PHYSICS BASED CHARGE AND DRAIN CURRENT MODEL FOR AlGaN/GaN HEMT DEVICES

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1 Journal of Electron Devices, ol. 14, 01, pp JED [ISSN: ] PHYSICS BASED CHARGE AND DRAIN CURRENT MODEL FOR AlGaN/GaN HEMT DEICES Gowin Raj 1, Hemant Pareshi 1, Suhansu Kumar Pati 1, N Mohankumar, Chanan Kumar Sarkar 1 1 Nano Device Simulation Laboratory, Electronics an Telecommunication Engineering Department, Jaavpur University, Kolkata , Inia SKP Engineering College, Tiruvannamalai, Tamilnau , Inia gowinraj@gmail.com Receive , online ABSTRACT A simple Physics base rain current moel of AlGaN/GaN High Electron Mobility Transistor moel (HEMT) is evelope. The Propose is useful for fast an accurate circuit simulation an analysis of Microwave an DC Characteristics. This moel inclues Channel length moulation an elocity Saturation ect. Derive moel results are compare with 1µm gate Al Ga N/GaN HEMT structure an 0.1 µm gate Al 0. 5 Ga N/GaN HEMT structure eperimental ata. The preicte Drain current are 1.3A/mm for 0.1µm gate an 5.3A/mm for 1µm gate length, which are in goo agreement with eperimental ata. Keywors: AlGaN/GaN HEMT, compact moels, sheet charge ensity, -D electron gas (DEG) I. INTRODUCTION GaN is the ecellent caniate for high power, high temperature an high freuency applications [1-]. The capacitance an c characteristics moel is thus very important for accurate simulation of high-spee igital an analog circuits in AlGaN/GaN HEMT. Among various numerical moels only limite moels are available in physics base [3].The variation of -D electron gas (DEG)

2 channel ensity n s with gate voltage an the physical ects shoul be moele for accurate simulation. The asymmetric triangular well confine DEG channel region is solve using Schroinger euation. In this moel lowest conuction ban energy level is consiere because E1 3E0 [4]. So low ban parameter from [5] γ 0 is consiere in this moel. The physics base moel presente here has minimal set of parameters. Channel length moulation (CLM) an velocity saturation ects are consiere in this moel an eplaine with reference. The paper is arrange as follows. Moel structure in accorance to eperimental imensions is given in Section II. Section III gives etaile epression for rain current moel for AlGaN/GaN with physical ect of velocity saturation an channel length moulation. Moel eperimental comparison (MEC) is eplaine for long an short gate length evice is given in Section I. II. MODEL DESCRIPTION The cross-sectional view of AlGaN/GaN HEMT for two ifferent eperimentally etermine gate length evice structures are shown in Fig. 1. The layer seuence, from bottom to top, is GaNunope/UID-AlGaN/n-AlGaN/metal, with DEG channel forme at the interface between GaN-unope/UID-AlGaN. The ifference between these two eperimental structures is 0.1 µm gate length with Al mole fraction of Al. 5 Ga. 75 N, with 100µm [6] an 1µm gate length evice with 75µm with, Al mole fraction of Al. 50 Ga. 50 N [7-8]. Table 1: List of symbols Symbol Physical meaning Electron charge Permittivity of AlGaN D Density of states th Thermal voltage g Gate to source voltage n s Charge ensity of DEG Thickness of n-algan layer i Thickness of UID AlGaN = + i Total thickness of AlGaN C g = / Gate capacitance per unit area III. MATHEMATICAL MODEL FOR DRAIN CURRENT III. 1 Charge Density Moel The unifie n s moel is given as [9] C g ns g0 C 3 0 g g0 g 0 th[1 ln( gon)] 3 3 th C 0 g g0 g 0 1 go 3.. (1) The thermal voltage th in this euation has less impact on n s (Charge Density), thus we propose to neglect th from the above ns euation. In Fig, region 1 is having E 0 greater than E f, corresponing to g0 < 0.9, an Region II is having E 0 less than E f corresponing to g0 0.9 [9]. Fig- gives the comparison between the moels of region-1 an region-, ns moel with th, an n s moel without th. So new charge ensity moel neglecting th can be written as e () Fig 1: Cross-sectional view of AlGaN/GaN HEMTs with Gate length L g. i spacer layer thickness an n- AlGaN layer thickness. n s Cg go where go gs off /3 Cg o go go - 3 C o ggo go 3 /3..(), gs is the gate to 1156

3 source voltage, off the cut off voltage, the channel potential along -irection, C the gate capacitance, the electronic charge an o is an eperimental ata for E 0 [5]. Fig-.: Comparison between the moels of region-1 an region-, n s moel with th, an n s moel without th. Region-1 (go<0.9) an region- (go>=0.9), where go= gs off (where off =-3). III. Current Moel The rain current ( I ) for this evice can be written as I where w n (, ) v( E ) g s g g g..(3) w =with of the evice, ve ( ) =electron rift velocity. In the low-fiel region, the longituinal electric fiel along the channel E is less than the critical fiel E T, thus the electron rift velocity can be given as ve ( ) LF E E 1 ua ET..(4) where u a is constant etracte from eperimental ata, LF is low longituinal fiel mobility epens on the vertical electric fiel in DEG of GaN. Longituinal fiel mobility is given as 0 LF 1 p1 E y, p Ey,.(5) where 0 is the low fiel mobility, p1 an p are the eperimental etermine parameters, Ey, is the vertical electric fiel of DEG. E y, can be calculate from average of Q w n along the lateral g s DEG g, irection i.e Q E y DEG..(6) We efine E an substitute (), (4) an (5) in euation (3). After substituting, integration of euation (3) is one from source to rain, giving the rain current as Lg - I 1+u a 0 ET /3 - μ w 0 gcg go-βgo = go - R /3 s +β Where go go Lg is the channel length, source an rain potential, 1 p1 Ey, p Ey,...(7) s an are c o g 3 /3 an. After integrating (7) the rain current is obtaine as e β Log (t)-816β t 1 t 3 upperlimit = g - off - +β I=α +480β t -00β t..(8) t 3 lowerlimit = g- off - s +β +5.5β t -7.8βt +0.5t 0wgcg s where an 1ua Lg EL T g III. 3 elocity Saturation The obtaine rain current moel is best fitte for linear region. For saturation region I is 1157

4 ifferentiate with respect to s. The ifferentiation gives zero, since the current is remain constant in saturation region. To calculation of, sat from (8) is too ifficult. Thus a smoothing function, is use in place of, while calculating I., gs off, sat, sat..(9) where, sat, gs is the gate potential m applie, off the cut off voltage an m the boy co-icient. Table II Parameters use in the Calculation for ifferent Devices Parameter Quantity Fig 3a Fig 4a Fig 3b Fig 4b off () Offset ol Rs(Ω) Par Source R R(Ω) Par Drain R W(µm) Gate With L g (µm) Gate Length E T Crit electric fiel u a Parameter u 0 Parameter p 1 Low fiel 1.13e-9-1.1e-1 µ Parameter p Low fiel 15e-18 14e-10 µ Parameter λ( -1 ) CLM Para. 1e-6 1e-6 m Boy Coicient 3.8 γ 0 (1e-1) Ep. Parameter[5].1.19 the saturation region. For short channel evices the n s moel shoul be solve using D Poisson s euation The final rain current moel with CLM is given in (10). I. RESULT AND DISCUSSION The moel an eperimental ata compare in this section. The MECs (moel-eperimental comparison) are one for 1µm 75µm gate an 0.1µm 100µm gate lengths from the eperimental ata in paper [6-8]. Table II gives the parameters use in these evices. The eperimental results an propose moel results show ecellent concurrence in the I - an I - g characteristics after incorporation of velocity saturation an CLM ects. Fig. 3a: Comparison of moel I - characteristics with eperimental ata for Al. 50 Ga. 50 N/GaN for L g =1µm evice. Eperimental ata taken from [7-8]. III. 4 Channel length moulation Increase in gate bias leas to increase the output conuctance in saturation region when CLM ect occurs. The simple observation of I with CLM ect in first orer euation is [10] I I (1 )..(10), CLM, where is the CLM etracte parameter from Fig. 3b: Comparison of moel I - g characteristics with eperimental ata from [7-8] measure at =5 for Al. 50 Ga. 50 N/GaN L g =1µm evice. 1158

5 Fig 3a shows the I - characteristics compare with MEC for Al. 5 Ga. 5 N/GaN L g =1µm. Results are goo agreement with eperimental ata [7-8]. Fig. 3b shows I - g characteristics with =5 [8], ehibiting ecellent matching For further investigation of SCE (Short Channel Effects) an CLM in this moel, comparison of the moel against eperimental ata for the L g =0.1µm is one. Fig. 4a shows the comparison of I - characteristics of the moel, compare with eperimental ata [6] for Al. 5 Ga. 75 N/GaN with L g =0.1µm, inicating a goo agreement. Fig. 4b shows I - g characteristics with =8 an eperimental ata in paper[6], inicating goo agreement.. CONCLUSIONS Fully physics base analytical moel for rain current in GaN HEMT evice is presente. The moel ehibits ecellent agreement with eperimental results for both long an short gate length AlGaN/GaN HEMTs. elocity saturation an channel length moulation ects are also inclue in the moel. Etraction of physical parameters from the propose moel is convenient. This moel can be use to evelop GaN HEMT compact moel. Acknowlegments The authors woul like to thank the Department of Science an Technology, Govt. of Inia for the financial assistance in carrying out research activities. References Fig. 4a: Comparison of moel I - characteristics with eperimental ata of Al. 5 Ga. 5 N/GaN HEMT with L g =0.1µm. Eperimental ata taken from [6]. Fig. 4b: Comparison of moel I - characteristics with eperimental ata for Al. 5 Ga. 5 N/GaN HEMT having L g =0.1µm. Eperimental ata taken from [6]. 1. Yi-Feng Wu, Kapolnek D, Ibbetson J.P, Parikh, Keller B.P, Mishra, U.K. ery-high power ensity AlGaN/GaN HEMTs, IEEE Transactions on Electron Devices. 48, (001).. Nguyen C, Nguyen N.X, Le M, Grier D.E. High performance GaN/AlGaN MODFETs grown by RFassiste MBE, Electronics Letters. 34, (1998). 3. Asgari M, Kalafi L, Faraone. A uasi-twoimensional charge transport moel of AlGaN/GaN high electron mobility transistors (HEMTs), Physica E: Low-imensional Systems an Nanostructures. 8, (005). 4. X. Cheng an Y. Wang. A Surface-Potential-Base Compact Moel for AlGaN/GaN MODFET, IEEE Transactions on Electron Devices. 58, (011). 5. Ho Ki Kwon, C.J. Eiting, D.J.H. Lambert, B.S. Shelton, M.M. Wong, T.G. Zhu, an R.D. Dupuis. Raiative recombination of two-imensional electrons in a moulation-ope Al 0.37 Ga 0.63 N/GaN single heterostructure., Appl. Phys. Letters. 75, (1999). 6. Kumar, W Lu, R Schwint, A Kuliev, G Simin, J Yang, M Asif Khan, Ilesanmi Aesia. AlGaN/GaN HEMTs on SiC With f T of Over 10 GHz, IEEE Trans. on Electron Dev. 3, (00). 7. Sippel J.C, Islam S.S, Mukheijee S.S. A physicsbase analytical moel of a GaN/AlGaN HEMT incorporating spontaneous an piezoelectric polarization Electrical an Computer Engineering, IEEE Canaian Conference. 3, (004). 8. Wu Y.F, Keller S, Kozooy P, Keller B.P, Parikh P, Kapolnek D, Denbaars S.P, Mishra U.K. Bias epenent microwave performance of AlGaN/GaN MODFET's up to 100, IEEE Transactions on Electron Devices. 18, 90-9 (1997). 1159

6 9. Khanelwal S, Goyal N, Fjelly T.A. A Physics- Base Analytical Moel for DEG Charge Density in AlGaN/GaN HEMT Devices, IEEE Transactions on Electron Devices. 58, (011). 10. T. Ytteral, Y. Cheng an T.A. Fjelly. Device Moelling for Analog an RF CMOS Circuit Design., John Willey an Sons (003). 1160