THE ELECTRICAL AND OPTICAL PROPERTIES

OF

THE SEMICONDUCTOR ALLOY SYSTEM

SaxGe1-xSe

by

THOMAS ABRAHAM, B.Sc., M.Sc.

A Thesis submitted for the degree of

Doctor of Philosophy in

the University of London.

Department of Electrical Engineering,

Imperial College,

London.

Dedicated

TO MY PARENTS.

ACKNOWLEDGAINTS.

I would like first and foremost, to thank my

supervisor, Dr. C. Juhasz, for his help and advice over the

past three years.

I am also grateful to Professor J.C. Anderson for

his invaluable help and support during the course of this

study, and all the other members of the materials section

for their many helpful criticisms and suggestions.

Finally I would like to thank Mrs. Pam.Dingley for

typing this thesis.

CONTENTS.

Page.

Chapter 1: INTRODUCTION 1

1.1. IV-VI Semiconductors 3

1.1.1. Stoichiometric Effects 3

1.1.2. Transport Properties 4

1.2. Layer Compounds 7

1.2.1. Electrical Mobility 7

1.2.2. Conductivity Switching. 8

Chapter 2: PREPARATION AND STRUCTURE OF ALLOYS 10

2.1. Introduction 10

2.2. Sample Preparation 12

2.2.1. Bulk Samples 12

2.2.2. Evaporated Films 14

2.3. X-ray Analysis 16

2.3.1. Powder Diffraction Data 16

2.3.2. Laue Back Reflection Data 20

2.4. Electron Microscope Analysis 22

2.5. Crystal Structure and Chemical Bonding 25

2.6. Stoichiometric Deviations 27

Chapter 3: ELECTRICAL PROPERTIES 30

3.1. Introduction 30

3.2. Basal Plane Transport Properties 33

3.2.1. Resistivity and Hall Coefficient ;:ieasurements 33

3.2.1.1. Experimental Procedure 33

3.2.1.2. .Eesults aad Discussion

3.2.2. Hall Mobility

3.2.2.1. Results

3.2.2.2. Mobility Scattering Mechanisms

3.2.2.3. Analysis of Data

3.2.3. The Thermal Effect

Page. 47

47

47

60

68

3.2.3.1. Experimental Procedure 68

3.2.3.2. Results 68

3.2.3.3. Discussion 75

3.2.4. The Seebeck Coefficient 77

3.2.4.1. Results and Dismission 77

3.3. Conduction Parallel to the c-axis 79

3.3.1. Experimental Procedure • 79

3.3.2. Results 81

3.3.3. Theory of Possible Conduction Mechanisms 93

3.3.3.1. Impurity Band Conduction 95

3.3.3.2. Conduction in Disordered Systems 103

3.3.3.3. Field Dependent Conductivity 105

3.3.4. Discussion 109

3.4. Electrical Properties of Evaporated Films 121

3.4.1. Experimental Procedure 121

3.4.2. Results and Discussion 122

3.5. Mossbauer Effect in SnxGel_xSe 130

3.5.1. Simple Mossbauer Theory 130

3.5.2. Results and Discussion 131

Chapter 4: OPTICAL PROPERTIES 134

4.1. Introduction 134

4.2. Theory of Optical. Transitions 140

4.3. Experimental Procedure 147

4.3.1. Transmission iileasurements . 147

• Page.

4.3.2. Reflectance MeaSurements 148

4.4. Bulk Optical Properties 153

4.4.1. Results 153

4.4.2. Discussion 162

4.5. Optical Properties of Thin Films 167

4.5.1. Results 167

4.5.2. Discussion 168

4.6. Photoconductivity of Evaporated Films 170

4.6.1. Theory 172

4.6.2. Experimental Procedure 174

4.6.3. Results and Discussion 176

Chapter 5: CONCLUSION. 181

Bibliography. 185

ABSTRACT. (i )

This work is concerned with the characterisation of the

IV-VI pseudo-binary semiconductor alloy system SnxGel_xSe.

The investigation of the electrical and optical properties was

carried out on several alloys, ranging from Sn.9GeaSe up to

SnaGe.9Se.

The alloys were prepared by heating a stoichiometric

mixture of high purity Sn, Ge and Se in their elemental states

up to a temperature of 10500C, and leaving the ampoule at this

temperature for a period of fifty hours. The charge obtained

consisted of a mass of easily separable, interleaved crystals.

These crystals possessed a distinct cleavage plane indicating a

high degree of orientation. Like the two terminal compounds

SnSe and GeSe, the alloys also had an orthorhombic crystal

structure, and powder X-ray data indicated that Vegard's law is

obeyed, with a small deviation in the case of the 'a' axis. The

long 'c' axis was easily discernible since it was perpendicular

to the cleavage plane and this property was used to obtain the

electrical properties perpendicular and parallel to this axis.

Films of various alloy compositions were deposited on Sodium

Chloride substrates using vacuum evaporation techniques. The

films thus obtained showed no definite orientation and were poly-

crystalline in nature.

The electrical properties are a function of the stoichiometric

deviations in the sample, and the carrier concentrations obtained

were in the range 1017-1018icm3. Basal plane transport

measurements gave a Hall mobility temperature dependence of about

T-2 at te:nceratures greater than 150°K. This deviation from the 3 .

normal T law was ascribed to non-polar optical phonon scattering.

G0

Measurement of the conductivity along the 'c' axis resulted in

three types of behaviour;

i) normal band behaviour for SnSe rich alloys

ii) a certain degree of carrier localization for

alloys around the Sn.5Ge.5Se region

andiii) an amorphous type conductivity behaviour for the

GeSe rich alloys possibly due to an intercalated

amorphous phase.

A similar thermal effect to that observed in the end compounds

by other workers was also found in the alloys, where the transport

properties showed an irreversible change with heat treatment.

The electrical properties of the thin films seem to be dominated

by the potential barriers at the grain boundaries. The Mossbauer

results on various SnSe rich alloys were analysed in terms of a

varying Sn s electron contribution to the bands and bonding.

Optical transmission and reflectance measurements were

carried out on various bulk and thin film samples of the alloy.

Allowed indirect transitions seem to predominate at the funda-

mental absorption edge. The band gap variation with co:dposition

was virtually linear and of the non-zero type. Photoconductivity

measurements on some of the alloy films seems to corroborate the

results from the transmission and reflectance data.

1 CHAPTER 1.

INTRODUCTION.

The pseudo-binary semiconductor system SaxGel_xSe results

from the alloying of the IV-VI layer compounds SnSe and GeSe in

varying proportion. The IV VI semiconductors of the chalcogenide

series, consist of nine binary compounds. These are presented

in Table 1.1 which also lists some of their properties (S5). In

terms of crystal structure they are almost equally divided between

the cubic-B1 structure exhibited by the lead compounds, SnTe and

GeTe, and the orthorhombic or B29 structure of the tin and

germanium, sulphides and selenides. The compounds with the B-29

structure are reported (01) to be isomorphous, and exhibit similar

optical and electrical properties. Several pseudo-binary alloys

have been investigated, but the two which have received most

attention are PbxSni_xTe and PbxS-n1-xSe, because of their use as

generators and detectors of infra-red radiation (S6). This is a

consequence of their zero bandgap variation with composition which

is schematically represented in Fig.1.1. For comparison the non

zero bandgap behaviour is also illustrated. The only optical and

electrical work reported on an orthorhombic alloy system has been

that of Albers et al (A1) on SnSxSel _x. This was found to show

non-zero bandgap behaviour. One of the reasons for investigating

SnxGel_xSe was to ascertain the variation of bandgap with composi-

tion. This system has not been studied in any detail. In fact

the only published data is that of Krebs and Langer (K7) who found

that the alloy exhibited complete solid solubility across the

composition range.

The layer like characteristics of the orthorhombic compounds

and alloys arise from their structural. anistropy, and is manifested

in the presence of a•unique cleavage plane perpendicular to the

2

Compound Melting Point oc. •

Structure at 300°K.

Energy Gap at 300°K ev.

.Conductivity type

undoped.

GeS 674 B-29 1.8 p

GeSe 670 B-29 1.13 p

GeTe 724 Cubic -0.1 p

SnS 881 ' B-29 1.08 p

SnSe 860 B-29 0.9 p

SnTe 806 Cubic - Bl -0.2 p

PbS 1111 B1 0.41 n,p

PbSe 1081 Bl 0.29 nl p

PbTe 924 Bl 0.32 n,p

Table 1.1.

ae

Zero'

'Non-Zero'

Fig. 1.1.

long axis. This property is exhibited by other semiconducting

materials including the Zinc and Gallium chalcogenides and the

transition metal di-chalcogenides (W3). An interesting aspect

of investigating these layer compounds was to find whether or not

their structural anistropy was reflected in their electrical and

optical properties. These compounds are also known to exhibit

conductivity switching behaviour. Some of the properties of the

IV-VI semiconductors and layer compounds will be described in more

detail in the subsequent sections.

The main purpose of the work described in this thesis was to

characterize the alloy system SnxGel_xSe with respect to its

electrical and optical properties. The preparation and structure

of various compositions of the alloy, including both bulk and thin

film samples, are presented in the next chapter. This is followed

in Chapter Three by a description of the basal plane transport

properties, conduction mechanisms along the c-axis and various other

effects. The penultimate chapter deals with the optical properties

of the alloy. For purposes of comparison and reference the

properties of the terminal compounds were also investigated. The

results of other workers for these compounds are described at the

beginning of the chapters, and later related to the results

obtained by the author.

1.1. IV-VI Semiconductors.

1.1.1. Stochiometric effects.

A compound will in general be stable over a

range of composition, or homogenuity region, which may or may not

include the stoichiometric composition specified by the formula.

These deviations from stoichiometry are important because they have

a dominant effect cn the electrical properties of the IV-VI_ systems.

This is because, for almost any sample which is not intentionally

doped, the deviations are large enough compared to the impurity

content and intrinsic carrier concentration, that at room tempera-

ture and below, the type and concentration of charge carriers are

determined primarily by the nature and magnitude of the deviations.

In most of the IV-VI compounds and alloys the electrical conductivity

is predominantly due to one type of carrier, so that the carrier

concentration can be obtained from the measured Hall coefficient

using the simple.one carrier formula. This may then be used as a

measure of the stoichiometric deviation. It is however not

possible to apply this to some samples of p type PbTe, SnTe and

GeTe since the one carrier formula is no longer applicable to the

room temperature data, because of the presence of two types of

holes. Finallyi the lattice defects responsible for deviations

from stoichiometry are completely ionized at all temperatures, so

that each defect supplies an integral number of charge carriers (S7).

1.1.2. Transport Properties.

In describing some of the electrical properties

of the IV-VI compounds and alloys, these with the cubic structure

will be dealt with first, and then the orthorhombic systems.

• The lead chalcogenides generally exhibit a constant Hall

coefficient and a decreasing' resistivity below room temperature (A5).

Above room temperature the Hall coefficient shows an increasing

tendency. The compounds SnTe and GeTe also exhibit this property,

and in all these cases it is reversible (A6). This has been

explained by Allgaier (A4) on the basis of the double valence band

model. This model is based on two valence bands at different pointb

in the Brillouin zone, whose extrema are separated by a small energy

At low temperatures it may be assumed that the carriers are

5

confined to the higher band. As the temperature is increased, the

most energetic carriers (holes) will at some point have an energy

greater than QE, and consequently they may be scattered into the

second band. If this band is characterized by a high effective

mass and low mobility, then these scattered holes will be effective-

ly removed from the conduction process. The Hall coefficient will

then increase with increasing temperature. This model has also

been used to explain the observed Hall coefficient in bulk (D6) and

film (Fl) samples of the alloys PbxSni_xTe and (PbSe)x (SnTe)i_x (,14).

The other interesting feature of these systems is the mobility

variation, with temperature and composition. The mobility variation

with temperature in nearly all these compounds shows a high tempera-

ture dependence with a slope of This departure from the

normal acoustic phonon scattering dependence of -1.5, has been

explained on the basis of the temperature dependence of the effective.

mass (it increases with increasing temperature) (A4). As far as the

non zero bandgap alloy PbTexSel_x is concerned, the mobility variation

with composition showed a decreasing tendency with composition with a

minimum at x = 0.5. This has been attributed to the influence of

alloy scattering (El). For the zero bandgap alloys PbxSni_xSe and

PbxSni_xTe (W1), in addition to this type of scattering there is

additional carrier scattering, especially as the bandgap tends to

zero. Additional complexities arise, due to the fact that the

effective mass dependence on temperature decreases, because of the

weaker temperature dependence of the related energy gap (B6). All

these materials are characterized by a high mobility of the order of

103-104cm2/volt-sec.

In the case of the two alloys mentioned above, there is corn-

plate mutual solid solubility for Fo„:Sni _xTe. For tAe alloy

6

PbxSn1-xSe complete solubility exists only in the range 1 x 0.57,

and it must also be pointed out that SnSe takes up a cubic structure

in this system. The mutual solid solubility of most of the binary

ternary and quaternary IV-VI systems have been comprehensively

reviewed by Strauss (S5), Nikolic (N1, N2) and Krebs and Langer (K7).

The orthorhombic IV-VI compounds SnS and GeS are of interest

with respect to the system under investigation because of their

apparent similarities. Most of the work on SnS was carried out by

Alberset al (A2, A3) who observed very similar transport properties

to the lead chalcogenides. There was however one unusual aspect

about the Hall coefficient of SnS at higher temperatures, and that

was its irreversible character. Heat treatment at temperatures

greater than 230°C resulted in an increase of the room temperature

carrier concentration. As will be described later, Strauss and

Brebich (S7) attributed this to the presence of elemental micro-

precipitates. The variation of the Hall mobility with temperature

showed a dependence of -2.2 at the high temperature end. This is

less than that of that of the lead chalcogenides and it is not known

whether the carrier effective mass of SnS is temperature dependent.

It may however be possible to explain this high value on the basis

of scattering due to optical phonons polarized perpendicular to the

basal plane. Albers et al (Al) have also reported mobility data on

the ternary systeM SnSxSel_x, which shows a decreasing mobility with

alloying,the result most probably of alloy scattering. It was also

observed that at the higher temperatures, the mobility dependence of.

ShSo. 5Se0.5 was less marked than those of the end compounds.

.There is no published data on single cryotal specimens of GeS.

D'Amboise et al (Dl) have investigated the conductivity of polycrystal-

line saples and observed an activated behaviour at high temperatures

7

with a 'flattening' tendency as the temperature is reduced. Van Den

Dries et al (V1) obtained an activated dependence for needle-like

polycrystalline samples, but also found that measurements on plate-

like GeS crystals showed non linear I-V characteristics. He

obtained an activation energy of 0.56ev while Yabumoto (Y1) has

reported an activation energy of 0.74-1.0ev for the dark conductivity.

.a The reported conductivities at room temperature varied from 10-10 -1

cm-1 (Y1) to 10-3//-lcm-1(D1), while Van den Dries (111) obtained a

value of 10-6.(1-1cm-1. These results will later be correlated with

the results obtained for Snx Ge1-x Se.

1.2. Layer Compounds.

1.2.1. Electrical Mobility.

In this section the properties specifically result-

ing from the layer structure of various semiconductors will be briefly

considered. Unfortunately data on the IV-VI layer compounds is

scanty and so the discussion will centre on other types like the •

Gallium Chalcogenides and some of the dichalcogenides of the transi-

tion elements.

The electrical properties of layer compounds have only been

studied extensively in recent times. Most of the work has been done

by Fivaz (F2) who has analysed the experimental mobility behaviour in

terms of a theoretical model dependent on carrier lattice interaction.

He postulated that for strong interaction, the carriers would be self

trapped within the layers, while for weak interaction they could be

considered as free quasiparticles. In the event of self trapping,

the charge carrier distribution in the presence of an electric field

can be expected to relax predominantly through scattering by optical

phonons polarized parallel to the c-axis. For the case of weak

interaction Schmid (S2) has proposed that non-polar optical phonons

6

will dominate the carrier scattering processes. This model has

been used to explain the large mobility temperature dependence

for various layer semiconductors, which are shown below:

Temp.dependence Carrier of. type.

Optical phonon energy hw(ev).

MoS2 (FW) -2.5 n 0.06

MoSe2 ( " ) -2.4 n 0.05

WSe2 ( " ) -2.4 - n 0.05

GaS (K) -2.4 p 0.05

GaSe (F) -2.0 p 0.04

GaTe (M) -2.0 p 0.033

The experimental data and theoretical analyses of conduction

along the c-axis in layer compounds in sketchy. Tredgold and

Clark (T4) haVe investigated c-axis conduction in GaSe and found

that the n-type material exhibited a hopping behaviour while the

p-type showed band characteristics. From this it was concluded

that the top of the valence band was three dimensional in character .

while that of the conduction band is two dimensional. Milne (M10)

on the basis of results obtained for GaTe proposed a Poole-Frenkel

mechanism to explain the c-.xis conductivity. Said (S1) however

found that in SnSxSe2_x the predominant mechanism is of the thermally

activated hopping type. This was also presumably the case in

n-type SnSe according to Atakishiev and Akhundov (A10). Before

any consistent theory can be formulated, however, more experimental

results will be required.

1.2.2. Conductivity Switching.

Conductivity switching involves a non-destructive

change from a low conductivity (off-state) to a high conductivity state

(on-state), on the application of a voltage above a certain threshold

value.

9

If the low conductivity state can be recovered (e.g. by application

of a high current pulse) then the device may be cycled between these

states. There are numerous types of conductivity switches but the

one of interest as far as this system is concerned would appear to

be the current controlled negative resistance (C.C.N.R.) device.

Some examples of layer compounds exhibiting this type of switching

are SnS2, ZrS2, CdI2, CdS and ZnS. Most of the evidence for this

type of switching seems to suggest that it is due to a filamentary

growth (H3) where the high conductivity state arises from the

presence of low-resistance filaments interconnecting the layers of

the crystal. The low conductivity state may be retrieved by the

thermal rupture of this filament. However, the 'switching

mechanism' for SnxGel_xSe seems to result from a different process,

which will be described in detail in a subsequent chapter.

10

CHAPTER 2.

PREPARATION AND STRUCTURE OF ALLOYS.

2.1. INTRODUCTION.

The structure and physico-chemical properties of the two

terminal compounds SnSe and GeSe have been investigated by various

workers (01, Kl, D8, Li, 02, M12, N4). The earliest work on these

compounds was carried out by Okazaki (01, 02) who found that they

both possessed the orthorhombic crystal structure. The lattice

constants were obtained from x-ray diffraction data and the results

are shown in Table 2.1. An analysis of the crystal structure revealed

that the observed reflections conformed to the following rules,

hkl present for all

hk0 present only for h t k even

and Okl present only for 1 even.

16 Both compounds were also assigned the space group D2h Pcmn.

Each unit cell contained four molecules of GeSe or SnSe. The

various bond angles, nearest neighbour distances and atomic co-

ordinates are all given in Table 2.1.

GeSe SnSe

a

b

4.38

3.82

10.79

4.46

4.19

11.57

Yl 0.879 0.882

Y2 0.148 0.145

zi 0.105 0.103

z2 0.503 0.479

1 x h 2.54 2.77

2 x 1 2.58 2.82

2 x 11 3.30 3.35

1 x h1 3.39 3.47 0(c) ,0

105°,10' 0,0 ,340 2 1 ,

11

Note: a, b and c are lattice constants expressed in Angstroms;

yl, zl, y2 and z2 are dimensionless parameters indicating the

distribution of the atoms for the cations and anions, respectively;

h, 1, 11 and hl denote the distances to the six nearest neighbours

in the structure, 04 is the angle between the bonds in the

horizontal chains, /3 and 2/ are the angles between the horizontal and vertical bonds for the anions and cations respectively.

Novoselova et al (N4) reported a phase transition for GeSe at about .

540°C while Dembovskii et al (D4) also observed a phase transition

for SnSe at the same temperature. Neither are specific about the

type of transition and there has been no verification of these

observations. Novoselova et al (N4) also investigated the tempera-

ture-composition and Pressure-temperature projections of these

compounds. It is interesting to note that Azoulay et al (All) who

analysed amorphous GexSel_x compounds, found that the formation of

glasses begins at pure selenium and goes up to x = 0.43.

A simple method for the preparation of crystalline samples of

these selenides has been described by Asanabe (A8, A9). Stoichiometric

amounts of the elements were heated in an evacuated ampoule to a temper-

ature of 10000C and left fcr about fifty hours, in order to ensure

complete chemical reaction. It was then possible to obtain samples

possessing a high degree of crystallinity, from the melt, by using a

slow cooling process.

Thin films of these 'compounds have received less attention than

the bulk. The structure and electro-physical properties of SnSe films

deposited on various substrates were studied by Mikolaichuk and

Freik (M8). They found that the best orthorhombic crystalline

structures were obtained by using an alkali halide (e.g. NaCl) single

crystal substrate, at a substrate temperature of 20000. They also

reported that for substrate temperatures greater than 397°C, the SnSe

films exhibited a cubic structure with a lattice constant of 5.82A°.

12

According to Kosevich (K6) who analysed the grain boundary structure

in SnSe films, the grains were oriented so that their (001) planes

were parallel to the (001) planes of the alkali halide subStrate.

He also found that neighbouring SnSe grains joined in mach a way as

to leave unfilled channels and faceted voids. Polycrystalline

orthorhombic films of GeSe on NaC1 substrates were obtained by

Goswami and Nikam (G3) for substrate temperatures greater than

200°C. They have not reported any phase change of the SnSe type,

although it does not seem that substrate temperatures greater than

300°C were used. An amorphous to crystalline phase change at 418°K

has however been reported for GeSe films by Zakarov et al (Z1).

The only reported work on the alloys, was the solid solubility

analysis carried out by Krebs and Langer (K7). They found complete

solid solubility across the whole composition range, with the lattice

constants obeying Vegard's law, except for 'a' which showed a slight

deviation.

In this chapter, the preparation of both bulk and thin films

of the system SnxGel_xSe for the range 04 x 41, will be described.

The structure and crystallinity of the alloys, bulk and film, will be

analysed, and the possible stoichiometric deviations inherent in

these systems, discussed in the final section.

2.2. - Sample Preparation.

2.2.1. Bulk Samples.

Various compositions of SnxGel_ySe were prepared

for the values of •x corresponding to 0.0, 0.1, 0.2,.0,25, 0.3, 0.4,

0.5, 0.6,_ 0.7, 0.75, 0.8, 0.9 and 1.0. Stoichiometric amounts of the

three elements were placed in a silica jlass astpoule, which was

evacuated to a pressure of 1U-7 torr, then heated to a te7Iperature

of 1050°C. The melting points (,P) atld aIomio weights of the

constituent'a ,mants ar as Colic:vs:-

Atomic 7:01:2-ht. rF.

Sn 118.70 232°C

Ge 72.60 937°C

Se 78.96 217°C

In order to obtain the stoichiometric weights of the elements the

following equations wore used,

WSe = 118.70 x x ) • f

Wore = 72.60 x (1-x) (2.1)

) wSe = 78.96

where f is any arbitrary number depending on the total weight required.

In this case it was usually either twenty or ten. The purity of the

elements ranged from 5N for Sn (Metals Research Ltd.), 5N for Ge

(Metals Research Ltd.) and 4N for Se (Norando Co.). The required

amounts were weighed to an accuracy of 0.1 mg by using an electronic

balance. The ampoule containing the mixture was heated in a

commercial Gallenkamp furnace where it was taken up to the stated

temperature over a period of three hours. The charge was left at

this temperature for about fifty hours to ensure complete chemical

reaction. It was shaken occasionally to enhance the diffusion

processes. The ampoule was then slowly cooled down to room tempera-

ture over a period of twenty-four hours. Some of the earlier samples

were quenched from the melt in order to reduce the possibility of

internal precipitation (this is described in detail in the next

chapter). These specimens, however, exhibited a low degree of

crystallinity and the cleavage plane (an inherent physical property of

layer compounds) was not recognisable. On the other hand the slow

cooling method resulted in a mass of easily separable interleaved

crystallites.

—11

14

The alloys were all silvery grey in colour, with the basal planes

exhibiting a metallic lustre. The crystallites were flaky in

character and possessed a distinct cleavage plane. All the alloys

for 1 > x ,;(:).5 showed these properties. The alloy compositions

corresponding to x = 0.2 and 0.1 also showed similar properties

although the samples were not as flaky as the SnSe rich ones. The

crystallites were fairly large with typical dimensions being 4cm by

3cm by 0.1cm. For compositions in the range 0.25 ts. x 4 0.4, the

crystallites were much smaller. For all these compositions, the

samples showed few visual crystalline defects. This was however

not the case for the GeSe sample.obtained, which although having a

distinct cleavage plane, yielded specimens with coarse surfaces.

In general the SnSe rich alloys showed a much higher degree of

crystallinity and a stronger flaky character than the GeSe rich

ones. Electron probe micro-analysis tests on the alloys indicated

that they were homogenous.

2.2.2. Thin Films.

Films with compositions x = 1, 0.8, 0.7, 0.5, 0.3, 0.2

and 0.0, were deposited on Sodium Chloride substrates using the

vacuum system shown schematically in Figure 2.1. The system

consisted of a rotary pump, diffusion pump, and vacuum chamber, iso-

lated from each other by means of valves. The chamber was first

evacuated by the rotary pump, and when a pressure of about 2 x 1071

torr was attained this channel was closed. The diffusion pump was

then used to obtain the required vacuum, by opening valves two and

three. Chamber pressures as low as 10-7 torr were obtainable. In

the chamber itself, the arrangement consisted of a source heater

situated below a kanthal wire subStrate heater. The ternr_orat-ares

were measured by means of an iron-constantan thermccoutle.

15

In order to obtain films with as high a degree of crystallinity

as possible, freshly cleaved single crystal NaC1 substrates were

used. They were cleaved along the 100 plane, and although care was

taken to ensure that the surfaces were defect free, it was not

possible to eliminate all the strain lines. This resulted in a

slight impairment of the films which were all deposited on the

100 face of the substrate.

The procedure used for the vacuum deposition will now be

described. A small source tube was filled with the powdered bulk

material and placed in the source heater. The surface of the

substrate was swept using a very fine brush to get rid of any

debris. It was then positioned under the substrate heater.

Following this, the vacuum chamber was pumped down to a pressure of

10-6 torr. In order to obtain a uniform temperature, the

substrate was heated for five hours prior to evaporation. The

source heater was then switched on, with the substrate shutter closed.

The reason for this pre-evaporation, which lasted a couple of

minutes, was to drive off any of the more volatile impurities present.

The films were then deposited, the process taking about twenty

minutes depending on the thickness required. After evaporation the

films were annealed. The special patterns required for the

electrical measurements were obtained by using a Hall shaped mask.

The experimental details (like-the source and substrate temperatures

which were extrapolated from the values used by other workers for

SnSe and GeSe films) for films of various representative compositions

are shown in Table 2.2.

16

Composition. Vacuum Pressure.

Source Temperature.

Substrate Temperature.

Annealing Time.

SnSe

Sn.8 Ge.2 Se

Sn.5Ge.5Se

Sno3Ge.7Se

GeSe

8x10-7torr.

lx10-6torr

6x10-7torr

lx10-6torr

1x10-6torr

607°C

607°C

56000

512°C

512°C

205°C

230°C

250°C

220°C

207°C

18 hrs.

16 hrs.

15 hrs.

15 hrs.

15 hrs.

Table 2.2.

The films were, like the bulk, silvery grey in colour, with the

thickness in the range 0.2 ton- 5tom. The thinner films were

measured using the interferometer, while the thickness of the rest

were estimated from the interference fringes of the optical trans-

mission data.

2.3. X-ray Analysis.

2.3.1. Powder Diffraction data.

The Powder diffraction patterns of all the bulk

compositions as well as some of the films were obtained by using the

Debye Scherrer method. Small samples of the alloy were finely ground

and then 'rolled' on to a silica glass fibre coated with canada balsam.

This fibre was positioned at the centre of a Debye-Scherrer camera,

which was then placed on an X-ray spectrometer. Cu- Ka radiation with

a nickel filter was used as the X-ray source. The exposure time

varied between five and ten hours depending on whether the alloys were

GeSe or SnSe rich. The patterns obtained for the two terminal

compounds corresponded to those of other workers (L2, 01, K1).

1 7

The alloys showed similar patterns as can be seen in Plate 1

(which shows a representative selection), with a gradual change from

one end of the composition range to the other. The lines obtained

for the alloys were coarser and more diffuse than those of the

terminal compounds. This is most probably a consequence of alloy

disorder, which has the effect of broadening the lines (C5).

From the line spacings it is possible by using simple geometry

to obtain the angle (e) subtended at the centre by the diffracted

beam. This is related to the spacing (d) between the planes by the

equation,

2d sin e = A

(2.2)

where A is the wavelength of the incident radiation. The value d

may be used to find the lattice parameters from the equation

1 1 h2 k2 12 2 = k

a 172.

(2.3)

where (hkl) specifies the plane and a, b and c are the lattice

constants. All the lines of SnSe and GeSe have been indexed and the

data is available on ASTM cards. Since the diffraction patterns for

the alloys are not very different, it may be safely assumed that they

also possess the orthorhombic structure, and the lines can be indexed

by comparing them with those of the terminal compounds. From

different values of (hkl) and d, the lattice constants can be calcu-

lated. The results obtained and their variation with composition is

shown in Fig. 2.2. Both parameters'c' and'b' seem to obey Vegard's law,

while'a'shows a small deviation. This compares well with the results

of Krebs and Langer (K7), but it must be admitted that the coarse line

widths tend to compromise the accuracy, especially since the differences

between the two end points are small. In spite of this, the overall

variation is consistent with complete solid solubility.

18

4C-011,1111 Sn .6GP 2

e

Sn ,Ge ,Se •,. • f

G eS e

PLATE 1

19

FTr; Variation of Lattice parameters with compoSition (x).

20

The powder diffraction patterns of some of the films were also

investigated. The patterns obtained corresponded very well with

those of the bulk samples. This is not surprising, since the two

end compounds have large dissociation energies (i.e. for SnSe the

value is 86Kcal/mole and for GeSe it is 115Kcal/mole (H7)) and both

SnSe (H7) and GeSe (L3) have been reported to vaporize predominantly

as the molecular species. The alloys would not be expected to be

very different from the terminal compounds, and it may be reasonably

assumed that the films do correspond to the stated alloy compositions.

This does seem to be the case from the diffraction patterns.

2.3.2. Laue Back reflection data.

The purpose of the Laue back reflection data was

to assess the crystal perfection of the samples. All the data for

the alloys was obtained with the beam parallel to the c-axis. For

SnSe, a Laue'pattern with the beam perpendicular to the c-axis was

also obtained. The results (three representative patterns are

shown in Plate 2) seem to divide the composition range into three

categories, which coincide with the (a), (b) and (c) types mentioned

in the next chapter. The compositions corresponding to these are

0 1 0.8, ii) 0.7 x > 0.4, and iii) 0.3 x > 0.0.

These will be considered in turn and compared with each other.

i) The data for 1 ?:x .. 0.8 showed a high degree of

crystallinity, and exhibited the four fold symmetry characteristic

of the 100 direction. The spots were sharp although there was a

tendency to broaden out as the alloying increased. These samples

showed a high degree of orientation and good crystallinity. The

pattern for the SnSe sample with the beam parallel to the basal plane

consisted of a series of superimposed Laue patterns. This may be due

to the rcugh disordered surface of the samPle used. viith saLiples

which were shaped to give a smooth surface in this direction the Laue

patterns were almost circular,. indicating the distortion effects of

the shaping action.

ii) The patterns for 0.7 x 0.4 were similar to the

previous ones, except that the spots were more diffuse and showed a

tendency to streak. This is most probably the result of the

increased lattice distortion arising from the greater degree of

alloying. The four fold symmetry indicated that the high degree of

orientation is still present.

iii) The range 0.3 0.0 yielded patterns which indicated

a much greater degree of disorder. Generally for polycrystalline

specimens of random orientation a complete ring is formed. For single

crystals which are deformed, only fragments of this ring appear. The

high degree of orientation is still maintained, and this of course is

also apparent from the easy cleavage plane. There is however a source •

of disorder which is random and independent of alloying effects. In

the next chapter anomalous conduction characteristics obtained for

these compositions are described, and attributed to a possible inter-

layer amorphous phase. It would appear that the Laue patterns are

distorted by the presence of this phase, which may be considered as

the source of disorder.

2.4. Electron Microscope Data.

The electron diffracticn patterns and micrographs were

obtained for thin films with compositions x = 1.0, 0.8, 0.5, 0.7, and

C.O. The films were first removed from the substrate by dissolving

the latter in water, and then carefully placed on to a fine grid.

The film specimen on the grid was examined under the electron micro-

scope, and some of the results are shown in Plate 3.

23

Electron Diffraction Pattern SnSe

Electron Diffraction Pattern

Sn .) „Ge

I,Se

Electron Micrograph Sn ,Ge

el r;Se

1146 X5OK

PIATE 3

24 -

The analysis of the micrographs is complicated by the structural

anisotropy of the material. Since nearly all the films are poly-

crystalline, it is not clear how the anisotropy is reflected in the

structure. The electron diffraction patterns however yielded more

information on the preferred orientation and relative grain size.

The pattern for the SnSe crystal seemed to indicate a high degree of

orientation. It is possible that the film was deposited in the basal

plane orientation, although from the presence of the double spots it

would appear that the layers are not in perfect alignment. The

electron micrograph was rather hazy and difficult to analyse. The

Sn.8Ge.2Se pattern showed a distinct lack of preferred orientation.

It also indicated a coarse grain size, since the circles tend to be

broken up, and this seems to be reflected in the micrograph. The

Sn.5Ge.5Se film showed no preferred orientation and a fine grain size.

The Sn.3Ge.7Se seems to show an interesting behaviour. From the

micrograph it would appear that the film consists of highly oriented

single crystals. Although the diffraction patterns seem to corroborate

the crystallinity, the preferred orientation is not obvious. This is

probably the result of a lack of layer alignment. Since theta! andib;

lattice constants differ, each layer contributes its own set of spots,

and a whole series of these spots superimposed on each other will

result in the type of pattern obtained. The micrograph on careful

examination, shows non-aligned layers stacked on each other. Finally,

the diffraction pattern of the GeSe film showed a complete lack of

preferred orientation, but the fine spots indicate coarse grain size.

This GeSe film seems to be more crystalline than that of Goswami and

Nikam (G3).

When the whole .comDosition range is considered, it would appear

that the higher the degree of alloying the smaller the grain size

(with the exception of Sv.3Ge.7Se). the same may apply to the

25 preferred orientation although with a lesser degree of certainty.

It must also be pointed out that for the samples Sn.8Ge.2Se,

Sn.5Ge.5Se and GeSe, the diffraction patterns varied as the films

were scanned. This is probably the result of the absence of any

preferred orientation.

2.5. Crystal Structure and Chemical Bonding.

Since the alloy structure basically consists of the

SnSe or GeSe parent lattice with Ge or Sn substitutional atoms, it

may be fully described by the structure of the terminal compounds

(both of which have the same structure and type of bonding).

The detailed structure is shown in Fig.2.3. The first diagram

Fig.2.3a shows the unit cell, the valence bonds are indicated by the

double lines (the double dashed lines indicate vertical bonds).

In Figure 2.3(b) and (c) the view of the crystal structure down the b •

and c-axes are shown. The double lines have the same notation while

the single broken lines denote the weak interlayer bonding and the

arrows indicate the cleavage plane. In all these diagrams the large

circle stands for the selenium atom while the small one may be either

Sn or Ge depending on the alloy composition.

This type of compound (alloy) has a structure belonging to the

D21h6 Pcmn space group in the orthorhombic crystal system. The unit

cell contains four Sn or Ge atoms and four Se atoms; each of these

has a co-ordination number of six. Along the c-axis the structure

consists of double layers, with the bonding between adjacent double

layers characterized by weak Van der Waals forces, resulting in a

marked (001) cleavage. The unit cell contains two double layers,

the distance between these being greater than the distance between

the atoms within a double layer. Each of the double layers consists

of two slightly corrugated-neighbouring layers, giving rise to the

glide plane symmetry. All the three nearest neiEnbcurs of each atom

9E

350

3911"S

(r) 00 00 35

0000 ''P'°"-5 d d 5

oanl.onags Tcoro.ga-c

3910 "50

35 0

co)

c • -

27

lie in one double layer, two are located in one layer at equal

distances 1, and a third in another layer at a distance h. The

lower double layer is obtained from the upper, by a reflection across

the (010) plane; therefore the corresponding angles and distances

are the same in both layers.

A model for the chemical bonding in these compounds has been

proposed by Gashimzade and Khartsiev (G1). Each Sn or Ge-Se pair

contains six p electrons in the outermost shell. They assumed

that the bonds were formed by three hybridised p-functions with a

small s-state contribution (Fig.2.3d). In this process one of the

s-electrons 'transfers over' to the Sn or Ge atom; this transition

is associated with the hybridization of the wave function, with

utilization of the free p-orbit of the neighbouring atom. Thus

there are three stable orbits with definite localized orbital

directions, two of which are located in corrugated planes and form a

chain, and the third of slightly different length ties up the infinite

chain of bonds in double layers (Fig.2.3a). The angles between

similar bonds are those denoted by c(in Table 2.1, while the angles

between the similar bonds and the third are denoted by /9 and )/

respectively. The distortion in the structure is associated with the

partial participation of the s-function in the bond. This type of

structure has been described by some workers (01, K2) as being of the

distorted NaC1 type.

2.6. Stoichiometric Deviations.

As stated in Chapter One, the electrical properties of

these semiconductors are controlled by the deviations from stoichio-

metry. There is no published data on either the homogenuity region

or the type of stoichiometric deviations for either of the terminal

compounds. In this section the results obtained for SnTe and SnS by

28

other workers will be described, and possible point defects for the

Sn xGel Se system assessed.

Brebick (B5) has investigated the homogenuity region for SnTe,

and found that it lies on the Te rich side between the limits 50.1 and

51.1 atomic percent Te, resulting in p-type conductivity. The

carrier concentration shows a linear variation with composition,

increasing as the deviation gets larger. Correlating the changes

in density and lattice parameter for various compositions in the

homogenuity region Brebick (B5) concluded that the predominant point

defects are tin vacancies, although there is the possibility that a

few Te-intestitials may also be present.

Rau (R1) has postulated a model based on doubly negatively charged

tin vacancies for atomic disorder in SnS. This was based on the

variation of the sulphur pressure with the variation of sulphur

content. The experimental procedure involved extracting small

quantities of sulphur from SnS, within the homogenuity region, and

simultaneously determining the equilibrium sulphur pressure. The

results obtained for the change in sulphur pressure were found to be

consistent with the assumption of doubly charged tin vacancies as

being the dominant source of point defects. It was also found, as

was to be expected from the predominance of p-type conduction in SnS,

that the homogenuity region lay on the S-rich side.

In considering the possible point defects in SnSe the rea_lts of

Rau (R1) for SnS, may be more relevant because of the striking

similarity between the two compounds. However the main type of point

defects in both of the tin chalcogenides seem to consist of Sn

vacancies. It may therefore be assumed that SnSe would also have a

t:renonderance of tin vacancies as the point defects. Whether they are

29

doubly charged or not would have to be verified, but the probability

is that they would be. The homogenuity region would be expected to

lie on the selenium rich side. There is no data available for the

atomic disorder in the Germanium chalcogenides. It is however

reasonable, on the basis of the similar p-type carrier concentration

behaviour between SnSe and GeSe that Germanium vacancies will

dominate the deviations from stoichiometry. In the alloys as well,

the defects are likely to be Sn or,Ge vacancies. Since the dissoc-

iation energy of SnSe is less than that of GeSe, the 'formation

energy' of tin vacancies is likely to be less than that of Germanium

vacancies. If this is the case then the tin vacancies will dominate

the observed carrier concentration in the alloys. This would seem

to be consistent with the variation of the hall coefficient (which is

a measure of carrier concentration) with composition shown in Fig.3.8.

Finally the homogenuity region for the alloys is also likely to lie

on the Selenium rich side.

30

CHAPTER 3.

ELECTRICAL PRCPERTIES.

3.1. INTRODUCTION.

The electrical properties of SnxGel_xSe will be governed by

its layer like orthorhombic crystal structure, and the deviations

from stoichiometry implicit in the alloying or compounding process.

There were no attempts made to rigidly control these deviations and

this accounts for a certain randomness in the carrier concentrations

of the different alloys. An additional factor influencing the electri-

cal properties is introduced by the degree of alloying. Whether or

not the strong structural anistropy is reflected in the electrical

properties is not clear. In layer compounds like GaSe, GaS, cd I2

and HgI2, Minder et al (M11) who investigated the drift mobility along

the lc' axis, have observed a definite three dimensional character.

The transport properties of the two terminal compounds SnSe

and GeSe can be expected to influence the alloys. The compound SnSe

has been extensively investigated by Asanabe (A8) and Mitchell (M12),

and GeSe by Asanabe and Okazaki (A9). The Hall coefficient, resistivity

and Hall mobility results obtained for single crystal SnSe by Asanabe

(A8) are shown in Fig.3:1. The resistivity (e) increases as the

temperature is increased, reaching a maximum at about 200°C and then

exhibits intrinsic behaviour. The Hall coefficient (Rh), which is a

measure of the carrier concentration, is constant at low temperatures,

then shows an anomalous behaviour at around 200°C, and finally decreases

at higher temperatures. The Hall mobility (ii4d0 shows a lattice scat-

tering type characteristic with a temperature dependence of -2. Asanabe (A8) investigated this anomalous Hall coefficient, and found

that the room temperature values of RH and e changed after the sanples

were heat treated. The mobility however remained unchanged. He

further found that with heat treatment below 200°C, RH and e increased,

and above 200°C they decreased.

10 1 1

Transport Properties of Single crystal SnSe.

al io

10

10 5 (!p ) oi< r

10

e) = C IO CI o

r

FIG. 3.1.

5 3 eT l2 0K-1 I

0

FIG.3.2. Transport Properties of Single crystal GeSe.

a to

t * • ID

10

FIG.3.3. Transport Properties of Polycrystalline GeSe.

32

These effects have been observed in other IV-VI systems and has been

explained by Strauss and Brebick (S7) on the basis of internal

precipitation of the elements. Similar electrical results were

obtained by Mitchell (M12) for SnSe although he has not reported

any anomalous behaviour. The transport properties of GeSe (Fig.3.2)

were similar to those of SnSe although the resistivity showed a

discontinuous behaviour as the temperature was reduced. Asanabe and

Okazaki (A9) also measured the electrical properties of polycrystalline

GeSe and these are shown in Fig.3.3. The resistivity shows an

activated temperature dependence, while the mobility exhibits both a

lattice and ionized impurity type scattering behaviour.

In this chapter the results obtained for the alloy system

SnxGe1-xSe are presented, as follows:

i) Basal plane transport properties - the resistivity, Hall

coefficient and Hall mobility results are discussed in this section.

The observed thermal effect and the variation of the Seebeck

coefficient with composition is also described.

ii) Conductivity along the c-axis - this section deals with the

electrical conduction mechanisms parallel to the c-axis, including the

field dependence and conductivity change exhibited by some of the

alloys.

iii) Electric properties of SnxGel_xSe evaporated films - the

transport properties are described and analysed in terms of the

crystalline structure of the films.

iv) The Mossbauer effect - in this section the Mossbauer chemical

shifts and quadropole splitting observed for various alloys are related

to their electrical properties.

Finally, in the concluding chapter the transport properties

obtained for this system are compared with those of similar semi-

conductors.

33

3.2. BASAL PLANE TRANSPORT PROPERTIES.

3.2.1. Resistivity and Hall Coefficient.

3.2.1.1. Experimental Procedure.

The resistivity and Hall coefficient measurements

were carried out on freshly cleaved rectangular samples of SnxGel_xSe,

for x = 1, 0.9, 0.8, 0.75, 0.7, 0.6, 0.5, 0.4, 0.3, 0.25, 0.2, 0.1

and 0.0. A sample length to width ratio of about four was used in

order to inhibit any shorting of the Hall field by the current

electrodes (P2). In general thin samples were used in order to

maximise the Hall voltages, with the thickness varying between 0.05mm

and 0.25mm. Electrical contacts were made by soldering 'five thou'

gold wire using high purity Indium, and these were found to be both

ohmic and mechanically strong. These contacts were made across the

sides of the samples, as shown in Fig.3.4, in order to ensure the

predominance of basal plane conduction through each double layer.

Two different procedures were used for the measurements, one

for the temperature range 77°K (liquid nitrogen temperature) to 300°K

(room temperature) and the other for the range 300°K to 420°K. The

second method involved placing the samples in a vacuum to prevent the

formation of oxide layers, which might interfere with the electrical

measurements. There were no observable differences between the room

temperature resistivity and Hall coefficient of the sample, in air and

under vacuum.

For temperatures between 77°K and 300°K the samples were

mounted on a holder which was then surrounded by a tight fitting copper

can ( ) . This arrangement was put in a dewar, placed between the poles

of an electromagnet which supplied a field of 1.36KG (measured by an

electronic Hall probe fluxmeter to an accuracy of 1L). Liquid nitro-

gen was then poured into the dewar and the sample'and holder cooled to

77°K. The temperature was measured using a chromel-alumel thermo-

couple placed close to the sample. The resistance and Hall voltage were

Sample shape and contact points.

D. V M.

000 v;

06 id Ir 1- Vit

•■•

O

POWER SUPPLY

FIG.3.5. Switching circuit for the measurement of the Transport properties.

obtained by measuring the current through the sample, and the voltages

between contacts 2 and 3, and contacts 2 and 5 across the sample.

Four sets of readings were taken with different directions of

current and field, and the resultant average was used for the

calculations. The measurements were carried out using the switching

arrangement shown in Fig.3.5, and a digital voltmeter with an input

impedance >5000 ma and a resolution of 2.5eon the most sensitive

range. The current was obtained by noting the voltage drop across

a hundred ohm resistor with a tolerance of placed in series with

the sample. The readings for various temperatures in the range 77°K

to 300°K were taken as the sample warmed up, after the liquid nitrogen

had been poured out.

In order to find the resistivity and Hall coefficient above

room temperature the sample was placed in a cryostat connected to a

vacuum system consisting of a one inch diffusion pump and a rotary

pump. The cryostat was positioned between the pole pieces of an

electromagnet with a maximum field of 4.8KG. Using different fields

did not affect the Hall voltage, since it showed a linear variation

with magnetic field. The cryostat was then evacuated to a pressure

of 10-3 torr after which the sample was slowly heated by using a 2.5

watt, 250 ohm resistor embedded in the copper bar holding the sample

block. The measurements were carried out as in the previous case.

The resistivity ((>) and Hall coefficient (RH) were obtained

by using the following expressions:

p = V2_3wt (3.1) Id

and RH = VHt

(3.2) 11' I

where V2_3 is the voltage across contacts 2 and 3, w is the width,

t the thickness, d the distance between contacts 2 and 3, VH the Hall

voltage, B the magnetic field and I the current.

36

3.2.1.2. Results and Discussion.

The resistivity curves for the different alloys (Fig.3.6)

show a decreasing dependence on temperature. This is indicative

of extrinsic behaviour in the temperature range considered. In

general e is characterised by a rapidly decreasing high temperature

end giving way to a more gradual decrease at lower temperatures, and,

in some cases becoming temperature independent at liquid nitrogen

temperatures. Unlike the PbxSni_xTe alloys (D6) none of the curves

showed any distinctive linear regions. According to Dixon and Bis

(D6) multiple valence band models yield non linear variations of

resistivities, and in this respect it is interesting to note that a

triple valence band model has been suggested for SnSe by Takahashi (T1),

on the basis of its optical properties. The resistivities in the case

of the alloys are affected by the degree of alloying, and this is

clearly apparent in the value of the low temperature resistivity as

x tends to 1-x. While most of the curves are fairly smooth, some of

them show discrepancies in the form of kinks. These kinks were

present for samples of GeSe, Sn.Ge.5Se and Sn.7Ge.3Se. While the

latter two are probably due to the thermal effect, the discontinuities

in the GeSe curve are more difficult to explain.

The Hall coefficient variation with temperature (Fig.3.7)

was well behaved below room temperature and showed p-type conduction

for all the alloys. While most of the alloys exhibited little or no

variation with temperature, some of the GeSe rich alloys showed a

tendency to increase as the temperature was reduced. Above room

temperature the anomalous behaviour is observed, with the Hall

coefficient increasing as the temperature is increased. This effect

was apparent for all the alloys and will be dealt with in more detail

in a subsequent section.

rl'Pmr,erature ciepondence of for 1 ?.x 0.5.

37

38

a5 8 0 K .1

T T,J;:-.perature dopend,7.o of rosizr,tivity for 0.4 x 0.0.

39

. 5. Han coefficient variaticr:- with te::IL?rz.-..ture for 1 O.5.

a. 5 11 lip

X soo p o—o 0.0 6o

40

o.

8

I13 ) 0K - T/

0

.7 ( r ) Hall coefficient variation with temperature for

0.4 > x 0.0.

41

From the Hall coefficient curves it appears that the

activation energy of the acceptor level is virtually zero. In fact

this is the case for SnSe, where Hall coefficient measurements by

Hashimoto (H5) up to liquid helium temperatures show little or no

change. For those alloys, especially on the GeSe rich side where

the carrier concentration decreases as the temperature is reduced,

there is a likelihood that carrier compensation takes place. This

could occur either through a deep lying donor level or through traps

in the forbidden gap. Since the observed variation seems to pre-

dominate in the alloys, the inherent disorder suggests that traps are

more likely to be the compensatory mechanism.

The reproducability of the results was checked by carrying

out measurements on different samples for the compositions x = 0.75,

0.5 and 0.25. In the case of x = 0.5 (Fig. 3.8) samples of three

different bulk specimens were also used. The results show little

variation in the Hall coefficient of tne different compositions.

The resistivity showed larger differences, but this may be attributed

to variations in the aegree of crystallinity of the samples. In

general, the reproducability was very good.

The variation of the liquid nitrogen temperature Hall

coeificient and the room temperature and liquid nitrogen temperature

resistivities with composition is shown in Figs. 3.9 and 3.10. The

Hall coefficient is fairly constant on the SnSe rich side up to

Sn.5Ge.Se, and then gradually increases up to Sn.iGe. Se, where it

presumably starts to increase sharply. Since no measurements were

carried out for x in the range o.1 > x > 0, it is not possible to

ascertain the exact nature of tne variation in this region. Over the

range considered the Hall coefficient (which is a measure of the

carrier concentration) does not change by much, even for the GeSe rich

alloys.

81- 1?11 o era 188 • 678 isc • 978 III. ▪ era 8

0.5

42

• X

* a 4 44.f f f a 4 a L i

f a ao if i 4, CI • dio0 0 a 4? 0 el 4 cs .s C

a A It a a • 0 10 - • 4 l'a 104 a

° 4 a tie 0 4.

10

to a BIB MR

o BTU 1'18 o.15

10 i? 9 o .11 13 Br (4 0K-s T/

FTC . 3.9 . Resistivity jptendence on te:.Aperatuf.i? for (.1. 1fferent

0,717%p1c, s of x correcndir„.7 to 0.2-), C. :-tod 0.75.

4 04

10 11 1d 1 3 14 6 7 9

coo.ffici.i):at deronder.oe te:Er;orature for different of x 0.22, G. and 0.77.

x 10 o. as

1 0

4 12,̀ ....4 g 404 4'4; b̀ 13 d i= Ss 0 t 00

• d e a A A o a a 0 °o

+ Bra lia o era ifs a 0T8 igc

BT814. panie

04

+ 114 C•t

*64,0 0 0 0

I0

BT131/A

o eTB11713 O 4 0

4 4 4 4 0 0 0 :15

00

1 • 4 it

a I .5 .6 -7 .g .9 1 0 .1 a .3

JO'

0

10

3. Variation of FlAti, CoePri CI.NT ith }don.

/14

l0

o Room TEMP. 0 Li g. NIT. TEMP.

.3 .5 .6 .1 .8 .4 I.

x

16

0

-3 I0

-a. 10

Vuriaticn cf with coT.rc:-;ition.

45

•

46

Mossbauer measurements (which will be described in detail later)

carried out on the tin content in SnxGel_xSe have resulted in

chemical shifts which indicate that the Sn atom is the main

carrier contributor in this system. This may explain the Hall

coefficient variation with composition.

The room .temperature resistivity (QM) increases sharply

in the range 1 > x 3 0.5 and then tends to level off for 0.4

The resistivity may be defined by the expression

1 = pfaiA ... (3.3)

(3

where p is the carrier concentration, x the electronic charge and p.

the mobility. The carrier concentration can be obtained from the

expression

• • • (3.4)

where a is the Hall coefficient.

Since the carrier concentration in the first range is fairly

constant, the increase in ea,. must be due to a change in mobility

resulting from the alloying effects. The high resistivity values

in the second range may then be explained in terms of the decreasing

carrier concentration. Again, the behaviour in the range 0.1 > x> 0

is unknown since these compositions were not investigated. The

liquid nitrogen resistivity curve shows a sharper increase as x tends

to 1-x (i.e. 'the alloying increases). This is apparent both at the

GeSe and SnSe rich ends, and indicates that the alloying effects are

more pronounced, than at room temperature. The curve exhibits a

maximum at x = 0.4. An interesting feature of the two resistivity.

. curves is their convergent tendency as the degree of alloying is

increased.

x 0.1.

47

3.2.2. Hall Mobility.

3.2.2.1. Results.

The Hall mobility ( pm) is calculated from

the equation

RH ... (3.5) e.

where RE is the Hall coefficient and e the resistivity. The results

obtained are shown in Fig.3.11. The curves are all characterised by

a high temperature straight line region which tends to flatten out as

the temperature is decreased. This is more noticeable in those

alloys with a high degree of alloying, where a distinct nearly

temperature independent flat portion is observed. The straight line

region can be represented by the equation

cm /V sec. ... (3.6)

where F= mobility at temperature T,

Fo= mobility at temperature To taken as room temperature,

and n = temperature dependence of mobility, denoted by the slope

of the straight line.

The variation of n with composition is shown in Fig.3.12.

The main factors controlling the mobility are the various carrier

scattering mechanisms present in the system. These will now be

discussed in detail.

ScatteringLmechanisms.

In considering the dominant scattering mechanisms,

two factors have to be taken into account. These are the crystalline.

anisotropy, which is important for lattice type scattering, and the

degree of alloying,which will tend to dominate the mobility at lower

temperatures. The theoretical derivation of the basal plane mobility

will now be considered in terms of these factors.

I b 7 sr 5 10 11 111311. OK -

48

03 X

10

Hall mobility variation with t8-nperatlre for x = 1.0, .0.8 and 0..

JO 14-

49

3 10

1 0 a 4 5

( 1 0 ) T /

Hall Mobility variation with tearatura for x - 0.4, 0.c. and 0.7.

to;

50

X

10 oi< -1

3 10

10

I 0

Hall ..lobility variation with temperature for x = 0.0, 0.1,-0.2 and 0.3.

1 1

10 0.9 0.8. 01 0.6 I I

0.1 0.0 0.11. 0.3 0.s

Z1.3.5.12. Variation of mobility temperature' coefficient n with composition x.

53

i) Lattice Scattering.

The lattice structural anisotropy may be expected to

play a significant part in determining the nature of the scattering.

Layer semiconductors can be viewed as loose assemblies of thin plane

objects stacked up on each other. In spite of their strong

physical anisotropy, it is not clear whether this is reflected by

their optical and electrical properties.

Fivaz (F2) has analysed the mobility dependence on tempera-

ture for strongly anisotropic layered structures while Schmid (S2) has

considered the case of weak carrier-lattice coupling and moddrate

anisotropy. The two methods and their applicability to the system

SnxGel_xSe will be discussed in the following section.

In deriving his theory Fivaz (F2) assumed, on the basis of the

structural anisotropy, that within each layer but outside the atomic

cores the potential is low-and varies slowly, while between the layers

the contributions add up to high and fairly wide potential barriers

(Fig.3.13). The charge carriers can then be considered to move in a

series of parallel potential wells, their local energy levels depending

on the width of the well. Since the width varies with the deforma-

tion of the lattice, the interaction between the charge carrier and

the lattice may be described by means of a deformation potential (Ed)

given by

Ed a(.j_EcT) ... (3.7)

where E,is the energy of the local level and a the width of the well.

Approximating the potential within one layer by a deep square well,

one obtains

hYr (3.8) as rla

where m is the carrier effective mass, n an integer and Plank' s

constant. Using these two equations Ed can be related to E, , with

the result,

La = E,

54

Figure 3.13 SCHEMATIC REPRESENTATION of the

FFECTIVE POTENTIAL in a LAYER 5 TRU C TUR E

55

Since a is a few angstoms for this system, the deformation potential

may be as high as several electron volts. Width changing deforma-

tions of this type result in optical phonons polarized perpendicular

to the layers. In the presence of an electric field, the inter-

action between these optical phonons and the charge carriers will be

the dominant relaxation process. A further aspect to be considered

is the carrier lattice coupling. If it is weak the excess charge

carriers behave as free quasiparticles, but if it is strong they are

self-trapped in the layers.

The Hamiltonian for this electron phonon system will be

given by

H = Hel + Hint + Hlat

(3.10)

where Hel is the Hamiltonian of the carrier in the perfect lattice,

Hlat the Hamiltonian of the isolated lattice and Hint the Hamiltonian

describing the interaction between the carrier and the lattice. Hel

and Hlat are represented by standard equations, but the evaluation of

Hint was carried out within the terms of the layer structure. Fivaz

defines the specific lattice vibrational modes involved, as 'homopolar'.

This is because, since the layers have a plane-mirror symmetry, a pair

of identical atoms on each side of the plane can vibrate in counter

phase, and no first order dipoles result from this motion even if the

atoms are charged. The interaction Hamiltonian is then given by

Hint :" ah JZ'xf) k t c.)

(3.11)

where cc. stands for the unperturbed cell coordinates, and the first

term denotes the deviation from the equilibrium interatomic distance,

in the c-axis direction, of an oscillator (representing a unit cell

containing a pair of identical atoms) of reduced mass M. Using

variational methods the spectrum of the coupled carrier in the weakly

coupled limit was found. To define the limits of strong and weak

56

coupling a dimensionless coupling constant g was introduced,

g =( niVz )( cl Ea- ) Tr R

a-

(3.12)

where Nx is the number of unit cells per unit area. In the

weak coupling limit g2 < 1. This limit corresponds to the theory

of perturbations, and the mobility can now be readily evaluated

in the relaxation time formalism of transport theory. The calcu-

lation in the two dimensional limit has been described in detail by

Fivaz and iIooser (F3) and yields if the small effect of phonon

emissions is neglected, the simple result for the relaxation time T :

= [4. rr g'co iTud

The basal plane mobility may now be obtained and is given by

4.7rM x g?. f:L; - VI =

where m is the electron mass and lico the optical phonon energy

measured in units of 10-2eV. Equating this with equation (3.6) an

expression can be obtained for the mobility temperature dependence n,

of the form;

n = (h-1717. j2/zP(-:4.)

(24T - Iht, - I)

(3.15)

Thus the value of n can be related to the associated phonon energyLcu

and this variation is shown in Fig.3.14. This serves as a test for

the validity of the theory for a given semiconductor system.

The method just outlined, however, assumes a high degree of

dimensionality and a virtual two dimensional model is used. Schmid (S2)

considered layer semiconductors in the limit of weak coupling and

moderate anisotropy. In developing his theory, he assumed the

presence of non degenerate broad bands (bandwidth much larger than

the phonon energy lay), a large bandgap (so that interband transitions

can be neglected) and ellipsoidal constant energy surface around k = 0.

( 3.13)

( 3.14)

g

57

0

004. 0.06 • 0.08

(eAr)

The dependence of the mobility temperature dependence on phonon energy.

x

FIG.3.15. Variation of Residual Mobility 1.1.R with composition x.

It was also assumed that the scattering was of the non-polar optical

phonon type.

The Hamiltonian for the electron-phonOn system in this

case is the same as in the previous instance except for the

interaction Hamiltonian which is now given by,

HINT 1,17.7r 5 ca$ a13 Cr hM C A

r ) As

(3.16)

where a_s,, cil-c4.1 and ck represent creation and anhilation

operators pertaining to the wavenumbers denoted by the subscripts,

and g is a coupling constant given by

a 3i £ Iirtx a II TI MN. (k

where £ defines the deformation potential per unit displacement.

The reciprocal lifetime of a carrier which undergoes

scattering by phonons is evaluated, and found to be (at k = 0),

-1 2g2wn1

(3.18)

where n1 represents the number of virtual phonons. Schmid (S2)

then shows that the Boltzman equation has a relaxation time solution

for this type of scattering. Furthermore the relaxation frequency

is given by the reciprocal lifetime shown above. The scattering

time may now be obtained, by considering the energy-weighted

average of the relaxation time over all occupied states:

/77 -60 du.

O

( 3 . 1 9)

(3.17)

where pct = 41. 2k2

a)-rt„kT

Jr

The temperature dependence of T can be evaluated by

numerical method's and the following results were obtained,

for kT << hw

for KT = hw

for kT >> hw

c's 1- cu )

T. aa4ic.,"

(--kwY'' vir

... (3.20)

Hence the mobility may be obtained, and the resulting

variation of the temperature dependence (n) on the associated phonon

energy is shown in Fig.3.14. It must however be noted that this

variation is not a very sensitive means of determining the energy of

the optical phonon.

ii) Alloy Scattering.

As the alloying is increased the randomly distributed

Sn and Ge atoms will give rise to an additional scattering factor

generally referred to as 'alloy' scattering. It is independent of

temperature and has the effect of reducing the mobility by a constant

amount. Nordheims rule (M6) which states that

. 1 f4R 0C

x(1-x)

(3.21)

where kt, is the residual mobility and x the alloy fraction, may be

used to give an empirical correlation between this type of scattering

and the degree of alloying. It must however be pointed out that this

rule describes the dependence of residual mobility on alloy scattering

for simple, binary metal alloy systems, and the conditions under which

it may be applied to a system like SnxGel_xSe have not been established.

iii) Crystalline defect, Neutral impurity and Ionized Impurity

Scatterinfi.

.There are other types of scattering mechanisms, which affect

the carrier mobility. Among these are Crystalline defect scattering,

-7!

60.

which as its name suggests arises from crystalline defects, and

neutral impurity scattering resulting from the unionized impurities.

Both these types result in a temperature independent limitation on

the mobility.

The final scattering mechanism to be considered is the

ionized impurity type. It is probable that the charge carriers

arising from the inherent deviations in stoichiometry will give rise

to an ionized impurity type scattering mechanism. In the non-

degenerate case this type of scattering has a temperature dependence

of T3/2 , but where degeneracy exists it is temperature independent.

An overall equation describing mobility (fri.) may be obtained

by considering the scattering mechanisms just described. Assuming

that the reciprocal collision times (T) for the several scattering

processes can be summed (D5), the overall reciprocal mobility may be

expressed as follims since 1,-L= »n„,

1 = 1 + 1 •4. 1 + 1 + 1

/-4 PL PA ILI D PN pi

(3.22)

where lattice scattering limited mobility

alloy scattering limited mobility

crystalline defect scattering limited mobility

neutral impurity scattering limited mobility

ionized impurity scattering limited mobility.

The relative degree of importance of these scattering

mechanisms will vary, depending on the temperature range and alley

composition.

• 3.2.2.7, Analysis of Hall Liobility..

In analysing the mobility curves, the end compounds

SnSe and GeSe will be considered first and then the alloys. Since

there is more published data on SnSe, the discussion will be centred

on this rather than GeSe (GeSe can, be expected to be similar to SnSe),

61

in considering the applicability of the lattice scattering dependent

mobilities.

The mobility temperature dependence (denoted by n) for both

compounds is -2. From optical measurements on SnSe, (T1, M13) the

phonon energies associated with the indirect optical transitions, for

the electric vector polarized along the three crystallographic axes

(a, b and c - the long axis) were found to be

0.022eV 0.047eV

E'llb 0.009eV 0.022eV

0.021eV 0.055eV

In order to find the phonon energy associated with 'n' the phonon

energies forellc would have to be considered. Using the theory

developed by Fivaz (F2) a value of n = -1.6 or n = -2.3 is obtained (Fic 3.19

for the two phonon energies. Neither of these correspond to the

experimental value. With Schmid's (S2) analysis, however, the

value of n for the lower phonon energy is -2, which agrees well with

the observed value. This implies a low degree of anisotropy which

is in keeping with the results of other workers (Al, AB). In fact

Takahashi (T1) has analysed the low-degree of optical anisotropy

cbtained, on the basis of a three rather than two dimensional model,

thus effectively ignoring dimensional effects. It must however be

pointed out that the non-rigorous method used here to identify the

phonon involved in the collision process, and a reported temperature

dependence of- T°.12-0.16(E13) of the effective mass, to some extent

compromises the close agreement between the experimental and theore-

tical values of n. This latter aspect (A5) has been used, with some

success, to explain the large values of n obtained for the lead

chalcogenides. In their paper, Allgaier and Houston (Ad) also showed

that this dependence decreased as the carrier concentration was increased.

62

The carrier concentration used to obtain this value for SnSe

(itrucT-0•12) was about 1017/00, whereas in this case it is 1018/00,

which would result in a smaller temperature dependence of the effec-

tive mass. Thus the part played by this dependence in determining

the value of n would be minimal.

A similar analysis may be applied to GeSe although any

detailed description is hampered by the lack of data on its phonon

spectra.

The essential features of the variation of n with alloy

composition shown in Fig.3.12, may be summed up as follows:

a) On the SnSe side n takes well ordered values which start to

decrease between x = 0.8 and x = 0.7, and assumes a value of --1.6

between x = 0.7 and x = 0.5,

b) there seems to be a distinct discontinuity between x = 0.5

and x = 0.4,

c) on the GeSe side the value of n is more random, but the

general tendency seems to be for n to increase as the alloying is

increased.

Since the principal factor governing the value of n is the

phonon energy perpendicular to the layer, the variation of n with .

composition may be the consequence of a changing phonon energy.

From the graph, it would then appear that the phonon energies are

higher for 0.1 < x s 0.4 and loWer for 0.5 4. 0.7, compared to

the terminal compounds. In the alloying process the Ge or Sn atoms

are expected to enter the lattice as substitutional atoms. Since

Sn atoms are slightly bigger than Ge atoms, alloying would result in

lattice distortions which could modify the associated phonOn energies.

Even if these modifications are small, they would still affect the

temperature dependence of mobility. Because of the difference in

size, it is possible that the effect of the Ge substitutional. atom on

63

the parent SnSe lattice would be tocompress the lattice framework

while Sn atoms in a GeSe lattice would tend to have an expansive

effect. Furthermore from the graph it appears that the lattice

distortions on the SnSe side are ordered while on the GeSe half

they seem to exhibit a certain degree of randomness. If this is

the case, then it could explain the observed discontinuity in the

variation of n between x = 0.5 and x = 0.4. There may however be

other explanations for the behaviour of n with composition. The

model just described assumes a changing phonon energy but this may

not necessarily be the case. The difference between the theory of

Schmid and Fivaz lies in the degree of dimensionality assumed.

The evidence for the terminal compounds is that they exhibit these

dimensional effects in spite of the crystalline anisotropy, which

when translated into carrier motion means that the directional

influence on conductivity is relatively small. In the case of the

alloys however because the interlayer disorder may be expected to be

larger than the basal plane disorder, there will be a tendency for

carrier localization within the layer to occur. In that event

lattice dilations along the c axis (i.e. optical phonons polarized

perpendicular to the basal plane) would provide the main carrier

relaxation process. For such a case the theory of Fivaz would be

more applicable. The corresponding phonon energy for 0.7 > x > 0.5

would be about 0.02eV (from Fig.3.14) which is the same as that of the

terminal compounds. In the case of the GeSe samples the results of n

are probably distorted by the presence of an intercalated amorphous

phase (see next section). It must however be stated at this

juncture that both these models are speculatory, and before any firm

conclusions can be drawn, more experimental evidence will be required.

64

From the results of Albers et al (Al) on SnSxSel_x it

appears that there is a distirict difference in the lattice scatter-

ing dependence of SnS.5Se.5 compared to the end compounds, with the

dependence in the former case being smaller. This agre6s with the

results obtained for Sn.5Ge.5Se is this system.

The behaviour of the mobility curves as the temperature is

reduced becomes less dependent on lattice scattering, and shows a

greater dependence on the other scattering mechanisms mentioned

earlier. The relative influence of the various scattering mechanisms

on this residual mobility ( 11.) will now be considered(Ecb 3.a1).

The variation of 1.J.,1 with composition is shown in Fig.3.15.

The smooth curve represents Nordheim's rule normalized to a

mobility of 60cm2/Vsec at x = 0.5. There is fairly good agreement

for most of the alloys except for x = 0.7 and x = 0.8. The

deviations may be due to the inherent limitations described earlier.

Another indicator of alloy scattering is the variation of the

residual mobility slope (BC) with composition (Fig.3.16). The

linearity of this part of the mobility temperature curve is more

pronounced, the greater the alloying. The graph in Fig.3.16 shows

a definite decreasing tendency with a minimum at x = 0.5. There

is some experimental evidence, admittedly of a negative nature, to

show that this slope is a function of the degree of alloying, rather

than other types of crystalline imperfections. In Fig.3.11,tthe

mobility variation with temperature for two samples of Sn.25Ge.75Se

are shown. They were deliberately chosen such that one of the

samples (BTB21A) showed visual evidence of a greater degree of

crystalline imperfection than the other. It may be observed that

although the mobility for the former was less, the slope BC of the

residual mobility curve remained virtually the same.

0 • •

• 0 •

• •

' • • 0 RE

SID

UAL MO

BIL

ITY SL

OP

E B

C

0.6 .

0.5

o. .

0.3 .

0.1 .

0.9

• • •

•

• 0 * '

'0

• 0

ag

• • v. • • G'

0.0 1.0 0 0.8 01 0.6 0. 5 0.3 0.a 0.1 0.0

Variation of secondary slope BC with composition.

66

The mobility limitations arising from crystalline. imperfec-

tions and neutral impurities will be considered together since it

is difficult to differentiate between the two in a system such as

this one. The variation of the breakpoint temperature TB with

composition may be an indication of the influence of this type of

scattering. The breakpoint temperature is defined as that

temperature at which the residual mobility scattering mechanisms

start to dominate the conductivity process. It is obtained from

the intersection of the two slopes describing the mobility curves,

and the.variation with composition of TB is shown in Fig.3.17. In

the case of the Sn.25Ge.75Se samples described in the preceding

paragraph it was found that the value of TB was greater for the sample

exhibiting the more marked crystalline imperfection. Considering the

variation of TB with composition on the SnSe rich side, it seems that

the defect scattering does piay a significant role, since TB is

increasing. However in the range 0.5 c x 0.8, the decreasing

lattice scattering slope shifts the intersection point to lower

temperatures, and a decreasing TB characteristic is obtained. On the

GeSe side TB increases as the alloying is increased indicating a

decrease in crystalline perfection with alloy fraction. However,

this analysis is subject to the limitation imposed by the difficulty

of extracting the various temperature independent mobility components

from the overall residual mobility.

Finally, the scattering arising from the ionized impurities

will also have to be considered. The effect of this scattering does

not, however, appear to be significant except maybe in some of the

nearly degenerate SnSe rich alloys. It is more likely though, that

the other scattering mechanisms mask out the mobility limitations due

to ionized impurity scattering.

O •

•

•0

•

• •

kto

a60

aao

300

ae0

0 O aoo

140 •

160

1.0 aq 0.8 0.'1 06 0.5 O.I. 0.3 02. 0.1 0.0

21f.;.3.17, VaL.iation of the breakpoint temperature TB with composition.

68

3.2.3. The Thermal Effect.

The anomalous behaviour of the Hall coefficient mentioned

earlier was investigated for the samples corresponding to x = 1, 0.75,

0.5, 0.2 and 0.0.

3.2.3.1. Experimental Procedure.

The resistivity and Hall coefficients of freshly

cleaved samples with the stated compositions were measured at room

temperature using the experimental techniques described in a previous

section. The samples, which were mounted on strips of mica, were

then put in a porcelain boat. This boat was carefully positioned at

the centre of'a long pyrex tube placed in a horizontal furnace. An

inert atmosphere was maintained over the samples by passing argon.

through this tube. The samples were subjected to heat treatment at

different temperatures for varying periods of time. After each heat

treatment period, the samples were rapidly cooled down to room

temperature. Their resistivities and Hall coefficients were then

measured using the same procedure described earlier. The maximum

heat treatment temperature used for these experiments was 350°C.

Heat treatment above this temperature resulted in the resistivities

being affected by strains in the sample set up by the rapid cooling.

These would interfere with the thermal effects.

• 3.2.3.2. Results.

The variation of the Hall coefficient (%) and Hall

mobility (14) with heat treatment time at different temperatures is

shown in Fig.3.18 (a - e). Since the mobility remains virtually

constant, the change in resistivity (p) is a consequence of the

change in the Hall coefficient which is inversely proportional to the

carrier concentration) since they are related by the expression,

HJ

35 Se'3 51,*N5 Ng HT/

35 N5 ( b)

FIJ.').13. Variation cf Hall coefficient and mobility with heat tiz,e for ,:lLffrent

O 09 Of 1. ,

0 ti

0t/ 09 09 I

0

Ow

9e

OE

0E.

.7,01£ ZO9 £ lout

09 0 09 0 Or/

oh,lut - 31411 09 on 09

01.

ob )0001

01

1

FI G.3. 18 (e).

Z2

This in effect means that the observed change is afUnction

of a changing carrier concentration resulting from shifts in

stoichiometry, and that the samples do not undergo any major

structural changes.

The main features of the thermal effect may be described

as follows (Fig.3.19a);

i) With heat treatment below a stated temperature Tc (which is

a function of alloy composition) the carrier concentration increases

and assumes a saturation value after a period of time. The Hall

coefficient values seem to be independent of cooling speed.

ii) For temperatures above Tc, the heat treatment results in an

increase in the carrier concentration. Rapid cooling was necessary

to ensure that the observed changes were not affected by heat treat-

ment at temperatures below Tc. As in the previous case RH assumed a

saturation value after a period of time.

This feature was not observed for Sn.5Ge 5Se presumably

because Tc is greater than 35000 for this alloy. The curve did

however show a distinct tendency to a minimum value, and by extra-

polation a value of T equal, to 365°C may be assumed for this alloy.

iii) As previously stated the Hall mobility remains virtually

constant-through all the heating cycles.

iv) The variation of Tc with composition shown in Fig.3.19(b)

exhibits a definite increasing tendency as the degree of alloying is

increased.

Asanabe obtained similar results for SnSe (AB) and GeSe (A9).

In addition he also found that the carrier concentration again

decreased with heat treatment below Tc, following heat treatment above Tc.

_ _ _

73

- - •-•-• - —. $1475 Cr.)s S-E — . _.0

a ••■•••••

ID ....-0 ---I

..----". . i" - - I'

. ...

'kU\ • .+' / ....•" ..- - .* ....6 —

\ . . , ... ..- ..- --

,, .. • -- ...- ...-

..- . .-- -.. r 0

GE Se

16

a•0 a4. .24 o4 3.0 3. a 3.3

(10 °/<-' T Variation of saturated carrier coc-,centration values

with heat treatent te;:iperature.

1.6

LIQ

74

0.5 N )C

FIG.3.20. Temperature-coMposition projection for binary IV-VI semiconductor near x = 0.5.

x

Variation of To with composition.

75

3.2.3.3. Discussion.

In order to explain the observed effect Asanabe

postulated an impurity diffusion model. This model is based on the

assumption that a certain number of acceptors are generated under

thermal equilibrium with heat treatment above To. On quenching

these acceptors are left generated. They gradually disappear to

establish a new condition of thermal equilibrium. This process is

enhanced by heat treatment below Tel which therefore results in a

reduced carrier concentration. As a possible acceptors_ generation

mechanism he has suggested the diffusion of impurity atoms into Se

vacancies.

The validity of this theory is doubtful since the indications

are that the carrier concentration results from the presence of

ionized metallic vacancies.

This thermal effect has also been observed in other IV VI

compounds like SnS, and the most likely explanation according to

Strauss and Brebick (S7) is that it is caused by internal precipitation.

The mechanism causing internal precipitation is illustrated in Fig.3.20.

This shows the temperature composition (T-x) projection near x = 0.5

• for a IV-VI binary semiconductor (referred to as MN - M for the metal

and N the chalcogenide). If the EN sample which has been N saturated

at the temperature and composition given by point A on the solidus

curve, is cooled at this point, the sample would be supersaturated in N

since the line AB lies outside the homogeneity range. The excess N

can be removed from the lattice either by loss to the vapour phase or

by the formation of microprecipitates of N at sites dispersed throughout

the crystal. The precipitation can occur much faster, since it

generally requires diffusion over a distance much shorter than the

distance to the surface of the sample. Therefore a cooling rate may

be fast enough to prevent loss of N to the vapour phase but not to

prevent internal precipitation. In this case the cooling carve for

76

the lattice will coincide with the solidus curve, as shown by the

arrows in the diagram, down to a temperature at which the diffusion

rate has been reduced sufficiently to prevent further precipitation.

Below this effective quenching temperature, which is indicated by

point C, the composition of the lattice remains constant, and the

cooling curve is given by CD. The carrier concentration in this

system is determined by the shift in stoichiometry, and the nature

of the charge carriers (holes or electrons) depends on whether there

is excess N (which would result in p -type behaviour) or excess M

(for ntype behaviour). The microprecipitates which previously

formed part of the excess N no longer contribute charge carriers and

hence a change in carrier concentration is observed.

Relating 'this to the system SnxGel_xSe and considering the

results obtained, it would appear that heat treatment below Tc results

in internal precipitation of Se, causing a decrease in the carrier

concentration. The dispersed microprecipitate phase is too small to

cause any appreciable change in the mobility. Heat treatment above

Tc probably results in the microprecipitates dissolving back into the

lattice, and contributing charge carriers again, thus causing an

increase in carrier concentration. At high temperatures stoichiomet-

ric shifts resulting from other processes (e.g. an increase in

metallic vacancies) cause a continuing increase in the carrier

concentration. This analysis will also explain the increase in Tc

as the alloying is increased, since internal precipitation is likely to

be more prevalent and for a larger heat treatment temperature range in

the alloys, than in the terminal compounds. A full qualitative analysis

of the thermal effect is precluded by the fact that the exact homogeneity

range for this systeM is not known.

77

3.2.4. The Seebeck coefficient.

The Seebeck coefficient (a) was measured by means

of the apparatus described by Green and Lee (G4). The light probe

set up was used, and d was calculated by means of the formula

oC = ( 40Vc + 21 rvioc

\ VA-Vc

(3.23)

where VA is the voltage at the 'hot' end and Vo that at the cold end.

All the voltages were positive, indicating p-type semiconductors.

3.2.4.1. Results and Discussion.

The Seebeck coefficient (a) was obtained for

various alloys right across the composition range. Its variation

with composition is shown in Fig.3.21(a). The spread of readings

obtained is probably due to crystalline defects in the different

specimens. Taking an average value it would appear that oe decreases

initially as x decreases, but then starts. to increase with further

alloying. In order to ascertain its thermoelectric efficiency, the

simplified expression used by Wasscher et al (W2) for the thermo-

electric (Z.3) figure of merit of the system SnSxSel_x will be used

here. This expression is as follows:

ZJT = 4.02 x io-9(si-- ) exp(11600..)xT ... (3.24) A

where a- is the conductivity in ohm-1cm-1, A the thermal conductivity

in W-cm-ldeg-1 and e< in V deg-1. • The thermal conductivity of SnSe

is 1.9 x 10-2Wcm-ldeg-1 (W2) and according to Krestovnikov et al (K8)

GeSe has virtually the same value. The thermal conductivity will

vary with composition, but it will be assumed here that this variation

is small enough to be neglected. The variation of ZJT against

composition is shown-in Fig.3.21(b). It is similar to that of the

Seebeck coefficient, except that towards the GeSe end, the decrease

is much more rapid. In conclusion, the low values of ZJT•mse the

use of these alloys as thermoelectric devices unlikely.

78

1.0 O. 0.‘ 04 0.X

0.0

FIG.3.21(a). Variation of Seebeck coefficient with composition.

0.3

A 04-

0.1

0.0 1-0

013 0. 04

04 0.0

X r_U.:.tion cf Thenacelectric figure of fr.orit zjT with

79

3.3. ELECTRICAL CONDUCTIVITY PARALLEL TO THE C-AXIS.

3.3.1. Experimental Procedure.

Samples for conductivity measurements were obtained

from freshly cleaved crystallites showing few visual defects. They

were typically about lcm by lcm with the thickness varying between

0.08cm and 0.005cm,. The SnSe rich alloys yielded thicker and better

crystals than those on the GeSe rich side. In order to obtain good

electrical contacts, gold was first evaporated onto each surface of

the sample. The masks used for this evaporation were shaped to

ensure. that as much of the basal plane surface as possible was

covered, without the sample being shorted. This was done in order

to obtain a uniform electric field across the sample. Gold wires

were then soldered to each surface using high purity (5N) Indium.

These contacts were mechanically strong and exhibited ohmic behaviour

for SnSe and the alloys up to and including Sn.4Ge.6Se. The alloy

compositions corresponding to x = 0.3, 0.2, 0.1 and 0.0 showed ohmic

behaviour only for a small range at low fields. As the field was

increased a distinct non ohmic behaviour was observed.

The variation of electrical resistivity with temperature, in

the range 77°K-420°K was obtained for alloy compositions given by

x = 1.0, 0.9, 0.8, 0.75, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1 and 0.0.

For the last four compositions small fields were used to ensure a

linear variation of current and voltage. These measurements were

carried out using the circuit shown in Fig.3.22(a). The current was

obtained by measuring the voltage across a hundred ohm resistor (Ri),

while the sample voltage was measured directly using a D.V.M. The .

temperature was obtained by means of a chromel-alumel thermocouple

positioned close to the sample. The contact resistance was found to

be negligible compared to the sample resistance, since resistivity

measurements using a four probe method on a thick SnSe sample gave

virtually the same result.

100 XI.

05C 1 tin TOR

D. V. /1. I

-0 - 0

L •■• MID ...II

SLY/ITC 1-1

Fly ConfrA crs

80

FIG.3.22(b). Circuit for measuring frequency dependence of c-axis c-onductiVity.

F1G.5.22(a). Circuit for e-aKis resistivity measurement.

81

The field dependence of the conductivity for the samples

showing non ohmic behaviour was obtained up to the limit of current

stability. This was repeated for various temperatures. It was

also noticed for these samples that the passage of a high current

300mn) resulted in a complete change in the behaviour of the

conductivity. It was no longer field dependent (the samples

showing perfect ohmic behaviour throughout the temperature range)

and also showed an increasing tendency with temperature. This

'current annealing' treatment was carried out on samples of GeSe,

Sn,IGe.CISe and Sn.2Ge.8Se, and their resistivity variation with

temperature measured using the procedure described earlier.

In order -co ascertain the sort of processes responsible for

electrical conduction along the c-axis, the conductivity variation

with frequency was also investigated in the range 10Hz to 106Hz.

This was done using the circuit shown in Fig.3.22(b), with the voltage

across the sample being measured by an oscilloscope, which was also

used to measure the voltage drop across a hundred ohm resistor from

which the current was deduced. A sine-wave oscillator with a

maximum range of 109Hz and an output voltage of 10V was used for the

supply.

3.3.2. Results.

The resistivity versus temperature curves (Fig.3.23) show

three distinct characteristics across the composition range:-

a) the resistivity decreasing with temperature, similar to the

basal plane case - this was exhibited by SnSe, Sn.9Ge.1Se

and Sn.EiGeaSe.

b) the resistivity showing a temperature independent or slightly .

activated behaviour over at least part of the temperature

range - as shown by the alloys Sn.7Ge.3Se Sn.4Ge.6Se,

Sn.50-e.5Se and Sn.ele.6Se

and c) the resistivity increasing rapidly as the temperature is

FIG.3.25(a). C-axis resistivity dependence on temperature for x = 1.0, 0.9 and 0.6.

sN_,GE.6ss

SpL6 CE.4 gE 0 0 0 63 0 0 G)

Sei.5 6E-5 LE (I)

fi 1 I.

(f)

ro°

I?

IWO

lab

FIG.3.23(b). C-axis resistivity dependence on temperature for x = 0.7, 0.6, 0.5 and 0.4.

Id

r

is 14• a oi<

FIG.3.23( ). C-axis resistivity dependence on temperature for x = 0.3 and 0.2.

FiG.3.23(d). C-axis resistivity dependence on temperature for x = 0.1 and 0.0.

reduced and then levelling off at lower temperatures - this

tendency is shown by the GeSe rich alloys for x in the

region 0 c x c 0.3

The last type corresponds to those compositions which

exhibited a conductivity field dependence.

The Hall mobility variation with temperature shown in

Fig.3.24 was obtained from the resistivity and the basal Hall

coefficient, using the equation

„ R. PZ

(3.25)

This of course assumes that the carrier concentration is independent

of direction, and that the scattering constant lz in the expression

RH . (where p is the carrier concentration and e the electronic charge),

is unity. The results, although similar to the corresponding basal

plane case, differ inasmuch as they show a well-defined nearly

'temperature independent' region. In the high' temperature limit the

mobility starts to decrease showing a temperature dependence of -2 --

similar to the corresponding basal plane mobility variation. The

Hall mobilities for the other two types of alloys were not calculated,

because possible carrier localization effects along the c-axis meant

that the carrier concentration was not necessarily independent of

direction and temperature.

The results of the conductivity field dependence for the

type (c) alloys are shown in Fig.3.25. The alloys Sn.2Ge.eSe showed

a different conductivity variation with field compared to Sn.1Ge,9Se

and GeSe. The field dependence of the latter showed a near ohmic

66

(3.26)

P7 s

3 4 5

8 9. I I

(101°K-' T/

FIG.3.24. Hall mobility variation with temperature for x = 1.0, 0.9 and 0.8.

10

10

• 101

.1 .3 .4. .5 .6 -7 •9 •

v (eld) 1.0 2-0

FIG.3.25(a). Non-linear I-V behaviour of GeSe.

10

10

c N.1 CE.9 SE

104 V ..1. .5 .6 I .9 9 LO .2.0

V (JaCtg) FIG.3.25(b). Non linear I-V behaviour of Sn.iGe 9Se at different

temperatures

SN.x G E .8 SE

.2 .3 .4. .5 .6. 3 .5' 7 s .0

-11

V (vatti.) FIG.3.25(c). Non-linear I-V behaviour of Sn.2Ge.8Se for

varying temperatures.

V (wet)

FIG.3.25(d). Non-linear I-V behaviour of Sn.3Ge 7Se for varying temperatures. -

92

behaviour at low fields, followed by a power dependence as

the field was increased, and finally a sharp increase just prior to

the current stability limit. For the other two alloys the field

dependence showed a larger deviation from ohmic behaviour at the

lower fields, followed by a region with a power dependence > 2.

As the field was further increased, a distinct trap filled limit

appeared, which gave way at higher currents to a current controlled

negative resistance region (C.C.N.R.). The deviation from ohmic

behaviour and the C.C.N.R. effects were more pronounced at lower

temperatures.

The reproducability of the resistivity characteristics varied

across the composition range. At the SnSe end, the differences

between various samples were not very large (-- X2), but they become

more significant as the degree of alloying increased. For x = 0.5,

the maximum change observed was about a factor of ten. The

resistivities of two samples of Sn.5Ge.5Se are given showing two

different types of temperature variation. These differences are

not surprising since the resistivity in this direction is highly

structure sensitive, and any crystalline defects present in the sample

will have a profound effect. In fact microcleavages could be

introduced into the crystal either during the cooling process, or when

cleaving to obtain the samples for measurement. Wide variations for

this component of resistivity have been reported by Milne (M10) for

GaTe and Hargreaves et al (H3) for ZnS. Milne reported a factor of

ten difference while Hargreaves also mentions a factor of about the

same order. For the resistivities (in the range 1 x > 0..4)

presented here, the samples exhibiting the smallest values were used.

For the type (c) alloys the reproducability was very poor

with difference factors as high as 102. It was also observed that the

higher resistivity samples showed a more marked conductivity field

93

dependence than the low resistivity ones. In view of this the low

resistivity samples were used ror the resistivity variation with

temperature, and high resistivity samples for the field dependence

measurements. The resistivity variation with temperaturd for the

latter is shown in Fig.3.26. The change in the behaviour of these

samples after the 'current annealing' treatment is also shown in

this diagram. In order to check whether the carrier concentration

had changed, basal plane Hall effect measurements at room tempera-

ture, were carried out on the Sn.1Ge.9Se and SnaGe.BSe samples.

A new value of 1.5 x 1018/cm3 (compared to 5.2 x 1017 for

Sn.1Ge.9Se and 4.5 x 1017 for Sn.2Ge.8Se) was obtained for both

specimens.

As stated earlier, the frequency dependence of conductivity

between 10 and 106Hz was examined at various temperatures down to

liquid nitrogen temperature, across the composition range. In

neither the alloys nor the end compounds was any distinct change of

conductivity with frequency observed.

3.3.3. Theory of Possible Conduction Mechanisms.

There has been little or no work reported on the

detailed theoretical analysis of electrical conductivity along the

axis in layer semiconductors. The experimental results and

observations of this conductivity component are in themselves sketchy.

Any theoretical interpretation would have to take account of

the Van der WFolls bonding between the layers. The energy scheme

for this type of bonding consists of discrete energy levels with a.

high degree of carrier localization (p1). For layer semiconductors

this would mean that the carriers are virtually self trapped in the

layers (i.e. the two dimensional limit). The resulting electrical

conductivity would then be very small. The experimental results

X 0.;

■M,

& - 115 GROWN SAMPLES

__.0.1

I O

10

0

0 CURRENT ANNEALED SRMPLE5

3 6 - '

0. 1 I I ; I I I I

(101 °K-1 ‘ T FIG. .26. C-axis resistivity variation with temperature for

as-grown and 'current annealed' samples.

I0

0

95

contradict this both for this system (e.g. 0; SnSe = ohm/cm), as

well as SnSxSel_x (A1), and III-VI layer compounds like GaSe and

GaS (1111).

It would thus appear that the localizing influence of the

Van der Waal's bonding is superseded by some other conductivity

process. A possible mechanism is impurity band conduction and this

will now be considered in detail.

3.3.3.1. Impurity Band Conduction.

The idea of impurity band conduction was first.

advanced by C.S. Hung (H8) to explain the flattening of the

resistivity, and the occurence of a maximum in the Hall constant at

low temperatures in germanium samples. Since then this type of

conduction has been extensively investigated for both germanium

(F5, C3, D3) and Silicon (M14, 01). The actual conduction mechanisms

involved depend on the carrier concentration, i.e. whether it

corresponds to the high, intermediate or low concentration region.

These regions may be described as follows:

i) High concentration region: When the carrier concentration

is high, the associated wavefunction overlap is large and 'an

impurity band' results. The charge carriers behave like a degenerate

Fermi gas in the band and the transport properties are metallic in

nature. The main cause of scattering is the random distribution of

the impurities (M5, K3).

ii) Intermediate concentration region: As the concentration

decreases the wavefunction overlap gets smaller and the carriers tend

to become localized. However there is a range of concentration where

the resonance energy between the carrier results in the formation of

a band. This range corresponds to the intermediate concentration

region and the bandwidth is determined mainly by the resonance energy (N3).

Carrier compensation is a requirement for this sort of conduction.

iii) Low concentration region: With little or no wavefunction

overlap the carriers are localized at impurity sites and electrical

conduction takes place by means of hopping processes. These may

be phonon-assisted in which case the carriers hop from occupied to

unoccupied sites with the aid of phonons, provided vacant neighbour-

ing sites are available as a result of compensation (M9).

The exact values of carrier concentrations corresponding

to the high, intermediate and low regions are specific to a given

semiconductor. It is possible though to differentiate between the

regions by considering various aspects of their conductivity

behaviour. The last two types result in an activated conductivity

dependence on temperature, while in the first case the behaviour will

be non-activated. The fact that the dominant 'hopping process'

pertaining to the low-concentration region is frequency dependent,

may be used to differentiate this from the intermediate region.

The three regions will now be considered in detail:

i) High Concentration Region:

According to Mott the transition irom this region to a

region showing activated behaviour is sharp, and the carrier concen-

tration (NA) at which it occurs is related to the hydrogenic radius of

the impurity centre (the hydrogen like impurity model is assumed here)

by the expression

NA = 4aH (3.27)

This corresponds to the concentration at which the :Lott type

localization will occur, a result of weak carrier interaction. This

type of localization may however be superseded by carrier localization

resulting, from the inherent disorder in t'ae system. This is known as •

the Anderson localization. To describe this (D2) one starts with a

96

97

crystalline three dimensional array of potential wells of depth H

separated by a distance such that for each well an electron can

occupy an s-state at a depth W (Fig.3.27(a)). The wavefunction (y)

falls off with distance r as

= const r-1 exp (-0( r)

(3.28)

wherecA2 = 2MW, m being the effective mass and h Planks constant.*

h2

According to the tight-binding approximation the bandwidth J (<< W)

is given by azI, where z is the co-ordination number and I can be

written as,R2Am*a2. A random potential V is now added to each

well so that there is a gaussian distribution of width Vo (Fig.3.27(b)).

Then if W z> Vos7 J the new band width will be Vo. The carrier states

will then be localized if Vo/j exceeds a critical value-5, but will

otherwise be delocalized. This critical value, however, is a func-

tion of the connectivity of the lattice.

Davis (D2) has described the conductivity for a system where

the transition from metallic to activated behaviour results from

Anderson localization. This was done by making an estimate of the

conductivity starting from the Kubo-Greenwood formula in the form

<0-- 69) (a u2,11- in) <11A> [N(E))

ht ( 3.29)

Here or (0) is the d.c. conductivity, S1 the sample volume, and D the

average matrix element for transitions between all pairs of states.

The signs < > indicate an average overall configuration of the ensemble.

Assuming that the extended wave functions peak at each centre but with random

phase an expression for D was obtained, of the form; •

= 77-(m )(ail ) - I)

.m" ( 3.30)

where ail is -writt,,n f.r the avera7e intersite separtion, m is the free .

(145).

o.;.5 0.5 1 X k g 16

P uNct.H

FIG.3.28. Variation of L-1 with carrier concentration

(a-) J. -.

FIG.3.30. Mott and Davis density of states model.

N (E)

(Q)

FiG.3.27. Anderson localization.effects.

1000

500

L ' 100

SO

Cc) ym.3.3o. Cohen density of

states model.

I l ;

electrcn mass and raK Lye carrier efftive mass. The denSity of

states :V,E) ;-, y be written as

N(E)= (3.31)

where Vo is related to J by the expression for the limit of

localization

Vo 5

J

Now. J is given by,

(

,?-771*.a.)

J = 2z

3.32)

Using these equations and making the relevant substitutions an

expression is obtained for the conductivity of the form;

cr(c) = 0.06e2 (3.33)

as Matsubura and Toyozawa (M5) used a different approach to

obtain the conductivity for the actual high concentration region.

They considered the particular case of the random distribution of

impurities. By utilising the Green function formalism the electrical

conductivity (a- ) can be expressed as the product of two Green

functions connecting impurity sites. A graphical model was developed

to calculate the Green functions, and using the results obtained in

conjunction with the simple hydrogenic impurity model the following

expression was obtained:

Cr = 2e2al,/ 1 x L-1

(3.34)

where L-1 is a complex 'Fo_urier function whose dependence on the

carrier concentration p ) and hydrogenic radius es is shown in

Fig.3.28.

100

Another theory based on the assumption that Boltzthan's

relaxation time approximation was not valid for impurity band

conduction, was developed by Kasuya (K3). A general transport

equation was derived, and this was subsequently used to obtain

expressions for conductivity in both degenerate and non degenerate

systems. In the limit of degeneracy, Cr is given by,

= (e÷0%

4 FF

( 3.35)

where Y is the density of states energy dependence, 71 describes the

drift velocity and BF is the fermi energy, and all the other letters

have the same notation as stated previously. For the non-degenerate

case cr is given by,

)1- cr- Ti y r) o; (KT)

J•-t-i T ( Ytil EF

where N. ) denotes the gamma-function.

(3.36)

ii) Intermediate Concentration Region:

The exact nature of. the type of conduction in this region is

not clear, although several models have been proposed. The main

feature of this type of conductivity (cr ) is that it can be

represented by the equation

Cr = C7; ivxf (e) Kr

( 3 37 )

where a; is the extrapolated value of cr for 1/1- -P. 0, and E is the

activation energy. It is the exact nature of this activation energy which

is uncertain. Fritzsche (F5) has suggested that it may be associated with

energy required to put a second electron on to a neutral impurity site.

101

Mott and Twose (M19) have considered the non-conducting to metallic

transition, as the distance between the impurities decreases, and

have suggested that the magnitude of the overlap integral for

carriers on two different sites may increase to such an extent that

long range order may exist. Under these conditions it is possible

that the lowest energy state of the system will be non-conducting

but separated from this by a small energy will be a conducting state

which can be reached by thermal excitation from the ground state.

It should be noted however that as the carrier concentration increases,

(the overlap increases), the activation energy decreases, finally

resulting in the high concentration region conduction described in the

previous section. Mikoshiba (M7) has developed a theory based on

Fritschels idea, and obtained an expression for E given by

E = E, - ( t.¢3-s) [1 1. So" alef ir-sc" (3.30

ct. ko a_ a

where s is a screening parameter, n is the number of nearest neighbours,

a the effective Bohr radius of the ionized impurity state, E, the activa-

tion energy for this type of conduction in the absence of the band

formed by the negatively charged impurities, and ko the permittivity

of free space.

Another theory proposed by Mycielski (M20) is that E may be

due to a hopping over a coulomb barrier separating an oc:.upied donor

site and an unoccupied one. The expression he obtains for the

activation energy is

E. c, -(3e) Ko

(3.39)

While Mycielskiis (20) theory may explain the conduction at

the lower end of the intermediate concentration re,Eion, 1:asuya (::3) has

102

suggested that at the higher end the band is more likely to be formed

by resonance between the states of the charged impurities (i.e.

negatively charged donors or positively charged acceptors).

Nishimura (N3) has obtained an expression based on this given by,

E= Jr_ [E,-t- C N 0- (3.40)

where El is the energy required to make an isolated ion from a neutral

donor or acceptor, C a constant describing the energy spectrum of the

resonance band, N the donor or acceptor concentration, and K'is the

carrier compensation factor. It is implicitly assumed here that at

this end of the intermediate concentration region resonance effects

are stronger and more dominant than the carrier correlation effects

considered by Mott and Twose. Nishimura also states that, the main

cause of carrier scattering is inherent in the resonance band formed

by the random array of impurities. For this type of scattering the

mobility will be nearly temperature independent.

Another aspect of this type of conduction was considered by

Davis and Compton (D3) who analysed the effects of compensation in

Germanium for a given carrier concentration. As the compensation was

increased for the intermediate carrier concentration region, the

activation energy also increased. This observed effect was attri-

buted to stresses and strains (i.e. general lattice disorder) being

set up due to_the compensation process (in their case it involved

irradiation with fast neutrons).

iii) Low Concentration Region:

The main feature of this reiiion is the localization of the

carriers. Here, again, the conductivity may be expressed as,

cr .12,:xf, EL

ky

103

where E. is the activation energy associated with this region.

This term E,, has been ascribed (M9) to the energy associated with

the transition of an electron from an occupied to an unoccupied

donor site. Compensation is thus an essential requirement for

conduction in this region. Although the transition is considered

to take place by tunnelling, an activation energy still exists

because of the need to overcome the Coulomb barriers associated with

the compensating impurities. Another mechanism for this type of

transition is hopping. One of the differentiating features of

hopping conductivity is its frequency dependence.

3.3.3.2. Conduction in disordered systems.

Another mechanism of electrical conduction which

will be briefly considered is conduction in amorphous (disordered) semiconduc-

tors. The reasons for discussing this will become more apparent when the

conductivity behaviour of the GeSe rich alloys are analysed.

Amorphous semiconductors are characterized by their lack of any

long range order. In order to account for the inherent disorder present

in these systems Mott and Davis (L118) proposed a density of states band

model shown in Fig.3.29(a). . This is essentially that of a crystalline semi-

conductor modified by a small degree of tailing at the band edges, and the

existence of a defect band, near the gap centre. The shaded area indicates

that the states are localised in this region, and the non shaded portion

corresponds to states beyond the 'mobility edge'. The mobility edge

(Fig.3.29(b)) defines the transition between transport due to normal band

conduction and that due to carriers in the localized states.

The electrical conductivity variation with temperature for this

density of states model is as shown in Fig.3.29(c), assuming that the

Fermi level is pinned over a wide range of temperature. With reference

104

to the diagram, in region A conductioi would occur by carriers being

excited beyond the mobility edge, in region B by carriers being

excited into a localized state at a band edge, and in region C by

thermally assisted tunnelling between states at the Fermi level. At

lower temperatures this last branch can be expected to show the

exp(-const T4) behaviour predicted for variable range tunnelling.

According to Cohen (C2) however, this model will have to be

modified for amorphous covalent alloys such as those based on the

chalcogenides Se and Te. Cohen (C2) postulates that the disorder in

these alloys is greater than in the elements or compounds for two

reasons. First there is compositional disorder in addition to trans-

lational disorder and second, since the connectivity of the valence--

banded network at each site changes randomly with the valence of the

atom occupying the site, the translational disorder is enhanced by the

compositional disorder. The resulting density of states variation is

as drawn in Fig.3.30, which shows that the valence and conduction bands

have broadened so as to overlap appreciably. The Fermi energy E is

fixed by the requirement that the number of empty states in the tail

of the valence band above EF equals the number of occupied states in

the tail of the conduction band. Since valence states are electri-

cally neutral when occupied and conduction states electrically neutral

when empty there is a random (overall neutral) distribution of

localized charges throughout the material, positive trapped holes and

negative trapped electrons. In this diagram the uppermost valence

band tail states act as donors, and the lawermost conduction band tail

states as acceptors.

105

The conductivity variation with temperature for this model

is expected to be the same as for the previous case, except that

the transition between regions B and C in Fig.3.29(c) will

probably be smeared out.

Conduction in the localized states takes place mainly by the

process of hopping. Hopping conduction can occur in several ways

some of which are described below:

i) the thermal activation of a carrier from one localized

site to another - this is known as thermally activated

hopping;

4a the movement of carriers with the help of phonons - \ known as phonon assisted hopping;

and ii) the carrier tunnelling to another 'energetically' equiva-

lent site - known as variable range hopping.

The characteristic features of hopping (M19) include a

conductivity temperature dependence of T-W and a frequency depend-

ence given by

(3.42)

where G-H is the hopping conductivity, ui the frequency, and s the

frequency dependence;which normally lies between 0.8 and 1.2. The 14 it

temperature dependence, however, tends to obey a T- law if the

hopping involves carriers in deep trap levels excited to the band

(HO.

3.3.3.3. Field dependent ccnductivitz.

A generalised I-V characteristic is shovn in Fig.3.51.

•r DONOR LEVEL

k.‘

Generalized I-V characteristic.

1c6

FIG.3.32. The Poole-Frenkel Effect.

107

It exhibits a complex behaviour which includes a linear region,

I 041/(1); a low power-law region, I 0c Vn where n = 1.5-2.0(2);

a Poole-Frenkel law or Schottky law region,ln I 041/2(3); a high

power-law region, I ocVn where n > 2(4); and finally a current

controlled negative resistance region (C.C.N.R.) just before

breakdown (5). In the presence of space charge limited currents,

region 2 will show a Inc V2 variation, and in the trap filled

limit (TFL) region (4) will exhibit a linear increase in current

for no change in voltage.

From the results obtained for SnxGel_xSe the two regions of

particular interest would appear to be the Poole-Frenkel law region and

the C.C.N.R. region.

i) The Poole Frenkel Conduction Process;

When an electric field interacts with

the coulombic potential barrier of an impurity centre or trap (s3)

the height of the barrier is lowered as shown in Fig.3.32. This

lowering known as the Poole Frenkel attenuation ( zNqw) is given by,

6 Cipp. F. = e F p r. F Treo k

( 3.43 )

where K is the dielectric constant, F denotes the electric field,

A?F, is known as the Poole Frenkel constant, and the other sub-scripts have the standard notation.

According to Frenkel (F4) the ionization potential E, of the 0

atoms is lowered by an amount given by equation 3.43 in the presence

of a uniform field. Thus the conductivity is then field dependent

and of the form,

(i"„r akri

(5.44)

106

where go-0 is the low field (i.e. ohmic region) conductivity. This

equation may be written in the form

J = Jo exp (StpF

(3°45) 2kT d2

where Jo is now the low field current density, V the voltage and d

the thickness of the sample. A plot of In J (or In I since J is the 1

current density) against V2 will yield a straight line from.the

slope of which the Poole Frenkel constant ApF may be obtained. Since

this constant can also be theoretically calculated, it is possible to

test the applicability of the Poole Frenkel law to a given system.

However, the experimental and theoretical values of Ppp do not

generally coincide due to various anomalous factors. Milne (M10)

gives a comprehensive review of these anomalous effects.

ii) C.C.N.R. effect:

After a maximum voltage is reached, any

further increase in current results in a decrease in voltage. This

is known as the current controlled negative resistance region. It

has been observed in several materials that exhibit switching

properties and may be analysed in terms of impact ionization, double

injection, zener breakdown, thermal breakdown, tunnelling, avalanche

injection, trap emptying and numerous other electrothermal and

electronic mechanisms (C4). In the particular case of SnxGel _xSe,

the main cause of the observed C.C.N.R. is probably due to an electrother-

mal mechanism.

109

3.3.4. DISCUSSION.

In discussing the c-axis conductivity in the system

snx Ge1-x' Se, the three types of behaviour described in Section 3.3.2.

will be considered in turn.

i) Type 'a' alloys.

From the temperature dependence of resistivity it

would appear that the compositions SnSe, Sn.9Ge./Se and Sn.SGe.2Se

exhibit 'high carrier concentration' type (i.e. metallic) conduc-

tivity throughout the temperature range investigated. This would

seem reasonable since the carrier concentration, which may be

considered to be isotropic for these alloys, is in the region of

1018/cm3. The observed resistivity behaviour is characteristic

of normal band conductivity, as it is similar to the basal plane

resistivity dependence. The resistivity anistropy ratio for SnSe

is about 25 which is larger than that of Albers et al (Al) who

found the c-axis resistivity to be about five times that of the

basal plane. They ascribed this to the anistropy of the effective

mass, and assumed an isotropic relaxation time. The difference

between the two resistivity anistropy values may be due to the

presence of microcleavages and other interlayer crystalline defects

in the samples used here. On the other hand, since the back reflec-

tion Laue data for these samples showed a high degree of crystal-

linity, it may be that the measurements of Albers et al (Al) were

subject to 'contact shorting'. It may be pointed out, however,

that large deviations in c-axis conductivity measurements are an

inherent problem encountered with layerlike semiconductors (:.:10, H3).

It should be possible to calculate a value for the resistivity on

the basis of the theory outlined by laisabura et al (!:.:;). This is

hoaever Precluded by the fact that their calc,,lations v;sro based on

110

the tight binding model and does

action between the impurity band

these compositions we are on the

action cannot be neglected.

not take into account the inter-

and conduction band. Since for

limit of degeneracy, this inter-

The Hall mobility variation with temperature, obtained on

the basis of an isotropic carrier concentration, is characterized

by two regions,.a low temperature nearly constant region and a high

temperature portion where the mobility decreases, with a slope of

about -2. This is in effect the same temperature dependence

constant (n) as for the corresponding basal plane samples. From

impurity band theory the main cause of scattering at high concen-

trations result from the carrier collisions with the randomly

distributed impurities. This gives a nearly temperature independent

mobility characteristic, which for these samples seems to appear at

the low temperature end. At higher temperatures it is likely that

the impurity band 'merges' with the valence band (since holes

constitute the charge carriers) and the scattering mechanisms are

now the same as those which would prevail in a normal band. In

this case it would be the lattice type scattering described in

section 3.2.2.1.

ii) Type b alloys.

The alloys in the range 0.7 x 0.4 seem to exhibit

a complicated resistivity variation with temperature. Sn.7Ge.3Se

and the high resistivity Sn.5Ge.5Se (2) samples show an activated

behaviour at the low temperature end, while at higher temperatures

the dependence is distinctly non-activated and metallic in nature.

The resistivity of Sn.7Ge.3Se becomes less temperature dependent

towards the liquid nitrogen temperature end. The composition

Sn. AGe.c Se shows an activated behaviour throughout the te:]rerature

ranee investigated. The activation eher:rics involv&d S :7 al

ran;:inE from 0.005eV for Sn,4Ge.uSe .004,Z1 fcr (2)

111

to 0.012ev for Sn.7Ge.3Se. In the case of Sn6(.4e.4Se and the low

resistivity sample of Sn.5Ge.5Se (1), at the higher temperature the

resistivity shows a metallic behaviour, but the main feature is the

large temperature independent region (which appears to be a transi-

tion characteristic between the activated and metallic resistivity

dependence). The principal factor governing the changing resis-

tivity variation would seem to be the increased disorder resulting

from the alloying process. At the higher temperature; the carrier

interaction effects would offset the Anderson localization tendencies

inherent in alloy disorder, resulting in the 'high carrier

concentration' type behaviour observed. As the temperature is

reduced the carrier concentration slowly decreases (from the basal

plane Hall coefficient variation shown in Fig.3.7) until a value is

reached where the carrier interaction and the Anderson localization

balance out, resulting in a temperature independent resistivity.

This is apparent in the Sn.6Ge.4Se and Sn.5Ge.5Se (1) samples, where

a comparison with the Hall coefficient curves shows that the flat

c-axis resistivity portion corresponds to the minimum low tempera-

ture carrier concentration values. For this explanation to be

valid, the resistivity should be highly dependent on the carrier

concentrations - an inherent assumption in the impurity band model.

For the Sn.7Ge.3Se sample, the (basal planed carrier concentration

is smaller than for the previous samples, and it decreases right

across the temperature range - hence the observed resistivity varia-

tion. The Sn.AGe.6Se sample has a carrier concentration which is

again slightly smaller than that of the other samples and an activated

resistivity behaviour is observed throughout.

The preceding discussion has been centred on the effect of the

changing carrier concentration on the carrier interaction and conse-

quent band formation. It was assumed here that the degree of

disorder is constant, and that the chanc::in.rsistivity characteristics

112

are a result of changes in carrier concentration, but this is not

necessarily true. The degree of disorder will vary between

samples of the same composition as the results for the two

Sn.5Ge.5Se specimens seem to indicate (this is however tempered

by the fact that the carrier concentration shows a slight variation

from specimen to specimen). It would therefore appear that the

resistivity behaviour is controlled by the interplay between the

variables of crystalline disorder (which results in Anderson

localization) and carrier concentration (which affects the inter-

action between the carriers).

It may be possible to obtain some idea of the resistivity

values on the basis of the theory outlined by Mott who considered

the effect on impurity band conduction, of the onset of Anderson

localization (Section 3.3.3.1.). The value of the hydrogenic

radius aH can be calculated from the expression,

QH

a K 1 "

(3.46)

where K is the dielectric constant and 4the ionization energy

which is given by

= 13.6 m

(m*) ) — 2 (eV)

7

(3.47)

where m* is the effective mass and m the electron mass. From the

long wavelength reflection data a value of about 10 may be ascribed

to IAT1). According to Albers et al (A2) the hole effective mass

in SnSe is 0.2m, and substituting these in the above equation a

value of 0.027eV is obtained for . The resulting hydrogenic

radius would then be --5501,°, which would give a resistivity from

equation (5.53) of 0.23 ohm cm. The resistivity in two cases

113

where the limit of localization is exhibited, is.— 2 ohm cm for

Sn.5Ge.5Se (1) and — 3.7 ohm cm for Sn.6Ge.4Se. These are

about 10 to 15 times the calculated value. There may be several

reasons for this discrepancy but the most likely ones are

i) The effect of the weak lattice connectivity (due to the

weak Van der Waals forces) which has not been taken into

account in deriving equation (3.33),

and ii) the inherent deviations in the experimental value of the

resistivity.

If a more realistic estimate of the conductivity is to be obtained

these two factors will have to be taken into account.

The activated resistivity behaviour of Sn.7Ge.3Se, Sn5Ge.5Se

and Sn.4 Ge .0 -Se may be explained on the basis of conduction in the

'intermediate carrier concentration range'. The activation energy

may be obtained from the equations presented in section 3.3.3.1.

However, the fact that the various parameters involved are not known

for this system, plus the structural anistropy, which has not been

taken into account in developing the theory, preclude any rigorous

analysis of the experimental data.

iii) Type 'c' alloys.

The GeSe rich alloys which show a field dependent

conductivity, possess several interesting properties. It was more

difficult to obtain crystals of the same size and quality as for the

SnSe rich alloys.' This is to be expected since from their relative

positions in the periodic table it is apparent that SnSe is more

easily compounded than GeSe. There is some evidence from the

electron probe microanalysis that a second possibly amorphous phase

may be present for the GeSe rich alloys. Ths. will not show up

114

distinctly in the diffraction patterns of these alloys. The back

reflection Laue photographs of the crystals along the 'c' axis

however show a greater degree of crystalline disorder than for the

SnSe rich side.

It was also observed that, whereas wide disparities were

obtained for resistivity measurements along the c-axis (in the order

of 102), basal plane properties tended to remain fairly constant

and were reproducable. This seems to suggest that any amorphous

phase present is likely to be in the interlayer gaps, rather than

in the basal plane. It is a possibility given credence by the ease

with which layer compounds can be doped using the process known as

intercalation (W3). In intercalation atoms of an additional

element are taken into vacant Van der Waal's sites. The existing

evidence in this case indicates the presence of an intercalated

amorphous phase in the alloy system for 0.3 x 0. This phase

would be randomly distributed throughout the interlayer gaps.

The resistivity curves seem to have three distinct regions, a

high temperature non-activated region, followed by a region showing

a distinctly activated behaviour, and as the temperature is reduced

further a tendency to flatten out is observed. From the values of

the resistivity and the shape of the curves it would appear that the

amorphous phase dominates the conductivity process. Therefore in

analysing the results, use will be made of the density of states

models described earlier. The various samples will now be considered

individually with the resistivities being related to the characteris-

tic shown in Fig.3.29(b):

GeSe: The resistivity curve for this sample may be analysed

on the baSis of the Mott and Davis - density of states model. The high

temi=ature section denoted by A snows a non activated resistivity

del,endence.

115

This would be reasonable since if, as stated, the carriers' are excited

beyond the mobility edge they will behave as charge carriers in a

normal band. It is in keeping with the results of SnSe rich alloys

since the behaviour in the normal band (i.e. impurity band), in this

temperature range is non-activated. The resistivity passes through

a minimum and then starts to increase with an activation energy of

0.06ev. This part probably corresponds to section B in Fig.3.29(b).

The low value of the activation energy may, since the impurity level

is virtually degenerate with the valence band, represent the energy

required to excite the carriers from the localised levels into the

main band. The resistivity curve then starts to level off and this

most probably corresponds to thermally assisted tunnelling between

states in the Fermi level with an associated energy of 0.004ev.

Sn.1Ge.9Se. The. resistivity dependence on temperature for

this alloy can be explained in exactly the same way as for GeSe.

The only difference is that the activation energy associated with

the low temperature behaviour is 0.006ev. Since these energies

depend on the randomly distributed intercalated amorphous phase,

variations from sample to sample are to be expected.

Sn.2Ge.8Se. The high temperature behaviour of the resistiv-

ity is similar to the previous two cases, but although the activated

part shows the same general tendency, the dependence is more

graduated. This is probably the result of a greater degree of

inherent disorder introduced by the alloying process. If this is

the case, then the Cohen model is more applicable in this instance

than the Mott and Davis model. The folwer would result in a more

Eroded resistivity variation such as the one observed here, because

of the distribution of the localized states throuhout the bandgan.

Sn.3Ge.7Se. The resistivity characteristic is similar to

116

that of SnaGe.E5Se, with the graded behaviour resulting from the

alloy disorder being emphasised even more than in the previous case.

The field dependence exhibited by these alloys may be analysed

in terms of the complex I-V characteristic described in Section 3.3.3.3.

From the log I versus log V curves in Fig.3.25, it would appear that

GeSe and SnaGe.9Se exhibit a similar behaviour while Sn.2Ge.8Se

and Sn.3Ge.7Se also show similar properties. In discussing these

alloys the former will be considered first and then the latter.

For the compositions GeSe and SnaGe.9Se, the field dependence

seems to consist of several distinct sections. The linear region

I ...eV is not obvious but it does exist at very low fields. The low

power law and high power law regions are denoted by B and D. The

high power law region shows a definite tendency to a trap filled

limit dependence, and is probably just a transition region. In

order to investigate the presence of a Poole Freakel law region a

graph of In I versus Vi was plotted and is shown in Fig.3.33. The

region denoted by C of the log-log I-V characteristic seems to show

a linear behaviour for the Poole Frenkel law. From the slope s of

the linear portion, the Poole Frankel constant 1.-1F. can be calculated

using the equation

S= ggr x I

akT

(3.45)

where d is the thickness of the sanple. The values obtained are

1.06 x 10-2eVcm1V-2 for GeSe and 1.17 x 10-2eVcInV--8- for

SnaGe.9Se(where the slope was virtually the same at all temperatures).

The value of &F can also be theoretically obtained from the equation;

3 PPF.

71 Ec,

(3./-19)

-3.0

-3.5

.0 0

0 0 0

V a‘ (1fuet4)4.

0

117

-D.5

0

0

FIG.3.33(a). Plot of ln— versus V2 for GeSe.

0

A

4.

A

0

0

0

-3

-3.5 a a a

a a a 0

- 11.5

- 5

0 .6 .8 V (wetA l

FIG.3.33(b). Plot of 14versus V2 for Sn.1Ge.9Se.

1.0 c)-

119

where Eo is the vacuum permittivity and K* the dielectric constant.

For GeSe, Yeargan and Taylor (Y2) give a value of 8 for the dielec-

tric constant, and the resulting value for

1 cm-2V-2. A similar result for SnaGe.9Se can be expected since K*

will not differ by much.

Although experimental values of XF are generally different

from the theoretical values, they are usually less and not as in

this case greater than the calculated value. This apparent

anomaly may however be resolved if it is assumed that the P.F.

mechanism occurs only within the intercalated amorphous phase.

The value of d used here (140 for GeSe and 170ponfor Sn.1Ge.9Se)

will not then correspond to the P.F. value of d required for

equation 3.48. However if the theoretical value of Ppris used in

this equation then the effective thickness of the amorphous phase

can be obtained. The slope s = 1.8 gives an effective thickness

of 900°A for GeSe. A similar value can be expected for Sn.1Ge.9Se

since the slope remains virtually the same.

Implicit in the discussion of the preceding paragraphs is the

assumption that at higher fields the intercalated amorphous phase

acts principally as a source of carrier traps. Thus in the event

of all these traps being filled, the current will show a nearly

voltage independent linear increase. This is evidently the tendency

as the graphs in Fig.3.25(a) and (b) show.

The field dependence curves for Sn.2Ge.8Se and Sne3Ge.7Se do

not seem to possess any distinctive linear regions and a plot of

LaI versus V2 showed no recognisable linearity. It would appear

though that the general shape could be fitted into the framework of

the com.nlex 1-V characteristic described earlier. A problem of

delineatin the various regions arises, beeauze tn:::,Isi-

tions between the regions results in a smearinj out of the lineality.

PAr is 2.7 x 10-4eV

120

The explanation for this behaviour probably lies in the increased

inherent disorder, due to the greater degree of alloying. There

is one major difference compared to the previous case, and that is

the presence of the C.C.N.R. region. This probably results from

detrapping caused by the Joule heating effect of the high currents.

It is possible that the amorphous phase was tending to crystallize,

thereby releasing carriers trapped at localized levels. It was

also observed that the resistivity of a sample decreased slightly

after it exhibited the C.C.N.R. effect.

The final aspect to be considered is the 'current annealed'

temperature dependence of resistivity for GeSe, SnaGe.9Se and

Sn.2Ge.8Se shown in Fig.3.26. The graphs show the same general

behaviour as the SnSe rich alloys and it may be presumed that the

conduction is of a similar 'high concentration' impurity band type.

Although the basal plane carrier concentration of ,-- 1.5 x 1018/cm3

would be in keepingwith the non activated resistivity behaviour,

it is different from the value of the carrier concentration prior

to the 'current annealing'. This is probably due to the generation

of carriers resulting from the 'thermal effect' described earlier.

The observed resistivity behaviour may be explained on the basis of

- the crystallization of the intercalated amorphous phase, due to the

current 'annealing' treatments. This is supported by the fact that

the resistivity decreases by a few orders of magnitude, and also

exhibits a linear field dependence. If this hypothesis is correct

it may be possible to retrieve the high resistivity state by passing

a large current through the sample. This would hopefully cause

localized melting of the crystalline phase, and if a rapid cooling

process is employed, it may result in the reaurearance of the inter-

calated amorphous phase. This could form the basis of switching

applications' for the GeSe rich alloys.

121

The general behaviour observed here is given credence by the

work of Braun (B4) and Zakarov et al .(Z1) on GeSe films. Braun

reported the presence of conductivity switching, while Zakarov found

a phase transition from the amorphous to the crystalline state at

145°C, with a subsequent change in resistivity. Further evidence

for the theory outlined here comes from the work of Tredgold et al

(T4) on the switching mechanisms on a similar layer like semi-

conductor, GaSe. According to them, the weak Van der Waal's bonding

is susceptible to basal dislocation and faults such as microcracks

and inter-crystallite boundaries. The large number of such stacking

faults could produce an essentially disordered structure viewed along

the c-axis. The existence of such a high degree of disorder due to

dislocations and faults could give rise to a continuum of localized

energy levels within the forbidden band. This would correspond to

the Cohen density of states models, which was used here to describe

the behaviour of SnaGe.8Se and Sn.3Ge.7Se.

3.4. Electrical properties of thin Films.

The transport properties of thin films of the system

Sn•• Ge1-xSe were investigated. There is very little data on the

electrical properties of thin films of GeSe and SnSe. The reported

work is limited to resistivity measurements on crystalline films of

SnSe (G2, MO, and the analysis of electrical conduction mechanisms

in amorphous GeSe films (F6, B4). The structure of the films used

for these measurements were analysed in an earlier chapter. In this

section the results obtained for films of SnSe, Sn.BGe.2Se,

Sn.5Ge.5Se and GeSe will be described.

3.4.1. Experimental Procedure.

Electrical contacts were made to the films usins-

high purity Indium solder and sold wire. The substrate was mounted.

cn a copper block, which was then placed in. a cryostat connected to

122

a vacuum system. The electrical measurements were carried out

under vacuum 163torr) in order to reduce any surface effects.

The experimental procedure used was the same as for the bulk

samples. A field of 4.8KG was used to obtain the Hall voltage.

The current was measured by a nanaeter and the voltage by using

a D.V.M., on the range with an input impedance > 5000M SI.

3.4.2. Results and Discussion.

The results of the various films are shown in

Figs.34-37. The one common feature of all the films is the

activated resistivity dependence on temperature. These transport

properties appear to be different from that of the corresponding

bulk basal plane. The Hall coefficients of SnSe and Sn.8Ge.2Se

are orders of magnitude larger than those of the bulk basal plane.

The Hall mobilities of the films SnSe, Sn.2Ge.8Se and GeSe, unlike

for the bulk basal plane, show two distinct regions which indicate

both lattice type and ionized-impurity type scattering.

The various films will now be considered in turn:

SnSe: The Hall coefficient exhibits an exponential increase which

tends to a constant value below about 400°K. Above this temperature

an anomalous behaviour is observed. The room temperature Hall

coefficient gives a valUe of 1.5 x 10164which is nearly two orders

of magnitude smaller than the bulk. This is not surprising since

stoichiometric deviations tend to be less marked in evaporated films.

Mitchell (M12) has in fact reported a .carrier concentration of 101//cm3

for a highly purified SnSe sample. The electrical results obtained

by Mitchell for his sample are very similar to those of the SnSe film.

The resistivity temperature dependence shows an activated

behaviour with an activation energy of 0.27ev. As in the case of

the Hall coefficient, the resistivity shows aq anca:alcus tendency

Joa

'of

10° a 3 iO 3

°K., r/

FIG.3.34. Transport properties of SnSe film.

3 I 0

50

40

30

10

104—

I I 10

so

4

30

.20

10 3 4 5 6

0.192)

51,11 GE.?, SE 10

ft

•

1oI 10

tam

rr

o RH

Qe 10

3 10 ram

•

/00

FIG. 3.35. Transport properties of Sn.8Ge.2Se film.

SN5GE5 E

6

• .

FIG.3.36. Resistivity dependence on temperature for Sn.5Ge.5Se.

60

40

3°

10

40 7

•K -1 It 5 1 2

T, T

FIG.3.37. Transport properties of SGeSe film.

12T

above 400°K. A very similar effect was observed by Goswami and

Nikam (G3), and it may be ascribed to the 'thermal effect'.

The Hall mobility shows a lattice scattering limited mobility

above 375°K, with a temperature dependence of -1.9 (the accuracy

is limited by the lack of sufficient experimental points), which is

very similar to the bulk. It is likely that as in bulk SnSe,

optical phonons constitute the dominant scattering mechanism.

Below 375°K the mobility seems to show an exponential decrease with

temperature. This is probably the result of potential barriers

arising from grain boundaries. The grain boundary regions which

give rise to these barriers will have high resistivities compared

with that of the undisturbed crystal, whose resistivity can be

assumed to be the same as that of the normal bulk basal plane

(-- 0.04ohm cm). The energy associated with these grain boundaries

is about 0.27ev (as obtained from the slope of the resistivity

curve) and this agrees very well with the results of Goswami et al

(G3).

Sn.5Ge.2Se: The results are as one would expect, similar to those

of SnSe. The room temperature Hall coefficient gives a value of

1.6 x 1015/cm3. The anomalous effect is not apparent possibly

because the temperature was not high enough: The energy associated

with the grain boundaries is (from the slope of the resistivity

curve) about 0.22eV - of the same order as for SnSe. The lattice

scattering dominated mobility results in a temperature dependence of

1.7 which is slightly less than for bulk Sn.8Ge.2Se. The differences

between SnSe and Sn.EiGe.2Se films seems to stem from the added alloy •

disorder present in the latter.

Sn c.Ce This film exhibited a very high impedance throl:,:hout

the t=oerature range considered. This caused 1 -=rge standing - voltages

128

and prevented any reasonable Hall voltage from being observed.

The Sn.5Ge.5Se crytallites were smaller than those of the

other films. Thus the number of grain boundaries would be much

greater, and this would explain the very high resistivity values.

The resistivity curve gave a potential barrier energy of 0.21ev -

almost the same as that of Sn.8Ge.2Se.

GeSe: The general tendencies of the Hall coefficient and

resistivity were the same. Although they differ from the

crystalline bulk basal plane properties, they bear a high degree

of resemblance to the electrical properties of polycrystalline

GeSe obtained by Asanabe et al (A9). This seems to back the

general argument used in the preceding paragraphs, that the main

conductivity controlling factor is the potential barriers

associated with the grain boundaries. The resistivity activation

energy is about 0.09ev and the slope of the mobility at the lower

temperature is 1.6.

Finally it is interesting to observe that the temperature

dependence of the potential barrier limited mobility becomes less

pronounced as the energy associated with this barrier decreases:

Activation Mobility tempera- Energy. ture dependence.

SnSe 0.27ev +4.6

Sn .8Ge .2Se 0.21ev 43

GeSe 0.09ev 41.6

In considering the conductivity( fir ) both the carrier concentration

( p ) and the mobility limiting factors have to be taken into account,

since a- is given by the expression

p 11 1J.

(5.50)

where e is the electronic charge and the mobility. It would then

appear that the low conductivity (or high resistivity) of nSe

129

compared to the bulk would be the result of both the low carrier

concentration, and the mobility limiting grain boundary barriers.

In GeSe however, the latter factor seems to dominate the

conductivity expression, since the room temperature carrier concen-

tration is almost the same as for the single crystal bulk sample.

In conclusion it may be said that the overall picture of

the electrical conduction process in SnxGel_xSe films is one of

lattice scattering domination in the high temperature limit, and

of potential barrier limitation at lower temperatures.

130.

3.5. The Mossbauer effect in SnxGel_xSe.

3.5.1. Simple Mossbauer Theory.

Mossbauer Spectroscopy is concerned with transi-

tions between energy levels within the nuclei of atoms. The fre-

quency of the resulting radiation is in the Y region of the electro-

magnetic spectrum. If a sample is placed in the path of a X-ray

source with the same nuclear structure (i.e. same element) then

resonant reabsorption of this emission can occur. However because

of the very fine line widths involved, the recoil of the source

nucleus will result in a shift of the incident frequency, thereby

inhibiting any resonant absorption. Mossbauer overcame this

problem by using solid crystal lattices as emitters, in which the

emitting nucleus is firmly fixed to surrounding nuclei, and hence

has a large apparent mass within which the recoil energy can be

dissipated. Furthermore, the source and sample were cooled to low

temperatures so that thermal motions of the lattice atoms are

reduced to a minimum. In order that the precise absorption fre-

quency may be calculated (since 1018Hz is difficult to measure) the

Doppler effect was utilized and the absorption frequency could then

be related to the velocity of the source relative to the sample.

A geiger counter placed behind the sample gave a measure of the X-rays

and any absorption would be indicated by a sharp fall in the count.

The Mossbauer effect was used in this case, to obtain the chemical

shifts and quadropole splitting of the Sn atom in the system

snxGel-xsa-

i) The Chemical Shift:

Shifts were observed in the Mossba,ler

effect when the chemical environment surrcundinj; a ;riven nucleus

varied. • These -chemical shifts are relatiVe to a stand-,rd.

131

According to Greenwood (G5) the chemical shift (6) may.be expressed

as

c5 =Const• cOL- cilMe (3.31)

4

where r is the radius of the nucleus, Sr the change in radius for.

2- „ the excited state of the nucleus, and S 1 W0)/ is the change in s

electron density at the nucleus in going from the source to the

absorber. When is is positive, a positiie chemical shift

implies an increase in the s electron density at the nucleus.

Thus the observed chemical shifts may be used to obtain information

about the relative s-electron densities at the nucleus.

The Quadrupole effect:

In the preceding discussion, it has

been assumed that the nucleus is spherical, but this need not

necessarily be so. Any nuclear state with a spin I > -12- has a

quadrupole moment, Q, and this can align itself either with or

across an electric field gradient cb.. This effect is seen as a

doublet with a separation .6 , and for the excited state having

I = may be expressed as

6= const Q. cis.

(3.52)

Hence this may be used to obtain information about site symmetries

and field gradients within a crystal.

3.5.2. Results and Discussion:

The experimental work was carried out at Chelsea

ColleEe by Dr. Donaldson and the results obtained are shown in

Table 4.1.

132

Liquid Nitrogen Temp. Room Temperature.

Composition (x) (rams -1) (mm.-1) 6 (mms-1) 6 (mms-1)

1.o 1.29 0.83 1.27 0.73

0.9 1.15 0.84 1.32 0.50

0..8 1.76 0 1.54 0

0.7 1.49 0 1.23 0.67

0.6 . 1.26 0.79 1.29 . 0.51

0.5 1.29 0 1.29. 0.57

6 - Chemical Shift d- Quadrupole splitting

TABLE 4.1.

In going from SnSe to Sn.9Ge.1Se, a decrease in the chemical shift

occurs at liquid nitrogen temperature, although the quadrupole

splitting remains the same. Increasing the germanium content to

Sn.E1Ge.2Se results in a significant change in the Mossbauer parameters,

the chemical shift at 78°K increases to 1.76mm/sec. and there is no

longer any resolvable quadrupole splitting. The data for Sn.3Ge.7Se

still showed an unresolved, relatively narrow resonance line but the

chemical shift has decreased to 1.49 mm/sec. The parameters for

Ge.4Sn.6Se are close to those of SnSe itself.

The carrier ,concentration for this system, as was seen

earlier, stays fairly constant on the Sn rich side and then starts to

decrease as the germanium content is increased on the GeSe side. It

was earlier stated that since Sn vacancies are energetically more

favoured than Ge vacancies, one would expect a steady decrease in

going from SnSe to GeSe. That this is not the case, at least in.the

SnSe half, implies the presence of a carrier source, which from the

Mossbauer results .would seem to be the Si s-electrons. This would

acccunt for the initial decrease in the chemical shift at the licuid,

nitrogen temperature.

133

The anomalously large increase in cc for Sri p,Ge ,Se may be due to

the fact that the electronic environment of the Sn is more symmet-

rical than in the previous cases. Following this, the steady'

decrease in the s-electron density continues as the carrier

concentration values are kept at a fairly constant level.

An increase in temperature should result in an increase

in the chemical shift since the Sn-chalcogenide bonds increase in

length. This does not seem to be apparent in these results and

the reasons for this are not very clear.

134

CHAPTER 4.

OPTICAL PROPERTIES.

4.1. INTRODUCTION.

The variation of the energy gap values with composition

have been reported for several IV-VI ternary alloy systems (S5) and

for a few quaternary systems (N2). There is however no band gap

data on the alloy systems SnxGel_xSe. The main purpose of the work

carried out here was to determine the exact nature of the variation

of band gap (Eg) with composition (x). The alloy systems

PbxSni_xSe (S6) and PbxShl_xTe(B7) have been extensively investigated

because of their zero-band gap behaviour. Albers et al (Al) have

carried out transmission measurements cn SnSl_xSex , which is

structurally similar to SnxGel_xSe. From the shape of the absorp-

tion edge they concluded that the variation of Eg with x is linear

at 300°K, with the transitions being of the allowed indirect type.

Of the two terminal compounds, detailed optical measure-

ments have been carried out on SnSe, but existing data on GeSe is

sketchy. Mochida (1;113) obtained the variation of absorption

coefficient with photcn energy for SnSe crystals along the a and b

axes, using polarized light. The result shown in Fi6.4.1(a), has

however to be modified since the measured absorption coefficient

(c)(0) is the sum of absorption coefficients due to band to bond

absorption (0(), free carrier absorption (0(1) and scattering 0(2,

i.e. c<o = °C+c<1 +c•C2' The free carrier absorption is neL-ligibly

anall in the short wavelength rane near lrmaad tends to zero at

shorter wavelen,7ths. The componant4X2 due to optical scattering

arises from the inherent crystal iciferfections and is constant

thrceut the .velea:-th rala,:te. The 1:-.1d to band

' tccefficiaat caa 73 ol;tirled suAraci

et 0

O

K

1

10 9 8 7 6 g 10 9 e 7 6 W./AVE NUMBER WAVE Null EIE-R

(a) ]5r (2)

10

I

I

1

I I

I

I

4 /

of 1

.t .4 1.0 1.1

PHOTON ENERGY (.12/1r)

(c)

FIG.4.1. Absorption coefficient dependence of SnSe for Eire: and Ellb%

136

factor from the experimentally derived absorption coefficient.

The results obtained by Mochida (M13) are shown in Fig. 4.1(b).

A result consistent with allowed indirect transitions was 1

obtained by plotting a graph of (10(hv)2 against photon energy

(Fig. 4.1(c)). The curve consisted of a series of discontinuous

straight lines, the discontinuities corresponding to the emission

and absorption of phonons. The energy gap and phonon energies

were obtained using an analysis similar to that used by Macfarlane

et al (Al, M2) to explain absorption in Germanium and Silicon.

The energy gap thus calculated was found to be the same as the 'zero

absorption! energy Obtained from Fig. 4.1(b). The values were

(E' being the electric vector):

e.11 a Ellb

Eg 0.932 ev 0.889 ev

EThononi 0.022 ev 0.009 ev

E phonon2 0.047 ev 0.022 ev

Takahashi et al (T1) used a similar analysis to explain

their results for the absorption coefficient. with the electric

vector polarized parallel to the c-axis 4-2a). However in

this case there are four distinct regions and the bandgap and

Thonon energies were found by using the following relations:

E2(+) + E2(-) El(+) + E1(-) 0.948ev 2 2

E 21(-) - El(+) (-) - 217 = 0.0 5ev

2

E yhcnon2 = E-2(-) - E2(+) E2(-) 7 s7 = Q.C205ev

NOTE: El. ELEcrAIC vEcro4 or

ilvcipEAn- E. M. RADinTior

- gEfek'S To CRYSTAL IL[ES

X10

3

re

'6

0 I . 0

PHOTON ENERGY Ce r̂) (a.)

10

10

0 1.0

PHOTON-ENERGY (RA)

FIG.4.2. Absorption coefficient depaence of SnSe for c' .

138

Mitchell (M12) also carried out optical measurements on

SnSe single crystals but he used unpolarised radiation. By

plotting against photon energy and extrapolating the curve to

0.C= 0, a value for the indirect energy bandgap of about 0.9 eV

was obtained. Theo(0 relationship exhibited a straight line

behaviour without any of the discontinuities observed by

Mochida (M13). Mitchell (M12) also obtained a value for the

direct energy gap of 1.2eV, by plotting o(2 against photon energy

in the high absorption region.

Both Mochida (M13) and Takahashi (T1) observed the band-

gap variation with temperature, and obtained an isotropic direction

independent,energy gap temperature coefficient of - 4.3 x 10-4ev/oK.

The optical properties of GeSe have been investigated by

Kanneswurf et al (K2) and Lukes (L4). Kanneswurf (K2) used

unpolarised light for his measurements of reflectivity and trans-

mission of thin single crystal specimens of GeSe. Analysing the

absorption behaviour to determine the type of transitions, he

obtained a good fit for allowed indirect transition, at low

absorption, with an energy gap of 1.15Y(Fig.4.3a). For the higher

absorption region a good fit was obtained for (04hv)-z, against photon

energy, giving a direct.energy bandgap of 1.53eV (Fig. 4.3(b)).

This photon energy dependence of the obsor2tion coefficient for

direct transition indicates that they are of the Iforbiddent type (L7)

Kannerwurf (K2) also obtained a seactral respenee CUX70 for

evarorated GeSe films. The results were analysed using- a procedure

prescribed by ;loss (Ml)), and the threnold eeergias of the two bands

of responsivity corresponded closely to the energy gap values that

were determined for the direct aref, iudirect Land traeitione.

mO

>c, rbtiM

3

0 1.q a.3

Pnoros ENERGY &Ad Ls

33

O

Lit 1-24- 1.30

PHOTON ENERGY (e4r)

(0-)

FIG.4. 5 . Absorption coefficient dependence on photon energy for GeSe.

FIG.4.4. Schematic representation of indirect transitions.

140

In obtaining the optical properties for GeSe Lukes (L4)

used light polarized along the crystallographic axes. The

resulting absorption coefficient was analysed in terms.of indirect

3 forbidden transitions (i.e. °( S ocEph). The reasons for this are

not obvious and cast some doubt on the results. The energy band-

gap that he obtained (1.1 ± 0.02eV) ffas however of the same order

as that of other workers (K2, M3, AS).

The main purpose of investigating the optical properties

of SnxGel_xSe was to ascertain the variation of bandgap with

composition. The optical properties of both the bulk and

evaporated films were obtained. From the bulk properties, the

indirect bandgap could be found but the samples were too thick to

yield any information on the direct gap. The temperature variation

of this bandgap was found using bulk specimens of various composi-

tions. As will be pointed out later, the analysis of the thin

film optical data proved difficult, because of the uncertainties in

the various parameters. Thin films were however used for photo-

conductivity measurements, as the signals obtained were much larger

than for the corresponding bulk specimens.

The following sections will detail the various results obtained.

In order fully to investigate the observed behaviour, the theory of

the possible types ofoptical transitions will now be described.

4.2. Theory of Optical Transitions.

The response of a given medium tc the driving electromEignetic

field D = E. ,11,1 is described by the complex dielectric function given by

f (w) = £ l (w) iC2(w) (1)

This is related to the refractive index N(w) by the expression,

N(w) = n(w) ik(w) = e(w)-- (2)

where n is the real refractive index and k the attenuation index.

By equating the real and imaginary parts of these two equations,

141 £1 = - k2

2 = 2 nk

The optical constants n and k are real and positive numbers and can be

determined by optical measurement. Another quantity, which is easily

-obtained by experiment, is the normal incidence reflectivity

R= (n - 1)2 + k2

(n + 1)2 + k2 (5)

Only cubic crystals are isotropic in their linear optical response.

The optical properties of non cubic crystals, which include bire-

fringence and dichroism, are described by a tensor dielectric function

(H2). In layer compounds the tensor generally reduces to the two

componentsEl for polarization in the basal plane, andE 11 for polariza-

tion along the c-axis.

The dielectric function contains contributions due to excita-

tions of lattice vibrations, mainly in the infra-red region of the

spectrum, and to electronic excitations of both the intraband and

interband type. In semiconductors, intraband transitions give only

small contributions since the concentration of free carriers is small,

compared to that in metals. Interband transitions occur between filled

valence band states. and empty conduction band states, mainly in the near

infra-red region of the spectrum for the semiconductor system under

investigation.

The imaginary part of E (w) is proportional to the joint

(valence and conduction band) density of states function Jvc(w) and to

the square of the matrix element for the transition Mvcl;

2(w) oc 1 Jvc(w) x (6) -2

The function J vc depends strongly on dimensionality; at the

onset energy for transitions corresponding to the bandgap E (:) , it

exhibits (for parabolic bands E0o4k2) a square root behaviour for the

three dimensional case and a step function for the two

( 3)

(4)

142

dimensional case. This .can be expected to show up in £2(w)

provided the matrix element Mve does not vary strongly in the region

of Eo. Corresponding features should be observed in the real part

E i(w) which is connected with E2( w) through dispersion relations,

and in the optical constants n and k as well as in the reflectivity.

Bassani and Parravicini (B2) have investigated the optical

properties of the layer compounds GaSe and GaS on the basis of the

band structure obtained for these compounds. It was found that the

transitions above lev (after the free carrier contribution is

exhausted) are essentially determined by the two dimensional model,

and that it was not affected by the layer interaction, provided. this

interaction was small enough to justify a small variation of the

energies as a function of kz. This was however subject to a slight

modification due to the three dimensional (3-D) nature of these

compounds (arising from the presence of double layers), affecting the

layer interaction. The selection rules in the two dimensional

limit stipulate that transitions which are allowed when the electric

field is polarized perpendicular to the c-axis are forbidden when

the electric field is parallel to the c-axis and vice versa. These

rules are not exactly satisfied at the points of the Brilloun zone,

where kz 4 0 or kz /TI/c, because of the 3-D character. / The breakdown

of the selection rules because -of the interaction between different

layers, may be ascribed as being due to a small pertubation.

Consequently the 2-D model will be valid provided the matrix elements

for transitions which are forbidden are considered to be some order of

magnitude smaller than those of the allowed transitions. The step

function density of states dependence will therefore still be valid.

143

Dresselhaus (D7) has considered the optical absorption in

anisotropic crystals, and found that for indirect transitions the

shift of the absorption band edge with polarization should be very

slight, since for both allowed and forbidden transitions the photon

energy dependence is of the sane form,given by (for a one phonon

emission process);

lOYC (. U■ g - k9)2

rhereImis the photon energy, Es the energy difference from the top

of the valence band to the bottom of the conduction band, and ie is

the energy of the phonon emitted in the indirect transition. This,

however, is not the case for direct transitions. By considering

direct transitions at the centre of the Brillouin zone in a hexagonal

structure without inversion symmetry, and using a group theoretical

classification of energy levels, together with the requisite selection

rules, expressions for the photon energy dependence cf the absorption .

coefficient (cX,D) were obtained. These were for polarization parallel

to the hexagonal axis,

oc,(11) = 2 e2( ixt2+ it,E )2 IM11 2 • — • • (7) 77-rn`c

and for polarization pctrpendionler to the hexagonal axis.

x *. A / c<j) (1.) = -2. c/At /14.e. iut 7.1.e)1P1?.1 (-R _E g.) . . . . (10

nr-mL4c.g!w 3.4#

where is the matrix eicT2nt denotin --- th,:: probability cf tran2ition,

w th2. angular. velocity of ti olectrunasmetic rodiaticn and E- the tJ

dir:.,ctencrjy ''andz?p, with the other constants haviig the usual nota-

tion. The lonr;ituiinal and transvcro-3 (mt) a7a.

Jz.lot,13 in those equations by hand pitwh,21-..!

-1

= ?714 (mix ntio. )

nix" rnA Crn *

j -'4

144

The two expressions for oq are subject to a restriction which limits

their validity to a region near the absorption edge given by,

u - E AE

where 4E is the energy interval in which the perturbation expansions

of the wavefunctions involved are rapidly convergent.

The effect of the anisotropic crystalline structure on

optical transitions in orthorhombic'systems has so far not been fully

analysed. From the preceding paragraphs it would appear that

indirect transitions may be treated isotropically while direct

transitions vary with the direction of polarization. The validity

of this statement depends on the degree of anisotrophy.

Takahashi et al (T1) have however analysed the optical

properties of SnSe using the three dimensional model on the basis

that the experimental results did not show any evidence for the two

dimensional band structure (i.e. the optical properties for Elle were

not very different from those for Ella and Ellb). It was also found

that at liquid helium temperatures the absorption coefficient showed

two distinct absorption bands corresponding to, 0.52evand 0.74ev for

Ella and, 0.50ev and 0.71ev for Ellb and Elle. In order to explain the pre-

sence of these bands, it was assumed that the valence band consists

of three sub-bands; heavy hole band, light hole band and split off

band. Thus the absaption bands correspond to transitions between the

valence sub-bands.

In the case of the three dimensional model the photon

energy dependence (s4) for direct transitions (irrespective of the

direction of polarization) is given by

qp « (hw - Eg)i (11)

for allowed transitions and 3.

c<j) (hw - Eg)a (12).

for transitions which are forbidden. The corresponding expressions

145

for indirect transitions are .

(hV - Eg t Ep)2

exp Ep 1 kT

for allowed transitions and

0-(1. .°4.(hV - Eg t Ep)3 (14)

for forbidden transitions, where Ep denotes the phonon energy.

A more exact expression for the indirect allowed transitions, which

takes into account both phonon absorption and emission is given by

(B1),

c'q =A (hw - Eg - Ep)2 + (hw - Es + Ep)2 for hw > Eg + Ep 1 - exp I

(-Ep l exp (§) _ 1 \. kT/

= A (hw - Eg + Ep)2 for (Eg - Ep 4 hw 4 Eg + Ep)

exp ( Ep I - 1 (15)

kkTi

= 0 (hw Ep - Ep)

In this expression only one type of phonon has been considered,

but in practise account has to be taken of both longitudinal and

transverse acoustic modes and optical modes as well (if all these are

present). The overall absorption would then be given by the sum of

the various parts e.g. if the two acoustic modes are present,

0(i = dex i- ckat

where a and e refer to absorption and emission processes and 1 and t to

longitudinal and transverse modes.

In the event of multiphonon emission and absorption the plot

of the absorption coefficient against photon energy will not yield a

straight line. Macfarlane et al (Ml, M2) who investigated the

optical properties of Silicon and Germanium found that the ok 04(hw)2

curve could be represented by a series of straight lines separated by

distinct breaks. The discontinuities at the low energy end disappeared

(13)

146

at low temperatures, which indicated that they were the result of

phonon absorption processes (since few phonons are excited at these

temperatures making phonon absorption improbable), From the

values of the energy at the discontinuities, and the behaviour of oks

at different temperatures, the various phonon energies contributing to the

absorption process were deduced. This is of interest in this context

because both Mochida (M13) and Takahashi (T1) obtained similar

results for SnSe, and used the same sort of analysis.

147

4.3. EXPERIMENTAL PROCEDURE.

Transmission and reflection measurements were carried out

on both bulk and thin film samples of various compositions of

Snx Ge1-x Se. All these measurements were obtained using a Perkin

Elmer 450 spectrophotometer in the range 0.6 microns - 2.0 microns.

It was not possible to use polarized radiation since polarizers tended

to cause a significant reduction of the signals. This means that

the difference signals obtained after transmission through the bulk

specimens were so small that they were comparable to the inherent

noise, and thus could not be adequately processed. The thin films

did not exhibit any definitive planar orientations and as such the

light could not be polarized along a specific direction. In spite

of this limitation the low degree of optical anisotropy , coupled

with the fact that the main point of interest was the variation of

the bandgap with composition were factors in favour of carrying out

the measurements using unr,olarized radiation.

4.3.1. TRANSISSION MEASUREYIENTS.

In order to obtain the transmission through bulk samples

of SnxGel_xSe, it was necessary to reduce the aperture, since the

samples were much smaller than the incident beam. This was done

by using a special sample holder with a small slit across which the

sample was placed. A similar holder without a sample across it,

was placed in the reference compartment. This ensured that the

• difference signal actually represented the transmission through the

sample. With the thin films however this was not necessary a:I the

films completely covered the beam. The bulk samples . rLn7ed in

thickness from 50fm to 250r and were placed ir the sample compart-

ment such that the beam was perpendicuar to the basal plane.

148

All the samples used were freshly cleaved, and only those which

exhibited few, if any, visual defects were used. This helped

minimise the light scattering due to crystalline imperfections.

By using freshly cleaved samples the presence of any surface oxide

layerswereprecluded. The bulk compositions for which these

measurements were carried out included

x = 1, .9, .8, .7, .5, .2 and 0.1.

The results obtained are shown in Fig.4.5. It was not possible to

obtain GeSe samples which were reasonably free from surface defects acid

because of the large amount of light scattered no data for bulk GeSe

was obtainable. The film compositions for which the transmission.was

measured were SnSe, SnoGe.2Se, Sn.7Ge.3Se, Sn.5Ge.5Se, Sn5Ge.7Se,

Sa.90-e.8Se and GeSe. The results are shown in Fig. 4.6.

Most of the measurements were carried out at room temperature

but for four bulk compositions with x corresponding to 1, .75, 0.5

and 0.2, the transmission at lower temperatures was also obtained.

This was done by placing the samples in an optical cryOstat with quartz

windows (quartz transmits in the near infra range considered), and

pumping the system down to a vacuum of 10-3 torr using a normal

diffusion and rotary pump vacuum unit. It was necessary to carry out

the measurements under vacuum to ensure steady temperatures, with little

or no drift as the 'wavelength range was scanned. Both the room

temperature and low temperature results, for the various compositions.

are shown in Fig.4.7.

4• 3. 2 . REFL33TANCE 7,113ASUREIMTS

These measurements were carried out using a Perkin Elmer

specular reflectance accessory. The angle of incidence used to find

the reflectance is 45°. The reflection is .a function of the angle of

incidence and does tend to vary as this angle is changed. In order to

10 1.1

FIG.4.5—

Stv.a CE:, SE

30

cL. . 1— is

1.5 1.4 1-2 11 p.n.

Transmission results for bulk SnxGel_xSe.

10

Sell GC? CE Ct. '00 (3C-47‘

1,0 1.1 1.2 1.3 14 A /Av.

30 30— SN sE SN.s . 0i6

10

0

10

1.0 1.1 1.2 1.3 1. 14- X()

1.5 0

1-0 (-I 1.2 1-3 A

t.. f•5

ca..? 6E13 SE Ct. .00 g Chn

30

0

10

1

ID 1.1 (.2 1.3 1.4 1.5

A pm,

• • •

• • / •

• ►

SNICE.3 SE SW.5 GE.5 SE

10

1.1 1.0 1.2 1.3 A

1.4 1.5 1.6 1.7 18

•

• •

•-• • 1 ..1

1 •

•

SO

SN CE --- Sti.9

40

30

20

10

FIG.4.6(a). TransmissiOn results for SnxGel_xSe films for x = I.0, 0.8, 0.7 and 0..

50

30

I • ►

•

1 • • , • •

• •

•

1.0 1.1 1.2 1.3 Xtur,

1.4

100

90

$o

I

70

t I t k

go I t

So •

1

r

(po

30 GEcE Er SE

Sm.3 GE.7 SE

do

10 /

1.0 1.4 1.5 1.6

A

FIG.4.6(b). Transmission results for Snx Ge1-x Se films for x = 0.3, 0.2 and 0.0.

30 St4.7s CE.15CE

10 20a°K I

R T. F-

10

30 SU SE

AO P00'1‹ — R.T.

I-

10

■ 0 A f I I f o

1.0 1.1 1.2. 1.3 1.4 1.5 1.0 1.1 1.2 1.3 1.4 1.5

A fon ->

1.0 1./ 1.2 1.3 1.4

1.5 1.0 . 1J 1.2 1.3 1.4 A ton

FIG.4.7. Transmission measurements for bulk samples at different temperatures for x = 1.0, 0.75, 0.5 and 0.2.

153

ascertain whether the reflectance showed any. significant departure

at 450 eomnared to smaller angles of incidence, the reflection of

the various samples was measured on the 270 Perkin ElMer Spectrophoto-

meter. The specular reflectance accessory for this machine had an

angle of incidence pf 120. The difference in reflection between the

two angles of incidence was minimal.

The small size of the bulk samples necessitated the use of

black masks. These were used for both accessories in the sample and

reference compartment. Tha radiation was incident on the shiny basal

nlane surface of the samples in all the cases. For SnSe the reflection

for a sample with a defect free surface parallel to the Ict axis, was

also measured. No masks were necessary for the films as they were

large encuzh to cover the beam. All the films had shiny surfaces very

similar to those of the bulk.

The results of the reflectance measnaements for bulk camples is shown

in Fig.4.8 and those for the films in Fig.4.9.

4.4, BULK CPTICAL PROPERTIES.

4.4.1. Results.

From the transmission and reflectance results shown in Fig.4.5

and 4.8, the absorption coefficient ocean be found by using the

relationship.

T = (1 - R)2e-k4

1 - R2e-2 °(0 d

where T is the transmittance

R the reflectande,

and d the thickness of the sample.

Solving for o<, in equation (16),

3- Ok o = 1 In I (1-11)2 + (1_R)2 2 + R2

2T 2T d

(16)

(17)

50

If.0

?0 1 I 1 I I 1 1 4 l0 1.1 /.2 1.3 1.4 1.5 1.6 -8

10

5N4 G Ea EC

SO

0

30 7 -e 1.4 1.1 1.2 1.3 1 4 1.5 1.6

A turn

70

SN SE

60

Sp

40 .9 1.0 1.1 1.2 1.3 1 4 1-5 1.6 .7

FIG.4.8(a). Reflectance results for bulk SnxGel_ e with x = 1.0, 0.8 and 0.7.

50

E SE

1,0 E1G

30

20 1 .cf 1.0 1•I 1.2 1.3 1 4 1.5 1.6 .7

A rm.

50-

CE.9 SE

40

CC

3

20 1 r 1 I 1 1 1.0 1.1

tila

1.2 1.3 1.4 1.5 1.6

0

SNI.5GE.s SE 50

4.0

30 I I I 1 .7 •8 .q 1.0 H

X Pim

FIG.4.8(b). Reflectance results for bulk SnxGel_XSe with x = 0.5, 0.2 and 0.1.

1 I I 1 1 1.2 1.3 1.4 1.5 1.6

-11

50

CC.

t. 1

70—

LD

.o

L .

t

. t

30

.s CE.s CE

6.3 cE t

dO

JD 1 l f I 1 I )

•7 •$ •4 10 1.1 J2 1.3 /.5 1.6

A 114n

FIG.4.9(a) . Awn

Reflectance results for SnxGel_xSe films with x = 1.0, 0.8, 0.7 and 0.5.

-T!

GE CE

30

20

10

30

1 0

nc

7

EU-

1.0 A fkin

1 1 1.5 1.6 1.2 1.4

1.0 1.1 ia 1.3 1.4 1.5

A pfilt •

SN GE SE 4. .8

Ito

3

2

1 I I 1 I 1 I 1 1 .8 .9 1.0 1.1 1.2 1.3 14 1.5 (.6

pint

FIG.4.9(b). Reflectance results for Sn Ge1-x Se films with x = 0.3, 0.2 and 0.0.

158

and hence knowing d, T and R, the absorption coefficient can be

calculated. The results obtained for the various compositions are

shown in Fig.4.10. This absorption coefficient however contains

components due to free carrier absorption and defect scattering, just

as in the case of the terminal compounds. Assuming that the free

carrier absorption is negligibly small in the wavelength region

considered, and that the component due to defect scattering is

constant, the true band to band absorption (010() can be found. In

each of the curves the constant component is obvious (in the horizontal

position) and hence ocmay be found by subtracting this from the

calculated value,c40. The results obtained are shown in Fig.4.11.

(18) (n 1)2+ k2

where n is the refractive index

and k the extinction coefficient, which in its turn is given by

k= A ce.

(19)

?1 being the wavelength.

From equation (19) with Cc of the order of about 102cm-1 and A about

10-4cm, the value of R obtained will be such that k2. (n-1)2. Hence

equation (16) can be simplified to read,

R = (n - 1)2

(n + 1)2

From this solving for n,

n = 1 + R

(20)

1 -R

This equation was used to find the variation of refractive

index with photon energy, the results of which are shown in Fig.4.12.

The value of refractive index thus obtained is only an approximation

to the true value, since reflectance is much more sensitive to polariza-

tion effects than transmission.

The reflectance (R) is given by the equation

R= (n -1)2 + k2

1.1 E 62f)

FIG.4.10. Variation of absorption coefficient ( o(0) with photon energy for bulk samples. .

I.0

I 1.0

MEI

.9

100

50

0

1 50

E Oa) -> FIG.4.11. Variation of band to band .absorption coefficient ( o()

with photon energy.

0 0

S.-

St.-

6 -&. •L • L. .

11.-■•■•

3

a

X FIG.4.13. Variation of 'absorption' due to defect scattering

( o&.) with composition for bulk samples.

-V ;.o 1-1 1. ?- i • 3 r. ; • 5

1.6

E Ce/v)

FIG.4.12. Variation of refractive index with photon energy for bulk samples.

161

162

It was not possible to obtain the reflectance at low

temperature, arid so only a qualitative idea of the change in band

gap with temperature can be obtained from the results shown in

Fig.4.7. This was done by noting the shift in the wavelength at

low temperatures, compared to the room temperature point corresponding to

the band gap obtained from the absorption coefficient behaviour.

4 A 2

Discussion.

The absorption coefficients plotted in Figs.4.10 and 4.11

show a fairly well ordered behaviour with a distinct shift towards

higher energies as the germanium content in SnxGel_xSe is increased.

It was not possible to obtain the absorption at higher energies because of the

thickness of the bulk samples used. This precludes any analysis of the

absorption coefficient for the presence of direct transitions since the

reported value of this gap is 1.2ev for SnSe (M12) and 1.53ev for GeSe. •

An interesting point to note is the variation of the absorption coeffi-

cient ( o(a) component due to scattering with composition (Fig.4.14).

Initially as x decreases czo, decreases until it reaches a low value at

x = 0.7 and then it increases fairly sharply, the highest value

occurring at x = 0.1. From this, it would appear that this light

scattering factor reaches a minimum at the alloy composition denoted

by x = 0.7. Although cga.depends mainly on the specimen and will vary

from sample to sample, its variation with composition does show a

distinct trend. However before any firm conclusions can be drawn, the

behaviour of cAd.for various samples of different composition with varying

surface characteristics, will have to be fully investigated.

The behaviour of the absorption coefficient due to band-to-band trans-

itions.is very similar to those obtained for SnSe and GeSe by other workers

(M13, M12, A2, K2, L4). The alloys also show a similar behaviour to the

terminal compounds. In spite of the fact that non-polarized radition

was used, the variation of o< with photon energy does not differ much from

that for polarized radiation. The difference though, becomes more

10

let

5 8

ns 1.0 10 1. 03 1.1 1.15

. Plot of c< 2 against photon energy.•

164

apparent when the plot of of 5: against photon energy is considered.

Unlike the behaviour observed by Mochida (M13) whip used polarized

radiation, no distinct breaks in the straight line energy

dependence of 0( -L., is discernable. A possible reason for this is

the presence of a 'smearing out' effect caused by the virtual

averaging of all the 'energy breaks'. The straight line behaviour,

however, clearly indicates the predominance of indirect transitions

in this range, and compares very well with the results of Mitchell (M12)

and Kanneswurf (K1), who both used unpolarized radiation.

A value for the indirect bandgap can be found from the inter-

section of theot curve with the energy axis. This in effect gives

a value which is an averaged version of the bandgaps obtained for

light polarized along the 'a' and 'b' axes. Since these do not differ

very much anyway, the values obtained here can be regarded as an

adequate indication of the indirect optical bandgap, for light incident,.

perpendicular to the basal plane.

The variation of these bandgaps with composition is shown

in Fig.4.15. The bandgap of GeSe was taken as 1.12ev, as obtained

by Lukes (L4). The linearity of the variation seem remarkable and one

can only conclude that SnxGel_xSe represents an optically well behaved

system. The variation of the bandgap in this case, is a function of

the changing lattice constants and since these vary almost linearly

with composition (K7) the behaviour observed, is to be expected.

In order to investigate the temperature dependence of the

bandgap for various compositions, the criterion that the wavelength

corresponding to the onset of absorption represents the bandgap, was used

to obtain the requisite temperature coefficient. The justification for

this lies in the fact that the bandgap obtained from the absorption

curves corresponds to the onset of absorption as indicated by the

behaviour of the transmission.

1.0 .7 .5 )(

is'IC.!].15. Variation of bandgap with composition.

166

The values thus obtained of the temperature coeffiCient of the indirect

bandgap were as follows:

dt

SnSe

3.6 x 10-4 eV/°K

Sn.75G°.25Se

1.3 x10-4 eV/°K.

Sn.5Ge.5Se 5.7 x 10-5 eV/°K.

Sn.2Ge.8Se

2.7 x 10-4 eV/°K.

The accuracy of these results is limited by the wavelength resolution

of the spectrophotometer. In spite of this the value obtained for

SnSe compares quite well with that found by Mochida who reported a

temperature coefficient of 4.3 x 10-4 eV/°K. The interesting point to

note is that dEg decreases as the degree of alloying is increased. dT

This is probably due to the lattice strainsset up by the alloying

process, masking out the temperature effects on the lattice. From

the actual transmission curves it will be observed that the long

wavelength transmission is greater at room temperature than at the

lower temperatures, for each of the compositions considered. The thermal

strains set up in the crystal at low temperature will increase the amount

of radiation scattered, and thus reduce the overall transmission.

From the preceding discussion it would appear that the various

changes in bandgap are a lattice induced phenomenon.

The variation of refractive index with photon energy, for the

different compositions is shown in Fig.4.12. Tho accuracy is rather

limited due to its dependence on polarisation effects However the

results obtained here compare quite well with those obtained by

Mitchell (M12) for SnSe and Kannerwurf (K1) for GeSel both of whom used

unpolarized light. It may be observed that in the case of the alloys

the refractiVe index shows a tendency to increase in the indirect

absorption region. There is no adequate explanation for this at the •

moment.

167

THIN' FILM OPTICAL PROPERTIES.

4,5,L, RESULTS.

The results of the transmission ('.T) and reflectance (R)

through films of.varying composition, shown in Figs. 4.6 and 4.9

can be used to find the absorption coefficient (0<r). The equations

relating OC T and R are as follows (H1);

T ( ?- "c ÷ K n [61, +0-4- k.: Nri r I(

X. 16 ./..f) (- d7 d)

/-aR,Ram(°cr.° [a.rrnF JtSa)tR,R;eirpER.O... (21)

and

R n, 8-- R,.0 .6-[ (10 di A) - (dar e° -/2, Ra. .0.13( 0(4 cel [11.7r , 01,4,. . . . (22)

where of is the refractive index of the film, ns the refractive index

of the substrate, d the film thickness, )1 the wavelength of the

radiation and ke the extinction coefficient defined as

= oCr

In equations (21) and (22)

R12 = oiF - t Kea

(hF

R22 = (hP n s ) IL (11F inV t K-e.

c = twr: a Ke t Kea. /

- tan-1..? h Ke p *KA

The reason for the complexity of these equations is that reflections

at the various interfaces (air-film, film-substrate, substrate-air)

and the multiple reflections occurinp-' within the film, have all to be

taken into account. It is obviously net possible to solve equations

(21) and (22) using any analytical methods. However using a numerical

iterative method and a computer it is possible to solve them. The

computer program used gave the absorption coefficient, refractive index

and extinctiol coefficient for the transmittance and reflectance at

various wavelengths.

4.5.

and

166

The results obtained trough were not single valued due to the corina

functions appearing in the expression. Another problem arises from

the feet that the refractive index essccie+ed_ with the two directions

of Polarization in the basal plane have different values. Thus, when

non polarized radiation is used a modulated fringe pattern is

obtained. Traces. of this are evident for the interference fringe of

some of the samples. To overcome this the averaged values of the

reflectance and transmittance were used. In order to find the true

value of the absorption coefficient from the multi-valued result

obtained from the computer program, a rough idea of the refractive index

was calculated using equation (20). The absorption coefficient

corresponding to this value of refractive index was then taken as the

representative value. The plot of 0(-r. against photon energy for the various

compositions is shown in Fig.4.16.

4. C. 2 DTSCUSSION.

A detailed anelysis of the absorption coefficient is not

possible because the component due to scattering is not nhvious from

the curves. The absorption coefficient is in general much greater than

for the ccrrespueding bulk case, and also shows an increasing tendency

towards the tin rich end. At the GeSe rich end eeeshows a similar

behaviour with a gradual increase follewed by a much sharper increase at

higher energies. The tin rich end en the other hand shows a similar

though more graded behaviour, with the difference that at the highest

photon energies, the slope of a4 changes and takes a smaller value.

In the case of Sn.5Ge.5Se the transition between these two regions

becomes much sharper.

A value for the indirect bandgap may be deduced from the energy

at the lowest point of that portion of the eircurve,having the largest slope.

A graph of the energy thus obtained against composition is shown in Fig.4.17.

The values obtained for the Sn rich end up to and including x = 0.5

Opp .0>

AMP

lo' .6 8 tO 1.8

E (eAr) --> FiG.4.16. Variation of absorption coefficient ( di-) with

photon energy for film samples:

.o

8 • 10

FIG.4.17. Variation of ' direct' and I indirect' bandgap wil,h composition fcr f samples.

0 0 0

1.6 1.7

Ito() 171

►

1 goo

1Aoo

Woo

O

► r ► Co

4.00

1

6

•

/0

,o 0

o

0

0 .9 10 . 1.1 1.2 t 3

FIG.4.18. Photon energy dependence of oc.5 for film specimens.

_D - 0 0 —

172

correspond vary well with the values obtained for the bulk. However

the values for the GeSe rich end are larger with the compositions

corresponding to x = 0.3 and x = 0.2 showing anomalously large values.

In order to obtain an indication of the direct gap in these

materials, a method similar to that of Kennervurf (K2) was used.

The value of C416-(Fig.4.18) was plotted against photon energy,-and

the energy corresponding to the start of the straight line portion

was taken as representative of the direct gap. The validity of this

method is questionable since the actual selection rules depend on the

polarization of the incident radiation. However the values of the

bandgap obtained are not too far off from the quoted values, as far as

the two terminal compounds are concerned. The direct bandgap plot against

composition is also shown in Fig.4.17. The general tendency exhibited

is one of increasing bandgap with increasing GeSe content.

4.6. PHOTOCONDUCTIVITY MEASUREIZNTS ON THIN FILMS.

4.6.1. THEORY.

The Photoconductivity in thin films of SnxGel_xSe results

from the excitation of electrons to the conduction band when the film is

illuminated by light of a particular wavelength. This wavelength is

obviously related to the bandgap. To explain the photoconductivity in

the lead chalcogenides two theories were proposed. They were

1) Single crystal recombination theory. Here the equilibrium

excess carries concentration on irradiation is determined by the

respective rates of generation and recombination of hole-electron

pairs, and the photoconductivity is taken to be directly proportional

to the increase in the number of carriers, the mobility being the same as

in the dark.

2) Barrier modulation theory. Hera it is postulated that

potential barriers are set up between microcrystals during the evapora-

tion of the film. These barriers are modified by the production of a

173

few photoelectrons in their vicinity, so that large numbers of carriers

already present are permitted to flow across the layer. Thus the

carrier mobility should increase markedly with only slight changes in

overall carrier concentration.

The evidence is now conclusive in favour of the first theory

(M16). In a latter section the applicability of this to SnxGel_xSe

will be discussed.

The value of the energy bandgap can be obtained from the

spectral response curves using a procedure developed by Moss (M17).

The spectral response curve can be represented in the range between

the long wavelength and the maximum response, by the equation

S(E) = 1

1 + exp 19 (E0-41 (23)

where ills a constant, E is the energy at any wavelength, and Eo the

energy at the 'threshold wavelength'. Now it can be assumed that

the varying sensivity results from the distribution of energy levels

from which the photoelectrons originate. If the distribution is such

that there are N(E)dE levels between E and E+dE, then with radiation of

a given quantum energy EtaE, the sensitivity will be proportional to the EA

total number of centres of energy lower than E i.e. /N(E)dE. Hence 0

d(

EA

N 50 (47)

IV(E) = G 01.4 40(E

Using equation (23) N(E) becomes,

N(E) - GP p fr (re- 0}

The total number of electrons excited to the conduction band is given by:

n =fC [N(E))

ctE where C is a constant.

(c).KT/

Substituting for N(E) from (24) and using standard integral methods, a

solution is obtained where .1'

n C(1) ?" fo) (P1 alcr

where G is a constant.

(24)

(25)

174

where a = ritt_ ). 13KT

Thic corresponds in form to the expression occuring in the conductivity

for electrons excited into the conduction band, namely

r. co exp(Ervia) where Eg denotes the bandgap. • Hence by comparison

Eo = Eg, and thus when E = Eg the vane of S becomes;

S P t 2

This in effect means that the bandgap will be given by the wavelength

corresponding to the point where the sensitivity has fallen to half

its value. The values obtained for the SnxGel_xSe films using this

procedure will be outlined in a latter section.

. 6. 2. Expartir,TE:TTAL PROCEDURE.

The experimental set up is as shown in Fig.4.19. Light from a

tungsten light source was 'chopped' mechanically at mains frequency

and then passed into a monochromator which emitted radiation in the

wavelength range 2imn. to 0.6 pm . This range could be scanned at

Varying speeds and for the purposes of this experiment a speed of

0.1cm/sec was used (T 3). .

Two electrical contacts were made to the films using high

purity Indium and these were used to provide a bias across the film.

The filM was then mounted on a clamp and placed such that the thin beam

from the modochromator was incident on the area between the two contacts.

The wavelength range was then scanned starting from the long wavelength,

and the Photo-electric signal obtained was processed using a Leek-in

Amplifier. The processed signal was then recorded by means of a chart

recorder.

175

Tungsten Lamp

- - - Reference Diode

Hi ger Wat t s Monochr otnator

Pre -amp

Brook deal Lock-in Amplifier

— SAMPLE

Recorder

Motor

FI',;-.4.19. Experimental set-up for photoconductivity measurements.

176

4.6.3. RESULTS AND DISCUSSION.

The Spectral response obtained for the films of SnSe,

Sn.8Ge.2Se, Sn.5Ge.5Se and GeSe are shown in Fig.4.20. From these

curves a value for the indirect gap can be deduced using the method

described in the theory. The results are listed in Table 4.1, and

they compare very.well with the indirect gaps obtained for the films

from the absorption curves, except for the case.of GeSe. The

spectral response curve gives a smaller value than is normally associa-

ted with GeSe.

Another feature of the curves is the presence of a second

responsivity band which is smaller than the first one. This band

is fairly obvious in the case of SnSe and Sn.8Ge.2Se but although the GeSe

curve shows a slight bulge, it is not as distinct as for the two cases

mentioned. In the Sn.5Ge.5Se response curve this second band does

not appear. It is probably submerged by the inherent noise since

the overall signal is very small compared to the other films. This

second band is due to the absorption resulting from direct transition,

and hence using the method outlined, a value of the direct gap can be

obtained at least for SnSe and Sn.8Ge.2Se. The values, shown in

Table 4.1, compare quite well, within experimental limits, with those

obtained earlier.

By considering the values of the photoconductive signals

(Table 4.1) in conjunction with the electrical properties of these

films described in the last chapter, some idea of the relevant

mechanisms governing the photoconductivity may be obtained. The signal

obtained for SnSe is remarkable and as there does not seem to be any

reported photoconduCtivity data on this compound, one can only assume

that it has never been investigated. It is likely that SnSe may prove

to be a good photoconductor.

3.6

!•5 1.6 0

"1 77

0.7

pAn

h ifint

FIG.4.20(a). Spectral Response curves for films of SnSe and Sn.8Ge.2Se.

1.04

0

446 -

17:

.7 -e .4 1.0 11 1 • a 1.3 1.4 1.5

St4.5GE.5 SE

'so

150

co

30

GE SE

0 -......- 1 1 1 1 •

0.9 0.85 0.$ .6 1.5 1.4 1.3 /.3 1.1 ba

FIG.4.20(b). Spectral Response curves for films of Sn.5Ge.5Se and GeSe.

179 TABLE 4.1.

Energy . Energy Sample. correspcnding corresponding

to 1st Band. to 2nd Band.

Bias Signal Applied. Obtained.

SnSe 0.9eV 1.04e7 4V 2170 V

Sn.8Ge.2So 0.91eV 1.07eV 1.4V 134 V

Sn.5Ge.5Se 1.04eV 4.6eV 3.3

GeSe 1.02eV 1.4V 164 V

From the electrical measurements it is clear that of all the films, the

Sn.5Ge.5Se film contains the smallest grains and thus possesses the

largest number of potential barriers (as is evident from its

resistivity). If the barrier modulation theory is applicable, then

the photoconductivity would be largest in Sn.5Ge.5Se. This is quite

obviously not the case and hence this theory can be discarded as far

as SnxGel_xSe is concerned.

The first of 'numbers' theory seams more applicable in this

case. In SnSe it was observed that the signal obtained using bulk

SnSe was too small to be measured, while the film Produced a large

photo-electric effect. From the Hall effect measurements the bulk

carrier concentration was about 1018/cm3 while for the film it was

about 1016/c10. In keeping with the 'numbers' theory, the photo-

electrons generated would be more noticeable in the specimen with the

lower carrier concentration. In the bulk case the number of photo

electrons was probably swamped out by the free carriers present.

This comparison holds for the SnSe and GeSe films as well, with the

number of free carriers in GeSe ( 6 x 1010/cm3) exceeding those in

SnSe, with the result that the photo-response is much more pronounced

180

in the latter. Although Sn.8Ge.2Se exhibits a lower carrier

concentration than SnSe its photo-response is smaller. This is

probably due to the larger number of grain boundaries (arising

from alloying effects), diminishing the photo-electric signal.

On the whole the evidence seems to be in favour of the

'numbers' theory, as far as the photoconductivity of SnGel_xSo

is concerned.

181

CHAPTER 5.

CONCLUSION.

This work has involved the characterization of a new semi-

conductor alloy system SnxGel_xSe with respect to its electrical

and optical properties. The overall picture which has emerged is

of a semiconductor which exhibits similar properties to other

IV VI alloy systems, but also shows effects arising from the

layer like anisotropy of the crystalline structure.

The basal plane Hall coefficient and resistivity show a marked

resemblance to other IV-VI compounds. The Hall mobility however

seems to be affected by the layer structure. For most of the

compositions the temperature dependence of mobility (n) is

consistent with the theory developed by Schmid for materials

exhibiting a low degree of anisotropy. This assumes that the

carriers are not self trapped in the layers, and the scattering is

mainly due to non-polar optical phonons. For optical phonon

energies of --0.02ev, this would result in a value of -2 for n.

Since the optical results of other workers seem to indicate that

this is indeed the energy of the optical phonon for SnSe, it would

appear that this theory is valid. For those alloys in the range

0.7 x 0.5 the value of n is about 1.6. This may be correlated

with the measurements of the c-axis conductivity in this range which

indicate a certain degree of carrier localization within the layers.

If this is the case, then the theOry of Fivaz, developed on the

assumption that the carriers are self trapped within the layers,

would hold. Relating the value of n to the optical phonon energy

using : the graph in Fig.3.14, a value of -̂0.02ev is obtained, which

is or less the same value as befcre.

182

The randomness of the values of n for the GeSe rich alloys, may

be due to the presence of the interlayer amorphous phase, shown up

by the c-axis measurements.

The c-axis resistivity measurements indicate that for the range

1 > x 0.8, the conduction is mainly normal band type conduction,

'while with increased alloying, localization effects appear. The

fact that agreement between the theoretical derivations of the

impurity band model and the experimental obserVation is rather poor,

is probably due to the fact that this theory is not well developed

especially for the 'high' and 'intermediate' concentration regions.

The hypothesis that an intercalated amorphous phase is responsible

for the resistivity behaviour observed in the GeSe rich alloys seems

to be backed by existing evidence. In connection with this it is

.interesting to note the non-linear I-V characteristics and activated

conductivity behaviour obtained for GeS by Van den dries (111) and

other workers. From their relative positions in the periodic

table it may be assumed that the 'compounding ease' of GeSe is higher

than that of GeS. Since this 'compounding ease' may be related to

the formation of the amorphous phase (i.e. the harder it is to

compound the material the greater the probability of an amorphous

phase) it would seem logical to explain the observed results for GeS

on this basis. This would seem to be consistent with the data.

The thermal effect reported here has also been observed for SnS

by Albers et al (A2) and the explanation based on the presence of

microprecipitates would seem to be valid. The conclusion from the

Eossbauer data that the SnS electrons are the main source of carriers

seems to agree with the variation of Hall coefficient with composi-

tion. The thermaelectrdo measurements indicate that SnxGel_7Se is

nct likely to provide efficient thermcelectric devices.

183

The thin films obtained show disordered polycrystalline struc

tures. The eleCtrical properties are clearly affected by the

disorder resulting in grain boundary limited mobility especially

at lower temperatures. Comparison of the resistivity results of

the GeSe film with those of the bulk sample, gives an indication

of the influence of the intercalated amorphous phase in the latter.

The optical measurements were hampered by the fact that non-

polarized radiation was used. This however doep not seem to have

affected the accuracy of the basal plane absorption coefficient and

optical bandgap calculated from the reflection and transmission

results. These conclusively show that anxGel_xSe is a non-zero

bandgap system, with a virtually linear variation of bandgap with

composition. The optical results of the films compare well with

those of the bulk at least for the SnSe rich end. The photo-

conductivity response for SnSe is large enough to warrant further

interest. The results obtained seem to indicate that the 'numbers

theory' accounts best for the observed effect.

Finally, the project as a whole has contributed to the clarifi-

cation of certain theories with regard to the temperature dependence

of mobility and has clearly shown the effect of alloying on the

electrical properties of non-zero bandgap ternary. semiconductors.

While the results haVe been useful in elucidating various theoretical

aspects, they also have practical implications. First and foremost,

the behaviour of other orthorhombic IV-VI alloys can be predicted

with some degree of accuracy. This is important when considering

that some of the glassy semiconductors like GeS have possible uses

as memory devices, switching devices, resistors, photovoltaic devices

and as photosensitive components. There is in fact.a Japanese

ratent (K5) on the XerograTthic use of GeS, an evaporated film of

which is retorted to have revealed a cos }vin power of 1000 lines/-1

184

The practical applications of SnxGel_xSe can only be fully

ascertained after further study. This project will serve as

a useful base for further investigation into their possible

use as devices.

185

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