Electrical characterization and modeling of SiC IC test ...577752/FULLTEXT02.pdf · Electrical...

Master of Science ThesisStockholm, Sweden 2012

TRITA-ICT-EX-2012:181

G I O V A N N I F E V O L A

Electrical characterization andmodeling of SiC IC test structures

K T H I n f o r m a t i o n a n d

C o m m u n i c a t i o n T e c h n o l o g y

Electrical characterization and modeling

of SiC IC test structures

Giovanni Fevola

Master Thesis in Integrated Devices and Circuits

Supervisors: Prof. Carl-Mikael Zetterling, Prof. B. Gunnar MalmExaminer: Carl-Mikael Zetterling

July, 2012

Abstract

Ohmic contacts and resistor structures have been evaluated for a 4H-SiC ECL technology. Sheet resistance, contact resistance, transfer lengthand specific contact resistivity have been measured with the linear transferlength method. Values for such parameters are reported for each layer ofnpn bipolar junction transistors in the temperature range from 27 to 300C.Sheet resistance exhibits a 60% decrease with increasing temperature inthe p-type layer, while a non-monotonous dependence is found for the n-type layers, with values spreading in a range which is wide about 10% theroom temperature value. Strip and serpentine integrated resistors have alsobeen tested. Simulations of sheet resistance for n- and p-type layers arecompared to experimental data. Different sources for incomplete ionizationand mobility are considered. A good agreement is finally found for the p-type layer, while the need to model the metal-non-metal transition arises inthe n-type layer.

Contents

Contents iii

Acknowledgements v

List of symbols and acronyms vi

1 Introduction 1

2 Properties of silicon carbide 3

2.1 Crystal structure and polytypism . . . . . . . . . . . . . . . . 32.2 Electrical Properties . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Wide band-gap . . . . . . . . . . . . . . . . . . . . . . 52.2.2 High critical electric field . . . . . . . . . . . . . . . . 52.2.3 High intrinsic temperature and radiation hardness . . 62.2.4 High thermal conductivity . . . . . . . . . . . . . . . . 6

3 Electrical characterization 8

3.1 Parameters of interest . . . . . . . . . . . . . . . . . . . . . . 83.1.1 Contact resistance . . . . . . . . . . . . . . . . . . . . 83.1.2 Epi-layer sheet resistance . . . . . . . . . . . . . . . . 103.1.3 Transfer length . . . . . . . . . . . . . . . . . . . . . . 103.1.4 Specific contact resistance . . . . . . . . . . . . . . . . 11

3.2 Structures for resistive characterization . . . . . . . . . . . . 123.2.1 Integrated resistors . . . . . . . . . . . . . . . . . . . . 123.2.2 TLM structures . . . . . . . . . . . . . . . . . . . . . . 153.2.3 Kelvin structures and contact chains . . . . . . . . . . 16

4 Experimental results 19

4.1 Experimental procedure and measurement plan . . . . . . . . 194.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 23

4.2.1 Temperature Behaviour . . . . . . . . . . . . . . . . . 234.2.2 Parameter variation . . . . . . . . . . . . . . . . . . . 244.2.3 Design verification . . . . . . . . . . . . . . . . . . . . 27

iii

5 Simulation and modeling 31

5.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.1.1 Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . 315.1.2 Incomplete Ionization . . . . . . . . . . . . . . . . . . 335.1.3 Bandgap narrowing . . . . . . . . . . . . . . . . . . . 36

5.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . 375.2.1 Collector . . . . . . . . . . . . . . . . . . . . . . . . . 375.2.2 Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6 Conclusions and future outlook 43

Bibliography 45

List of Figures 50

List of Tables 52

iv

Acknowledgements

I owe sincere and earnest thankfulness to Prof. Carl-Mikael Zetterling forsupervising my work with grand patience and dedication. He has repliedmy questions and revised my scripts even when he was on vacation. Hisconstructive attitude is exemplary to me.

Prof. Mikael Östling and Prof. Niccolò Rinaldi are thanked for givingme the opportunity of being an exchange student at KTH.

Prof. B. Gunnar Malm and Dr. Reza Ghandi are also thanked for theirguidance in the laboratory.

Dr. Benedetto Buono has introduced me to the probestation and hasshowed me the measurement and simulation techniques. He has also alwaysbeen available to discuss my guesswork. I thank him and wish him the best.

Luigia Lanni has provided the wafer to characterize, technical informa-tion and material for this thesis, and good advices. Not to mention theamazing cakes. Thank you, Gina!

Dr. Christoph Henkel, with whom I shared office and laughs, is thankedfor the attention he has devoted to my work.

Without naming any in particular, I wish to thank all my friends fromStockholm and from home, and my fellow students; their support and esteemhave somehow contributed to this work.

The final acknowledgements go to my family, for their support and en-couragement throughout my study. To them I dedicate this thesis.

v

List of symbols and acronyms

Al Aluminum

C Carbon

d Contact spacing

ECL Emitter coupled logic

EA Acceptor energy level

EF Fermi Energy

EC Conduction band maximum

ED Donor energy level

EV Valence band minimum

gA Degeneracy factor for acceptors

gD Degeneracy factor for donors

kB Boltzmann constant

LT Transfer length

MNM Metal-Non Metal

n Free electron concentration

N Nitrogen

NA Acceptor concentration

N+A Ionized acceptor concentration

NC Effective density of states in the conduction band

ND Donor concentration

N−

D Ionized donor concentration

vi

vii

NV Effective density of states in the valence band

q Elementary charge

P Phosphorus

p Free hole concentration

Rc Contact resistance

RON ON-Resistance

Rs Sheet resistance

RT Total resistance

Si Silicon

SiC Silicon Carbide

T Temperature

t Thickness

TLM Transfer Length Method

VB Breakdown Voltage

χ Electron Affinity

∆EA Acceptor ionization energy

∆ED Donor ionization energy

ε Permittivity

Ec Critical electric field

φB Barrier height

φm Metal work function

µn Electron Mobility

µp Hole Mobility

ρ Resistivity

ρi Specific interfacial resistivity

ρc Specific contact resistivity

ζA Acceptor’s degree of ionization

ζD Donor’s degree of ionization

Chapter 1

Introduction

Since its inception, electronics has been more and more pervasive. Morerecently, this spread has not seemed willing to spare the harshest environ-ments. The most demanding applications, because of high temperatureor radiation presence, range from combustion monitoring (as in automotiveengines); process control (as in oil wells and chemical manufacturing); struc-ture health monitors in nuclear energy production, and in the aerospace andnaval fields; up to space exploration [46]. So far, where feasible, this has of-ten happened at the cost of additional parts or specially dedicated coolingsystems . This has increased size, weight and complexity (and chance offailure, on turn) of the overall system, suggesting the advantage of usingrobust independent electronics. Also, for instance, where a sensor could beplaced in a critical zone and the signal delivered to a safe one for controlor elaboration, huge advantages would come from placing the electronics asclose as possible to the critical zone. The ideal picture includes being ableto amplify and convert electrical analog signals into digital and eventuallyoptical ones in a hostile environment before transmitting them.

These are some considerations which have motivated the research inparticular on high-temperature electronics. The limits of Silicon (Si) andthe potentialities of wide bandgap semiconductors have been pointed outin the choice of the best suited material [31]. Silicon Carbide (SiC), afterovercoming Silicon in the domain of power electronics [8], is currently themajor candidate for this role. Different works have reported SiC integratedcircuit technologies for high temperatures, more or less recently [21].

This work is part of the latest one, which exploits an ECL-based bipolartechnology. The resistors in its circuits are crucial elements and representthe recipient of the study that was carried out on the test structures. Con-firming the assumptions made in the design phase is one of the goals. Thenone might be keen on gaining different kind of information from simple resis-tance measurements. However, the most interesting question concerns theirtemperature behaviour and the chance of predicting it. Incomplete ioniza-

1

2 CHAPTER 1. INTRODUCTION

tion makes it a not trivial one. Also, although SiC devices simulation hasbeen a research topic for years, the existing models mostly refer to powerelectronics and might not achieve the accuracy we desire.

After a brief due overview of SiC’s main properties in chapter 2, theparameters of interest, the methods and the structures for electrical charac-terization are described in chapter 3. Experimental data obtained accordingto the above mentioned aims are reported in chapter 4, while they are com-pared to simulations in chapter 5. Conclusions are drawn in the final chapterand a few suggestions for future work are given.

Chapter 2

Properties of silicon carbide

2.1 Crystal structure and polytypism

Silicon and Carbon are both fourth group elements and they occur in thediamond unit cell (Figure 2.1a). It consists of a face centered cubic cellwith four inner atoms, one per diagonal, at one third of the diagonal lengthfrom the vertex. In SiC the inner atoms are silicon and the others arecarbon, forming the so-called zincblende or sphalerite crystal (Figure 2.1b).In this structure every Si atom is covalently bonded to four C atoms (andvice versa) so that the basic building block is a tetrahedron in which thedistance between two carbon (or two silicon) atoms is 3.08Å and the distancebetween a carbon and a silicon atom is 1.89Å (Figure 2.3a), with the latterbeing fairly smaller than Si bond length.

A peculiarity of SiC is to crystallize in more than one form and suchfeature is called polytypism. In order to explain it, it is helpful to enhancea further way to describe a SiC crystal: it can be seen as double hexagonalclose packed sheets of Si and C stacked up according to a certain scheme(Figure 2.2), periodically repeating. Any specific scheme determines a spe-cific crystal structure, which is the polytype. The polytype name consists ofa number that indicates the length of the sequence and a letter that refers

Figure 2.1: Diamond (a) and Sphalerite (b) unit cell.

3

4 CHAPTER 2. PROPERTIES OF SILICON CARBIDE

Figure 2.2: Stacking sequences for 3C, 4H and 6H polytypes [47].

to the structure of the resulting crystal (e.g. C for cubic, H for hexagonal).Several hundreds of different structures are possible and have been identi-fied in nature, but commercially available wafers are mostly 3C, 4H and 6Hand, though incomplete, more accurate electrical parameters and parametermodels are available in literature or object of research for these polytypes.

Planes and directions within the crystal structure can be addressed byMiller indices [45]. For SiC four are needed. In fact, as usual for hexagonalcrystal structures and differently from cubic ones, four main directions areused: a1,a2,a3 lying in the close-packed plane, and c perpendicular to them(Figure 2.3b).

(a) (b)

Figure 2.3: SiC tetrahedrical structure (a) and principal axes for HCP crys-tals (b), [48].

It is clear that the crystal’s view in the c direction differs from that inthe a-plane. This anisotropy reflects on some of the polytype’s parametersas well.

2.2. ELECTRICAL PROPERTIES 5

2.2 Electrical Properties

2.2.1 Wide band-gap

Because of the short bond length SiC has a wide energy bandgap. Roomtemperature values are around three times larger than Si bandgap. Themain advantages of this material, such as high critical electric field, thepossibility to operate at higher temperature or radiation hardness, are allrelated to this very property. This and some other parameters of SiC fordifferent polytypes are summarized in Table 2.1.

Table 2.1: Material properties of Si and SiC [10].

(unit) Si 3C-SiC 6H-SiC 4H-SiC

Dielectric constant 11.8 9.7 9.7 9.7Energy gap (eV) 1.12 2.39 3.03 3.26Critical field (MV/cm) 0.3 1.5 3.2 3Electron mobility (cm2/V s) 1400 1000 3701,1002 8001,9502

Hole mobility (cm2/V s) 600 40 90 115Electron drift velocity (×107 cm/s) 1 2.5 2 2Thermal conductivity (W/cm K) 1.5 5 4.9 4.9

1: perpendicular to c-axis; 2: parallel to c-axis

2.2.2 High critical electric field

The critical electrical field is defined as the electrical field value at whichimpact ionization phenomena and hence breakdown occur. For SiC thisvalue is about 10 times higher than that of Si. This property makes SiCmore suitable for power electronics applications.

For instance, in a p-n junction, said W the depletion width and Ec thecritical electric field, the breakdown voltage VB is given by:

VB =EcW

2, (2.1)

so that with the same W a ten times higher VB can be achieved or, equiva-lently, if a non-punch-trough design is desired, the device can be made tentimes thinner keeping the same VB.

Then if we consider a p+-n junction the doping of the low-doped regionND is:

ND =2εVB

qW 2=

εE2C

2qVB, (2.2)

inferring that the doping can be made one hundred times higher. Hence,since the on-resistance is given by:

RON =W

qµnND=

4V 2B

εµnE3C

(2.3)

6 CHAPTER 2. PROPERTIES OF SILICON CARBIDE

Figure 2.4: Carrier concentration vs. temperature.

and also taking the lower values for mobility and dielectric constant of SiC inaccount, the final result is that much lower on-resistance can be achieved forthe same VB: roughly a factor between 200 and 400 depending on polytype[48].

2.2.3 High intrinsic temperature and radiation hardness

An electron-hole (e-h) pair can be created providing energy, thermally orby radiation. The p-n junction, the basic device, relies on the fact that onthe p-side there are almost only holes and on the n-side there are almostonly electrons. This assumption is correct (i.e. the device is extrinsic) andthe device works as long as the intrinsic carriers concentration is negligiblecompared to doping. If sufficient energy is available the intrinsic carrierseven outnumber the extrinsic ones: the material becomes intrinsic. Whenthat happens both the electron and hole concentration equal the intrinsicone, then the junction and hence the devices fail. The intrinsic temperaturesets the threshold between these two situations (Figure 2.4).

The energy bandgap is the minimum energy needed to create an e-h pair.Because of the wider bandgap, in SiC higher temperature or more intenseelectromagnetic fields compared to silicon are required to create e-h pairsor, equivalently, there are considerably fewer intrinsic carriers at any giventemperature (e.g. ≈ 10−7 vs. ≈ 1010 cm−3 at room temperature). Theintrinsic temperature of SiC is around 1000C [48], depending on polytypeand doping, while Si’s one is about 270C [36].

2.2.4 High thermal conductivity

SiC has a three times higher value for thermal conductivity compared toSi, meaning that a three times higher thermal flow is possible for the same

2.2. ELECTRICAL PROPERTIES 7

thermal increase at the junction. As previously stated, in power electronicsthe devices can be made thinner, but this on turn implies less power flow,so that higher thermal conductivity just mitigates this disadvantage. Whenit comes to integrated circuits, electric fields are usually much lower thancritical electric field, so that for SiC higher thermal conductivity just meansbetter capability to carry heat out of the device.

Chapter 3

Electrical characterization

3.1 Parameters of interest

3.1.1 Contact resistance

A contact is said to be ohmic if it can provide sufficient current with avoltage drop which is small compared to that in the active part of the device.Contact resistance is a measure of the quality of the contact and if it is smallenough the contact can be considered ohmic. Unfortunately such parameteris not really well defined since, beyond the metal-semiconductor contactresistance, it includes a part of the metal and the semiconductor adjacentto the interface, current crowding effects, spreading resistance under thecontacts etc.

The resistance at the actual interface stems from the barrier which ap-pears when metal and semiconductor1 are in contact, because of differentwork functions (Figure 3.1). The barrier height is given by:

φB = φm − χ, (3.1)

1A n-type semiconductor will be assumed.

Figure 3.1: Band diagram of metal-semiconductor structure. Separate (a)and in contact (b) [4].

8

3.1. PARAMETERS OF INTEREST 9

Figure 3.2: Conduction regimes in metal-semiconductor contacts [41].

and is basically independent of the semiconductor’s doping concentrationND

2.

Different mechanisms are responsible for conduction in metal - semicon-ductor contacts, depending on doping. They are illustrated in Figure 3.2.As the space-charge region width varies like N

−1/2D , for high doping it is

small enough to allow most of electrons to tunnel. This is the so-calledfield emission. For low doping, electrons pass from one side to another onlyby thermionic emission. This occurs when they are provided with thermalenergy high enough to exceed the barrier. For intermediate doping none ofthese mechanisms dominates and thermionic-field emission occurs. The spe-cific interfacial resistivity ρi accounts for the actual contact and is definedas:

ρi =∂V

∂J

∣

∣

∣

∣

V =0, (3.2)

with J and V being the current density and the voltage drop at the contact.For this parameter theoretical expression can be derived in all of the threeconduction regimes. In particular for field emission it is:

ρi ∼ exp(C/√

ND), (3.3)

where C is a constant. The expression above shows that for a good contactND should be as high as possible. Nonetheless it has to be mentionedthat the theoretical expression developed for ρi do not always agree withexperimental data [41].

The temperature dependence of contact resistance is usually observedthrough the specific contact resistivity (see section 3.1.4). We just pointout that, depending the current through the barrier on the number of freecarriers on the semiconductor side, a strong temperature dependence of thecarrier concentration affects contact resistance as well.

2Image force barrier can vary the barrier height but is usually neglected

10 CHAPTER 3. ELECTRICAL CHARACTERIZATION

3.1.2 Epi-layer sheet resistance

If we consider a rectangular slab of homogeneous material contacted at bothends by perfectly conductive plates its resistance is given by:

R = ρL

tW, (3.4)

where W,L,t are respectively width,length and thickness of the slab and ρis the material resistivity. Since integrated resistors can be modeled as filmsof constant thickness, ρ and t are usually combined into a single term Rs

named sheet resistance:Rs = ρ/t. (3.5)

It has to be noted that it is a technological parameter since both resistivityand thickness depend on the process that is being used. L/W is also calledaspect ratio and it yields the number of squares which the resistor is madeof. The advantage in introducing Rs is that it allows to think about resistorsin terms of number of squares, since their resistance is simply obtained bymultiplying it by Rs, and this is certainly more convenient when one isdealing with layouts.

In practice ‘the slabs’ are diffusions or epitaxially grown layers, so theycan hardly be seen as a homogeneous material. Because of non-uniformdoping, ρ is position-dependent, as well as the carrier concentration andmobility are. Assuming a monodimensional profile, varying along the x-axis, the sheet resistance can be evaluated as

Rs =1

∫ t0 q [µn(x)n(x) + µp(x)p(x)] dx

=ρ

t, (3.6)

where the average resistivity ρ also has implicitly been defined. For a n-typesample, neglecting the doping-dependence of mobility, the (3.6) reduces to

Rs =1

qtµnζDND, (3.7)

where the doping concentration and the incomplete ionization ratio fordonors, ND and ζD, are averaged as follows:

ND =1t

∫ t

0ND(x)dx, ζD =

1tND

∫ t

0ζD(x)ND(x)dx. (3.8)

It is clear from the (3.7) how mobility and incomplete ionization concur tomake Rs temperature-dependent.

3.1.3 Transfer length

It can be shown that only a portion of the contact is active during a two-dimensional current flow inside an integrated resistor and this portion hap-pens to be approximately equal to the thickness of the semiconductor sheet

3.1. PARAMETERS OF INTEREST 11

[17]. A transmission line model was applied by Murrmann and Widmannto planar devices in order to model current transfer and to be able to ex-tract contact resistance and sheet resistance [29]. The transfer length LT isdefined within this model, as the length where the voltage due to currenttransferring from the semiconductor to the metal or vice-versa as droppedto 1/e of its maximum value, which is located at the contact edge.

A more practical result is that, said L and Z the contact dimensions, ifL ≥ 1.5LT the effective contact area becomes LT Z and, since L can be muchhigher than LT , the effective area can be much smaller than the actual one.This on turn means that the current density is much higher than expectedin the close proximity of the contacts. This has to be considered whendesigning the contacts to prevent reliability problems.

The transfer length depends on the contact specific resistance (see sec-tion 3.1.4) and on the sheet resistance of the semiconductor underlying thecontact [41]:

LT =√

ρc/Rs. (3.9)

Such formula correctly suggests that the smaller the semiconductor resis-tance compared to the contact one, the more the current spreads below thecontact.

3.1.4 Specific contact resistance

Specific contact resistance, ρc, is sometimes also referred to as contact resis-tivity or specific contact resistivity. It is a contact area independent param-eter so it allows to compare contacts of different size. Differently from itstheoretical counterpart [9] ρi, it includes not only the actual interface butalso the regions immediately above and below. It can be expressed as:

ρc = RcAeff , (3.10)

where Aeff is the effective contact area.The effective contact area generally differs from the actual one because

part of the contact is not used by the current, especially in large3 contacts[19]. Plus, the ρc is usually an apparent value, as current crowding effects dueto misalignment between contacts (Figure 3.3) are included in the contactresistance. Different correction terms can be applied, depending on themeasurement method involved [41].

The temperature dependence of contact specific resistance is discussed in[44] for W-Si contacts. A complex, doping-dependent temperature behaviouris observed.

3The reference size is the transfer length.


Figure 3.3: Effect of misalignments between contacts. Ideal current flow (a)and current flow of misaligned contacts (b) [41].

3.2 Structures for resistive characterization

Passives are used in integrated circuits. Their resistance can be predictedbut the designer is usually also interested in verifying it, for several reasons.That is to say: some predictions rely on corrective factors that are notreally well known; the resistance values are prone to variability, because ofprocess and temperature variation, nonlinearity etc. The best test structureis of course the resistor itself but there are more convenient structures thatallow to extract the above mentioned parameters, providing more generalinformation.

3.2.1 Integrated resistors

Contact

Figure 3.4: Layout of a strip resistor [14].

The layout of a strip resistor is depicted in Figure 3.4. The drawn widthand drawn length are respectively the width of the strip of resistance ma-terial and the distance between the inner edges of the two contacts. If the

3.2. STRUCTURES FOR RESISTIVE CHARACTERIZATION 13

sheet resistance is known, the resistance can be roughly evaluated throughEquation 3.4. Because of outdiffusions, the actual dimensions might differfrom the drawn ones. Since resistors are usually much longer than wide theerror on length is neglected. The decrease in resistance is modeled as:

R = RsLd

Wd + Wb, (3.11)

in which the width bias Wb models the extra width added by outdiffusion.The effective width We is defined from that as the sum of the drawn widthand the bias one.

Equation 3.4 also implicitly assumes uniform current flow and that isclearly not verified in the resistor of Figure 3.4. Firstly the current mustcrowd near the contacts because they do not extend across all the width ofthe strip. This lateral non-uniform current flow increases the resistance by

∆R =Rs

π

[

1k

ln

(

k + 1k − 1

)

+ ln

(

k2 − 1k2

)]

, (3.12)

where k = We/(We − Wc), with Wc being the contact width. Secondly,placing the contacts on top of the strip makes that the current has to bendover, causing current crowding in the vertical dimension and so an increasein the overall resistance. However this effect is taken in account in thecontact resistance. It must be said that the error due to neglecting currentcrowding phenomena is less than 1% for ten squares long resistors [14], sothe designer’s concern is usually to avoid short resistors in the layout ratherthan properly evaluating the correction term.

(a) (b)

Figure 3.5: Serpentine resistors [14].

When large values for resistance are required, the layout of Figure 3.4becomes inappropriate. The more convenient layouts of serpentine or mean-der resistors are depicted in Figure 3.5. The turns can be either circular orrectangular. The contribution of the 180 end segment in the first case and


of the corner squares to the resistance is of interest. Such values are reportedin literature by different authors, but it is common to round their values to1/2 square for a corner square and 3 squares for the circular segment [14].

Figure 3.6: Dogbone resistor [14].

Resistors can also become so narrow that the contact cannot be accom-modated inside the strip without violating the design rules. The structuremust widen in proximity of the contacts so as to get the dogbone or dumbbellstructure, depicted in Figure 3.6. The resistance can be evaluated as in stripresistors according to the (3.11) but, like in strip resistors, current lateralflow occurs. Differently, since current spreads out near the contacts, the(3.11) overestimates the final value. The corrective term can be minimizedby making Wc the same as Wd and by minimizing the overlap Wo. Somevalues are published in [14] but, again, the correction is usually neglected ifthe resistor is longer than five squares.

The variability of integrated resistors is mainly due to process and tem-perature variation, to non-linearity and to contact resistance. Process vari-ation acts in two ways: photolitographic accuracies and non-uniform etchrates affect dimensions and fluctuations in film thickness; doping profilesand doping net concentration affect sheet resistance. The temperature de-pendence is a complex and non-linear one. Depending on the temperaturerange of interest and on the desired accuracy, it can sometimes be mod-eled as linear, so that only the so-called linear temperature coefficient ofresistivity and the resistance value at a certain temperature are sufficient todescribe such dependence. This is rarely the case for SiC because of the hightemperature ranges for which it is usually employed and because of the hightemperature sensitivity. Temperature behaviour will be widely discussed inthe subsequent chapters. Non-linearity is referred to the I-V characteristicexhibited by the resistor. Whereas an ideal resistor exhibits a linear rela-tionship between voltage and current, meaning that slope (i.e. resistance) isconstant, in actual resistors several factors, such as self-heating, high-fieldvelocity saturation and depletion region encroachment, concur to make itnon-linear. In other words, resistance becomes function of voltage, that isto say it is voltage modulated.


Figure 3.7: Schematic of a linear TLM structure [22].

3.2.2 TLM structures

The TLM test structures are used in order to determine the above men-tioned parameters of interest. Such structures are named after the transferlength method (TLM), originally conceived by Shockley [43], but are not un-related to the transmission line model, since the method, on turn, resorts tothe model’s approximations to evaluate the total resistance. In particular,according to the transmission line model, the contact resistance is given by:

Rc =√

Rsρc

Zcoth(L/LT ) =

ρc

LT Zcoth(L/LT ), (3.13)

where LT is given by the (3.9), and Z and L are respectively the contactwidth and length. If it is L >= 1.5LT the following approximation holds:

Rc ≈ ρc

LT Z. (3.14)

Figure 3.7 depicts the schematic of a linear TLM structure: it consistsof a semiconductor layer contacted with differently spaced pads. The totalresistance RT between any two adjacent contacts is given by:

RT = Rsd

Z+ 2RC ≈ Rs

Z(d + 2LT ). (3.15)

The method involves measuring these values and plotting them versus spac-ing d (Figure 3.8a, typical spacings are 5, 10, 15, 20, 25µm). Doing so enablesto extract:

• the sheet resistance through the slope of the interpolating line:

Rs = slope × Z;

• the contact resistance from the y-axis intercept: Rc = RT (0)/2;

• the transfer length from the x-axis intercept: LT = −12 d|RT =0;


(a) (b)

Figure 3.8: Total resistance vs. spacing (a), and four probes setting (b).

• the specific contact resistance from the contact resistance according tothe (3.14).

The total resistance can be measured with a two or a four probes setting.The latter (Figure 3.8b) is usually preferable because less sensitive to par-asitics, cable resistance and imperfect probes-contact. That is because cur-rent and voltage, which are measured independently, are both unaffected byextra-resistances on their own path. In fact, if an extra resistance is addedon the current probes an extra applied voltage is needed, but the currentis correctly sensed; similarly, if the extra resistance lies on the voltmetricpath, it has to be compared to the voltmeter in-resistance, hence resultingeasily negligible.

Some problems of the transfer length method are worth mentioning:the x-axis intercept is sometimes not very distinct, yielding incorrect valuesfor LT and ρc [41]; the (3.15) assumes constant sheet resistance for thesemiconductor, even under the contacts, where it might be different becauseof effects due to contact formation. Equations 3.15 and 3.14 should beslightly modified in this case [38]. Also, Li et al. [23] proved that the sheetresistance is a weak function of the spacing between contacts and observedan error on contact resistance for small contact spacings (< 0.1µm).

3.2.3 Kelvin structures and contact chains

Kelvin structures allow to measure contact resistance and specific contactresistivity. These structures have two main advantages. First they permitto measure very low contact resistances and second, differently from otherstructures, the measurement procedure for contact resistance is direct anddoes not require any knowledge about the semiconductor layer [41]. The sim-plest Kelvin structure is also known as cross-bridge Kelvin resistor (CBKR)


Figure 3.9: Four-terminal Kelvin structure: cross section (a) and top view(b) [41]; six-terminal Kelvin structure (c) [22].

and is depicted in Figure 3.9a,b. Current is forced through the contact be-tween pads 1 and 2 and voltage is measured between pads 3 and 4. If a highimpedance voltmeter is used, there is no current flow between 3 and 4 sothat they are at same potential as the contact surfaces. Contact resistanceis therefore given by:

Rc =V34

I, (3.16)

where V34 is the measured voltage and I is the applied current. The specificcontact resistance can be calculated multiplying by the contact area. It hasto be noted, though, that the value so obtained usually over-estimate thetrue one because it does not consider lateral current crowding effects [25].Figure 3.9c shows instead a six-terminal Kelvin structure [37]. If pads 5 and6 are ignored, it works as a CBKR. If voltage is sensed between contacts 5and 3 and current is still forced between 1 and 2, the voltage-current ratioyields the so-called end resistance [41].

Although coarser, contact chains (Figure 3.10) also provide a methodto measure contact resistance. The total resistance is the sum of the semi-conductor and contact resistance. They are also used to check the processdefectiveness. If contact resistance is higher than expected, though, it ishard to say whether one specific contact is faulty or all of them are.


Figure 3.10: Cross section and top view of a contact chain test structure[41].

Chapter 4

Experimental results

The test structures that were object of study belong to an integrated cir-cuit technology in 4H-SiC based on bipolar junction transistors [21]. Thecharacterization involved their three epitaxial layers: the n-type collectorand emitter, and the p-type base. The performed measurements had threemain goals: to investigate the temperature behaviour of resistive elements,the mapping of parameter variation, and the design verification. In the firstsection we describe how this was carried out and achieved, then in the secondsection the results are presented and discussed.

4.1 Experimental procedure and measurement plan

Because of unexpected events only a fragment of the wafer was availableat the end of the fabrication process and only eight dies were functioning(Figure 4.1a). In particular, each die has three blocks for ‘resistive’ char-acterization (I-R block), one per layer. Their position within the die ishighlighted in Figure 4.1b. The I-R block contains all of the test structuresdescribed in chapter 3 (Figure 4.2).

The temperature behaviour was obtained by testing the TLM structuresat seven different temperatures: 27; 50; 100; 150; 200; 250; 300C. Theparameters of interest were extracted from three TLM structures, one perlayer, on die r1c3 1. The parameter variation was evaluated through a wafermapping in which at least one TLM structure per die and per layer wastested at room temperature.

The TLM measurements were performed with a four probes setting.Current was forced from the outer pads, with voltage being sensed betweeneach couple of adjacent contacts. Current was swept in a certain range inorder to get the I-V characteristic of the two contacts plus semiconductorstructure. The current range should be as high as possible to get an easily

1Every die is referred to as rxcy. x and y denote respectively row and column numberof the die, having the flat on top.

19

20 CHAPTER 4. EXPERIMENTAL RESULTS

(a) (b)

Figure 4.1: Functioning dies (a) and die map (b).

appreciable voltage drop, but low enough to prevent local-heating phenom-ena, that might noticeably affect the resistance. Because of that a currentrange of [−10, +10] µA for the base layer and [−1, +1] µA for collector andemitter layers were chosen.

The resulting characteristic is a straight line if the contact is ohmic.However this is not ensured and a test sweep should always be run in orderto check that. Now, the I-V characteristic of a faulty contact usually appearsas a Schottky junction’s one (Figure 4.3), but with a narrow current range itwould appear as linear, not allowing to find out bad contacts. Therefore thecurrent was preventively swept in a wider range (up to [−100, +100] mA)and then in the above mentioned one for the measurement proper. Thisexpedient also improves the probe’s contact with the metal pad, where athin oxide layer might have formed.

The adopted measurement setting suffers in some cases from sensitivityto relative positioning of the probes. In practice, when two probes areplaced on the same pad, because of the non-uniform current distribution,the measured resistance is overestimated. That is the case when the outerspacings have to be measured. For the collector and emitter TLM values thisgenerally leads to overestimate on turn contact resistance, transfer lengthand contact resistivity (Figure 4.4a). Hence, only the values relative to innerspacings can be trusted. This luckily does not apply to the base layer, whereresistance values are considerably higher and less affectable by parasitics. Inthis case the measured values fit well on a straight line (Figure 4.4b).

All other structures on die r1c3 were also tested, at room temperature, inorder to get different kind of information. It is firstly of interest to know how

4.1. EXPERIMENTAL PROCEDURE AND MEASUREMENT PLAN 21

(a) Scheme. For the integrated resistors the number of squares is noted; for the Kelvinstructures and the contact chains, the contact and via dimensions.

(b) Optical image.

Figure 4.2: I-R test block.


−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

x 10−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

Current (A)

Vol

tage

(V

)

Schottky

Figure 4.3: I-V characteristic of a faulty contact

−10 −5 0 5 10 15 20 25

0

5

10

15

20

25

30

35

Spacing (µm)

Tot

al R

esis

tanc

e (Ω

)

Emitter 1, die r3c3.

(a)

−5 0 5 10 15 20 25

0

1000

2000

3000

4000

5000

6000

7000

Spacing (µm)

Tot

al R

esis

tanc

e (Ω

)

Base 1, die r3c3.

(b)

Figure 4.4: TLM measurements for emitter layer (a) and base layer (b)

much the actual resistances differ from the nominal ones. This holds bothfor the serpentine resistors, where uncertainty is also due to the correctivefactor discussed in chapter 3, and for the regular ones, some of which havesame number of squares but different width. For the latter, in particular,the over-etch on the sides of the semiconductor slabs might affect the narrowresistors more than the wide ones. The resistance was measured with a fourprobes setting in the narrow resistors (which have four pads, Figure 4.2) ofthe n-type layers, and with a two probes setting elsewhere.

Two kinds of comparisons involving integrated resistors are possible.When different kinds of resistors have equal number of squares their totalresistance can be compared directly. But also, since equally shaped resistorswith several different numbers of squares, Nsq, are available in the block (seeFigure 4.2) and their resistance is given by:

RT = NsqRs + 2Rc, (4.1)

the sheet resistance can be extracted from the slope of the interpolating lineand can be compared with the value extracted from TLM measurements.

4.2. RESULTS AND DISCUSSION 23

0 50 100 150 200 250 3000

50

100

150

200

Temperature (°C)

She

et R

esis

tanc

e (Ω

/squ

are)

Die r1c3, n−type layers.

Emitter 1Collector 2

(a)

0 50 100 150 200 250 3000

20

40

60

80

100Base 1, die r1c3

Temperature (°C)

She

et R

esis

tanc

e (K

Ω/s

quar

e)

(b)

Figure 4.5: Sheet resistance vs. temperature.

Finally, contact resistance and contact specific resistivity can be extractedfrom more than one structure and the values can be compared.

4.2 Results and discussion

4.2.1 Temperature Behaviour

Sheet resistance vs. temperature is plotted in Figure 4.5. Both the n-typelayers do not experience big variation: all values are in a range that variesaround 10% of the room temperature value. Conversely, sheet resistancedecreases in base of about 60% its room temperature value. A similar trendfor p-type 4H-SiC is reported by Balachandran et al. in [6].

The complex temperature dependence of sheet resistance has been high-lighted in section 3.1.2. The nonmonotonous trends for sheet resistance re-sult from those of ionization degree and mobility (see Equation 3.7). Becauseof incomplete ionization at room temperature the number of free carriers canincrease with temperature. Mobility instead is a decreasing function of tem-perature, for any doping, for temperatures above 300K [40]. The initialdecrease of sheet resistance is hence due to incomplete ionization prevailing.Eventually the latter begins to saturate, whereas mobility keeps decreasing,and a minimum for sheet resistance is reached.

The minimum point (i.e. the temperature at which the minimum isreached) is a function of the doping concentration and the dopant element,because mobility and ionization degree are. In particular, the higher theconcentration and/or the deeper the dopant element, the lower the ionizationdegree at a given temperature. Then, the higher the saturation temperatureand the higher the minimum point. The minimum point for sheet resistanceof emitter and collector (whose doping is quite close) is around 150C. Thatof base, whose dopant energy levels are much deeper, is supposedly over250C.


0 50 100 150 200 250 3000

2

4

6

8

10

Temperature (°C)

Con

tact

Res

ista

nce

(Ω)

Die r1c3, n−type layers

Collector 2Emitter 1

(a)

0 50 100 150 200 250 3000

200

400

600

800

1000

Temperature (°C)

Con

tact

Res

ista

nce

(Ω)

Base 1, die r1c3

(b)

Figure 4.6: Contact resistance vs. temperature.

The mobility drop does not in principle affect contact resistance, whichdepends, among the other things, on the number of available free carriersin the semiconductor. Therefore the trends are monotonically decreasingwith increasing temperature (Figure 4.6). Also in this case the extent ofvariations is much bigger in the base layer: the minimum value that hasbeen observed is about one fourth the maximum one in the base, while thesame ratio is 75-80% in the n-type layers.

The full set of measurements concerning temperature behaviour is re-ported in Table 4.1. Transfer length also appears as monotonically decreas-ing and, more importantly, it always stays very small compared to the con-tact length of the TLM structure (≈ 50µm), as assumed in chapter 3.

The same considerations made for contact resistance hold for specificcontact resistivity. Moreover, it is worth noting that despite its higher con-tact resistance compared to the emitter’s one, the collector TLM shows lowerspecific contact resistivity . This is because of shorter transfer length, whichon turn is consistent with higher sheet resistance (i.e. current spreading lessbelow the contact).

4.2.2 Parameter variation

The results of mapping are reported in Table 4.3. For die r1c3 it was possibleto extract parameters from both the TLM structures of every layer. Assum-ing low variability within die, their values give an idea of the reliability ofthe TLM-extracted parameters. In particular, the closeness of the two sheetresistance values in any layer suggests that the relative uncertainty of sheetresistance is probably the lowest compared to those of the other parameters.Conversely, specific contact resistance is the less accurate, as its uncertaintyincludes those of contact resistance and especially transfer length (see Equa-tion 3.13), but that is intrinsic to the transfer length method.

This must be taken in account when evaluating the variation within the


Table 4.1: Temperature behaviour

T Rs Rc LT ρc

(C) (Ω/sq.) (Ω) (µm) (10−5Ωcm2)

27 87.5 4.66 5.32 2.48

Emitter

50 85.5 4.46 5.22 2.33100 82.3 4.16 5.05 2.10150 78.7 4.15 5.27 2.19200 80.8 3.96 4.90 1.94250 81.8 4.05 4.95 2.01300 87.8 3.89 4.43 1.72

27 162 5.10 3.14 1.6050 156 4.98 3.20 1.59100 147 4.63 3.15 1.46150 144 4.40 3.06 1.35 Collector200 147 4.04 2.76 1.11250 150 3.91 2.60 1.02300 157 3.82 2.43 0.93

T Rs Rc LT ρc

(C) (KΩ/sq.) (Ω) (µm) (10−4Ωcm2)

27 59 706 1.20 8.44

Base

50 48 465 0.96 4.48100 34 319 0.93 2.96150 28 205 0.74 1.53200 25 191 0.75 1.44250 24 162 0.68 1.11300 23 181 0.77 1.39


Column

Row

Base Sheet Resistance vs. Position

3 4 5

1

2

3

4.5

5

5.5

6

6.5

x 104

(a) Base

Column

Row

Collector Sheet Resistance vs. Position

3 4 5

1

2

3

165

170

175

180

185

(b) Collector

Emitter Sheet Resistance vs. Position

Column

Row

3 4 5

1

2

380

90

100

110

120

130

140

(c) Emitter (d) Observed dies

Figure 4.7: Wafer mapping.

whole wafer. The mean value of each parameter, for each layer, is reportedin Table 4.3. Maximum and minimum indicate the parameter span. Thoseof contact resistivity are the biggest and reflect only partly a real differenceamong the contacts.

Some variations can be clearly interpreted. For instance, the collectorand base are obtained by etching epitaxially-grown layers [21]. The kindof etch that has been used for this batch is more aggressive on the edges,and the thickness of base and collector was in fact confirmed to be lower inthe outer dies by SIMS and profilometer measurements. This reflects on thesheet resistance values, where a quite clear pattern can be observed (Figure4.7a,b). Likely the variations are mainly due to different thicknesses, butalso non-uniform doping concentrations and measurement uncertainty mightplay some minor role.

The latters, instead, are responsible for the variations in the emitter asno etching is performed on its top surface (so smaller variation is expectedfor thickness) and as uncertainty affects the emitter’s measurements more


Figure 4.8: Correlation Rs-Rc. Dies are sorted by increasing Rs.

for the above mentioned reasons. However, there is no regularity in this case(Figure 4.7c) and it is hard to value any factor’s influence.

We note that the role of thickness variation could in principle be cut outthrough a temperature behaviour’s mapping. In fact the minimum pointin the Rsvs.T trend, for a given die, is thickness-independent2, then for agiven layer (dopant) it is a function only of doping concentration. As earliermentioned, the qualitative information that can be derived for each die isthat the higher the minimum point the higher the doping concentration. Ifaccurate models were available the minimum point could be precisely relatedto the doping.

About contact resistance, beyond the variation, it is interesting to seeif any kind of correlation with sheet resistance can be identified. If thethickness of the layer underlying the contact is uniform and the contactprocess is perfectly efficient both contact and sheet resistance are mainlyfunction of doping, hence there should be a direct correlation between thetwo sets of values. Figure 4.8 refers to the base values (the same happensin the other layers) and shows that this is not the case. That is mainlybecause of thickness differences, which affect sheet resistance and not thecontact one, but probably there is room for improvement of the contactprocess as well.

4.2.3 Design verification

The resistance of the narrow resistors with different number of squares isplotted in Figure 4.9, for different layers. Except for a few faulty resistorsin the n-type layers (Figure 4.9a), the trends appear to be linear. If their

2From Equation 3.7:∂Rs

∂T= 0 ⇐⇒

∂

∂T

1

µnζD

= 0.


0 5 10 15 20 250

1000

2000

3000

4000

5000

Number of squares

Res

ista

nce

(Ω)

CollectorEmitter

(a) Emitter and collector

0 5 10 15 20 250

500

1000

1500

Number of squares

Res

ista

nce

(KΩ

)

(b) Base

Figure 4.9: Narrow resistors.

resistance is neglected, sheet resistance can be extracted from these trendsand compared with the TLM-extracted ones. The same can be done forthe wide resistors. Their resistance value is clearly less reliable, though,because only two points are available. Table 4.4a summarizes the resultingvalues for comparison. The values from the base and the collector layers arecompatible, while the integrated resistors values in the emitter layer slightlymismatch the TLM-extracted ones.

A more direct comparison can be made looking at the 10-squares re-sistors. The total resistance for wide, narrow and serpentine resistors fordifferent layers is reported in Table 4.4b3. The serpentine resistor in theemitter layer shows significantly lower resistance than the others. The othervalues are compatible with each other if a relative margin of 10% is accepted.

Contact chains and Kelvin structures measurements do not match theexpected ones. For the contact chains, the base measurements suggest thateither the single segment resistance is about 10% overestimated, or onesegment in ten is shorted (Table 4.5). Leaning towards the second chance,likewise, we conclude that the defectiveness is quite higher in the n-typelayers: about half the segments are shorted.

The Kelvin structures in the base layer show non-linear I-V characteristicon a [−10, 10]µA current range, suggesting non-ohmic contact. Restrictingthe range eventually leads to a quasi-linear characteristic and, for [−1, 1]µA,a 31KΩ value is obtained for the 6 × 6 contact. It cannot be trusted thoughbecause it means specific contact resistivity 2-3 order of magnigude higherthan the TLM-extracted one. Similar results are found in the other layers.We conclude that these structures are still unreliable and, again, we foundthat the contact process might be improved.

3It has to be taken in account that whereas the narrow and serpentine resistors havethe same kind of contact, the wide resistor also has a wider contact.


Table 4.2: Mapping results.

(a) Base

Die StructureLT Rc Rs ρc

(µm) (Ω) (KΩ/sq.) (10−4Ωcm2)

r1c3B1 1.20 706 59.0 8.4B2 1.33 782 58.6 10.4

r1c4 B1 0.79 513 65.2 4.0r2c3 B1 1.16 504 43.4 5.9r2c4 B1 0.90 432 48.2 3.9r2c5 B1 0.70 465 66.8 3.2r3c3 B1 0.99 433 43.7 4.3r3c4 B1 1.04 493 47.4 5.1r3c5 B1 0.87 561 64.2 4.9

(b) Collector and emitter.

Die StructureLT Rc Rs ρc

(µm) (Ω) (KΩ/sq.) (10−6Ωcm2)

r1c3

C1 1.62 2.85 176 4.6C2 3.14 5.10 162 16.0E1 5.32 4.66 88 24.8E2 6.68 5.61 84 37.5

r1c4C1 1.94 3.46 178 6.7E1 2.23 2.54 114 5.7E2 2.46 2.75 112 6.8

r2c3C1 1.77 2.95 167 5.2E2 9.65 7.04 73 67.9

r2c4 C1 1.95 3.26 167 6.4

r2c5C1 2.02 3.54 175 7.2E2 1.25 1.57 126 2.0

r3c3C1 2.82 4.61 164 13.0E1 3.05 4.07 133 12.4

r3c4C2 1.92 3.49 182 6.7E2 1.85 2.60 140 4.8

r3c5C1 2.33 4.37 187 10.2E1 1.18 1.57 134 1.9


Table 4.3: Parameter variation statistics.

LayerLT Rc Rs ρc

(µm) (Ω) (Ω/sq.) (Ωcm2)

BaseMean 0.96 513 54736 4.97×10−4

Max 1.2 706 66808 8.44×10−4

Min 0.7 432 43357 3.24×10−4

CollectorMean 2.05 3.56 174 7.49×10−6

Max 2.82 4.61 187 13.0×10−6

Min 1.62 2.85 164 4.60×10−6

EmitterMean 3.5 3.44 115 17.1×10−6

Max 9.65 7.04 140 67.9×10−6

Min 1.18 1.57 73 1.85×10−6

Table 4.4: Resistors verification.

(a)

Layer sheet resistance TLM (1;2) Narrow resistor Wide resistor

Base (KΩ/sq.) 58.5; 59.0 58.0 59.5Collector (Ω/sq.) 176; 162 156 179Emitter(Ω/sq.) 87.5; 84.1 97.2 117

(b) 10 squares resistance (KΩ)

Layer Wide Narrow Serpentine

Base 62.5 60.1 58.1Collector 1.94 1.86 1.99Emitter 1.21 1.27 1.08

Table 4.5: Contact chains measurements.

Resistance (KΩ) Segment 10 segments 20 segments

Base 106 896 1802Collector 0.65 3.79 7.17Emitter 0.37 1.69 3.49

Chapter 5

Simulation and modeling

Simulations were run with the ISE-TCAD software [42]. The goal was toinvestigate the possibility of predicting correctly the temperature behaviourof sheet resistance. Before presenting and discussing the results, the physicalmodels that were more significantly involved are described.

5.1 Models

5.1.1 Mobility

In the simulation environment the Arora mobility model [3] is implemented.The low-field mobility for electrons and holes is given by:

µn,p(T, N∗) = µminn,p

(

T

T0

)αmn,p

+µdelta

n,p

(

TT0

)αdn,p

1 +

N∗

Nrefn,p

(

TT0

)αNn,p

Aan,p

(

TT0

)αan,p

, (5.1)

with N∗ being either the concentration of ionized impurities or the overalldoping. T0 is the reference temperature and is always set to 300K. Theexpression above models the doping dependence as the Caughey and Thomaskind [7], but here the temperature dependence is added.

The parameter values used by the simulator are taken from [5] and arereported in Table 5.1. They are based on measurements in [40]. In botharticles it can be noted how many parameters lack of any temperature de-pendence. Also because of this, other mobility models have been tested.

A more recent and complete reference for electron mobility in N-dopedSiC is [39]. It provides the parameter values for the main SiC polytypes,relying on several experimental data. Here the low field mobility is in factmodeled as by Arora and the temperature dependence of each parameter isconsidered. The only difference concerns the parameter µdelta but it can be

31

32 CHAPTER 5. SIMULATION AND MODELING

Table 5.1: Parameter values for eq. 5.1 by [5].

unit n p

µmin [cm2/Vs] 0 15.9µd [cm2/Vs] 947 108.1N ref [cm−3] 1.94 × 1017 1.76 × 1019

αm [1] 0 0αd [1] -2.15 -2.15αN [1] 0 0Aa [1] 0.61 0.34αa [1] 0 0

easily overcome with no big error1. The mobilty is given as a function ofthe overall doping, so N∗ = NA + ND must be set.

Table 5.2: Parameter values for Equation 5.1 from [39] and [26].

unit n p

µmin [cm2/Vs] 40 37.6µd [cm2/Vs] 910 68.4N ref [cm−3] 2 × 1017 2.97 × 1018

αm [1] -0.5 −2.75∗

αd [1] -2.58 −2.75∗

αN [1] 1 0Aa [1] 0.76 0.356αa [1] 0 0

The values with ∗ refer to N∗ = 1.4 × 1018 cm−3.

The reference for hole mobility in Al-doped 4H-SiC is by Matsuura etal. [26]. Here the temperature dependence is expressed as:

µp(T, N∗) = µp(300, N∗)(

T

300

)

−βp(N∗)

, (5.2)

where, also, and in agreement with [18], N∗ is the total doping concen-tration. µp(300, N∗) and βp follow a Caughey-Thomas doping dependence.

1µdelta(

TT0

)αd

is actually modeled as µmax(

TT0

)αmax

− µmin(

TT0

)αmin

. Values for

µdelta and αd were obtained imposing the two expressions equal at T=300K and T=573K.The difference is always less than 2.5%.

5.1. MODELS 33

Although the temperature dependence of the doping-related parameters ofEquation 5.1 (αN and αa) is not explicit within this model, a different dopingyields a different βp and, on turn, different temperature trend. Therefore,their temperature dependence is comprised in the β parameter. Table 5.2summarizes the “alternative” parameter values.

The electric field dependence of mobility is taken in account accordingto the Caughey-Thomas model:

µn,p(E) =µlow

n,p[

1 +(

µlown,p E

vsat

)β]1/β

, (5.3)

where β = 2 and vsat depends on temperature as follows:

vsat = vsat0

(

T

300

)αv

. (5.4)

vsat0 = 2.5 × 1017 cm/s and αv = 0.5 for both electrons and holes.

5.1.2 Incomplete Ionization

In Silicon at room temperature the thermal energy kBT/q is sufficient toionize all the dopant impurities. It can be assumed then that the concentra-tion of free carries equals doping. In SiC the impurity levels of the typicaldopants are deep enough to make their ionization energies not small com-pared to the available thermal energy. In such case the concentrations ofionized carriers (acceptors or donors), N+

A and N−

D , are given by the Fermi-Dirac distribution [35]:

N+A =

NA

1 + gAexp(EA−EFp

kBT ), (5.5)

N−

D =ND

1 + gDexp(EFn −ED

kBT ), (5.6)

with NA/D being the total active doping concentration, EFp/nthe quasi-

Fermi levels and EA/D the dopant energy levels. gA and gD are the degen-eracy factors for acceptors and donors and are usually assumed to be 4 and2 respectively2.

The ionization degree for acceptors and donors, ζA/D, is defined as theratio between ionized impurities concentration and doping concentrationand can be derived from Equations 5.5,5.6 expressing them in terms of thecarrier concentrations instead of the quasi-Fermi levels:

2Different choices can be made, though. In [6] is gA = gD = 3.


ζA =N+

A

NA=

1

1 + gAp

NVexp(∆EA

kBT ), (5.7)

ζD =N−

D

ND=

1

1 + gDn

NCexp(∆ED

kBT ), (5.8)

where ∆EA = EA −EV is the acceptors ionization energy, ∆ED = EC −ED

is the donors ionization energy, NC and NV are the effective density of statesof, respectively, electrons in the conduction band and holes in the valenceband. A handier expression can be easily derived for Equations 5.7 and 5.8:

ζA =N−

A

NA=

−1 +√

1 + 4gANANV

exp(∆EAkBT )

2gANANV

exp(∆EAkBT )

, (5.9)

ζD =N−

D

ND=

−1 +√

1 + 4gDNDNC

exp(∆EDkBT )

2gDNDNC

exp(∆EDkBT )

. (5.10)

The advantage consists in expressing the ionization degree explicitly as afunction of doping and temperature.

More precise information about the ionization energies is needed. In SiCtwo different lattice sites exist: one with cubic surrounding (k) and one withhexagonal surrounding (h) and a dopant impurity can be in either of them.In 4H-SiC it is usually assumed that the number of k-type impurities is thesame as the h-type one. Depending on which site the impurity occupies,it has a different energy level corresponding to different ionization energy.The dopant elements used in the tested samples are Al for p-type and Nfor n-type SiC. The difference between the two Al levels is negligible andonly the shallower one is usually considered. The situation is different for Nwhere the two levels EDk

and EDhare around 60 meV and 90 meV beneath

the conduction band minimum. In such case writing the total free carriersconcentration as the sum of the free carriers coming from the two sites andsolving the neutrality equation, leads to a slightly different formula for theionization degree [4]:

ζD =−1 +

√

1 + 2gDNDNC

exp(EC−EDk

kBT )

2gDNDNC

exp(EC−EDk

kBT )+

−1 +√

1 + 2gDNDNC

exp(EC−EDh

kBT )

2gDNDNC

exp(EC−EDh

kBT ),

(5.11)A simpler approach involves defining an effective donor level (Ed) for

Equation 5.10. This is accomplished in [5] imposing the actual number ofionized donors to equal the number of ionized donors for the single effective

5.1. MODELS 35

level at T=300K:

0.5ND

1 + gDn

NCexp(

EC−EDkkBT )

+0.5ND

1 + gDn

NCexp(

EC−EDhkBT )

=ND

1 + gDn

NCexp(EC−Ed

kBT ).

(5.12)Assuming EC − EDh

= 52.1 meV and EC − EDk= 91.8 meV [13, 12] and

solving for Ed, a value of 65 meV is obtained.As pointed out by Da Silva et al. [11], the effective energy level always

lies in between the two actual levels. It is closer to the shallowest one forfull ionization and vice-versa, meaning that the effective level is ζ-dependent.Since ζ does vary with temperature, it is also temperature-dependent. Suchconclusion can be drawn also by noting that Equation 5.12, from which onespecific effective level was obtained, holds for one specific temperature.

The ionization energies are also found to decrease with increasing dopingconcentration. Although several mechanisms describing such phenomenonare involved and have been theoretically considered [32], a simple modelrelating the ionization energy only to the average distance of the impuritiescan be used:

∆EA = ∆EA(0) − αAN1/3i , (5.13)

∆ED = ∆ED(0) − αDN1/3i , (5.14)

where Ni = NA + ND is the total doping concentration, ∆EA/D(0) is theionization energy for infinite dilution and α is a proportion constant. Thismodel is implemented by the simulator and

αA = αD = 3.1 × 10−5 meV cm

is chosen. Default values for ∆EA(0) and ∆ED(0) are instead 210 meV and65 meV. Since there is no general agreement in literature about values forboth ∆EA/D,0 and αA/D, different sources have been considered.

Table 5.3: Parameters for donor levels of N-doped 4H-SiC.

∆ED1(0) (meV) αD1(meV cm) ∆ED2(0) (meV) αD2(meV cm)

65 1.23 × 10−5 111 3.75 × 10−5

A reference for donors is [33], where values for the two nitrogen donorlevels in samples with different doping are reported. The parameters forEquation 5.14 can be extracted by interpolation and are reported in Table5.3. The extracted values are consistent with those reported in [15].

For Al ionization energies we referred to [18] and [26]. Unlike the former,the latter also models the deep level (Table 5.4). Interestingly, for the basedoping the deep level overcomes the shallow one.


Table 5.4: Parameters for acceptor levels of Al-doped 4H-SiC.

∆EA1(0) (meV) αA1(meV cm) ∆EA2(0) (meV) αA2(meV cm) Ref.

220 1.9 × 10−5 413 2.07 × 10−4 [26]265 3.6 × 10−5 - - [18]

5.1.3 Bandgap narrowing

Bandgap narrowing [35] occurs in heavily doped semiconductors. It is due totwo distinct effects: degeneracy and band tailing. Degeneracy occurs when,because of heavy doping, the wavefunctions of the electrons overlap, causingthe allowed donors or acceptor levels to broaden in a set of allowed energies.The bandgap is reduced when the doping is high enough to make this setmerge into the conduction, for n-type doping, or into the valence band,for p-type. The carrier-carrier interaction related to the high density ofmajority carriers also adds an extra-potential inside the crystal that movesthe allowed conduction and valence energy band states into the bandgap.The final effect is the lowering of conduction band minimum EC and theraising of valence band maximum EV and is called band tailing.

Narrower bandgap means on turn higher intrinsic carrier concentration.This is a negligible effect, though, if one is interested only in the free carrierconcentration of a doped sample, a fortiori in SiC. Instead, it is signifi-cant that both the dopant levels spreading and the band tailing reduce theionization energy of dopant impurities, increasing the majority carrier con-centration.

Table 5.5: Parameters for band edge displacement.

Ac Bc Av Bv

n-type −1.50 × 10−2 −2.93 × 10−3 1.90 × 10−2 8.74 × 10−3

p-type −1.57 × 10−2 −3.87 × 10−4 1.30 × 10−2 1.15 × 10−3

Lindefelt relates band displacements of n-type and p-type 4-H SiC to theionized impurities concentration [24]. The following formulas, together withthe parameters in Table 5.5, give the band edge displacements in eV:

∆Ec = Ac

(

N

1018

)1/3

+ Bc

(

N

1018

)1/2

(5.15)

∆Ev = Av

(

N

1018

)1/3

+ Bv

(

N

1018

)1/2

(5.16)

5.2. SIMULATION RESULTS 37

!"

#

# ""

$ $ %& %&

Figure 5.1: BJT. Cross section (a) and top view (b) [21].

where

N =

N+D for n-type

N−

A for p-type

It has to be noted that in a n-type semiconductor the valence band is evenmore displaced than the conduction band (and vice-versa for p-type) butsuch displacement does not affect the ionization energies. Also, in the testedp-type layer the band edge displacement is negligible compared to the initialvalue of Al ionization energy, whereas this does not apply to any tested n-type layer.

5.2 Simulation results

The attention was focused on the collector and the base layers. In particular,by collector layer we mean the deep and more heavily doped one in the crosssection of Figure 5.1. The TLM structures are built in these layers after anetching step which removes the overlying ones. In order to have a margina small portion of the target layer, the one that must be reached is etchedaway, hence the final thickness of the epi-layer in the TLM structure areslightly lower than the BJT’s ones.

The more complex structures in the emitter layer include two differentlydoped layers. Although their simulation is not more complex, the resultwould not provide simple information for model adjustments.

5.2.1 Collector

The collector layer was modeled as a 900 nm-thick, uniformly N-doped slab.Nominal concentration is 1 × 1019 cm−3. In order to mimic the TLM struc-ture, three different spacings were simulated. The contacts were conceived


as ideal and placed on top of the slab. Therefore the total resistance in-cluded the semiconductor resistance and the aliquot of contact resistanceaccounting for the complex current distribution near the contact.

The trend and the values predicted with the original parameters arequite unlikely and, of course, do not match the experimental data at all.Same unsatisfactory results were obtained in a previous work [20]. In seek-ing the reasons for that, we firstly note from Equation 3.7 that the sheetresistance trend is properly modeled if mobility and incomplete ionizationare. Secondly, we observe that from the same equation, for a given dopingthe following relation can be derived:

Rs(T2)Rs(T1)

=ζ(T1)µ(T1)ζ(T2)µ(T2)

. (5.17)

Then, knowing mobility, a “relative” trend for ionization degree can be ex-tracted from the measured sheet resistance. Such a trend, differently fromthe sheet resistance prediction of Equation 3.7, is immune from thicknessand doping3 uncertainty.

300 350 400 450 500 550 6000

20

40

60

80

100

Temperature (K)

Ele

ctro

n M

obili

ty (

cm2 / V

s)

Old mobilityRoschke model

Figure 5.2: Electron mobility for the collector layer.

We start with questioning the mobility model. The original mobilityvalues predict a ionization percentage rising of a factor ≈ 4, which sets anupper bound of about 25% for the room temperature value. Such a trend andespecially a so low upper bound is unlikely for two reasons. Firstly, takingbandgap narrowing into account with Equation 5.15 a value of ≈ 30 meVis, on first approximation, estimated for ionization energy of N impurities,which is quite lower than the available mean thermal energy, suggestingeven full ionization at room temperature; secondly, sheet resistance at roomtemperature is predicted by Equation 3.7 to be about 3 times the measuredvalue, which is hardly compatible with the accuracy of the other parameters.We conclude that the mobility model does not hold.

3The doping uncertainty affects a single value of mobility much more than the mobilityratio in Equation 5.17


As already mentioned in section 5.1.1, the mobility model for electronsfrom [39] was tested. The temperature trend of mobility for the collectordoping is reported in Figure 5.2. High difference arises at high tempera-tures, yielding a higher upper bound for room temperature ζD: about 50%.Still, the simulated trends do not agree the measured one but some progresscan be noted. Figure 5.3 sums up the simulations with the two mobilitymodels: resistance increases monotonically in both cases but less hotly withRoschke’s values.

Settled for the new mobility, we seek an explanation for disagreementin the incomplete ionization model. There is, in fact, a mismodeling of therelative trend of incomplete ionization (Figure 5.4). Since bandgap narrow-ing and temperature increasing concur to lower the ionization energy of Nimpurities, attempts to conveniently correct this trend by changing the ion-ization energy according to the previous sections (5.1.2 and 5.1.3) criteriawere made. Unfortunately that does not yield positive results.

This might be because in this case the incomplete ionization is probablynot due to insufficient thermal energy and donor levels depth. Instead, thehigh doping brings the Fermi-level up closer to the dopant states, causingthem, rather than the conduction band ones, to be likelier to be occupied.This phenomenon is dealt for P-doped Si by Altermatt et al. [1, 2]. Theyshow that, against the common assumption of full ionization, at room tem-perature up to 25% of dopants are nonionized when the dopant density isaround the Mott transition (metal-non metal) [28], whereas the percentageis negligible far above that point (Figure 5.5a).

Figure 5.5b shows instead that our incomplete ionization model, givenby Equation 5.10, does not take in account this phenomenon. ζD = 0.49 ispredicted by Equation 3.7 and Raman spectroscopy sets the critical electronconcentration for Mott transition around 5 × 1018 cm−3 [30]; moreover theapproximate expressions for degenerate semiconductors by Joyce and Dixon

0 50 100 150 200 250 300100

200

300

400

500

Temperature (°C)

She

et R

esis

tanc

e (Ω

/squ

are)

Collector 2, die r1c3

MeasurementsOld mobilityRoschke mobility

Figure 5.3: Collector layer simulations.


Figure 5.4: Incomplete ionization according to Roschke’s mobility model.

(a) The fraction between conduc-tivity mobility and Hall mobil-ity, reflecting incomplete ioniza-tion [1].

1015

1016

1017

1018

1019

1020

1021

1022

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ND

(Phosphorus, cm−3)

ζ D

(b) Incomplete ionization degree according toEq.5.10 for ND = 1 × 1019cm−3 and ionization en-ergy set to 45 meV.

Figure 5.5: Incomplete ionization in Si:P.

[16] give the following estimation for the Fermi level in our sample:

28 meV < EC − EF < 50 meV for T=300K, (5.18)

which is close to the shallower dopant level. These facts suggest that oursample undergoes the Mott transition when temperature is increased but ourmodel neglects this circumstance, underestimating the ionization percentageand giving the final monotonically increasing trend for sheet resistance.

Finally, a mere analytical fitting was applied to the relative trend ofionization degree extracted from measurements. gD = 0.157, ∆ED = 95.5meV give the best agreement with trend, but not with absolute values. Theconsequent trend for sheet resistance is depicted in Figure 5.6. However,these values are not coherent with the physical ones, and somehow confirmthe need of some drastic model adjustments.


300 350 400 450 500 550 600180

185

190

195

200

205

210

Temperature (K)

She

et R

esis

tanc

e (Ω

/squ

are)

gD

=0.157∆E

D=95.5 meV

Figure 5.6: Best fit to trend.

5.2.2 Base

The thickness of the base layer was set to 270 nm. The p-type dopants are Alimpurities and their nominal concentration is 1.4×1018 cm−3. Bandgap nar-rowing affects ionization energy in a very weak way and has been neglectedin this case.

300 350 400 450 500 550 6000

20

40

60

80

100

Temperature (K)

Ele

ctro

n M

obili

ty (

cm2 / V

s)

Old mobilityMatsuura model

Figure 5.7: Hole mobility for the base layer.

Simulations with the original parameters strongly underestimate thesheet resistance. Even considering the uncertainties of doping and thick-ness, there is room to believe that ionization percentage and/or mobility areoverestimated. In fact, an ionization energy value of 175 meV is used withthe original model, but both Matsuura and Koizumi models (see section5.1.2) reveal higher values: respectively 181 and 225 meV. This would resultin lower ionization degree. Also, Matsuura mobility model predicts lowervalues (Figure 5.7).

Simulations for different parameter values are plotted in Figure 5.8. Theline closest to the measurements was obtained using the old mobility modeland Koizumi’s parameters for incomplete ionization; the upper line resultsfrom the same values for ionization energy but uses Matsuura mobility model


0 50 100 150 200 250 3001

2

3

4

5

6

7

8x 10

4

Temperature (°C)

She

et R

esis

tanc

e (Ω

/squ

are)

MeasurementsMatsuura, KoizumiOld mobility, KoizumiOriginal parameters

Figure 5.8: Simulations of the sheet resistance in the base layer.

instead. Although more distant, the latter has a better agreeing trend andis therefore more promising for higher temperatures.

Furthermore, we note that the heavy doping and the high ionizationenergy of aluminum concur to very small ionization. About 85% of dopingat least is nonionized at room temperature. Matsuura models even predictsa < 5% room temperature value. This can be inferred from the relativetrends of ζA extracted from measurements (Figure 5.9). The wide range ofvalues is indeed one of the factors which make the modeling hard.

Figure 5.9: Ionization degree deduced from measurements.

This is also because the critical concentration for MNM transition, whichis around 2 × 1019 cm−3 for Al doped 4H-SiC [34], is definitely well abovethe hole concentration at room temperature, while it might be significantlyclose at high temperature if full ionization is approached.

Chapter 6

Conclusions and future

outlook

In this work a characterization of SiC test structures has been performed.Besides a design verification, it has provided valuable information concerningthe temperature behavior of SiC resistors and the impact of process variabil-ity. In particular, a complex temperature dependence for sheet resistance,and a strong one for most parameters of interest in the p-type layer ratherthan in the n-type ones, has been described in the 27 to 300C temperaturerange; some patterns in the die-to-die variations have been highlighted; afew evidences of not full efficiency of the contact process were given; andthe design criteria for integrated resistors have been proved correct in mostcases.

One of the main disadvantages included not being able to trust the re-sistance measurements from the outer pads of the TLM structures in then-type layers. This resulted in lower accuracy of the final parameters. Webelieve it would be useful to produce TLM structures with two further pads,devoted to force current. More generally, the characterization process shouldlook towards automation. The advantages would include the possibility of:accurate estimation of uncertainty, detection of the minimum point in thetemperature trend, and mapping for different temperatures.

Measurements have also been compared with simulations. New sourcesfor simulation parameters have been considered as no perfect match wasachieved with the original ones. The n-type sheet resistance trend was to-tally mismodeled. An improvement has been reached with different mobilityparameters and the reasons for that have been suggested. Borrowing con-siderations made for Si, the need to model the metal-non metal transitionin such case has been enhanced. The p-type sheet resistance simulationsyielded lower values compared to measurements. In this case, the changesin the incomplete ionization model have given the best agreement.

An other mobility model [27] has been brought to our attention and is

43

44 CHAPTER 6. CONCLUSIONS AND FUTURE OUTLOOK

worth testing. Where no improvement was achieved, direct mobility mea-surements would be useful. Finally, the natural course of this study wouldconsist in moving towards higher temperatures. Modeling would obviouslybenefit from that, allowing comparison in a wider range.

Bibliography

[1] P. P. Altermatt, A. Schenk, and G. Heiser. A simulation model forthe density of states and for incomplete ionization in crystalline sil-icon. I. Establishing the model in Si:P. Journal of Applied Physics,100(11):113714, 2006.

[2] P. P. Altermatt, A. Schenk, B. Schmithüsen, and G. Heiser. A sim-ulation model for the density of states and for incomplete ionizationin crystalline silicon. II. Investigation of Si:As and Si:B and usage indevice simulation. Journal of Applied Physics, 100(11):113715, 2006.

[3] N.D. Arora, J.R. Hauser, and D.J. Roulston. Electron and hole mobili-ties in silicon as a function of concentration and temperature. ElectronDevices, IEEE Transactions on, 29(2):292 – 295, Feb. 1982.

[4] T. Ayalev. SiC Semiconductor Devices Technology, Modeling, and Sim-ulation. PhD thesis, Technischen Universität Wien, Jan. 2004.

[5] M. Bakowski, U. Gustafsson, and U. Lindefelt. Simulation of SiC HighPower Devices. Physica Status Solidi Applied Research, 162:421–440,1997.

[6] S. Balachandran, T.P. Chow, and A.Agarwal. Low and High Temper-ature Performance of 600V 4H-SiC Epitaxial Emitter BJTs. MaterialScience Forum, 483-485:909–912, 2005.

[7] D.M. Caughey and R.E. Thomas. Carrier mobilities in silicon empiri-cally related to doping and field. Proceedings of the IEEE, 55(12):2192– 2193, Dec. 1967.

[8] V.E. Chelnokov, A.L. Syrkin, and V.A. Dmitriev. Overview of SiCpower electronics. Diamond and Related Materials, 6(10):1480 – 1484,1997. Proceeding of the 1st European Conference on Silicon Carbideand Related Materials (ECSCRM 1996).

[9] S. S. Cohen. Contact resistance and methods for its determination.Thin Solid Films, 104(3-4):361 – 379, 1983.

45

46 BIBLIOGRAPHY

[10] R. Estève. Fabrication and Characterization of 3C- and 4H-SiC MOS-FETs. PhD thesis, KTH, Stockholm, 2011.

[11] A. Ferreira da Silva, J. Pernot, S. Contreras, B.E. Sernelius, C. Persson,and J. Camassel. Electrical resistivity and metal-nonmetal transitionin n -type doped 4H − SiC . Phys. Rev. B, 74(24):245201, Dec. 2006.

[12] W. Götz, A. Schöner, G. Pensl, W. Suttrop, W. J. Choyke, R. Stein,and S. Leibenzeder. Nitrogen donors in 4H silicon carbide. Journal ofApplied Physics, 73(7):3332–3338, 1993.

[13] G.L. Harris. Properties of Silicon Carbide. INSPEC, 1995.

[14] A. Hastings. The art of analog layout. Prentice Hall, 2001.

[15] I. G. Ivanov, B. Magnusson, and E. Janzén. Optical selection rules forshallow donors in 4H −SiC and ionization energy of the nitrogen donorat the hexagonal site. Phys. Rev. B, 67(16):165212, Apr. 2003.

[16] W. B. Joyce and R. W. Dixon. Analytic approximations for the fermienergy of an ideal fermi gas. Applied Physics Letters, 31(5):354–356,1977.

[17] D. P. Kennedy, P. C. Murley, and R. R. O’Brien. A statistical approachto the design of diffused junction transistors. IBM Journal of Researchand Development, 8(5):482–495, Nov. 1964.

[18] A. Koizumi, J. Suda, and T. Kimoto. Temperature and doping de-pendencies of electrical properties in Al-doped 4H-SiC epitaxial layers.Journal of Applied Physics, 106(1):013716, 2009.

[19] A.Y. Kovalgin, N. Tiggelman, and R.A.M. Wolters. An area-correctionmodel for accurate extraction of low specific contact resistance. ElectronDevices, IEEE Transactions on, 59(2):426 –432, Feb. 2012.

[20] L. Lanni. SiC bipolar junction transistor circuits for low voltage andhigh temperature applications. Master’s thesis, KTH, Stockholm, 2009.

[21] L. Lanni, R. Ghandi, B.G. Malm, C. Zetterling, and M. Ostling. De-sign and Characterization of High-Temperature ECL-Based Bipolar In-tegrated Circuits in 4H-SiC. Electron Devices, IEEE Transactions on,59(4):1076 –1083, Apr. 2012.

[22] S.-K. Lee. Processing and Characterization of Silicon Carbide (6H-and 4H-SiC) Contacts for High Power and High Temperature DeviceApplications. PhD thesis, KTH, Stockholm, 2002.

BIBLIOGRAPHY 47

[23] Y. Li, H.B. Harrison, and G.K. Reeves. Correcting separation errorsrelated to contact resistance measurement. Microelectronics Journal,29(1-2):21–30, 1998.

[24] U. Lindefelt. Doping-induced band edge displacements and band gapnarrowing in 3C-, 4H-, 6H-SiC, and Si. Journal of Applied Physics,84(5):2628–2637, 1998.

[25] W.M. Loh, S.E. Swirhun, T.A. Schreyer, R.M. Swanson, and K.C.Saraswat. Modeling and measurement of contact resistances. ElectronDevices, IEEE Transactions on, 34(3):512 – 524, Mar. 1987.

[26] H. Matsuura, M. Komeda, S. Kagamihara, H. Iwata, R. Ishihara,T. Hatakeyama, T. Watanabe, K. Kojima, T. Shinohe, and K. Arai.Dependence of acceptor levels and hole mobility on acceptor densityand temperature in Al-doped p-type 4H-SiC epilayers. Journal of Ap-plied Physics, 96(5):2708 –2715, Sep. 2004.

[27] T.T. Mnatsakanov, L.I. Pomortseva, and S.N. Yurkov. Semiempiricalmodel of carrier mobility in silicon carbide for analyzing its dependenceon temperature and doping level. Semiconductors, 35(4):406 – 409, Apr.2001.

[28] N. F. Mott and E. A. Davis. Electronic processes in non-crystallinematerials. Clarendon Press ; Oxford University Press, Oxford : NewYork :, 2nd ed. edition, 1979.

[29] H. Murrmann and D. Widmann. Current crowding on metal contactsto planar devices. Electron Devices, IEEE Transactions on, 16(12):1022– 1024, Dec. 1969.

[30] S. Nakashima and H. Harima. Raman Investigation of SiC Polytypes.physica status solidi (a), 162(1):39–64, 1997.

[31] P.G. Neudeck, R.S. Okojie, and Liang-Yu Chen. High-temperatureelectronics - a role for wide bandgap semiconductors? Proceedings ofthe IEEE, 90(6):1065 – 1076, Jun. 2002.

[32] G. L. Pearson and J. Bardeen. Electrical Properties of Pure Siliconand Silicon Alloys Containing Boron and Phosphorus. Phys. Rev.,75(5):865–883, Mar. 1949.

[33] J. Pernot, W. Zawadzki, S. Contreras, J. L. Robert, E. Neyret, and L. DiCioccio. Electrical transport in n-type 4H silicon carbide. Journal ofApplied Physics, 90(4):1869–1878, 2001.

[34] C. Persson, A. Ferreira da Silva, and B. Johansson. Metal-nonmetaltransition in p -type SiC polytypes. Phys. Rev. B, 63:205119, May2001.

48 BIBLIOGRAPHY

[35] R. F. Pierret and G. W. Neudeck. Advanced Semiconductors Fundamen-tals, volume 6 of Modular series on solid state devices. Addison-Wesley,1989.

[36] R.F. Pierret. Semiconductor device fundamentals. Addison WesleyLongman, 1996.

[37] S.J. Proctor, L.W. Linholm, and J.A. Mazer. Direct measurementsof interfacial contact resistance, end contact resistance, and interfa-cial contact layer uniformity. Electron Devices, IEEE Transactions on,30(11):1535 – 1542, Nov. 1983.

[38] G.K. Reeves and H.B. Harrison. Obtaining the specific contact re-sistance from transmission line model measurements. Electron DeviceLetters, IEEE, 3(5):111 – 113, May 1982.

[39] M. Roschke and F. Schwierz. Electron mobility models for 4H, 6H,and 3C SiC [MESFETs]. Electron Devices, IEEE Transactions on,48(7):1442 –1447, Jul. 2001.

[40] W. J. Schaffer, G. H. Negley, K. G. Irvine, and J. W. Palmour. Con-ductivity Anisotropy in Epitaxial 6H and 4H SiC. MRS Proceedings,339, 1994.

[41] D.K. Schroder. Semiconductor material and device characterization.Wiley-Interscience, 1990.

[42] Sentaurus TCAD, Synopsys Inc. ver.X-2005.10, Available:http://www.synopsys.com.

[43] W. Shockley. Research and investigation of inverse epitaxial UHF powertransistors. Technical Documentary Report AL TDR 64-207, AF Avion-ics Laboratory, Research and Technology Division, Air Force SystemsCommand, Wright-Patterson AFB, Ohio, Sept. 1964.

[44] S.E. Swirhun and R.M. Swanson. Temperature dependence of specificcontact resistivity. Electron Device Letters, IEEE, 7(3):155 – 157, Mar.1986.

[45] N.G. Szwacki and T. Szwacka. Basic Elements of Crystallography. PanStanford Publishing, 2010.

[46] M.B.J. Wijesundara and R. Azevedo. Silicon Carbide Microsystems forHarsh Environments. Springer New York, 2011.

[47] N. G. Wright and A. B. Horsfall. Silicon carbide: The return of an oldfriend. Material Matters, 4, 2009.

BIBLIOGRAPHY 49

[48] C.-M. Zetterling. Process technology for silicon carbide devices. IN-SPEC, 2002.

List of Figures

2.1 Diamond (a) and Sphalerite (b) unit cell. . . . . . . . . . . . 32.2 Stacking sequences . . . . . . . . . . . . . . . . . . . . . . . . 42.3 SiC unit cell and principal axes for HCP crystals . . . . . . . 42.4 Carrier concentration vs. temperature. . . . . . . . . . . . . . 6

3.1 Band diagram of metal-semiconductor structure . . . . . . . . 83.2 Conduction regimes in metal-semiconductor contacts . . . . . 93.3 Effect of misalignment between contacts. . . . . . . . . . . . . 123.4 Layout of a strip resistor . . . . . . . . . . . . . . . . . . . . . 123.5 Serpentine resistors . . . . . . . . . . . . . . . . . . . . . . . . 133.6 Dogbone resistor . . . . . . . . . . . . . . . . . . . . . . . . . 143.7 Schematic of a linear TLM structure . . . . . . . . . . . . . . 153.8 Total resistance vs. spacing (a), and four probes setting (b). . 163.9 Four and six terminal Kelvin structure . . . . . . . . . . . . . 173.10 Cross section and top view of a contact chain test structure . 18

4.1 Functioning dies (a) and die map (b). . . . . . . . . . . . . . 204.2 I-R test block. . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3 I-V characteristic of a faulty contact . . . . . . . . . . . . . . 224.4 Sensitivity to probes relative position . . . . . . . . . . . . . . 224.5 Sheet resistance vs. temperature. . . . . . . . . . . . . . . . . 234.6 Contact resistance vs. temperature. . . . . . . . . . . . . . . 244.7 Wafer mapping. . . . . . . . . . . . . . . . . . . . . . . . . . . 264.8 Correlation Rs-Rc. . . . . . . . . . . . . . . . . . . . . . . . . 274.9 Narrow resistors. . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.1 BJT. Cross section (a) and top view (b) . . . . . . . . . . . . 375.2 Electron mobility for the collector layer. . . . . . . . . . . . . 385.3 Collector layer simulations. . . . . . . . . . . . . . . . . . . . 395.4 Incomplete ionization according to Roschke’s mobility model. 405.5 Incomplete ionization in Si:P. . . . . . . . . . . . . . . . . . . 405.6 Best fit to trend. . . . . . . . . . . . . . . . . . . . . . . . . . 415.7 Hole mobility for the base layer. . . . . . . . . . . . . . . . . 415.8 Simulations of the sheet resistance in the base layer. . . . . . 42

50

LIST OF FIGURES 51

5.9 Ionization degree deduced from measurements. . . . . . . . . 42

List of Tables

2.1 Material properties of Si and SiC . . . . . . . . . . . . . . . . 5

4.1 Temperature behaviour . . . . . . . . . . . . . . . . . . . . . 254.2 Mapping results. . . . . . . . . . . . . . . . . . . . . . . . . . 294.3 Parameter variation statistics. . . . . . . . . . . . . . . . . . . 304.4 Resistors verification. . . . . . . . . . . . . . . . . . . . . . . . 304.5 Contact chains measurements. . . . . . . . . . . . . . . . . . . 30

5.1 Original mobility parameters . . . . . . . . . . . . . . . . . . 325.2 Alternative mobility parameters . . . . . . . . . . . . . . . . . 325.3 Parameters for donor levels of N-doped 4H-SiC. . . . . . . . . 355.4 Parameters for acceptor levels of Al-doped 4H-SiC. . . . . . . 365.5 Parameters for band edge displacement. . . . . . . . . . . . . 36

52

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