Volume II, Issue V, May 2015 IJRSI ISSN

Transcription

1 Volume II, Issue V, May 015 IJRSI ISSN Analytical Modeling of Potential and Electric Field Distribution and Simulation of Large Signal Parameters for Dual Channel Dual Material Gate AlGaN/GaN High Electron Mobility Transistor Abstract A two dimensional analytical model based on solution of -DEG charge expressions for potential and electric field distribution in dual channel dual material gate AlGaN/GaN high electron mobility transistor (DCDMG HEMT) is developed to demonstrate unique features of this device structure in suppressing short channel effects (SCEs), reduction in overall drain current collapse with further improvement in device current drive capability. The model accurately predicts the channel potential and electric field distribution along the device channels. It is observed that work function difference of dual metal gate leads to a screening effect of the drain potential variation by second metal gate portion near the drain resulting in suppressed drain induced barrier lowering (DIBL) and hot carrier effect. This further improves carrier transport efficiency due to improved uniform distribution of electric field along both the channels of device. Improvement in device current drive capability is due to incorporation of lower channel in the device. The resultant double channel dual material gate device get improved transconductance that suppresses current collapse that normally occurs in GaN based conventional HEMTs. Since current collapse mainly occurs in upper channel closer to the device surface while graded profile lower channel in the device is at far distance resulting in minimal current collapse. The proposed model also considers trap concentration, a responsible factor, for current collapse for device analysis and characterization. Finally theoretical prediction of our model results compared with device simulation results and experimental data. Results are found to be in close agreement giving validity to our proposed model. Keywords DEG-two dimensional electron gas, SCE- short channel effect, DCDMG-Dual Channel Dual Material Gate, HEMT-High Electron Mobility Transistor, AlGaN/GaN-Aluminum Gallium Nitride/Gallium Nitride. B I. INTRODUCTION eing an important device for high frequency, high power application AlGaN/GaN hetrostructure based High Electron Mobility Transistors attracting a lot of attention of device scintists word wide. Better performance of AlGaN/GaN hetrostructures relies on high saturation velocity, Rahis Kumar Yadav 1, Pankaj Pathak, R M Mehra 3 Department of Electronics and Communication Engineering, School of Engineering and Technology, Sharda University, Gr. Noida, India thermal stability, high breakdown benefits of electric field and development of polarization induced high sheet charge density of DEG at hetrointerface []. This kind of hetrostructures can provide much higher output power density compared with conventional AlGaAs/GaAs-HEMT [3]-[6]. Long et al [6][7] has fabricated and characterized AlGaAs/GaAs HFET structure, named as dual material gate HFET, in which two different metals of different workfunction were selected and merged into a single gate by making them contact laterally. The work function of metal region M 1 was chosen to be greater than that of metal region M leading to reduction in SCEs and supressed DIBL. This structure got improvement in the carrier transport efficiency due to step function in the channel potential distribution. In order to enhance the current drive capability of HEMTs, efforts were made by scientists to construct AlGaN/GaN double-channel HEMTs. However, due to the additional AlGaN barrier between the two channels, accesses to the lower carrier channel w e r e usually inefficient thus doublechannel behaviors was not pronounced [1]. Fabrication of an AlGaN/GaN/AlGaN/GaN epilayer structure using a lower AlGaN barrier layer with smaller layer thickness and low and graded Al composition was proved to be an effective approach to implement the double-channel HEMT with the second channel of high electron density and acceptable access resistance Roanming Chu et al [1]. The resultant AlGaN/GaN double-channel HEMTs exhibit device performance better than or comparable to baseline AlGaN/GaN HEMTs in all aspects. However, so for no analytical model is developed to incorporate the effect of double channel with dual material gate using AlGaN/GaN hetero-interface. In our DCDMG AlGaN/GaN HEMT model we considered multilayer device structure which provide better device performance in comparison to base line GaN HEMTs structures. II. MODEL FORMULATION.1. -D Analytical model for Channel Potential Analysis: Following Fig.1 shows schematic cross sectional view of DCDMG Al m Ga 1.m N / GaN HEMT with Al mole fraction Page 49

2 Volume II, Issue V, May 015 IJRSI ISSN m=0.30, L 1 and L are lengths of the laterally merged gate metals M 1 and M respectively having different workfunction and forming single gate for the device. The source and drain + regions are uniformally doped at N d =10 6 m -3. The work function of metal gates M 1 and M are ф M1 =5.3 V and ф M =4.1V respectively. In normally on device the Al 0.3 Ga 0.7 N barrier layer are fully depleted under normal operating conditions and electons are confined to the DEG in upper and lower GaN layers forming hetrointerfaces for double channel effects. SOURCE In our analytical model the channel region it is devided into two parts each under metal gate M 1 and metal gate M. The - D potential distribution ф 1 (x, y and ф x, y in upper channel can be obtained by solving the -D Poission,s equation as d ф 1 (x,y ) N d d ф 1 (x,y) L 1 L M 1 GATE d c = 3 nm (undoped Al 0.3 Ga 0.7 N) d b1 = 18 nm (Si-doped Al 0.3 Ga 0.7 N) N d d s = 3 nm (undoped Al 0.3 Ga 0.7 N) Upper -DEG d ch1 = 14 nm (undoped GaN) d b = 1 nm Al m Ga 1-m N (m graded from 3% to 6%) Lower -DEG d ch =.5 µm (GaN) SAPPHIRE N d + Fig.1. Cross sectional schematic of DCDMG AlGaN/GaN HEMT based on double channel AlGaN/GaN HEMT epilayer on sapphire substrate [1], Total gate length (L)=L 1+L, L 1=L =0.5µm, work function of gate region M 1 (ф M1) =5.3V, work function of gate region M (ф M) =4.1V [6][7], Gate width (W) =100μm, N d=x10 4 m -3, =d b1+d s+d c+δ and d =+d ch1+d b+δd are distance of upper channel and lower channel from gate, Δ and Δd denotes DEG effective depth in upper and lowere GaN layers respectively. for 0 x L (1) where x and y denotes horizontal and vertical axis in the device cross section respectively, N d is doping density of the Al 0.3 Ga 0.7 N layer, ε(m) is the dielectric constant, q is the electronic charge of Al 0.3 Ga 0.7 N and L=L 1 +L is the effective channel length. Potential profile ф 1 x, y in vertical y M DRAIN direction for upper channel can be approximated by following parabolic function as ф 1 x, y = ф 1L x + C 11 x y + C 1 x y () Similarly, ф 1L x is the upper channel potential, = d b1 + d s + d c + Δ distance of upper channel from gate, d b1 the thickness of n-al 0.3 Ga 0.7 N, Δ depth of DEG in upper GaN layer from its top edge. Similarly, ф x, y in lower channel can be obtained as d ф (x,y) + d ф (x,y) ε a (m ) for 0 x L (3) Where ф (x, y) is and lower channel potential, Similar to as stated above the potential profile in vertical direction for lower channel can be apprximated by following parabolic function ф x, y = ф L x + C 1 x y d + C x y (4) ф L x is the lower channel potential, d = + d c1 + d b + Δd is distance of lower channel from gate, d c1 is thickness of upper undoped-gan layer, d b the thickness of lower n-al m Ga 1-m N and Δd is depth of DEG in lower GaN buffer layer. In expressions () and (4), C 11 x, C 1 x, and C 1 x, C x are arbitary coefficients. Since in DCDMG Al 0.3 Ga 0.7 N /GaN HEMT gate is formed by merging two different metal gates M 1 and M of workfunctions ф M1 and ф M respetively. Thus flatband voltages V FB1 and V FB of gates are given by expressions V FB1 = ф MS1 = ф M1 ф S (5) V FB = ф MS = ф M ф S (6) Where, ф MS1 and ф MS are metal to semiconductor work functins for gate region M 1 and gate regin M respectively. Also, ф S = χ a (m) + E g ф F (7) Were, ф S is work function of n- Al 0.3 Ga 0.7 N, χ a (m) is electron affinity, E g is band gap of n- Al 0.3 Ga 0.7 N at T=300K and ф F is fermi potential given by expression ф F = kt q ln N d n i (8) where n i is intrinsic career concentration and N d is donar concentration in the material. In the DCDMG Al 0.3 Ga 0.7 N HEMT structure gate has been partitioned in to two parts, hence potential under gate region M 1 and gate region M for upper channel will be given separately as ф 11 x, y = ф 1L1 (x) + C 111 x y + C 11 x y 0 x L 1 (9) ф 1 x, y = ф 1L x + C 11 x (y ) + C 1 x y L 1 x ( L 1 + L ) (10) Similarily potential under gate regions M 1 and M for lower channel will be given separately as Page 50

3 Volume II, Issue V, May 015 IJRSI ISSN ф 1 x, y = ф L1 x + C 11 x y d + C 1 x y d for 0 x L 1 (11) ф x, y = ф L x + C 1 x y d + C x y d for L 1 x ( L 1 + L ) (1) The Poisson equations are solved separately for upper channel and lower channel under each gate regions using the following boundary conditions 1. Channel potential at the interface of two dissimilar metals is continuous [9-11] ф 11 x, = ф 1 x, at x = L 1 (13) ф 1 x, d = ф x, d at x = L 1 (14). Similarily electric field at the interface of two dissimilar metal is also continuous [9], thus ф 11 x,y ф 1 x,y = ф 1 x,y = ф x,y at x = L 1 for upper cannel(15) at x = L 1 for lower cannel (16) 3. Taking gate to source voltage in consideration, potential ф 11 x, 0 = V g1 (17) ф 1 x, 0 = V g (18) ф 1 x, 0 = V g1 (19) ф x, 0 = V g (0) where V g1 = V gs V FB1, V g = V gs V FB, and V gs is gate to source voltage. 4. dф 11 x,y dф 1 x,y dф 1 x,y dф x,y y= = E int 11 (1) y= = E int 1 () y=d = E int 1 (3) y=d = E int (4) where E int 11 and E int 1 are fields at hetrointerface of upper channel under M 1 and M. Similarily E int 1 and E int are fields at hetrointerface of lower channel under M 1 and M [9-11]. Thus E int 11 = qn ns 11 E int 1 = qn ns 1 E int 1 = qn ns 1 E int = qn ns (5) (6) (7) (8) here n s11 and n s1 are sheet career densities for upper channel under M 1 and M respectively, also n s1 and n s are sheet career densities for lower channel under M 1 and M respectively [1]. These values can be obtained by [13] as n s11 = q V gs V t1 V c1 x for 0 x L 1 (9) n s1 = q V gs V t1 V c1 x for L 1 x (L 1 + L ) n s1 = qd V gs V t V c x for 0 x L 1 Page 51 (31) n s = qd V gs V t V c x for L 1 x ( L 1 + L ) (3) (30) Where, V c1 (x) and V c x are upper and lower channel potentials at any point x along the channel due to V ds as applied drain to source voltage, V gs is applied gate to source voltage. The thresold voltages V t1 of upper channel and V t lower channels respectively are given as V t1 (m) = χ(m) Δφ(m) q(n d N t ) d b1 V t (m) = χ(m) Δφ(m) q(n d N t ) d b σ pz (m ) σ pz (m )d (33) (34) Where, χ(m) as the Schottky barrier height, Δφ(m) as the conduction band discontinuity at the Al 0.3 Ga 0.7 N /GaN hetrointerface. N d is Si doping concentration of n-algan layer and N t is trap concentration [9], σ pz m net polarization induced sheet carrier density at the hetrointerfaces and obtained as σ pz m = [ P SP m P SP 0 + P pz ] (35) Where P SP (m) and P SP (0) is spontaneous polarization of Al m Ga 1-m N and GaN material system [13-15]. In our model piezoelectric polarization depends on the amount of strain developed at hetrointerfaces in order to accommodate the difference in lattice constants of GaN and AlGaN. For fully satrained device piezoelectric polarization dependent charge density is given as a 0 a(m P pz = e a(m ) 31 m e 33 m C 13(m) for 0 m 1 C 33 (m) a 0 a(m σ pz m = e a(m) 31 m e 33 m C 13(m) + + P C 33 (m) SP m P SP 0 for 0 m 1 36) Where a(m) is lattice constant e 31(m) and e 3(m) are piezoelecric constants and C 13(m) and C 33(m)are elastic constants[14-16]. Increasing Al mole fraction in barrier layer increases lattice mismatch that further results in stain relaxation. For partially relaxed device with Al m Ga 1-m N layer thickness in the range of 18nm to 40 nm piezoelectric polarization induced charge density depends on the Al mole fraction as [16]. a 0 a(m e a m 31 m e 33 m C 13 m C 33 m for 0 m 0.38 P Pz = m a 0 a(m a m e 31 m e 33 m C 13 m C 33 m for 0.38 m for 0.67 m 1 (37)

4 Volume II, Issue V, May 015 IJRSI ISSN In above equation (37) device remains completely strained for Al molefraction up to 38% and partially relaxed for m from 38% to 67%. Device is fully relaxed for m greater than 67%. The potential at source end for each channel is ф 11 0, = V bi1 = ф 1L1 0 (38) ф 1 0, d = V bi = ф L1 0 (39) WhereV bi1 and V bi is built in voltages. 5. Te potential at drain end for eac cannel is Ф 1 L 1 + L, d = V bi1 + V ds = Ф 1L L 1 + L (40) Ф L 1 + L, d = V bi + V ds = Ф L L 1 + L (41) the constants in (9), (10), (11) and (1) can be found from boundry conditions and on substituting their values in (9), (10), (11) and (1), We get ф 11 x, y = ф 1L1 x E int 11 x (y ) + Vg1 ф 1L1 x E int 11 y (4) ф 1 x, y = ф 1L x E int 1 x (y ) + Vg ф 1L x E int 1 y (43) ф 1 x, y = ф L1 x E int 1 x (y d ) + Vg1 ф L x d E int 1 d y d (44) ф x, y = ф L x E int 1 x (y d ) + Vg ф L1 x d E int d y d (45) Channels potentials ф 1L1 (x) and ф L (x) are obtained by substituting (4), (43) in (1) and (44), (45) in ()..On substitution we get d ф 1L1 d ф 1L d ф L1 d ф L + V g1 ф 1L1 (x) + V g ф 1L (x) + V g1 ф L1 (x) λ + V g ф L (x) λ + E int 11 (46) + E int 1 (47) + E int 1 d (48) + E int d (49) where = Page 5 characteristic length of upper channel and λ = d characteristic length of lower channel Introducing a new variable η 11 (x) = ф 1L1 x V g1 qn d + E int 11 η 1 (x) = ф 1L x V g qn d + E int 11 η 1 (x) = ф L1 x V g1 η (x) = ф L x V g qn d + E int d λ qn d + E int d λ (50) (51) (5) (53) on substituting (50) in (46), (51) in (47), (5) in (48) and (53) in (49), we get d η 11 (x) d η 1 (x) η 1 (x) = 0 (54) η (x) λ = 0 (55) using (50) and (51), η 11 (x=0) = η 111, η 1 (x=l 1 +L ) = η 1 and boundry conditions, similarly using (5) and (53) η 1 (x=0) = η 11, η (x=l 1 +L ) = η and boundry conditions we get η 111 = V bi V g1 qn d E int 11 (56) η 1 = η V ds V FB1 V FB b 1 b 11 (57) η 11 = V bi V g1 qn d E int 1 d λ η = η 11 + V ds V FB1 V FB b b 1 λ (58) (59) where b 11 = qn d E int 11 and b = qn d E int 1 for upper 1 for channel and b 1 = qn d E int 1 d lower channel respectively. and b = qn d E int d Solving (54) for η 11 (x) and η 1 (x) and substituting in (46) and (47) we get channel potential for upper channel as: Ф 1L 1 x = η 111 sin L1 x Ф 1L x = η 1 sin x L1 +η 11 sin x +η 11 +L x sin L +V g1 + qn d E int 11 +V g + qn d E int 1 Similarily solving (55) for η 1 (x) and η (x) and substituting in (49) and (50) we get potential for lower channel as: Ф L1 x = η 11 x +η 1 sin x λ λ λ Ф L x = η sin x L1 +η 1 +L x λ sin L λ +V g1 + qn d E int 1 d λ +V g + qn d E int d λ (60) (61) (6) (63)

5 Channel Potential (V) Volume II, Issue V, May 015 IJRSI ISSN Using boundry conditions (38), (40) and (56), (57) in (60) and (61) we get values of η 11 and η 11 as η 11 = η 111 sin L +η 1 + V g V g1 cos L +(b 1 b 11 ) sin L1 cos L sin L +cos L η 11 = η 1 sin L1 +η 111 sin L + V g1 V g sin L + b 11 b 1 sin L sin L +cos L Now using boundry conditions (39), (41) and (58), (59) in (6) and (63), we get values of η 1 and η 1 as η 1 = η 11 sin L λ +η λ + V g V g1 λ cos L λ +(b b 1 )λ sin L1 λ cos L λ λ sin L λ +cos L λ λ η 1 = η sin L1 λ +η 11 sin L λ + V g1 V g λ sin L λ +(b 1 b )λ sin L λ λ λ sin L λ +cos L λ λ (64) (65) (66) (67) Electric Field Analysis: The electron transport velocity through the channel is directly related with the electric field along the channel. The surface electric field component along the upper channel in x direction under the Gate M 1 is given as channels at the interface of M 1 and M orinates due to the work function differences of two gate metal regions of different work funtions. This further enhances drift velocity of -DEG carriers, reduces DIBL and result into screening effect by M suppressing short channel effects (SCE) in upper and E 11 x = dф 11 x,y (68) lower channel effectvely. E 11 x = = dф 1L1(x,y) y= η 111 x η 11 cos x and x component under M is E 1 x = dф 1 x,y E 1 x = = dф 1L(x,y) y= η 11 +L x η 1 cos x L 1 sin L (69) (70) (71) The surface electric field component along the lower channel in x direction under the Gate region M 1 is given as E 1 x = dф 1 x,y = dф L1(x,y ) y=d E 1 x = λ η 11 x λ λ η 1 cos x λ λ and x component under gate region M is given as E x = dф x,y = dф L(x,y ) y=d E x = λ η 1 +L x λ λ η cos x L 1 λ sin L λ III. RESULTS AND DISCUSSIONS (7) (73) (74) (75) To verify the present DCDMG Al 0.3 Ga 0.7 N/GaN -HEMT model, ATLAS TCAD [8] device simulator is used to analyse channel electric field, potential distribution, current voltage characteristics as well as transconductance of device. Also model and simulation results are compared with experimental data [1][6][7]. Fig. shows the potentials distribution along both the channels as extracted from the analytical model as well as simulated data. These results are in good agreement with pulished DMG AlGaN/GaN HEMT results [9]. In this figure, the solid lines shows model results and dash lines represent the simulated results which further depends on device biasing. The upper channel potential starts from 1.5 volts and increases with hump up to.0 volts. This figure clearly shows the step in the potential distribution along the The potential distribution plot shows that gate M 1 functions as control gate and gate M works as screen gate in device. Since potential begins to drop more in the channels under screen gate M under drain junction reions leading to more reduced DIBL. Plot also depicts that potential distribution in upper channel is higher than that of the lower channel. Fig.3 depicts longitudinal electric field variation along the channels for DCDMG Al 0.3 Ga 0.7 N/GaN HEMT model and simulation data for channel lenth L=1µm. Due to the peaks in electric field profile at the interface of two gate metals in DCDMG AlGaN/GaN HEMT structure, the electric field under M in both the channels get enhanced. Since the electron transport velocity is related to the electric field Page Upper channel Lower channel Normalised Channel Length (x/l) Fig. Variation of channel potential with normalized channel length in DCDMG Al 0.3 Ga 0.7 N/GaN HEMT solid lines shows model data and dash lines shows ATLAS simulation data.

6 Upper Channel Electric Field x10 5 (V/cm) Lower channel Electric Field x10 5 (V/cm) Volume II, Issue V, May 015 IJRSI ISSN distribution along the channels. The velocity with which charge carriers enter and drift in the channels also increases Upper channel Lower channel Normalized Channel Position (x/l) Fig.3 Longitudinal Electric Field variation with normalized channel position for DCDMG AlGaN/GaN HEMT. Solid lines shows model data and dash lines shows ATLAS data. leading to more efficient carrier transport along both the channels. Also presence of lower workfunction of gate metal M reduces peak electric field at the drain end leading to reduction in hot carrier effects in the device collapse due to presence of two channels in the device structure. Output current voltage characteristics also shows significantly higher darin current to that of the conventional GaN based HEMTs. The significant enhancement in transconductance of DCDMG Al 0.3 Ga 0.7 N/GaN HEMT has also been verified from Fig. 5. The simulated input characteristics plot for the device reveals a much higher drive current in comparison of conventional GaN based HEMTs [10] due to the increased carier transport velocity in the device and better gate controllability.thus our proposed DCDMG Al 0.3 Ga 0.7 N/GaN HEMT structure can improve current drive capabilty and overall device transconductance by reducing current collapse, SCEs and hot electron effects much effectively than conventional GaN HEMT structures [11-14]. A close matching between model results, simulation results and published experimental data as described above prove the accuracy and validity of our proposed device model. IV. CONCLUSIONS Analytical modeling concept of dual channel dual material gate Al 0.3 Ga 0.7 N/GaN HEMT has been examined first time by developing solid state physics baed -D analytical model and simulating device structure using industry validated ATLAS TCAD [8]. The analytical expressions for upper and lower channels potential distribution and electric field distribution have been obtained and found in good agreement. The results are further caliberated with published experimental data. Fig.4 shows current voltage characteristics of DCDMG Al 0.3 Ga 0.7 N/GaN HEMT for different gate to source biases when Fig.1 device structure simulated using ATLAS TCAD device simulaor. Plot clearly shows variation of drain current with variation on drain to source voltage at various gate to source biases in both linear and saturation regions. Simulated results shows that DCDMG AlGaN/GaN HEMT device has effective control on drain current with reduction in overall current It can be concluded with the above interpretations that DCDMG Al 0.3 Ga 0.7 N/GaN HEMT architecture provides screening effects in small channel devices thus suppressing short channel effects (SCE), reducing hot electron effects due to introduction of dual material gate and minimising overall current collapse due to introduction of double channels. In addition, due to enhanced channel potential distribution and step function in channel electric field distribution, the more uniform carrier drift velocity in both the channels is obtained that results in higher switching speed of the device. Page 54

7 Volume II, Issue V, May 015 IJRSI ISSN REFERENCES [1] Roanming Chu,Yugang Zhou, Zie Liu, Deliang Wang, Kevin J. Chen, AlGaN/GaN Double Channel HEMT, IEEE Transaction on Electron Devices, vol.5, no.4, Apr [] O. Ambacher, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M.Murphy, W. J. Schaff, L. F. Eastman, R. Dimitrov, L. Wittmer, M. Stutzmann, W. Rieger, and J. Hilsenbeck, Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures, J. Appl. Phys, vol. 85, no. 6, pp , Mar [3] Y. F. Wu, A. Saxler, M. Moore, R. P. Smith, S. Sheppard, P. M.Chavarkar, T. Wisleder, U. K. Mishra, and P. Parikh, 30-W/mm GaN HEMTs by field plate optimization, IEEE Electron Device Lett., vol.5, no. 3, pp , Mar [4] V. Tilak, B. Green, V. Kaper, H. Kim, T. Prunty, J. Smart, J. Shealy, and L. Eastman, Influence of barrier thickness on the high power performance of AlGaN/GaN HEMTs, IEEE Electron Device Lett., vol., no. 11, pp , Nov [5] K.Kasahara, N. Miyamoto, Y. Ando, Y. Okamoto, T. Nakayama, and M.Kuzuhara, Ka-band.3 W power AlGaN/GaN hetrojunction FET, in IEDM Tech. Dig., pp , Dec. 00. [6] W. Long, H. Ou, J. M. Kuo and K.K Chin., "Dual-Material G a t e (DMG) Field Effect Transistor, IEEE Trans. Electron Devices, vol. 46, pp , May [7] W. Long et.al. Methods for fabricating a dual material gate of a short channel field effect transistor, US Patent, US , Nov 000. [8] Silvaco TCAD, ATLAS Device Simulator, [9] Sona P.Kumar et all, Analytical modeling and simulation of subthreshold behavior in nanoscale dual material gate AlGaN/GaN HEMT Elsevier, Superlattices and Microstructures, vol. 44, pp , Mar [10] Jia-Chuhan Lin, Yu-Chieh Chen, Wei-Chih Tsai,Po-Yu Yang Structure design criteria of dual channel high mobility electron transistor, Solid-State Electronics, vol.51, pp , 007. [11] Sona P.Kumar, A. Agarwal, R Chaujar, S. Kabra, M. Gupta, R.S. Gupta, Threshold Voltage model for small geometry AlGaN/GaN HEMT based on analytical solution of 3-D Poisson s equations Microelectronics Journal, vol.38,pp , Oct.007. [1] Sona P.Kumar, A. Agarwal, R Chaujar, M. Gupta, R.S. Gupta, Performance Assessment and sub-threshold analysis of gate material engineered AlGaN/GaN HEMT for enhanced carrier transport efficiency, Microelectronics Journal, vol.39,pp , Aug.008. [13] Rashmi Modelin and characterization of spontaneous and piezoelectric dependent lattice mismatched AlGaN/GaN HEMT for microwave and millimeter wave applications PhD Thesis, UDSC, India, 001. [14] E.S. Hellman, The polarity of GaN: A critical review, MRS Internet J. Nitride Semiconduct. Res. 3, vol. 11, pp. 1-11, [15] Y.Zhang,I.P.Smorchkova, C.R.Elsass, S.Kellar, J.P.EIbbetson, S.Denbaars, U.K.Mishra ans J.Singh Charge control and mobility in AlGaN/ GaN Transistor:Experimental and theoretical studies J.Appl, vol.87, no11, pp , 000. [16] T.Li,R.P.Joshi and C.Fazi Montecarlo evaluation of degeneracy and interface roughness effects on electron transport in AlGaN/ GaN hetrostructures J.Appl,Phys vol.88, no., pp , Page 55