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We develop a new method to determine the edge and screw dislocation density in wurtzite n-GaN film. The method is to fit the van der Pauw variable temperature Hall-effect measurements with a analytic expression of low-field electron mobility in n-GaN. Our calculations take the comprehensive effect between the dislocation line and the shallow-donor defects as the main cause to depress the carrier mobility. Because of the crystal distortion near the dislocation line, the energy is so high that shallow-donor defects in the GaN crystal can be captured near the dislocation line. In other words, the shallow-donor defects distribute in lines along the dislocation line, but the shallow-donor defects along the screw and edge dislocation line have different energy levels. The shallow-donor defects take energy from lattice and the carrier, which is in relaxation process, then deliver the energy through ionizing. So, it is found that the following assumptions need to be made in order to obtain the model function for the mobility over a wide temperature range: i) there are 6 shallow-donor defect lines around one dislocation line; ii) two donor energy levels belonging to the screw and edge dislocation respectively must be taken into account; iii) the exchange energy between the carrier and the shallow-donor defect is ħωLO, the energy value of polar optical phonon. Under these assumptions, experiments indicate that our calculation function can fit the experimental curve best. The values of dislocation density from our model and others determined by x-ray diffraction or by chemical etching method are in good agreement, and the values of donor energy levels from our model and Rode iterative method to solve the Boltzmann equation are also in good accordance with each other. This method is applicable for the wurtzite n-GaN films grown by various preparation technologies under any condition, which is for the sample with the peak-mobility temperature about or under 200 K, not for the sample with the peak-mobility temperature about or above 300 K, which room-temperature mobility usually is about or less than 100 cm2/(V·s).
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Keywords:
- gallium nitride (GaN) /
- Hall mobility /
- dislocation density /
- rode iterative
[1] Kozodoy P, Ibbetson J P, Marchand H, Fini P T, Keller S, Speck J S, DenBaars S P, Mishra U K 1998 Appl. Phys. Lett. 73 975
[2] Stephen W K, Peter G B, Man H W, Erin C H K, Umesh K M, James S S 2012 Appl. Phys. Lett. 101 262102
[3] Heinke H, Kirchner V, Einfeldt S, Hommel D 2000 Appl. Phys. Lett. 77 2145
[4] Metzger T, Hopler R, Born E, Ambacher O, Stutzmann M, Stommer R, Schuster M, Gobel H, Christiansen S, Albrecht M, Strunk H P 1998 Philos. Mag. A 77 1013
[5] Ivantsov V, Volkova A 2012 Condens. Matter Phys. 18 4023
[6] Srikant V, Speck J S, Clarke D R 1997 J. Appl. Phys. 82 4286
[7] Zhang Y, Xie Z L, Wang J, Tao T, Zhang R, Liu B, Chen P, Han P, Shi Y, Zheng Y D 2013 Acta Phys. Sin. 62 056101 (in Chinese) [张韵, 谢自力, 王健, 陶涛, 张荣, 刘斌, 陈鹏, 韩平, 施毅, 郑有炓 2013 62 056101]
[8] Ibrahim M A M, Korotkov R Y 2005 J. Appl. Phys. 97 093715
[9] You J H, Lu J Q, Johnson H T 2006 J. Appl. Phys. 99 033706
[10] Weimann N G, Eastman L F, Doppalapudi D, Hock M N, Moustakas T D 1998 J. Appl. Phys. 83 3656
[11] Look D C, Sizelove J R 2001 Appl. Phys. Lett. 79 1133
[12] Look D C, Sizelove J R, Keller S, Wu Y F, Mishra U K, DenBaas S P 1997 Solid State Commun. 102 297
[13] Mavroidis C, Harris J J, Kappers M J, Humphreys C J, Bougrioua Z 2003 J. Appl. Phys. 93 9095
[14] Götz W, Romano L T, Krusor B S, Johnson N M, Molnar R 1996 J. Appl. Phys. Lett. 69 242
[15] Chen Z, Yuan H R, Lu D C, Sun X H, Wan S K, Liu X L, Han P D, Wang X H, Zhu Q S, Wang Z G 2002 Solid-State Electron. 46 2069
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[1] Kozodoy P, Ibbetson J P, Marchand H, Fini P T, Keller S, Speck J S, DenBaars S P, Mishra U K 1998 Appl. Phys. Lett. 73 975
[2] Stephen W K, Peter G B, Man H W, Erin C H K, Umesh K M, James S S 2012 Appl. Phys. Lett. 101 262102
[3] Heinke H, Kirchner V, Einfeldt S, Hommel D 2000 Appl. Phys. Lett. 77 2145
[4] Metzger T, Hopler R, Born E, Ambacher O, Stutzmann M, Stommer R, Schuster M, Gobel H, Christiansen S, Albrecht M, Strunk H P 1998 Philos. Mag. A 77 1013
[5] Ivantsov V, Volkova A 2012 Condens. Matter Phys. 18 4023
[6] Srikant V, Speck J S, Clarke D R 1997 J. Appl. Phys. 82 4286
[7] Zhang Y, Xie Z L, Wang J, Tao T, Zhang R, Liu B, Chen P, Han P, Shi Y, Zheng Y D 2013 Acta Phys. Sin. 62 056101 (in Chinese) [张韵, 谢自力, 王健, 陶涛, 张荣, 刘斌, 陈鹏, 韩平, 施毅, 郑有炓 2013 62 056101]
[8] Ibrahim M A M, Korotkov R Y 2005 J. Appl. Phys. 97 093715
[9] You J H, Lu J Q, Johnson H T 2006 J. Appl. Phys. 99 033706
[10] Weimann N G, Eastman L F, Doppalapudi D, Hock M N, Moustakas T D 1998 J. Appl. Phys. 83 3656
[11] Look D C, Sizelove J R 2001 Appl. Phys. Lett. 79 1133
[12] Look D C, Sizelove J R, Keller S, Wu Y F, Mishra U K, DenBaas S P 1997 Solid State Commun. 102 297
[13] Mavroidis C, Harris J J, Kappers M J, Humphreys C J, Bougrioua Z 2003 J. Appl. Phys. 93 9095
[14] Götz W, Romano L T, Krusor B S, Johnson N M, Molnar R 1996 J. Appl. Phys. Lett. 69 242
[15] Chen Z, Yuan H R, Lu D C, Sun X H, Wan S K, Liu X L, Han P D, Wang X H, Zhu Q S, Wang Z G 2002 Solid-State Electron. 46 2069
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