COMPARISON OF THE MODELS OF POLARIZATION USED TO SIMULATE I-V CURVES OF AlGaN/GaN STRUCTURES

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1 OMARISON OF THE MODELS OF OLARIZATION USED TO SIMULATE I-V URVES OF Al/ STRUTURES Jurj Rcko, Alen Grnová, eter Benko, Ldislv Hrth, Miroslv Mikolášek, Mgdlén Kdlečíková, Jurj Brez Slovk University of Technology, Ilkovičov 3, Brtislv, Slovki E-il: Received 03 My 2017; ccepted 18 My Motivtion olriztion effects t teril interfces ply key role in the perfornce of devices bsed on nitride terils. We hve focused on the effect of spontneous nd piezoelectric polriztion in rel etl//al/ heterostructure used in the production of vrious types of sensors. Spontneous polriztion is due to the intrinsic syetry of the bonding in the equilibriu wurtzite crystl structure. Mechnicl stress results in the so-clled piezoelectric polriztion. It is negtive in tensile nd positive in copressive strined Al lyers. The orienttions of spontneous nd piezoelectric polriztions re prllel in the cse of tensile strin nd ntiprllel in the cse of copressive stress. We deonstrte the effect of tensile nd copressive strin upon the I-V chrcteristics of etl//al heterostructures. 2. Theory T OT AL The effect of spontneous nd piezoelectric polriztion chrge AlG1 N is reflected in the oisson eqution deterining the shpe of the sheet bound totl interfce chrge d dψ( TOTAL D A D A 0 κ( Al G N( q p( n( N ( N ( Nt ( Nt (. (1) 1 dx dx Here, is the reltive perittivity, is the electric potentil, n nd p re concentrtions of free chrge crriers, N D+ nd N A re concentrtions of shllow ionized donors nd cceptors, N D+ t nd N A t re concentrtions of deep ionized donors nd cceptors expressed, nd is the olr concentrtion of Al. 2.1 Spontneous polriztion Spontneous polriztion is negtive for ll G-polrity heterostructures. The vlue of AlG1 N exhibits nonliner dependence on which is described by introducing bowing preter b into the usul liner interpoltion between the vlues for AlN nd b 1 AlN 1 1 Al, (2) where the bowing preter is clculted s b Al 2 AlN 2Al 0.5G 0.5N. (3) 173

2 Since the oisson eqution (1) contins the derivtive of polriztion, one cn eliinte spontneous polriztion in s it is considered constnt nd Eqn. (2) cn be rewritten s 1 b AlN Al 1 1. (4) reters of spontneous polriztion re surized in Tble 1. Tb. 1: reters of spontneous polriztion Mteril AlN b Al (/ 2 ) Reference [1] [1] [5] 2.2 iezoelectric polriztion Group III nitrides, such s, exhibit very strong piezoelectric polriztion effects, greter by one order of gnitude thn other III-V seiconductors [1]. Both in gnitude nd orienttion, piezoelectric polriztion is directly relted to the strin present in the teril. Higher strin cuses higher polriztion. opressive strin induces polriztion oppositely oriented thn tensile strin. This is illustrted in Fig. 1. pz Al pz Al Substrte ) Substrte b) Fig. 1: The gnitudes nd orienttions of spontneous nd piezoelectric polriztion coponents under tensile () nd copressive strin (b). iezoelectric polriztion sheet interfce bound chrge occurring due to the istch of the lttice constnts t the heterointerfces is deterined s c c 0 e 33 c0 0 0 Z 2e , (5) where e 33 nd e 31 re piezoelectric constnts. The reltion between the lttice constnts nd c in the hexgonl Al syste is given by elstic constnts 13 nd 33 s c c0 c (6)

3 Then the piezoelectric polriztion sheet bound interfce chrge cn be written s Z 0 e e 13 AlG N (7) 1 33 The elstic constnts 13, 33, piezoelectric constnts e 31, e 33 nd the lttice preter of the hexgonl unit cell of the wurtzite structure in dependence on the olr concentrtion of luiniu in Al G 1- N were linerly interpolted using the Vegrd lw by y y AlN 1 1 y. (8) reters for piezoelectric polriztion given in Tble 2 were obtined fro [1] nd revised in ccordnce with [2]. Tb. 2: iezoelectric polriztion preters Mteril e 31 e (Å) (/ 2 ) (/ 2 ) (G) (G) AlN Reference [4] [1] [1] [1] [1] The vlues provided in Tble 2 re inserted into Eqn. (8). This yields Al G1 N, (9) e31al G 1 N , e 31Al G1 N, (10, 11) 13Al G1 N, 33Al G1 N. (12, 13) Since the second ter is constntly negtive, it is cler tht E 0 under tensile strin, Al G1 N () > (0), nd E 0 under copressive strin, () < (0). 1 The totl sheet interfce bound chrge due to spontneous polriztion nd piezoelectric polriztion is given s Z Z. (14) TOTAL AlG N AlG1 AlG Siultion We hve focused on the effect of spontneous nd piezoelectric polriztion in rel etl//al/ heterostructure shown in Fig. 2. N 175

4 olriztion (/ 2 ) olriztion (/ 2 ) Metl (Au) 10n Al(25%-Al) 10n 2DEG AlN Spphire 1.2µ 20n 330n Fig. 2: Metl//Al/ heterostructure. The dependences of the gnitudes of spontneous nd piezoelectric polriztions of Al G 1 N on the olr frction of luiniu re shown in Fig. 3, nd the dependences of the totl polriztion under tensile nd copressive stress on the olr frction of luiniu re shown in Fig. 4. Due to the tensile stress induced chrge the bnd digr in therodynic equilibriu hs roof-shped xiu on the first /Al interfce, Fig. 5. This roof presents ighty brrier for the therionic eission-drift-diffusion electron current. This is why the siulted current densities of such structure re lower by ny orders of gnitude thn the experientlly observed vlues iezoelectrics polriztion opressive strin Spontneous polriztion Tensile strin Molr frction, ( - ) Molr frction, ( - ) Fig. 3: Dependences of spontneous (4) nd piezoelectric polriztions (7) on the olr frction of Al in Al G 1 N. Fig. 4: Dependences of the totl polriztion (14) under tensile nd copressive strin on the olr frction of Al in Al G 1 N. On pplying reverse voltge, the roof decreses nd finlly vnishes t V >1 V. However, if the spontneous nd piezoelectric polriztions re ntiprllel (the effect copressive stress), no roof-shped xiu is creted on the conduction bnd nd the siulted currents tch well with the experient, see Fig. 6. The further growth of the current is cused by the contribution of direct nd trp-ssisted tunnelling. For reverse voltges higher thn 1 V the contribution of tunnelling is higher thn tht of therionic eission-drift-diffusion. 176

5 Energy (ev) urrent density (A/c 2 ) Experientl current 1.5 Tensile strin opressive strin urrent with copressive strin urrent with tensile strin E Fn E c Distnce () Fig. 5: Bnd digr of etl//al/ structure in therodynic equilibriu under tensile nd copressive strin Voltge (V) Fig. 6: oprison of siulted reverse currents of etl//al/ structure under tensile nd copressive strin with experientl dt (circles) obtined t T=300 K. 4. onclusion A question rises bout the orienttions of spontneous nd piezoelectric polriztions. According to literture [3-5], Al lyers grown on buffers re lwys under tensile strin. Our siultions tch with the experientlly obtined I-V curves only under ssuption of copressive strin [6]. Acknowledgent The work hs been supported by projects VEGA 1/0651/16 nd AVV References [1] S. Vitnov: Siultion of high electron obility trnsistors, hd Thesis, TU Wien, Austri (2010). [2] F. Bernrdini, V. Fiorentini, D. Vnderbilt: hysicl Review B 63, (2001). [3] O. Abcher, B. Foutz, J. Srt, J.R. Shely, J.R. Weinn, K. hu, M. Murphy, A.J. Sierkowski, W.J. Schff, L.F. Estn: Journl of Applied hysics 87, 334 (2000). [4]. Ellinghus: Siultion of /Al heterostructures for HEMT siultor, Mster Thesis in Mtheticl Engineering, University of L'Aquil, Itly (2011). [5] I. Suprydkin, K. Abgryn, D. Bzhnov, I. Mutigullin: hysic Sttus Solidi 11, 307 (2014). [6] J. Rcko,. Benko, M. Mikolášek, R. Grnzner, M. Kittler, F. Schwierz, L. Hrth, J. Brez: Applied Surfce Science 395, 122 (2017). 177

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