AlGaN/GaN HEMTs

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    SUMMER PRACTICAL TRAINING REPORT

    AlGaN/GaN HEMTs andAnalysis of Transistors

    K. Gagandeep G. Singh3rd Year Undergraduate, Engineering Physics

    Indian Institute of Technology, Hauz Khas, New Delhi -110016

    Work from 12th May to 18th July at:Solid State Physics Laboratory, Timarpur, Delhi -110054

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    SOLID STATE PHYSICS LABORATORYDODO, MINISTRY OF DEFENCE

    GOVERNMENT OF INDIA21st July, 2014

    CERTIFICATE

    This is to certify that Mr. K. Gagandeep G. Singh, student of Engineering Physics (B. Tech)3rd Year at IIT Delhi has undergone training under Mrs. Seema Vinayak of Solid State PhysicsLaboratory (SSPL) for a period from 12th May to 18th July on AlGaN/GaN HEMTs andAnalysis of Transistors. He has completed their training successfully. This report does not containany secret information.

    Signature of the Supervisor(Dr. Seema Vinayak, Scientist G)

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    Contents

    1 Introduction 6

    2 Properties of GaN 72.1 Crystal Properties of GaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    2.2 Physical Properties of GaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Figure of Merit (FOM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

    3 Substrate and Growth Techniques 123.1 Growth Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

    4 AlGaN/GaN Heterostructures 14

    5 Transistors 155.1 Bipolar Junction Transistor (BJT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    5.1.1 Common Emitter Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    5.2 Characteristics of MOSFET (Metal Oxide Semiconductor Field Emission Transistor) . 185.2.1 Saturation Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.2.2 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2.3 Finding the Saturation Current . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    5.3 Characteristics of MESFET (MEtal Semiconductro Field Effect Transistor) . . . . . . 245.3.1 Saturation Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.3.2 Saturation Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    6 Simulations for MOSFET Using COMSOL MultiphysicsR 286.1 Model Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    6.1.1 Parameters Used during the Simulation . . . . . . . . . . . . . . . . . . . . . . 296.2 Energy Level Diagram of MOSFET along the center of the device form the Gate Contact 296.3 Current Density of MOSFET and n-channel . . . . . . . . . . . . . . . . . . . . . . . 306.4 Electron Concentration for different Drain to Source Voltages . . . . . . . . . . . . . 316.5 Surface Charge Density of MOSFET . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.6 Current(ID) vs Voltage Characteristics(VDS) . . . . . . . . . . . . . . . . . . . . . . . 33

    7 Semiconductor Heterostructures 337.1 Hetero junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

    7.1.1 Band Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347.1.2 Understanding the Notch Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 35

    8 HEMT Working Principle 36

    9 Conclusion 40

    10 References 41

    11 Important Points 43

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    Acknowledgements

    I sincerely express my sense of indebtedness to Dr. R. Muralidharan, Director SSPL, for grant-ing me permission to undergo the summer training at SSPL.

    I would like to sincerely thank my faculty coordinator Dr. Rajendra Singh, Professor IITD to provideme this humble opportunity to work at SSPL. I warmly thank him for his co-operation and guidance

    I would like to express my sincere thanks to Mr. Amit and Mr. Chandan Sharma for their helpextended.

    Finally I would like to sincerely express my thankfulness to our supervisor Mrs. Seema VinayakScientist G, for her guidance and for constantly motivating us to work harder.

    I would like to state that the visits to the SSPL laboratory were very helpful in giving me an in-sight into the practical work being done in the field of my project.

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    Objectives of Training

    The aim of the training program was to get familiarized with the components of fabrication of thinfilms at the laboratory and also to get the basic working principles behind the semiconductor deviceslike MOSFETs, MESFETs and HEMTs. The objectives for the training period were:

    To understand the basic operation principles and basic differences between MOS and MESFETs.

    Calculation of Energy Band Diagrams in MESFETs and MOSFETs.

    Understand the mechanism of current saturation in BJTs, MESFETs and MOSFETs.

    DC Characteristics of MOSFETs simulated in COMSOL Multiphysics R.

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    1 Introduction

    The continuously increasing need for electric power has led to development of new technology whichmakes it possible to increase the efficiency by miniaturization of device and by increasing power supplyBut now efficient use of the available energy has become the main concern of modern power electronics.

    For the past several decades Si based semiconductor devices have been the most exhaustively usedtechnology for handling power circuitry. But due to its physical and performance short comes likelow power handling capacity, breakdown voltage, maximum operating temperature etc. no furtheradvancements in power electronics can be done any further. In particular, due to the band gap andintrinsic carrier concentration of the material, Si devices are limited to work at a junction temperaturelower than 200 C which is less suitable for modern power applications. [1]

    Where else, wide band semiconductors (WBG), such as silicon carbide (SiC), gallium nitride (GaN)and related alloys, exhibit better physical properties which can serve better in satisfying the demandof increased power, frequency and operating temperature of the devices.

    Form these SiC technology is the most advanced technology amongst other wide band semiconduc-tors. This is so because first of all the size of SiC wafer has been continuously increasing and that toodefect free (especially micropipes). Furthermore, the device processing technology has reached a highlevel of maturity and some SiC devices like Schottky diodes or MOSFETs operating in the range of600-1200 V have already reached the market [2].

    While SiC is the most technically advance WBG semiconductor, GaN and related alloys (like AlxGaN)still suffer from the several physical issues related to both surface and interfaces [3]. Furthermorethe lack of good quality (and cheap) free standing GaN templates make also the material growth aserious concern, since heteroepitaxy on different substrates (like Al2O31-x, SiC, or Si) is requiredAlthough for long time GaN has been mainly attractive because of the optoelectronics applicationsthe recent improvement of the material quality of GaN-based heteroepitaxial layers provided the sci-entific community with considerable incentive to investigate the potentialities of this material also forapplications in power electronics.

    Although the low field mobility of bulk GaN is much lower than that of other III- IV materialslike GaAs, GaN has a much higher saturation velocity and wide band gap, which makes it favorablefor high frequency power devices. Another good reason to look into advancing GaN is its ability toform AlGaN/GaN heterostructures with a large band discontinuity which helps in the formation o2DEG (2 Dimensional Electron Gas). 2DEG is formed due to the presence of both spontaneous andpiezoelectric polarization of the material.

    The high polarizations and resulting electric fields in AlGaN/GaN heterostructures produce highinterface charge densities even for unintentionally doped materials. In particular, the 2DEG formedis AlGaN/GaN heterostructures can have sheet carrier densities in the order of 1-3x1013cm-2, i.e.well in excess of those achievable in other IIIV systems like GaAs. Moreover, the possibility to useundoped material results in a significant improvement of the electron mobility in the 2DEG, due tothe reduction of Coulomb scattering with ionized impurities.

    AlGaN/GaN heterostructures are particularly interesting for the fabrication of high electron mo-bility transistors (HEMTs), based on the presence of the 2DEG.

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    Figure 1: Crystal structure of Zinc Blend(Left), Wurtzite(Middle) and Rock Salt(Right)

    2 Properties of GaN

    The research activity on GaN dates back to the first 1930s. However, only in the 90s the materiastarted to attract interest for power and RF electronics, because of its superior properties such a highband gap, a high breakdown field and a high saturated electron velocity. In the next years, powerelectronics will play an important role for the reduction of the energy consumption all over the world

    Many discrete power electronic devices are used in the power modules for the transmission andthe conversion of electric power. For these devices, a reduction of the static and dynamic losses candirectly result in the overall lowering of power consumption of the system. Also the next generationof high-speed communication devices are becoming key technologies for network communication, re-quiring increasing operating frequency associated with portability and convenience.

    Si technology is approaching the theoretical limits imposed by the material properties, in terms ofmaximum operation power, frequency and temperature. Therefore new materials have to be lookedforward to in order to overcome Si limitations. The use of wide bandgap (WBG) materials can beconsidered as the best solution to meet the requirements of modern power electronics. In fact, WBGsemiconductors such as silicon carbide (SiC) and gallium nitride (GaN), have been known to exhibitsuperior electrical characteristics compared to Si because of their inherent advantages such as highelectron mobility, higher breakdown field strength and larger energy bandgap.

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    Figure 2: The wurtzite unit cell of GaN with lattice constants a0 and c0.

    2.1 Crystal Properties of GaN

    Any III-nitride material is expected to exist in one of the three forms namely rock salt, zinc-blendand wurtzite.

    Thermodynamically wurtzite is the most favorable structure for GaN at ideal temperature and pres-sure. [4] The basis consists of four atoms two Nitrogen and two Gallium atoms. The unit cell consistsof six atoms and is characterized by two constants a0(3.18A) and c0(5.18A). The Ga and N atoms arearranged in two interpenetrating hexagonal close packed lattices (HCP), each one with one type oatoms, shifted 3/8 c0 each other. The covalent bonds allow that each atoms is tetrahedrally bondedto four atoms of the other type. There is also a ionic contribution of the bound due to the largedifference in electronegativity of Ga and N atoms. On a wurtzite structure there is no inversionsymmetry on the [0001] direction (c-axis). This latter means that it is possible to distinguish twodifferent orientation of GaN crystals, i.e., Ga-face and N-face, depending if the material is grown withGa or N on top and corresponding to the (0001) and (0001-) crystalline faces as is shown Figure 3.

    Schematic drawing of the crystal structure of wurtzite Ga-face and N-face GaN. The spontaneous

    polarization vector is also reported.

    Now, because of the difference in the electronegativity of N and Ga there exists an ionic bond alongwith the already present covalent bond. This leads to a dipole moment in the (0001) direction. Thiseffect in known as spontaneous polarization, because it exists without the presence of any stress orstrain.

    The strength of the spontaneous polarization depends on the non-ideal (asymmetric) structure ofthe crystal. Not only covalent bond in the direction parallel to c0 plays an important role, but also

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    Figure 3: Ga-face and N-face structure of GaN

    the other three covalent bonds of the tetrahedral structure. Their resultant polarization is alignedwith c0 but in a0 opposite direction, compensating the polarization in the (0001) direction. For thisreason in a wurtzite structure, the c/a ratio plays a fundamental role for the spontaneous polarizationwhere the resultant Psp increases with reducing the asymmetry of the crystal, i.e. decreasing the c/aratio. For example a GaN crystal with a c/a ratio of 1.6259 will present a reduced Psp (-0.029 C/m2)with respect to an AlN crystal (-0.081 C/m2) with a c/a ratio of 1.6010.

    In this context, in the presence of factors that may change the ideality of the structure and the

    c/a ratio, as stress or strain, the total polarization will be modified. The additional contribution tothe polarization, due to the presence of strain and stress in the crystal, is the so called piezoelectricpolarization Ppe. This contribution is particularly important in AlGaN/GaN heterostructures for thegeneration of the two dimensional electron gas about which we will be seeing afterwards.

    2.2 Physical Properties of GaN

    Thanks to its superior physical properties, GaN is considered an outstanding materials for optoelectronics, high power and high frequency devices. Properties like the wide band-gap, the high valueof critical electric field and the saturation velocity can represent a big advantage in terms of electronicdevices applications. In Table 1, some of these properties, which are relevant for electronic devicesperformances, are reported and compared to other semiconductors counterparts. [5]

    The wide band-gap of GaN (3.39 eV) is responsible for the high critical electric field (3.3 MV/cm),which is one order of magnitude higher than that of Si. The high critical electric field gives the possibility to sustain the application of high bias values, thus making the material suitable for high-voltagedevices fabrication. A further implication of its wide band-gap is the low intrinsic electron concentration ni. The value of ni in GaN at room temperature is in fact several orders of magnitude lower

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    Properties Si SiC (4-H) GaN GaAs Diamond

    Bandgap Energy (Eg) eV 1.12 3.26 3.39 1.42 5.45

    Breakdown Field (Ec) MV/cm 0.3 3.0 3.3 0.4 5.6

    Intrinsic e- Concentration (ni) cm-3 1.5x1010 8.2x10-9 1.9x10-10 1.5x106 1.6x10-27

    e- Saturation Vel. (vsat) x107 cm/s 1.0 2.0 2.5 1.0 2.7

    e- Mobiltiy cm2/V.s 1350 700 1200 8500 1900

    Thermal Conductivity (k) W/cm.K 1.5 3.3-4.5 1.3 0.5 20

    Relative Permittivity 11.8 10.1 9.0 13.1 5.5

    Table 1: Properties of GaN compared with other conventional and wide band-gap semiconductors atroom temperature

    with respect to that of Si or GaAs, and comparable with that of SiC. This characteristic enables toincrease the maximum operation temperature of the devices made of this material and have reducedleakage currents.

    Other parameters that describe the quality of the material are the relative permittivity (epsilon r) andthe thermal conductivity (k). The relatively high permittivity value (epsilon r) is a good indicatorof the capacitive loading of a transistor and passive components. On the other hand, the thermaconductivity (k) describes the ease of heat conduction and, hence, the possibility to efficiently extractthe dissipated power from the device. Materials with a lower thermal conductivity typically lead to adevice degradation at elevated temperatures. Although III-V semiconductors typically have a moder-ate value of k, GaN has a thermal conductivity which is comparable to that of Si (but lower than SiC)

    The amazing properties of GaN include also a high electrons saturation velocity (v sat), which inturn is important for high current and high frequency operation of devices. Compared to other wideband gap materials that show high v sat, GaN can also reach a high electron mobility (u) compara-ble with Si. Undoubtedly, among wide band gap semiconductors, the unique feature of GaN is thepossibility to make band gap engineering considering the related AlxGa1-xN alloys. In particular, byvarying the Al content it is possible to tailor the band gap of the material. In this way, AlGaN/GaNheterostructures can be fabricated, allowing to reach carrier mobility up to 2000 cm2/Vs in the twodimensional electron gas (2DEG) formed at the interface.

    Coming to an example of application of GaN, there are electric power converters which are inte-

    grated practically in all the electronic systems to convert either DC or AC current. Their efficiency isalso related to the possibility to have fast switching elements with increased power density. Typicaapplications of efficient power converters are the energy conversion in solar systems, wind power sta-tions and modern electric vehicles as well as for power supplies in mobile base stations and computersystems. In all the aforementioned sectors, GaN represents today an attractive material. In fact, GaNbased switches have theoretically a better figure of merit with respect to Si and SiC. Figure showsthe comparison between the trade-off curves of the specific on resistance R ON vs breakdown voltagefor Si, SiC and GaN. [6]

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    Figure 4: On-Resistance vs Breakdown Voltage

    As can be seen, at a given operation voltage, the on-state resistance of GaN devices can, in princi-ple, outperform the competing Si or SiC devices. Since the specific on resistance is strictly related tothe power losses of the device, the use of GaN can significantly lead to a reduction of the losses and toan improvement of the efficiency of the electronic systems. However, as can be seen, the experimentaldata point are still far from the theoretical limits of the material.

    2.3 Figure of Merit (FOM)

    To better compare the potential power electronic performance for different semiconductors materialsfigures of merit (FOM) are commonly adopted. In particular, for high power and high frequencydevices three important FOM are considered, Johnson (JFOM), Baliga (BFOM) and Baliga high fre-quency (BHFOM). JFOM = (vsatEc)

    2 is an indication of the maximum capability to energize carriersby electric field, BFOM=u.Es.Ec3 measures the minimum conduction losses during DC operationand BHFOM=uEc2 give information about the minimum conduction losses during high frequency

    Figure of Merit Si SiC GaN

    JFOM (vsatEc)2 6x1010 3.6x1013 14.6x1013

    BFOM u.Es.Ec3 248 20.9x104 79x104

    BHFOM uEc2 84 7200 20800

    Table 2: Figure of Merit comparison

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    Figure 5: Typical operating frequencies and output power ranges of electron devices made using adifferent semiconductor materials.

    operation. All these figures of merit for GaN are reported in Table 2 and compared to Si and SiCclearly showing that GaN is potentially a superior material for the high power and high frequencyapplications.

    A comparison of the typical operating frequency and output power range for different semiconductormaterials is shown in Figure. In this case, it must be noted that with respect to SiC, GaN is moresuitable for higher frequencies but in a lower output power range.

    3 Substrate and Growth Techniques

    In spite of its outstanding material properties, the technological development of GaN has come laterthan in other semiconductors. The reasons of this delay were mainly related to the difficulty to havehigh quality free-standing GaN substrates and, consequently, the difficulty to fabricate vertical struc-tures for power devices. In fact, for the growth of GaN other materials must be used as substrateSince the perfect substrate does not exist, an ideal candidate must have physical and crystallographicproperties, such as lattice parameters and thermal expansion coefficients, close to those of GaN, inorder to avoid the formation of cracking of the film, or defects formation during the growth of thematerial. The lattice mismatch and the difference in thermal expansion coefficients (TEC) of thecommon substrates used for GaN growth are reported in Table 3.

    Out of the possible choices Sapphire is an interesting choice because it is insulating, it can with-

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    Substrate Latticce Mismatch Difference in Thermal Expansion Cofficient

    Al2O3 (0001) +16 % -25.3 %

    6H-SiC (0001) +3.5 % +33.3 %

    3C-SiC (111) +3 % +24.4 %

    Si (111) -17 % +55.5 %

    AlN (0001) +2.5 % +33.3%

    Table 3: Lattice mismatch and difference in thermal expansion coefficient of GaN with respect to themost common substrates

    stand the required high growth temperatures, and it is relatively cheap. Anyway the large latticemismatch (+16Silicon can be also a possible substrate for the growth of GaN layers. In the recentyears, GaN materials grown on Si is attracting a huge attention thanks to the low substrate costthe possibility of large substrate diameters and the potential integration with the well-developed Sielectronics technology. Despite a large lattice (+17The residual stress is depending on the growthcondition and cool-down procedure. Moreover there exists a dependence of the stress on the impurityconcentrations that lead to an increase of the tensile stress with increasing the doping concentration[8, 9]

    To relieve the tensile stress and achieve crack-free GaN heterostructures, several kind of transitionlayers can be used, such as low temperature AlN [10], graded AlGaN buffers [11] or AlGaN/GaNsuperlattices [12]. It has been seen that the dislocation density in the material strongly depends onthe choice of the transition layer, and can be partially mitigated by using a high temperature AlGaNintermediate layer that acts as a dislocation filter [13]. Moreover transition layers increase also the

    series resistance in the GaN layer, reducing the crack density and providing a good electrical insula-tion from the substrates.

    3.1 Growth Technique

    If the choice of a suitable substrate is an important issue for the development of GaN technologynot less important are the growth techniques employed to obtain a high quality material, with a lowconcentration of defects. The first technique used to grow epitaxial GaN layers was the Hydride VaporPhase Epitaxy (HVPE).

    Nowadays, the Metal Organic Chemical Vapor Deposition (MOCVD) has become the most usedmethod to grow GaN, owing its superior quality as high degree of composition control and uniformityreasonable growth rates (1-2 um/hr), the possibility to use high purity chemical sources and to growabrupt junctions. MOCVD uses the reaction of trimethylgallium (TEGa) and NH3 that occurs closethe substrate. To obtain high quality GaN film, during the deposition the substrate must be keptat a temperature of about 1000 C - 1100 C, to allow a sufficient dissociation of the NH3 moleculeat a pressure between 50 and 200 Torr. Moreover, another critical aspect is the control of the N/Gamolar ratio that must be kept high in order to compensate N losses due to the high partial nitrogenpressure at the elevated growth temperatures [14].

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    In fact the poor nucleation of GaN on Si at high temperatures results in a reaction of nitrogenwith Si and in a Ga-Si alloy formation which initiates a strong and fast etching reaction (melt backetching) destroying the substrate and the epitaxial layer [15]. The most established method to preventthe nitridation is starting the growth process with an AlN nucleation larger grown in the same reactorwith a few monolayers pre-deposition of Al. [16] The material doping can be tailored by the induction

    of extra precursor on the reactor, as silane (SiH4) for Si doping (n-type) or biscyclopentadienylmag-nesium (Cp2Mg) for Mg doping (p-type). Anyway the control of a low doping concentration (NDis less than 11016cm-2) is still a complex factor because the formation of nitrogen vacancies, whichact as donors leading to n-type doping of the material. Also the oxygen impurities present duringthe growth process can act as donors, leading to an n-type material [17]. To improve the crystallinequality of the grown GaN, pre-treatments can be required. For example the deposition of a thin lowtemperature buffer layer can be an advantage. The use of this layer, generally AlN or Si, can reducethe lattice mismatch, providing a benefit in terms of defects density (dislocations, oxygen impurity,nitrogen and gallium vacancies, etc).

    To reduce the defects density in the grown material, a different process called lateral epitaxial over-growth (LEO) has been also developed [18]. It consists in the deposition of GaN on a patterneddielectric substrates (like SiO) followed by the lateral expansion and coalescence of the grown ma-terial. Although this technique can lead to a significant reduction of the dislocation density (up to6107cm-2) the extremely high cost of the process (which require the employment of lithographic stepsfor the substrate preparation) has limited its practical application for GaN growth.

    The Molecular Beam Epitaxy (MBE) is a slow (1 um/hr) but efficient technique for GaN growth,that show comparable material quality to those grown by MOCVD. A problem is that the NH3 isvery stable at the low temperature (700-800 C) used in MBE. To solve this issues reactive species ofnitrogen, generated by electron cyclotron resonance (ECR) or radio frequency (RF) plasmas with lowenergy, are generally used [19].

    4 AlGaN/GaN Heterostructures

    One of the most interesting aspects related to GaN materials is the possibility to grow AlGaN/GaNheterostructures, in which a two dimensional electron gas (2DEG) is formed at the heterojunctionThe peculiarity of AlxGa1-xN alloys is the possibility to tailor the lattice constant and the energygap by varying the Al concentration x.

    In particular, the in-plane lattice constant a of AlxGa1-xN alloys depends on the Al concentration xand is also related to the lattice constant of GaN and AlN by the relation [20]

    aAlGaN(x) =xaAlN + (1 x)aGaN (1)

    On the other hand, also the band gap of a AlxGa1-xN alloy can be expressed as a function of the Almole fraction according to [21]

    EAlGaNg (x) =xEAlNg + (1 x)E

    GaNg x(1 x) = [x6.13 + (1 x)3.42 x(1 x)]eV (2)

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    Figure 6: Dependence of the band gap energy (a) and of the lattice parameter a (b)on the Al molefraction for the AlxGa(1-x)N.

    The dependence of the band gap energy and the lattice parameter with respect to the Al molefraction for the AlxGa1-xN is shown below.

    The big advantage of AlGaN/GaN heterostructures consists in the formation of a two dimensionaelectron gas (2DEG) at the interface, generated by the strain induced by the lattice mismatch betweenGaN and AlGaN. The presence of the 2DEG allows the fabrication of an innovative device called HighElectron Mobility Transistor (HEMT).

    5 Transistors

    In order to understand more about working of High Electron Mobility Transistor(HEMT), the basicknowledge of working principles of different transistor can give a better view about how the HEMTswork.

    5.1 Bipolar Junction Transistor (BJT)

    When BJT is setup as shown in the following figure it is said to be in forward active mode. TheEB(Emitter-Base) junction is forward bias and the BC(Bas-Collector) junction is reverse bias.

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    The energy band diagram of this npn BJT under 0 bias and forward active mode is given as

    When EB is forward bias the barrier height as seen by carrier reduces and the thermal excitationenergy kbt provide sufficient energy to the electron permitting them to cross the region I and enterregion II. In region II there is an established gradient (approximately linear) of electron concentrationdue to the majority carrier electron of region I which came into region II and are minority carrier here.Due to gradient we get e- diffusing towards the interface of region II and III where because of reversebias configuration of electric field is easily able to drift away the e- at the interface. So, eventually wecan understand that the current through collector is dependent only on the barrier height on regionI and region II interface. Which in turn depends on the voltage between BE.

    ic= eDnABEdn(x)dx =eDnABE

    nB(0) 00 xB

    (3)

    ic =eDnABE

    xB.nB0.exp

    VBE

    Vt

    (4)

    ic = Is.exp

    VBEVt

    (5)

    5.1.1 Common Emitter Configuration

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    As we have discussed earlier the transistor will work (i.e. generate current through collector) iffthe CB junction is reverse bias. So keeping this in mind we write the KVL equation for loop 1.

    VCC=I R+VCB +V BE=I R+VCE (6)

    Now if Vcc is large enough and Vr(=IR) is small enough then Vcb is greater than 0, that is BCjunction is reverse bias and thus the transistor is in the forward active region of operation.

    Again as the forward bias BE voltage increases the collector current and hence Vr will also increase.Increase in Vr results to decrease in the magnitude of Vcb. At some point Vr + Vcc may become0 and at that point if the Ic is increased slightly further the setup will become forward biased andflow of minority carrier through base collector barrier will be obstructed by the electric field whichis opposing their flow. Thus we get a saturation current when the gradient of e- concentration isnot able to supply sufficient force to the e- to move through the electric field and contribute to thecurrent. The following thing can be understood using this Ic Vce graph.

    The reverse bias is shown by linear region. The non-linear region before saturation shows thatsome e- are able to pass through the negative electric field and contribute to the current. And over

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    the saturation region even if we increase Vce we wont be able to increase current any further.

    VCE=VCC ICRC (7)

    Ic=VCC VCE

    RC(8)

    [24,25]

    5.2 Characteristics of MOSFET (Metal Oxide Semiconductor Field Emission Transistor)

    Let us consider the region below the oxide layer under normal condition (No applied Voltage to thegate) the energy band diagram is as follows

    When a positive voltage is applied with respect to S the holes due to the field move away andleave behind some negative charge. The band diagram of which is as follows

    When a positive voltage is applied whit respect to S the holes due to the field move away andleave behind some negative charge. The band diagram of which is as follows.

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    The excess of e- near the interface makes the band to bend such that Ef gets closer to Ec. Wheneven higher positive voltage is applied then there will be a situation where in the Efi will be crossed byEf. This is the situation when the region near the interface starts behaving as an n-type semiconductor(as in n-type the Ef is abve Efi) and we get an inversion region. When seen this region in the followingdiagram, the region appears as to be a channel of n-type semiconductor. The voltage above whichthis happens is the threshold voltage (Vt).

    So, under this situation n-channel is formed which can easily conduct electricity ids if small voltageis applied over the drain. The n-channel has some conductance and for small values of Vds has itsconductance or resistance characteristics similar to a resistance. So,

    ID =gdVDS (9)

    gd=W

    Ln |Q

    n| (10)

    IC=VCC VCE

    RC(11)

    So, form previous discussion we have

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    5.2.1 Saturation Current

    When Vds increases to the point where the potential drop across the oxide ot the drain terminal isequal to Vt, the induced inversion charge density is zero at the drain terminal. The following figuresshow these effects

    When Vds Becomes large than Vds(sat) value, the point in the channel at which the inversioncharge is just zero moves towards the source terminal. In this case, e- enter the channel at the source,travel through the channel towards the drain and then, at the point where the charge goes to 0, the

    e- injected into the space charge region where they are swept by the E-field to the drain contact. Theregion of Id vs Vds characteristic is referred to as the saturation region. When Vgs changes, the Idvs Vds curve will increase so we have

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    5.2.2 Derivation

    From Ohms law we haveJx= Ex (12)

    where = enn(y) (13)

    The total current is found by

    Ix=y

    z

    Jxdydz (14)

    So,

    Q

    n=

    en(y)dy (15)

    where Qn is inversion layer charge per unit area. So,

    IX= W nQ

    nEx (16)

    From Charge neutralityQ

    m+Q

    ss+Q

    n+Q

    sd(max) = 0 (17)

    From Gausss law s

    EndS=QT (18)

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    Now, from surfaces 1 & 2, we assume that Ex is essentially a constant along the channel length. Thecontributions of surfaces 1 & 2 cancel each other. Surface 3 is in the neutral p-region, so the electricfield is zero at this surface. Only surface 4 contributes.

    sEndS= 0xEoxW dx= QT (19)

    Where, epsillon ox is the permitting of the oxide. The total charge enclosed is

    QT = (Q

    ss+Q

    n+Q

    SD(max))W dx (20)

    So, from the previous two equations we have

    0xE0x = Q

    ss+Q

    n+Q

    SD(max) (21)

    Now,EFP EFM=e(VGS Vx) (22)

    Considering the potential barriers we have,

    VGS Vx= (V0x+

    m) (

    Eg stfp)

    VGS Vx= V0x+ 2fp+mx

    where, phi ms is the metal semiconductor work function difference.

    s = 2fp

    for the inversion condition.

    The electric field in oxide isE0x =

    V0xt0x

    On combining the equations we have

    0xE0x = 0xt0x

    [(VGS Vx) (ms+ 2fp)]

    So,

    Ix = W nC0xdVxdx

    [(VGS Vx) VT] (23)

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    Where Ex = -dVx/dx and Vt is the threshold Voltage.So, on integrating

    L0

    Ix= W nC0x

    Vx(L)Vx(0)

    [(VGS Vx) VT]dVx (24)

    Assuming mu n to be a constant above.

    For the n-channel device the drain current enters the drain terminal and is a constant along theentire channel length. Letting Id = -Ix the equation becomes

    ID =W nC0x

    2L [2(VGS VT)VDS V

    2DS] (25)

    which is valid for VGS VT andVDS(sat) VDS.

    5.2.3 Finding the Saturation Current

    The above equation of current through the drain can be plotted as follows

    Since Id is valid below Id(sat)

    Id sat can be found by taking the maxima of the above plots. So, from

    dIDdVDS

    = 0

    we getVDS=VGS VT (26)

    The value of Vds is just Vds(sat). For Vds is graVds(sat) the ideal drain current is a constantand is equal to

    ID(sat) =W nC0x

    2L (VGS VT)

    2 (27)

    So, finally the plots we obtain are

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    [24,25]

    5.3 Characteristics of MESFET (MEtal Semiconductro Field Effect Transistor)

    When negative voltage is applied to the gate the e- below the gate feels repulsion and positive chargeis left near the schottky junction. This region thus forms a depletion region where no free chargeis present. As the negative voltage magnitude increases the width of depletion layer increases andfinally covers completely the n channel. Thus making the gate to close the conduction. Such gatesare active low gates which are activated only at zero magnitude of applied potential.

    Now when n-channel is not depleted then even on the application of small positive voltage at thedrain the majority carrier negative move from the source through n-channel to the drain and thusconduct electricity and cause current flow. Now, if Vd(Drain Voltage) is increased then the regionnear the drain will become reverse biased and thus the depletion region width near this region willincrease.

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    Now if Vd is increased further then a voltage will come at which the depletion region near thedrain will completely cover the n channel. At this condition it is presumed that current will halt atonce, but due to strong electric flied the e will be pulled. Under this condition we reach the saturationcurrent value and even on any further increase of Vd we wont get any increase in value of Id. Thuswe get the saturation region.

    5.3.1 Saturation Voltage

    The depletion region width will vary with distance h(x) throughout the channel. hi is function oVbi(built In Voltage) and Vgs(Gate Voltage) and hm(max. depletion region width) is given by

    hm =

    2s(Vbi+VDS VGS)

    eNd(28)

    Pinchoff occurs when hm = a. At this point we reach the Saturation condition. So,

    a=

    2s(Vbi+VDS(sat) VGS)eNd

    (29)

    Or,

    Vbi+VDS(sat) VGS=ea2Nd

    2s=Vp0 (30)

    So,VDS(sat) =Vp0 (Vbi VGS) (31)

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    5.3.2 Saturation Current

    From Ohms Law, the differential resistance of the channel at a point x in the channel is

    dR= dx

    A(x) (32)

    where p is the resistivity and A(x) is cross sectional area.

    Also,

    = 1

    enNd

    A(x) = (a h(x))W

    So,

    dR= dx

    enNd(a h(x))W (33)

    also

    dV =ID1dR(x)

    where Id1 is the constant current throughout the channel.

    So,

    dV(x) = ID1dx

    enNdW(a h(x)) (34)

    Idx= enNdW(a h(x))dV(x) (35)

    Using,

    h(x) =2

    s(V(x) +V

    bi V

    GS)

    eNd1/2

    Where V(x) is the potential in the chennel due to the drain-to-source voltage. Solving for V(xand taking differential we have,

    dV(x) =eNdh(x)dh(x)

    s(36)

    and using this in Id1 equation we have

    ID1 =n(eNd)

    2W

    s[ah(x)dh(x) h(x)2dh(x)]

    On Integration, we have,

    ID1=n(eNd)

    2W

    s

    a

    2(h2m h

    2i )

    1

    3(h2m h

    2i )

    (37)

    Using

    h2m=2s(VDS+Vbi VGS)

    eNd

    h2i =2s(Vbi VGS)

    eNd

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    and

    Vp0 =ea2Nd

    2s

    We can rewrite the above Idq equation as,

    ID1 =n(eNd)

    2W a3

    2sLVDSVP0

    2

    3VDS+Vbi VGS

    Vp03/2

    +2

    3Vbi VGS

    Vp03/2 (38)

    we say,

    IP1 n(eNd)

    2W a3

    6sL

    as the pinch off current.And thus we have

    ID1 = IP1

    VDSVP0

    2

    3

    VDS+Vbi VGS

    Vp0

    3/2+

    2

    3

    Vbi VGS

    Vp0

    3/2

    (39)

    The above equation is valid for0 |VGS| |V|

    and0 VDS VDS(sat)

    Now, as we have shown earlier that the drain becomes pinched off, for the n-channel MESFETwhen

    VDS=VDS(sat) =VP0 (Vbi VGS)

    So, in the saturation region the saturation drain current is determined by using Vds=Vds(sat)

    ID1= ID1(sat) =IP1

    1 3

    Vbi VGS

    Vp0

    1

    2

    3

    Vbi VGS

    Vp0

    (40)

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    For MESFETs the pinchoff voltages are known as threshold voltages so we have

    VT =VbiVP0

    So,Vbi= VT+VP0

    Using this value in the previous equation we have

    ID1(sat) =IP1

    1 3

    1

    VGS VT

    Vp0

    + 2

    1

    VGS VT

    Vp0

    3/2 (41)

    The above equation is valid for Vgs is greater than Vt.

    When transistor turns on, we have (Vgs-Vt) is less than Vp0. So, the above equation can be expanded using Taylor Series and we obtain

    ID1(sat) IP1 3

    4

    VGS VT

    VP0

    2

    (42)

    Substituting Ip1 and Vp0 the above equation becomes

    ID1(sat) =nW

    2aL (VGS VT)

    2 (43)

    This can further be written as

    ID1(sat) =kn(VGSVT)2 (44)

    kn=nsW

    2aL

    The factor kn is called conduction parameter. [24,25]

    6 Simulations for MOSFET Using COMSOL Multiphysics R

    In order to get a better picture of how the device is going to perform for a given set of device param-eters, various simulation softwares are available which can help us get a glimpse of how the devicemay react on application of certain parameters. This enables us to drive away many of the possibleerrors which might come due to petty human error. Such errors can cause huge waste of both humanlabour and money. Thus they can increase the manufacturing time significantly. To overthrow thesesorts of errors, we can rely on good simulation softwares like Comsole Multiphysics R.

    Now in the following semiconductor device simulation, we will be simulating the DC characteris-tics of a MOSFET.

    6.1 Model Specifications

    This model calculates the DC characteristics of a MOS (metal-oxide semiconductor) transistor usingstandard semiconductor physics. In normal operation, a system turns on a MOS transistor by applyinga voltage to the gate electrode. When the voltage on the drain increases, the drain current alsoincreases until it reaches saturation. The saturation current depends on the gate voltage.

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    6.1.1 Parameters Used during the Simulation

    Vds = 0[V] is the Drain-to-source voltageVbs = 0[V] is the Base-to-source voltageVgs = 2[V] is the Gate-to-source voltagephim = 5.0535[V] the Metal work function

    Na = 1E17[1/cm3] is the Background dopingNd = 1E18[1/cm3] is the Maximum donor doping concentrationW mos = 1e-6[m] is the width of MOSFETh mos = 0.2[um] is the height of MOSFETL mos = 1[um] is MOSFET lengthLg = 0.24e-6[m] is Gate lengthL s = 0.32[um] is Source lengthL d = 0.32[um] is Drain lengtheps ins = 4.2 is Insulator relative permittivityd ins = 5E-9[m] is Insulator thickness

    6.2 Energy Level Diagram of MOSFET along the center of the deviceform the Gate Contact

    Form the above figure obtained we can see the energy diagram along the center of the devicefrom the gate contact for Vgs = 2 V and Vds = 3 V. This figure shows the separation of the quasi-Fermi levels (size of the depletion region) as well as the inversion region where the intrinsic energylevel crosses the electron quasi-Fermi level (Efn).From this figure one can see the length of invertedregion starting from the surface (y = 0) to the crossing of the intrinsic energy level with the electronquasi-Fermi level (y approx - 0.03 um).

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    6.3 Current Density of MOSFET and n-channel

    The above figure displays the logarithm of the norm of the current density in the device underthe specified conditions. In the figure, one can notice the inverted region that allows the current topass between the n-doped regions (drain and source). Here we can clearly see the inverted n-channebetween the two n-doped regions.

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    6.4 Electron Concentration for different Drain to Source Voltages

    The above figure shows the logarithm of the electron concentration along the inverted channel fordifferent drain-to-source voltages. We can clearly see that a reduction of the electron concentrationnear the drain creating the saturation of the drain current. The figure shows the electrons pinched-offas the charge near the drain end is reduced by the channel potential, i.e. as the drain-to-source voltageincreases.

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    6.5 Surface Charge Density of MOSFET

    The figure shows the inverted channel (in blue) as well as the depletion region (orange). The redregions show the close-to neutral areas. The drain-side of the device shows a larger depletion regionto compensate the vanishing space charge at the pinch-off point. We can see a larger depletion widthon the drain-side of the MOSFET compared to the source side. This is a consequence of the electronsdrawn from the drain-side of the inverted channel.

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    6.6 Current(ID) vs Voltage Characteristics(VDS)

    The above figure shows the ID vs VDS curve of the device where a the current rises linearly atlow drain-to-source voltage to slowly saturates as the electron concentration vanishes at the pinch-offpoint

    7 Semiconductor Heterostructures

    The previous sections helped us get a good understanding of how the basic transistors work. For

    us to understand this we must be clear with what is the physics associated with SemiconductorHeterostructures.

    7.1 Heterojunctions

    Heterojunctions are two types

    Iso type Conductivity types are same bot n or both p.

    Aniso type Conductivity types are different. One is p and other is n.

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    For Heterostructures to form, both the joining materials must have similar thermal properties. Sothat while operation one might not crack over the operation of other.

    For Heterojunction the most important requirement is that their lattice should match. If not sowe will have defective regions. And if the interface is defected we have mobility effects which is notpermissible. Similar to what happens during high doping AlGaN/GaN have perfect match of lattice

    Homojunctions are formed from same material doped differently. Heterojunctions are formed bydifferent materials which may or may not be differently doped.

    7.1.1 Band Diagram

    Let us consider two semiconductors with X1 is greater than X2; Eg1 is smaller than Eg2; then

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    So, here we see a discontinuity in the energy band diagram. This 5 or notch is caused due toNotch Effect which is explained below.

    7.1.2 Understanding the Notch Effect

    Let us first take the example of homojunction. The diagram below describes p-n homojunction (The

    conduction band only)The e- will keep transferring from the n side to p side till the maximum energy of e- concentration

    on both sides are equal. And that is when we get the built in potential.

    Now in Heterojunction

    If notch was not to be considered then only Vbi would have been the built in potential but dueto the notch the built in potential is actually increased.

    So, band bending in case of heterojunction is more that that of homojunction. Now, as were thecase in MOSFET here too due to the extra band bending the notch might cross the fermi level and

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    so the portion lower to the fermi level will be accumulated of e-. So, basically we try to maximize thedelta Ec. So that e- concentration in unbiased condition increases.

    Due to the discontinuity delta Ec in the conduction band of AlGaAs and GaAs, the band bend-ing in the undoped GaAs is more than in the GaAs homojunctions of similar doping levels.Due to this effect, large concentration of e- are present at the GaAs surface adjacent to AlGaAs and

    they remain there due to the notch in the cconduction band.The e- have been supplied form the doped layer to undoped region (or where doping concentration islow) as a result ionied impurity scattering effect is absent.

    8 HEMT Working Principle

    The HEMT is a peculiar device, since it can offer optimal characteristics in terms of both highvoltage, high-power and high frequency operation. Its operation principle is founded on the presenceof the 2DEG at interface of an heterostructure, like for example an AlGaN/GaN system. It is athree terminal device where the current between the two Ohmic contacts of source and drain, flowingthrough the 2DEG, is controlled by the electrode of gate (typically a Schottky contact). Practicallythe bias applied to the gate controls the flow of electrons through the channel. The figure shows aschematic of an HEMT device. To confine the electron flow in the 2DEG and isolate HEMT devicesdeep trenches (cutting the 2DEG) or ion implantation are typically used.

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    The below figure illustrates, in a schematic band diagram of an AlGaN/GaN HEMT structurehow the 2DEG is influenced by the different gate bias conditions. This schematic is reported for thecase of a n-type doped AlGaN barrier layer. At Vg = 0V there are allowed levels below the Fermi levelin the subbands of the quantum well, resulting in the presence of a high sheet carrier concentrationand in the on-state of the device. By increasing the gate bias (Vg is greater than 0 V), the Fermlevel rises, increasing the density of allowed states below the Fermi level in the conductive band

    and therefore increasing the sheet carrier concentration of the 2DEG. By decreasing the gate biasV towards negative values (V is less than 0 V) the Fermi level drops depleting the 2DEG, until theposition of the Fermi level lies below the quantum well Under this condition, the level in the energysubbands are completely empty and the device is in the off-state.

    In the following figure we can see the Ids vs Vds characteristics of a HEMT. In the Ids-Vdscharacteristics by applying a positive potential difference between source and drain (Vds ), the currentwill start to flow in the 2DEG. By increasing the drain bias, the current flow in the channel will increaselinearly up to certain value. After this value the current through the channel starts to saturate. Themaximum saturation value Idss depends on the sheet carrier concentration n of the channel. Lookingat the trans characteristics, for a fixed Vds the drain current I rises with a parabolic behaviour withincreasing gate bias.

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    The drain current(Ids) can be controlled by the bias applied to the gate electrode. In particularIds decreases with increasing the negative value of the gate bias (Vg), since the region of the channelunder the gate is depleted. The value of Vg which determines the pinch-off of the channel (where thesheet carrier concentration in the channel becomes zero) is called threshold voltage (Vth) of the device

    In a AlGaN/GaN HEMT at any point x along the channel, neglecting the extrinsic series resistanceof source and drain, the sheet carrier concentration depend by the applied Vg

    ns(x) = 0AlGaNqdAlGaN

    [V g V th V(x)] (45)

    where dAlGaN is the distance of the gate to the 2DEG channel, corresponding to the AlGaNthickness. The gate-to-channel capacitance (per unit of area) can be approximately assumed asindependent ofns using the expression C2DEG = 0AlGaN/qdAlGaN.

    It is now possible to define the threshold voltage of the device, as the gate bias necessary to turn-offthe 2DEG, resulting in ans=0. Looking at the AlGaN/GaN schematic band diagram showed in abovefigure, it is clear that the threshold voltage depends on different parameters like the Schottky barrierheight B, the conduction band offset at the AlGaN/GaN interface delta Ec, the concentration of

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    donor atoms in the AlGaN layer ND, the relative dielectric constant AlGaN, the thicknessdAlGaN andthe Al concentration of the AlGaN. Besides these parameters, in order to have a complete expressionof the threshold voltage the contribution of the polarization induced charge density must be takeninto account. Thus simply the threshold voltage can be expressed as

    Vth= B EC

    qNDAlGaNd2AlGaN

    20AlGaN

    dAlGaN (46)Assuming a constant mobility and remembering the Ohmic law, for a two-dimensional electron

    gas the conductivity of the channel will be directly proportional to the sheet carrier concentrationns and to the electrons mobility in the channel

    = q.ns. (47)

    It is possible to write the drain current as:

    ID = .W.Q(x)dV(x)

    dx (48)

    where Q(x) is the charge considered in the channel. Integrating both sides in the all length of thechannel and considering the expression of Q(x) we have

    ID = .W

    L.C2DEG

    Vg Vth

    VDS2

    VDS (49)

    The drain current of a HEMT in linear region is often expressed in a form similar to that used fora MOSFET, i.e., :

    ID = .W

    L.C2DEG

    Vg Vth

    VDS2

    VDS (50)

    IncreasingVDSupto certain value calledVDSsat, the drain currentIDis constant and so the derivateofID will be zero.

    dIDdVDS

    =qWL

    C2DEG(Vg Vth VDS) = 0 (51)

    andVDSsat is given byVDSsat = Vg Vth (52)

    At bias condition ofVDSsat the ID will be expressed as

    IDSS=1

    2

    W

    LC2DEG(Vg Vth)

    2 (53)

    The above equation is approximation valid for long channel devices. However, for HEMTs witha short gate length (l is less than 10 um) the electron transport occurs under high electric fields and

    the expression of the saturation current is different. If the electric fields exceeds a certain criticavalue, the speed of the electrons in the 2DEG begins to saturate. Taking into account the effects ofthe saturation velocity model the saturation current is expressed as

    IDSS=q.ns.vsat (54)

    Considering the expression of the drain current, it is also possible to define the transconductanceof the device as the change in drain currentID resulting from a variation of gate voltage Vg for a fixedVDS:

    gm=IDVg

    (55)

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    at constant VDS.

    Similarly the output conductance of the device is defined as the ID response to a VDS variationfor a fixer gate bias Vg

    gd= IDVDS

    (56)

    at constant Vg. [26]

    9 Conclusion

    As the need for power is ever growing, present technology based on Si is not able to provide sufficientpower handling and high frequency operation capabilities. Therefore better alternative to the dominant Si based technology has to be looked forward to. For this purpose we explored some alternativesand came to the conclusion that WBG semiconductor like GaN can help us in this deed.

    We saw that 2DEG which is formed at the interface of AlGaN/GaN heterostructure can be usedto make high power, high frequency transistors, based on HEMT principle. In order to understandabout the working principle of HEMTs we went to the basics and started with BJT then proceedingto MOSFETs, MESFETs and finally came to HEMT. On understanding the working principles of althe devices we came to know that in both MOSFET and HEMT 2DEG are formed, but because inMOSFET the 2DEG is formed in the doped region, the scattering there is high, which results in lowersaturation velocity. Where as in HEMTs the 2DEG is formed in the undoped region which leads tolack of ion scattering and thus the mobility can be raised highly. Although the low field mobilityof GaN is lower as compared to other III-IV materials, but the high saturation velocity and higherbandgap makes it ideal candidate for high power and high frequency device.

    We compared the various figure of merits for different capable contenders and again came to theconclusion that our choice for GaN was the best. Further the possibility increasing the polarization (piezoelectric polarization) by inducing stress or strain on the material makes route for furtherpossibilities which can help in tweaking or enhancing the properties of AlGaN/GaN HEMTs.

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    10 References

    [1] J. Millman and C.C. Halkias in Electronic Devices and Circuits, Tata McGrawHill

    Publishing Company Ltd., New Delhi, 1991.

    [2] http://www.cree.com/LED-Chips-and-Materials

    [3] Wide Energy Bandgap Electronic Devices Fan Ren and John C. Zolper (Pg. 13 15)

    (Book Source: books.google.co.in/books?isbn=9812382461)

    [4] http://www.ioffe.ru/SVA/NSM/Semicond/GaN/bandstr.html

    [5] GaN-Based RF Power Devices and Amplifiers By Umesh K. Mishra, Fellow IEEE,

    Likun Shen, Thomas E. Kazior, and Yi-Feng Wu. (Source: http://ieeexplore.ieee.org/

    stamp/stamp.jsp?tp=&arnumber=4414367)

    [6] Power Electronic Europe Issue 4, 28 (2010), Alberto Guerra and Jason Zhang,International Rectifier, El Segundo, USA (Source: http://www.power-mag.com/pdf/

    feature_pdf/1283339996_IR_Feature_Layout_1.pdf)

    [7] Growth of GaN on SiC(0001) by Molecular Beam Epitaxy

    (Source: http://onlinelibrary.wiley.com/doi/

    10.1002/1521-396X(200112)188:2%3C595::AID-PSSA595%3E3.0.CO;2-S/pdf)

    [8] High quality AIN and GaN epilayers grown on (00-1) sapphire (100) and (111)

    silicon substrates (Source: http://scitation.aip.org/content/aip/journal/apl/

    66/22/10.1063/1.114242)

    [9] Effect of Si doping on strain, cracking, and microstructure in GaN thin films

    grown by metalorganic chemical vapor deposition (Source: http://scitation.aip.org/

    content/aip/journal/jap/87/11/10.1063/1.373529)

    [10] Metalorganic Chemical Vapor Phase Epitaxy of Crack-Free GaN on Si (111)

    Exceeding 1 m in Thickness (Source: http://iopscience.iop.org/1347-4065/39/11B/

    L1183)

    [11] Metalorganic chemical vapor deposition of GaN on Si111: Stress control and

    application to field-effect transistors (Source: http://scitation.aip.org/content/

    aip/journal/jap/89/12/10.1063/1.1372160)

    [12] The nature of arsenic incorporation in GaN (Source: http://scitation.aip.org/

    content/aip/journal/apl/79/20/10.1063/1.1418030)

    [13] AlGaN/GaN High Electron Mobility Transistors Grown on 150 mm Si(111)

    Substrates with High Uniformity (Source: http://iopscience.iop.org/

    1347-4065/47/3R/1553)

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    [14] Influence of sapphire nitridation on properties of gallium nitride grown by

    metalorganic chemical vapor deposition (Source: http://scitation.aip.org/content/

    aip/journal/apl/68/11/10.1063/1.115687)

    [15] GaN-Based Devices on Si (Source: http://onlinelibrary.wiley.com/doi/

    10.1002/1521-396X(200212)194:2%3C361::AID-PSSA361%3E3.0.CO;2-R/pdf)

    [16] Effect of the N/Al ratio of AlN buffer on the crystal properties and stress

    state of GaN film grown on Si(111) substrate (Source: http://

    www.sciencedirect.com/science/article/pii/S0022024803017433)

    [17] Activation energies of Si donors in GaN (Source: http://scitation.aip.org/

    content/aip/journal/apl/68/22/10.1063/1.115805)

    [18] Thick GaN Epitaxial Growth with Low Dislocation Density by Hydride Vapor Phase

    Epitaxy (Source: http://iopscience.iop.org/1347-4065/36/7B/L899)

    [19] Wide Energy Bandgap Electronic Devices Fan Ren and John C. Zolper (Book

    Source: books.google.co.in/books?isbn=9812382461)

    [20] Two-dimensional electron gases induced by spontaneous and piezoelectric

    polarization charges in N- and Ga-face AlGaN/GaN heterostructures (http://

    scitation.aip.org/content/aip/journal/jap/85/6/10.1063/1.369664)

    [21] Optical constants of epitaxial AlGaN films and their temperature dependence

    (Source: http://scitation.aip.org/content/aip/journal/jap/82/10/10.1063/1.366309)

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    content/aip/journal/apl/77/7/10.1063/1.1288817)

    [23] Spontaneous polarization and piezoelectric constants of III-V nitrides

    (Source: http://journals.aps.org/prb/pdf/10.1103/PhysRevB.56.R10024)

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    11 Important Points

    Si based technology has lived through its glorious period and because of its low power handlingcapacity, its low band gap and intrinsic carrier concentration of the material it has a to have a

    junction temperature less than 200 C to work properly.

    WBG semiconductors like SiC, GaN etc. overcome the above short comes of Si and can copeupwith increased power, frequency and operating temperatures. SiC technology is the most ad-vance amongst all the WBG SCs but it too suffers from micropipes crystal defect.

    GaN and its alloys have not been able to advance as much as SiC because of various physicalissues realted to their surface and interface. Also, because of the lack of free standing GaNsubstrate heteroepitaxy has to be performed on substrates like Al2O3, SiC or Si.

    Although the bulk mobility of GaN at low fields is much lower than that of other III-IV materialsbut the high saturation velocity and higher band gap makes it an ideal contender for highfrequency power devices. Also ability to form heterostructures of AlGaN/GaN leads to theformation of 2DEG at the interface which can be further used in the fabrication of HEMT

    devices.

    2DEG is due to the formation of both spontaneous and piezoelectric polarization. Which canbe used to make HEMTs.

    There are three possibilities for III-Nitrides namely zinc-blend, wurtzite and rock salt, of whichGaN exists in the wurtzite form which is thermodynamically most stable at room temperatureand pressure.

    Because of the absence of inversion symmetry along the c-axis it is easily possible to distinguishbetween different orientations of GaN namely G-faced and N-faced, depending if the materiais grown with Ga on top or N on top corresponding to (0001) and (0001-) crystalline faces.

    There exists a polarization in the GaN crystal due to the difference in the electronegativityof the atoms. This leads to a polarization known as spontaneous polarization which in turndepends on the c/a ratio. The less the ratio the more the polarization.

    There exists another polarization because of the induced stress and strain which leads to changein the c/a ratio. This becomes considerably important in AlGaN/GaN heterostructres for 2DEG

    The wide band gap of GaN (3.30 eV) is responsible for the high value of critical electric field(3.3 MV/cm) which is order of magnitude higher than that of Si. The high critical electric fieldmakes it suitable for high voltage devices.

    Also, because of low intrinsic electron concentration the maximum operation temperature canbe made to rise without leading to rise in leakage current.

    The relatively good value of relative permittivity makes it a good contender for capacitive loadingof transistor and passive components. Also, the thermal conductivity value being almost equato that of Si makes it capable to better transfer the heat produced and thus not making it todegrade at high temperature working conditions.

    Also, its capability to form AlGaN alloys makes the band gap alteration easy which comes handyfor the formation of heterostructures needed for the formation of 2DEG.

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    In principle the on state resistance at a given voltage of GaN can outperform competing Si andSiC devices. Which will reduce the power losses.

    In order to better compare the power electronic performance for different semiconductor ma-terials figure of merit are employed. In particular for high power and high frequency JFOM isan indication of the maximum capability to energize carriers by electric field, BFOM measures

    the minimum conduction losses during DC operation and BHFOM give information about theminimum conduction losses during high frequency operation. On comparing these values withSi and SiC we can easily come to the conclusion that GaN is a better choice.

    The inability to form free standing GaN substrate, other materials must be used as substratefor the growth of GaN.

    Hexagonal silicon carbide (6H-SiC) can be used as a substrate as the lattice mismatch for (0001)oriented GaN films is small and the thermal conductivity is higher. But the catch here is thehigh defect density (107 cm-2 for screw dislocations and 109 cm-2 for edge dislocation density).

    Si can also be used as a substrate. But owing to large lattice and thermal expansion coefficient

    mismatch can lead to defects and cracks on the material.

    To relieve the tensile stress and achieve crack-free GaN heterostructures, several kind of tran-sition layers can be used, such as low temperature AlN, graded AlGaN buffers or AlGaN/GaNsuperlattices.

    MOCVD is now the most popular method to grow GaN owing to its good quality and reasonablegrowth rates.

    By the formation of 2DEG at the junction interface we have a pool of electrons captured in thequantum well which is free to flow in the plane parallel to the junction interface.

    The benefit of 2DEG is that because of the absence of ionic counterparts in the well the scatteringis reduced significantly which contributes to better efficiency.

    It is because of the piezoelectric polarization the formation of high sheet charge density ispossible even without using undoped layers.

    Saturation of current in BJT (NPN) happens when base is higher than emitter, but collector isnot higher than base.

    Saturation in case of MOSFET happens when the width of the channel below the oxide layernear the collector becomes zero, this width is related to Vds and Vgs.

    Saturation current in case of MESFET is because of the depletion of n-channel below the Gatewhere on the application of required voltage Vgs the width of n-channel can be controlled. Alsothe potential difference Vds causes the n-channel to pinch off near the drain.

    It is the formation of Notch near at the interface of heterojunction which acts as the place forformation of 2DEG.

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