An Introduction to Thin Films

AN INTRODUCTION TO THIN FILMS Y. R. Reddy *

[email protected] [email protected]

Professor in Physics, E.I.T, Eritrea, North-East Africa This article provides a basic knowledge in thin films and was written keeping in view of under graduate and post graduate students who are having thin films in their curriculum. This lecture notes contains method of nucleation, types of growth, sputtering process, methods of growth which includes vacuum evaporation, flash evaporation and chemical vapour deposition. Methods for measurement of thickness of thin films are also included. Finally electric and optical properties of these films are illustrated. ______________________________________________________________________________________

1. Introduction: Thin film is a branch that deals with very thin structural layers of different materials. In recent years, thin film science has been grown world wide in to a major research area. The importance of thin film coating leads breakthrough in micro electronics, optics and nano technology/1/. Thin films with thickness ranging from one to several microns are very essential for thermal barrier coatings and to protect materials from thermal and atmospheric influences/2/. The film science and technology plays an important role in high tech industries. Thin film technology has been developed primarily for the need of the integrated circuit industry. The demand for development of smaller and smaller devices with higher speed especially in new generation of integrated circuits requires advanced materials and new processing techniques suitable for future giga scale integration (GSI) technology. In this regard, physics and technology of thin films can play an important role to achieve this goal. The production of thin films for device purposes has been developed over the past 40 years. Thin films as a two dimensional system are of great importance to many real-world problems. Their material costs are very small as compared to the corresponding bulk material and they perform the same function when it comes to surface processes. Thus, knowledge and determination of the nature, functions and new properties of thin films can be used for the development of new technologies like solar cells/3/, sensors/4/, optical applications/5/, electronic engineering/6/ ferroelectrics/7/etc.

2. Thin film nucleation and growth:

A thin film does not grow as perfect slabs of bulk like materials. When compared with the bulk material, physical properties of thin films on substrate may strongly differ, depending especially on development of morphology and structure. Features like grain size, shape, orientation and other are determined to a large extent at an early stage of nucleation and growth and can be influenced by deposition conditions/8/. The individual atomic process which determine film growth in it initial stage is shown in fig.1.

Fig.1 The substrate atoms are given in open circles and film atoms are shown in dark circles. Condensation of new material from the gas phase can be described by an impinging rate. The number of particles per cm2 per second is given by r = P (2π MKT0)-1/2 …….. (1). Where P is the vapour pressure, M the molecular weight, K Boltzman Constant and T0 is the temperature. Once a particle is condensed from a vapour phase, it might immediately re-evaporate or it may diffuse along the surface. This diffusion process might lead to absorption particularly at special sites, edges or other defects or the diffusion particles may re-evaporate. In all these processes characteristic activation energy has to be overcome. i.e., the number of particles being able to participate in a particular process is given by the expression

* Permanent address: Department of physics, Kakatiya Government College, Warangal, India.

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mailto:[email protected]

mailto:[email protected]

Introduction to thin films- Y.R.Reddy

KTEdis

Vα e ……… (2) Where v is the desorption rate and Edes is the activation energy for the desorption. The corresponding activation energy for the absorption and diffusion depends upon the atomic details of the particular process.

Fig.3 This layer-by-layer growth results 1. High crystal quality 2. Film atoms are more strongly bound to each other and fast diffusion. Island growth: Island growth is shown in Fig.4. If the interaction between the neighboring film atoms exceeds the over layer substrate interaction leads to island growth. In this case an island deports always near a multilayer conglomerate of absorption atoms. The first few atomic layers usually grow as islands of a depositing material centered on nucleation site. The island grows until they touch each other (percolation threshold).This percolation threshold typically occurred between 5 to 10 nm. The thin film properties around percolation threshold and below percolation threshold will be very different from bulk properties.

Fig.2 Beside the absorption of special defect sites and surface diffusion, nucleation more than one absorption particle might occur, as might further film growth by addition of particles to an already formed island. The islands formation is shown in the fig.2. In order to obtain a smooth film surface during the growth, sufficient high surface mobility of the diffusing species and elevated temperatures are needed. In thermodynamically equilibrium, condensation and re-evaporations are equal and hence no net growth is result. As there is a crystal growth, it must be clearly is a non-equilibrium process/8/. Mainly there are three types of thin film growth phenomena is observed. 1. Layer-by-layer growth 2. Island growth and 3. layer-plus-island growth Layer-by-layer growth:

Fig.4 The film atoms in islands growth are more strongly bound to each other than the substrate with slow diffusion. Layer-plus-island growth: The layer-plus-island growth is an interesting one and is shown in Fig.5. After formation of one or several complete layers, first island formation can occurs. A 3D island grows over the top of the first full layer. In this case a lattice mismatch between the substrate and the deposited film may occur. It may not occur in epitoxial growth.

The layer-by-layer process of growth of thin film is shown in the figure.3. In this method the interaction between the substrate and layer atoms is stronger than between neighboring layer atoms .First a layer of layer atoms is formed on a substrate substance. Lateran a second layer is formed on the first layer and completes the growth on the first layer. A third layer forms on the second layer and soon. Each new layer starts to grow only when the last has been completed.

Fig.5

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Introduction to thin films- Y.R.Reddy

Effect of grain size: The grain size of the thin film formed on substrate depends on deposition rate and Temperature/9/. Dependence of grain size on various factors is shown in the figure.6. Grain size increases with substrate temperature up to certain temperature and then becomes constant Fig.6 (a).Grain size is more for the thick sample than thin sample. Up to entertain temperature, the grain size did not show any difference on the thickness of the sample. The grain size with deposit rate is shown in fig .6(b).Grain size is constant up to certain deposit rate. On further increasing the deposit rate, grain size decreases.

Fig.6 Grain size versus annealing temperature in shown in the fig.6 (c). As the temperature going on decreasing the grain size also decreases. A graph between grain size and the film thickness at constant temperature is shown in fig.6 (d).On increasing the grain size, the thickness of the film increases. 3. Sputtering process: Sputtering a physical process where by atoms in a solid target material is ejected in to a gas phase due to bombardment of material by energetic ions. This process is commonly used for thin film deposition, as shown in the fig.7.

When an ion strikes the target cluster of closed packed atoms, in the first collision, pushes the atom deeper in to the cluster. Subsequent collisions between the atoms can

Fig.7 result in some of the atoms near the surface being ejected away from the cluster. The number of atoms ejected from the surface per incident particle is called sputter yield. This is an important parameter to measure the efficiency of the sputtering process. The ions for the sputtering process are supplied by plasma that is induced in sputtering equipment on an ion or electron accelerator. Mostly organ ions are used for the sputtering process. 3.1. Sputter yield:

It is defined as the mean number of atoms removed from the surface of the solid per incident ion. It is given by Sputtering yield, S = (Atoms removed/incident ions)

Sputtering is called by the interaction of incident particles with the target surface atoms. The sputter yield will influenced by the fallowing factors 1. Energy if incident particle 2. Target material 3. Incident angle of particle and 4. Crystal structure of the target surface.

Sputter yield can be measured by the fallowing methods: 1. Weight loss of the target 2. Decrease of target thickness 3. Collection of sputtering material etc.

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An introduction to thin films- Y.R.Reddy

Plasma is sent between two plates. One plate is made with the source called target, and kept negative potential. The target is made with the material, of which the thin film has to be prepared.

Fig.9The plasma positive ion Ar+ strikes the target by the force of attraction and knocking the atom loose, the target atom then land on the wafer (substrate) .The process is continued and more and more atoms are deposit on the substrate to form a thin film. 4. Thin film preparations: Thin films can be prepared by depositing the materials on an insulating substrate with

coating to a thick ness from few to

100 . Many methods for thin film thickness deposits exit. Here depicting some of the widely used methods for the preparation of thin films.

0A

0A

4.1 Vacuum evaporation: This method is used to prepare the thin films of variety of substances in a high evacuated chamber in which the material is heated by electric means as shown in the figure.10.

Fig.10

3.2 Sputter yield- ion energy: A graph between sputter yield(S) and ion energy (E) is shown in the Fig.8.

0E

S

E

Fig. 8 There is no sputter yield up to certain energy and after that sputter yield increases and becomes maximum between 10Kev and 100Kev.After that sputter yield decreases. E0 is the thresholds energy for the sputtering .Sputter yield is maximum at high energies .It decreases at very high energies (> 100Kev) because the ions loose much of their energy far below the surface. The sputtering yield very less depends on the temperature of the target surface. 3.3 Advantages of sputtering: Sputtering is well emerges as cleaner, more flexible and controllable means of deposition than other means. The main advantages of the sputtering are: 1. The ability of transfer of material from the solid unheated source in the absence of Possibly reactive crucible or container. 2. With suitable precautions the source cathode composition is preserved in the growing film and 3. This technique is having high advantage of deposition of material over substrate to form thin film. A simple experimental technique is shown in the figure.Fig.9. Generally argon gas is used for the sputtering process, and is kept between the two electrodes, which is kept in a vacuum chamber. When a high energy electron is strikes the argon atom, it is ionized forming an Ar+ and an electron. By using the high energy field, low pressure plasma is formed between the plates.

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A vacuum pump is connected to a chamber to be evacuated. Inside the chamber masked wafer is suspended by a supporting stand and material to be evaporated is kept on another support. Heating coils are arranged to heat the material. Due to electrical heating, the material is radiated in straight lines in all the directions from the source and deposit on the wafer. This process is continued until a thin film of requires size is deposited on the wafer. When the process is completed, the vacuum is released and the wafer is removed, this process leaves a thin uniform film on the deposition material on all parts of the wafer. This vacuum evaporated technique is most suitable for deposition of highly reactive material such as aluminum, which is difficult to work with air. The method is clean and allows a better contact between the layer of deposited material and the substrate surface. In addition, because, evaporation travels in straight lines, very precious pattern is produced. Kinetic theory of gas and emission condition:

The deposition condition of thin film is better understood by the kinetic theory of the gas/10/. When a solid substance is melted or heated in vacuum, form vapour atoms or molecules enclosed in a space and create a vapour pressure. At a steady state of evaporation, these molecules will have equilibrium vapor pressure.

PV = NKT or

P = )(VN

KT …….. (3)

Where N is the total number of vapour atoms or molecules, V the volume of the chamber, T the absolute temperature and K is the Boltzmann constant. These molecules or atoms can colloid with one another in a mean time τ and let l is the average distance of travel before suffering a collision with other. Then

N = 12 ]2)[( ……. (4) −πσ

VN

From equation 1,KTP

VN

=

Substituting in equation 2,

l = 12 ]2)[( −πσKTP

l = KT/ ( 12 ]2[ ……. (5) −πσPt It is observed that , if the vapour pressure is

lowered the more will be the collision distance l .If the value of pressure P is very small, l is very long and even collision may not takes place ( l is greater than the dimensions of the container.).If P is very small, the value of

22πσKT

is nearly becomes 5. Or l = 5/P (in

cm.).Hence in high evacuating chambers, pressure is very minute and l is very high. At equilibrium condition, the vapour pressure of the gas molecules is also saturated, and the number of molecules, n, striking the surface of a substrate per unit area per unit time is given as n = P/ ( )2 MKTπ …… (6)

As 1/ (2 )Kπ = 3.513x1022

n = 3.513x1022 P/ MT ……. (7) Where m is the molecular mass and M is the gram molar weight. The corresponding mass evaluated per cm2 per sec. is given by the equation

G = 5.833x10-2 PTM

(in gm cm2/sec.) ... (8)

Similarly, the corresponding saturated vapour pressure

P = 17.44 GMT

……. (9)

The volume of the vapour

V = 3638MT

……. (10)

According to the above equations, it is clear

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An introduction to thin films-Y.R.Reddy

that the rate of deposition is proportional to P and )/( TM . It increases with pressure P

and as ell as M but decreases with T . i.e., at high substrate temperature there will be decrease in the rate of deposition.

It is assumed that the gaseous molecules incident on the substrate will condense to build a film, but this is not true in the real case. All impinging molecules do not condense to form the deposit layers, some are reflected back in to the gaseous state ands some other may be re-evaporated. Hence suitable correction factor has to be induced and this is known as the ‘sticking coefficient’ which has a maximum value of 1, for all the molecules are assume to condense on the substrate. Distribution of deposit:

The evaporating molecules coming out from heater source will spread in all the directions but the velocity distribution depends on the nature of the source, which are broadly classified in to three groups. Point source:

If the source is tiny sphere comparing to the distance from a receiving substrate is called a point source. The emitting vapour stream from the point source will be having same velocity distribution in all the directions.

Surface source:

If the emitted vapour molecule velocities are directional, then the source is called as a surface source. The velocity of molecules is maximum along the source-normal direction but it decreases with increasing the angle of inclination Ψ of the direction with source-normal. The velocity distribution fallows the cosine law and decreases with increasing of . If = 0, the surface source resembles a point source except it is not a spherical.

Ψ Ψ

Cylindrical source: The emission of vapour stream will be from

the surface of the cylinder and can be approximately between the point source and surface source Expression for material deposition: The amount of the material deposition on the substrate depends not only on the nature of the source but also on the inclination of the wafer stream (θ ) and on the substrate – normal direction.

Substrate

hψ

r

x

source

Fig.11 Let us now consider the amount of material(dm) that will emit through the solid angle (dw)of a source in the form of appoint surface source. If m is the total amount evaporated , the deposited amount is directly proportional to total mass of the evaporation(m), solid angle (dw)and the cosine of the angle of incidence (ψ )to the normal between the source and substrate. i.e., dm α m α dw α Cosψ dm α m dw Cosψ dm = (m dw Cosψ )/4π The above equation is valid for the surface source. If the source is a point source, ψ = 0

and hence, dm = π4

mdw …… (11)

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If 0≠θ

t = dr

m24π

cosθ … (19)

For the surface source: If θ = 0,

t = dr

m2

4π cos ψ …..(20)

If 0≠θ ,

t = dr

m24π

cosψ cosθ …… (21)

Now let us consider the thickness variation of deposit at different points on horizontal plane PQRS, which is at a distance of h from the source. Let point A and B are at the distances of h and r from the source respectively. If we consider a point source and let t0 and t are the thickness of the films at two points. Then, on substituting r =h in equation (19)

t0 = dr

m24π 2

1h

……(22)

Similarly we can get

t1 = 24 dhmπ

23

2 ])(1[

1

hx

+…… (23)

Dividing equation (23) by equation (22),

t1/ t0 = [1+ 23

2 ])( ……..(24) −

hx

where cos rh /=θ For surface source: we can write the ratio as fallows,

t0 = d

mπ4 2

1h

and ………

(25)

t1= d

mπ4 222 )(

1xh +

…… (26)

Let dA is the unit area of the substrate at a distance r from the source along the vapour direction. In this case, the amount of the material deposit also depends onθ . Hence for the surface source:

dm = dAr

m θψπ

coscos2 … (12) 4

If θ = 0,

Dm = dAr

m ψπ

cos4 2 …… (13)

For a point source: ,0=ψ then

Dm = dAr

m θπ

cos ……. (14) 4 2

For θ = 0,

Dm = dAr

m24π

……. (15)

If θ = 0, and ,0=ψ then

Dm = dAr

m24π

…….. (16)

The substrate receives a maximum amount of deposits. Hence, position of the substrate with respect to the source as well as the nature of the source, considerably effect the film thickness. Considering the point source and surface source, let is examining the thickness of the film. The density d of the film material, D = dm/V …….. (17) Where V is the volume of the film which is equal to t dA, where t is the thickness of the film. D = dm/(t dA) or dA = dm/( d.t) For a point source:

Dm = dAr

m24π

, substituting for

dA

Dm = td

dmr

m.4 2π

,

Or t = dr

m24π

…… (18)

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An introduction to thin films – Y .R.Reddy

Dividing equation (26) by equation (25) one can get

t1/ t0 = (1+ 22

2

)−hx

…..(27)

where cos rh /cos == ψθ .

B. Flash evoperation:

This method is generally adopted when the material has a tendency to decompose or dissociate during evaporation.

Fig.12 In this process, a small amount of charge in powder form is fed at a time to a whiter hot boat made with tungsten or molybdenum, so that instantaneous evaporation of the total charge takes place with out remains any residue. This process is shown in the fig.12. Because of the high temperature of the

boat and limited amount of charge fed at a time to the boat, there will be no time for contribution to build up the different vapour pressure. This method of deposition is called flash evaporation.

The charge is in a powder form is fed from a reservoir to the heater boat through a cute. The cute is made vibration which is connected to a vibrator. The vibrator is adjusted such that only small amount of charge falls on the boat; so that it can evaporate completely by the time of next charge falls on it. By this method a constant composition film can be produced. 5. Thinfilm thickness measurements: Thickness plays an important role in the film properties unlike a bulk material. The film properties are thickness dependent. The application of thin films in optical devices like interference filters anti-reflection coatings etc. are highly dependents on film thickness. In all thickness measurements, it is generally assumed that the films are homogeneous and more or less uniformly deposited on the substrate, and hence assumed to have mean thickness t. Film thickness measurement techniques are based on different principles such as mass difference, light absorption interference effects etc. 5.1 Mass method:

This method depends on increase of mass of a film due to deposition of film and is shown in the figure. The increase in film weight can be measured by a suitable micro balance. This balance is made up of quartz and deposits are formed on a pan which is suspended from the end of the beam by means of a quartz fibre.

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An introduction to thin films – Y.R.Reddy

The other end of the beam carrying a counterpoise. A pointer or a mirror is attached to the beam of the balance. With increasing of weight during the deposition, the pointer moves and its displacement can be measured by a traveling microscope. If mirror is fixed in the place of the pointer, with deposition of the mass mirror rotates and the rotation can be measured

plate N the frequency constant depends on nature of the crystal and t is the thickness of the thin film. For quartz cut at 35 , the value of N is 1670mm.kc/s.

020 ′

On depositing the material on quartz substrate, the frequency going on changes. The change of frequency df = -Cf t dfilm …….(32) Where dfilm is the density of the film deposited, Cf is the sensitivity of the mass determination. From the above equation, t = df/( Cf dfilm ) ….(33) In the above experiment, the temperature of the quartz crystal can affect the frequency of oscillations. While depositing the film on quartz, the temperature increases. To avoid this effect, crystal is cooled before taking the measurements. The sensitivity of the thickness measurement by this method is about 10-8 g.cm-2

5.3 Optical method (photometric method): There are several thickness measuring methods which depends on optical properties such as reflection, transmission, interference etc. The more commonly used method is photometric method, bases on transmittance of light/12/. This method depends on change in transmittance of light at normal incidence. If Io is the intensity incident light normally on a film and I is the intensity of the transmitted light, then,

Fig.13 by lamp and scale arrangement. Before doing the experiment the balance is standardized with known weights. Let m is the mass deposited due to the formation of thin film, V the volume of the film formed, then density of the material of the thin film, d = m/V …..(28) If A is the surface area if the film and t is the thickness, V = t.A …..(29) Then density can be given by the expression d = m/t.A or t = m/d.A …..(30) By knowing the mass m, film area A and the density of the material d, the thickness of the film can be measured. 5.2 Crystal Oscillator Method: This method was investigated by Suerbrey/11/. In this method, thickness measurement depends on oscillations of quarts crystal when excited, and the frequency of the oscillations depends on thickness by the equation

teII α−=0

…. (34)

Where t is the thickness of the film and α is the absorption coefficient (Lambert’s law). This ratio of I/I0 is called transmittance T. Then T e α= ….(35) t−

Taking logarithms both the sides, log T = - tα …..(36) That is, a transmittance versus film thickness graph on a semi-log scale will be a straight line. Hence, if one can measure the transmittance, film thickness can be measured. This method can be used for the film which can not absorb the light.

When light falls on the thin film which

F = v/2t = N/t …..(31) Where f is the frequency of the crystal is the velocity of the transverse wave normal to

l

9

is coated on a substrate, both transmittance T and reflectance R will show maxima and minima, and vice versa. The position of maxima and minima for both transmittance and reflectance can be recorded in a spectrograph as a function of wave length. Let the maximum and the minimum occurs at wavelengths 1λ

and 2λ in the transmission case, then

2 n f t = 21

21

λλλλ−

or

t = )(2 21

21

λλλλ−fn

…..(37)

Where nf is the refractive index of the film. From the above equation, the thickness of the film can be measured. 5.4 Interferometry- method: Film thickness can be measured accurately by interference fringes using multiple beam interferometers. A film, thickness of which is to be determined, deposited on flat surface, so as to leave sharp edge between the film and uncoated region of the substrate. A microscopic Slide can be used as a substrate. This complete substrate and the film are coated with silver coating for a good reflection. It is having a sharp step at the film edge. Another flat glass slide known as a reference plate, coated with Ag as in the case of film plate, is then placed over the specimen as shown in the fig.14 (b).A monochromatic parallel bean of light is allowed to fall normally on these plates. The arrangement for this is shown in the figure14 (a), which is the similar arrangement as that of the wedge method to find a thickness of the wire. The reflected light is then observed through the microscope. A set of sharp fringes perpendicular to the step with equal displacements will be observed as shown in the figure 14(b). The thickness can be measured by the equation,

T = a

b2λ

…… (38)

Where the λ is the wavelength of the light

used, b the displacement of the fringe at the step and a is the fringe width.

Fig.14 The sharpness of the fringe depends on the reflectivity of the metal coating, air gap etc.The metal coating on the two plates should be same. Thin thick ness of the thin film can be measured

up to the order of 30- 20,000 . 0A

6. Chemical Vapour Deposition (CVD): Chemical vapour deposition is a versatile process suitable for manufacturing of coatings, powders, fibers etc.This technology is now an essential factor in the manufacturing of semiconductors and other electronic components, optical, optoelectronic/13/ etc. Chemical vapour deposition may be defined as a solid on a heated surface from a chemical reaction in the vapour phase. It belongs to the class of vapour-transfer process which is atomistic in nature that is the deposition species are the atoms or molecules or the combination of these. The process can be defined in general form as fallows: The deposition of film from gaseous phase by thermal decomposition or chemical reaction on substrate surfaces at high temperature is known as chemical vapour deposition process or vapour plating . This technique is used for the preparing various

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Fig.16 are used for the formation of film deposit on the surface of the wafer (Substrate). The remaining waste gas is pump out by an exhaust pump, after waste treatment. 6.1. thermal decomposition: Many compounds when heated to high temperatures decompose results in the formation of solid as well as a gaseous phase. When an organic compound such as tetra ethylene orthosilicate which is in liquid form is heated to a temperature, a dielectric film of SiO2 is formed. Si(OC2H5)4 SiO2 + 4C2H4 + 2H2O (On decomposition) Some times oxygen can also be introduced in to the reactor to control the characteristic of the film. Silicon or germanium when heated to 700-9000C at a pressure of 10 Torr, it decompose to form Si and Ge films. SiH4 Si + 2H2 GeH4 Ge + 2H2 Silicon film can also be prepared by the reduction of tetrachloride silicone vapour with an n alkali metal hydride in the presence of organic solvent tetra ethylene glycol dimethyl ether SiCl4 + LiAl5 SiH4 + LiCl + AlCl3 SiH4 Si + 2H2 The reaction for the preparation of carbon film for carbon resistors can be prepared by

inorganic and organic compounds. The basic principle involves decompositions of vapour phase species and their subsequent deposition on substrates or reactions among the vapour species in a neutral atmosphere. Some times a carrier gas also used either to control rate of the reaction or to prevent undesired reactions at the prevailing elevated temperatures. Some of common reactions for formation of films as given below: AB A + B AB + CD AC + BD 2AB AB + A 2 4 (AB) nA + nB n

Where A, B, C, D are the different constituents and n is an integer. The rector for the CVD is shown as fallows:

Fig.15 In this reactor, there should be a gas inflow and an out flow should be provided for waste products. The pressurized gas should be sent to deposition chamber through a gas metering from gas cabinet. Gas metering device is used to control gas flow in to the chamber. Gas chamber contains a substrate at the bottom which is provided with a heater (Fig.16).The plasma or the incoming stream line gas decompose and the atoms or molecules which

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passing benzene vapours to a temperature of 500- 10000C. C6H6 C + Gaseous products 6.2 Vapour phase reaction: Silicon oxide (SiO2) films can be produced by the reaction of SiCl4 vapour with carbon dioxide in the presence of hydrogen. SiCl4 + CO2 + H2 SiO2 + C Cl4 + H2 SnO2 film often used in metal oxide resistors can be prepared from SnCl4 vapour in presence of water and HCl vapour. SnCl4 + 2H2O + HCl SnO2 + 4HCl + HCl 6.3 Vapour transportation method: In this method, vapours of two reacting constituents are passed over substrate kept at high temperature region when the reaction takes place to form the desired film. These techniques are generally used for the preparations of very thick films and even flat shaped crystals of several mm sizes.

Formation of CdS and CdSe by passing Cd and S or Se vapour through the furnace kept at high temperature can be achieved. Cd + S CdS Cd + Se CdSe In this technique, their will be three temperature zones, two for vaporization of two constituent elements and bring them together to react at a third zone to form direct product. 6.4 Disproportional method: This depends on the difference in the stability of polyvalent metal compounds at two temperatures. Both SiI2 and GeI2 are stable at lower temperatures where as SiI2 and GeI2 at comparatively high temperatures. By preparing SiI2 vapour at high temperatures (11000C) and passing them through a tube kept at lower temperature (9000C), a reaction cycle will

takes place as fallows: SiI4 + Si (at 11000C) 2SiI2 2SiI2 (at 9000C) Si + SiI4 SiI4 thus formed can again be connected to SiI2 by recycling. For the formation of the germanium film the two temperature regions should be 2000C and 3000C only which are much lower than the silicon iodides. 6.5 Applications of CVD: CVD has applications across a wide range if industries. Coatings: Coatings for a variety of applications such as wear resistance, corrosion resistance, high temperature protection, erosion protection etc. Semiconductors and related devices: CVD can be used to produce integrated circuits, sensors, and opto electric devices. Dens structure parts: CVD can also be used to produce components that are difficult or un-commercial to produce using conventional fabrication techniques. Optical fibers: For telecommunications. Composites: these techniques are used to reproduce ceramic composites such as carbon-carbon, carbon silicon carbides silicon carbides- silicon carbide composites. This process sometimes called as chemical vapour infiltration. Powder production: This technique is used to produce the novel powders. These techniques are also used in catalysts and nanomechines. 7. Electrical properties of thin films: In the case of thin metallic films, its resistively has been found to be much higher to that of corresponding bulk material, and it decreases with increasing film thickness and attains a value after approaching the bulk and then becomes constant as shown in the fig.17.

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film from which the electrons scattering in all the directions. There are three regions of scattering 1) between 0 and 1θ , the electrons will not able to travel their mean free path (mfp) l , and hence they strike the surface. In

region (2) between b

`

21 θθ and ,the electrons will

travel their full mfp l and in region (3)

betweenb

πθ and2 , the electrons once again hit

the surface as mfp is less than . blThe ratio of the conductivity of the film fσ to

the bulk l is given as fallows: b

b

f

b

f

ll

=σσ

= tl

lt

lt b

bb

log21

43

+

If klt

b

= , then one can write the equation as

k

kk

b

f 1log24

3+=

σσ

…. (39)

According to Sondheimer, the relation between conductivity of film and bulk is given as, for t ‹

and k ‹ 1, bl

]1[log4

3k

k

b

f =σσ

…… (40)

For thick films, › l ,and k › 1, t b

1]831[ −+==kf

b

b

f

ρρ

σσ

kb

f

831+=

ρρ

=tlb

831

ρ

+

On expanding in power series and neglecting the higher order terms,

]831[ b

b

f lt −=ρρ

…… (41)

t

A

Conductivity ρ against thickness t

Fig.17 Thin films are classified as continuous and discontinuous media. If the thin film is continuous with out any break or gap in between the adjacent regions and has some crystalline structure that of bulk material, is called continuous film, if not, it is called discontinuous film. 7.1. Conduction in continuous metallic film: If the thickness of the film is at the order of the mean free path of electron, then the conduction electrons will be more frequently scattered by two surface boundaries. Consequently, its conductivity decreases. This decrease of conductivity due to reduction of the material size is called size effect.

t

Film surface

Film surface

Fig.18 The conductivity of thin film fσ depends on the thickness of the film t .The scattering of electrons can be explained as fallows: Let us consider an arbitrary point with in the

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df .ρ

d

sc Na

bR

K

Fig.20 A graph between tf .ρ versus where t is the The slope of the graph gives gives the value of fρ . 7.2. Temperature coefficient of resistivity: The temperature coefficient of resistivity can be defined as the ratio of the change of the resistively per unit rise of the temperature to its initial resistivity. If bρ is the resistively of the bulk, bdρ is the change in resistivity in dT rise of temperature , then Temperature coefficient of resistance of the bulk

bTCR)( = bb

b dTd

αρ

ρ=

1 ……

(44) Similarly, the temperature coefficient of resistance for the film can be written as

tt

tf dT

dTCR α

ρρ

==1)( …… (45)

Dividing the equation (45) by the equation (44)

b

f

f

b

b

f

ddT

dTd

ρρ

ρρ

αα

..=

For a small rise of temperature, the change in bulk resistivity and the change in film resistivity is almost equal and hence,

It is observed that bσ is always greater than fσ . Let P is the fraction of electrons is secularly scattered from two surfaces and the rest are diffused with complete loss of their energy. Then, one can write

)1(831 pkf

b −+=σσ

….. (42)

From the equation (42) ,it can be observed that , when p=1, fb σσ = , that is the conductivity of the film is independent of the thickness, and same as that of the bulk.. If p ‹ ‹1, or nearly equal to zero,

k

bf

831

1

+= σσ

tlb

bf

83

1

1

+= σσ …….(43)

The values of fσ decreases with decreasing the

thickness. A graph betweenb

f

ρρ

against k is

shown in the figure.19, for different values of p. These experimental curves show a reasonable agreement with predicted values.

P=0

P = 1b

f

ρρ

k Fig.19 Thickness of the film, for different elements is shown in the figure.20.

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b

f

f

b

b

f

σσ

ρρ

αα

== …… (46)

This ratio of TCR of a film to its bulk is proportional to the ratio of their conductivities. 7.3. Conductivity and activation energy A thin film generally exhibits a high resistivity. Conduction can be takes place in high electric fields for the electrons to overcome the potential barrier between the islands. The variation of resistance with temperature can be represented as

KTE

eTAR γ−= 0 ..(46)

Where γ,0A the constants for a particular metal film and E is the activation energy for the conduction. The resistance of such a film decreases with temperature. In the high fields, the resistance of the film linearly dependent on the field. The value of conductivity σ versus 1/T, where T is the temperature in Kelvin for the thin films coated on Pyrex substrate at different thickness is shown in the figure.21.

Decreasing d

Log σ

1/T Fig.21 It is interesting to note that the activation energy also depends on the film thickness. On increasing the film thickness, the activation energy decreases continuously, and becomes constant after certain thickness. Beyond that, the activation energy and conductivity behaves like a bulk material.

8. Optical behavior of thin films: Optical properties of films have been studied extensively because of their applications in various optical and electro-optical deviances and it has been found that there is often a considerable deviation of optical parameters from that of bulk material. 8.1. Reflection, transmission, absorption and energy gap: When a beam of light passes through a thin film, it is partially reflected, transmitted and absorbed. Let R, A and T are the reflected, absorbed and transmitted light and is the intensity 0f the incident light, then

0I

TARI ++=0 ….. (47) Reflectance can be defines as the intensity of light reflected to the intensity of incident light. If is the intensity of the reflected light, the reflectance

rI

R = 0I

I r …… (48)

Absorbance can be defined as the ratio of intensity of the light absorbed to the incident light. If is the intensity of light absorbed, the absorbance,

aI

0I

IA a= ….. (49)

Transmittance can be defines a s the ratio of intensity of light transmitted to the intensity of incident light. If is the intensity of light transmitted, then, the the transmittance,

tI

0I

IT t= ….. (50)

Adding the equations 48, 49 and 50,

0/)( IIIITAR tar ++=++ =1 …. (51)

For perfectly non-absorbing material, 0=aI and hence, R + T = 1.

15

An introduction to thin films – Y. R .Reddy

When a monochromatic beam of light incident on a medium at a normal incidence, the relation between R, n and K are given as

22

22

)1()1(

knknR

+++−

= ….. (52)

And

t

t

ReRT α

α

2

2

1)1(−

−

−−

= … (53)

Where α is the coefficient of absorption, t is the thickness of the film through which the light passes and k is the extinction constant. An absorption spectrum of a thin film material is shown in the fig.22.The absorption of light by the film may takes place broadly by two processes:

logα

νh

Fig.22

1. By raising the electrons from valence band to the conduction band and

2. By exciting the lattice vibrations of the material by photon energy, or by both processes.

The lattice provides the information of bond length, effective charges and lattice vibrational frequencies. Electronic bond structure can be studied by process 1.

Optical methods provide very simple way of finding the band gap comparing to electrical methods.

Even in the absence of any thermal energy at 0Konly possible absorption that t can takes place is when the incident radiation has sufficient energy to excite valence electrons across forbidden energy band gap in to the conduction band.

The resulting absorption spectrum is

however, is continuous of intense absorption at shorter wavelength. A plot between energy versus wave vector k is shown in the figure. 23.

gE

direct indirectE

k Fig.23 The transition is said to be direct when the conduction band minimum and the valence band maximum occurs at the same wavelength. The absorption edge may occur at h gE=ν where , the minimum width of the forbidden energy band of the material. If the minimum of the conduction band and the maximum of the valence band do not coincide, the transition is said to be indirect.

gE

Thus the electronic transitions between the valence and conduction bands can be a direct or indirect. The transition probably related with absorption coefficient α as ……..(54) p

gEhA )( −= ναWhere p is called transition probability. A graph for log α and log νh is shown in fig.24. All the graphs are straight lines and the slope of the graph gives the value of p. The p has discrete values like ½, 1, 3/1, 2 ….. Let us now consider the case of metals where the absorption is primarily due to free charge carriers leading to the interband

16

An introduction to thin films – Y. R.Reddy

transitions involving no change of energy. Then the absorption coefficient is given as

)1(

422*

2

τωτπα

+=

mNe

nc ….. (55)

Where n is the refractive index, c the velocity of light, N free charge concentration,τ relaxation time and is the reduced mass. If ›› 1, then

*m 22τω

22*

24τωτπα

mNe

nc=

τω

π2*

24m

Nenc

=

As λπω =

c2

On substituting and simplification,

τπ

λαnmc

Ne*3

22

= ….. (56)

where λ is the wavelength of the light used. A graph between α and is shown in the fig.24. 2λ

α

2λ

Fig.24 It shows that α and is linearly dependent. This generally happens in visible and infrared region .The linearity generally observed for metals and semi metallic substances.

2λ

Refraction and transmission by single film: Let us consider a thin film PQ, RS on their boundaries, let a light is incident at A with an angle of 0θ . A part of the light is reflected and the rest is transmitted through the film and emerges out from other side of the film of thickness . Let 1d 1θ is the angle of refraction. The ray at C can also be reflected in to the same medium and suffers number of reflections as shown in the fig.25.

Fig.25 Combination of parallel reflected beams represented by 1,2,3,4…the transmitted beam of light rays cam be represented by 1’,2’,3’,4’…. These rays may lead to constructive or destructive interference depending on optical path length traveled by the rays, before their combination. Let DB is perpendicular to AB, then the path difference of the two rays = (AC+CD)-AM = cos2 111 θd ……….. (57) nWhere id the thickness of the medium (thin

film) and is the refractive index. The point D 1d

1n

17


And M will be in the same phase. Then the optical path difference, 111 cos2 θλ dn= …… (58) Where λ is the wavelength of the light used. Now if we consider all the reflected rays1,2,3…, there will be a constant phase difference 1δ between the successive rays due to extra optical path traversed by the medium in the film. And is given by

λπδ 2

1 = 111 cosθdn

The summation of the amplitudes of the reflected rays ........2211 ++= rarar = ∑ 11raWhere ……. Are the amplitudes of the reflected waves 1, 2, 3…..

2211 , rara

The total reflectance or the reflectivity® is given by the equation,

1212

22

1

1212

22

12

2cos212cos2δδ

rrrrrrrrrR

++++

== ..(59)

Similarly, the transmittance T is given by

22

21121

22

21

0

12

2cos21 rrrrtt

nn

tT++

==δ

…….(60) 9. Magneto resistance: The application of magnetic field alters the electrical resistance of a thin film. This change in the resistance of material due to the application of the magnetic field provides information regarding the shape of the Fermi surface of the thin film. When electrons are moving in a substance, and a magnetic field is applied perpendicular to the current direction, a Hall field will be built up to counterbalance the Lorentz force. All these electrons will not have same velocity. As a result the Hall Effect can compensate the Lorentz force and the net current in the direction is zero. Fast electrons which deviate one way or other under go more collisions. As the result their mean free along

The length of the sample will reduce causing increasing of its resistance. The change in the electrical resistance due to applied magnetic field with reference to zero magnetic fields can define as magneto-resistance. The magneto-resistance of a material can be defined as the change in resistively due to the applied magnetic field to the resistively at zero field. If Hρ and 0ρ are the resistivities of a substance at field H and field zero, then The magneto resistance

= 0

0

ρρρ −H =

0ρρΔ

…… (61)

As the resistivity is the reciprocal of conductivity and let Hσ and 0σ are the conductivities at field H and zero respectively, Magneto resistance

= 0

0σ σ H

σ−

…… (62)

When magnetic field is small, the magneto resistance is proportional to the square of the field, and hence,

2

0

AH=Δρρ

….. (63)

Where is is known as coefficient of magneto resistivity. For higher fields, the magneto resistance fallows the quadratic law

2

2

0 1 CHAH+

=Δρρ

….. (64)

Where c and 2μ= μ is the electron mobility. If H=0, equation (64) converts to equation (63) In the case of transverse magnetic field, the coefficient of magneto resistance

20 )2

(ne

Aσ

= …. (65)

Where n is the number of electrons per unit volume and e is the charge of the electron. Substituting the value of A in equation (63)

=Δ

0ρρ 20 )

2(

neσ

H …..(66) 2

18


Kohler showed that the magneto resistance depends on temperature, magnetic field and even on sample purity and geometrical consideration. According to him,

=Δ

0ρρ

f ( )0ρ

H …..(67)

F is a function depending on geometrical consideration and field direction. The

dependence of magneto resistance on 0ρ

H is

shown in the figure .26.at different temperatures.

1 2

3

0ρρΔ

0ρH

(1)78K (2) 195K (3)219K

Fig.26 Wilson-Summerfield theory gives the relation between resistivity in the magnetic field H as

)273.01( 220 HH μρρ += Or

)273.01( 22

0

HH μρρ

+= …. (68)

It indicates that, the magneto resistance is a strong function of mobility. Higher the

mobility, higher the ratio of0ρ

ρH . This

parameter depends on geometry of the sample.

For a rectangular sample, 0ρ

ρH varies on length

to breadth ratio (l/b). For a smaller value of

(l/b), 0ρ

ρH is a larger one. If the (l/b) value is

less than ¼, the magneto resistance is independent of its dimensions (Reverse in the case of Hall Effect). The magneto resistance of thin film decreases with decreasing of particle size/14/ 10. Sheet Resistance: Sheet resistance is the measure of resistance of thin films that has uniform thickness. For a rectangular three dimensional conductor, the resistance of a conductor is directly proportional to its length and inversely proportional to the area of cross section. If L is the length and A is the area of cross section, resistance

R α AL

or

ALR ρ= …. (69)

where ρ is the resistivity of the material. If W is the width and t is the thickness of the thin film, then we can write,

WtLR ρ=

WL

tR ρ=

WLRR s= …. (70)

Where is called sheet resistance and can be

defines as resistivity per unit thickness. As

sR

WL

is a dimensional less quantity, the unit of sheet resistance must be ohm. To differentiate from resistance, the unit of sheet resistance is considered as ohm/square. If L=W, for a square, R= for a square lamina, the sheet resistance is equal to the resistance of the lamina.

sR

Measurement: Sheet resistance can be measured by four-point probe method. A geometrical correction factor (CF) is usually required to convert the

19


Applications: factor accounts according to the sample size, shape and spacing. The sheet resistance measured by the four-probe method

)(CFxIVRs = ….. (71)

Where V is the measured DC voltage across the voltage probe and I is the DC current passing through the two current probes. The value of CF for samples of various sizes and shapes can be found in the reference books.

The sheet resistance of a thin film with different doping concentrations is shown in the fig.27.

It is usually used to evaluate the out come of semiconductor doping, metal deposition and resistive paste printing. This application can also be used in screen printing and hybrid micro circuits. References: 1. J.A.Venables, Rep.Prog.Phys.47 (1984)399 2. C.Ratsch, J.A.Venables.Jour.Vac.Science& Tech.A21 (2003) S96 3. J. Poortmans and V. Arkipov, thin film solar cells, John Wiley & sons publications (2006) 4. Joachim.P et al Sensors 4(2004)156 5. Mereno, etal. Optics letters30 (2005)914 6. H.Okimura. 17(1980)5359 7. Reza moazzami, IEEE tras. Elct. dev. 39 (1992) 2044 8. Thin film processes: Elsevier Publishing, 1991 9. M.Yamaguchin and T Nagotoma Jpn. Jour. Phys. 37(1998)5166 10. Hand book of thin film deposition processes and techniques. Krishna sheshan, William Andrew Publishing, 2002. 11. G. Sauerbrey, Zeitschrift für Physik, 155 (1959) 206-222 Fig.27 12. B. A. Nikitin et.al. Measurement techniques, 30 (1987)196 On increasing the doping concentration, the

sheet resistance decreases continuously. The value of sheet resistance is less for n-type doping than p-type doping for the same doping concentration.

13. Hideki Matsumura et.al, Thin Solid Films, 501(2006) 58. 14. B. P. Zot’’eV, Russian physics journal, 18(1975)69

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An Introduction to Thin Films

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