The role of dislocation-induced scattering in electronic transport in GaxIn1-xN alloys
© Donmez et al.; licensee Springer. 2012
Received: 16 July 2012
Accepted: 21 August 2012
Published: 31 August 2012
Electronic transport in unintentionally doped GaxIn1-xN alloys with various Ga concentrations (x = 0.06, 0.32 and 0.52) is studied. Hall effect measurements are performed at temperatures between 77 and 300 K. Temperature dependence of carrier mobility is analysed by an analytical formula based on two-dimensional degenerate statistics by taking into account all major scattering mechanisms for a two-dimensional electron gas confined in a triangular quantum well between GaxIn1-xN epilayer and GaN buffer. Experimental results show that as the Ga concentration increases, mobility not only decreases drastically but also becomes less temperature dependent. Carrier density is almost temperature independent and tends to increase with increasing Ga concentration. The weak temperature dependence of the mobility may be attributed to screening of polar optical phonon scattering at high temperatures by the high free carrier concentration, which is at the order of 1014 cm−2. In our analytical model, the dislocation density is used as an adjustable parameter for the best fit to the experimental results. Our results reveal that in the samples with lower Ga compositions and carrier concentrations, alloy and interface roughness scattering are the dominant scattering mechanisms at low temperatures, while at high temperatures, optical phonon scattering is the dominant mechanism. In the samples with higher Ga compositions and carrier concentrations, however, dislocation scattering becomes more significant and suppresses the effect of longitudinal optical phonon scattering at high temperatures, leading to an almost temperature-independent behaviour.
KeywordsGaxIn1-xN In-rich GaxIn1-xN Mobility Electronic transport 72.10.Fk 72.20.Fr
In the last decade, after the revision of the band gap energy from 1.9 to approximately 0.7 eV, intensive research has been carried out on InN and In-rich GaxIn1-xN alloys in order to re-determine the fundamental properties[2–4]. Despite much interest on the optical properties of InN and GaxIn1-xN[5, 6], there has been a relatively small number of investigations to explain temperature-dependent electronic transport properties in GaxIn1-xN alloys[7, 8].
In this article, we report the electronic transport properties of nominally undoped GaxIn1-xN alloys with different Ga concentrations (x = 0.06, 0.32 and 0.52). Hall effect results show that all the alloys are highly n-type, and the free carrier concentrations are independent of temperature.
The samples with different Ga concentrations (x = 0.06, 0.32 and 0.52) were grown by a Varian GEN-II gas source molecular beam epitaxy chamber on (0001) c-sapphire substrates with a 200-nm-thick GaN buffer layer. The growth temperature was varied from low to high with increasing Ga composition[9, 10]. The thickness of the GaxIn1-xN layer was determined from the growth parameters and verified by backscattering spectrometry at nearly 500 nm. The GaxIn1-xN samples were fabricated in Hall-bar geometry, and ohmic contacts were formed by diffusing Au/Ni alloy. Hall effect measurements were carried out at temperatures between 77 and 300 K.
Modelling of carrier mobility
High-frequency dielectric constant
Static dielectric constant
Electron effective mass
Density of crystal
Electron wave vector at Fermi level
The electromechanical coupling coefficient
Occupied volume by an atom
The formulas of major scattering mechanisms used in 2DEG mobility calculations
Definition of variables
K, electromagnetic coupling coefficient; JPE(k), electron wave vector dependent integral.
ρ, crystal density; v s , longitudinal acoustic phonon velocity; Ξ, deformation potential constant; m*, electron effective mass; JDP(k), electron wave vector dependent integral. b, Fang-Howard expression; qs, reciprocal screening length; f(0), occupation probability; F11(q), ground-state Fang-Howard wave function.
, polar optical phonon energy; and, high- and low-frequency dielectric constant; Z0, effective width of triangular well formed at the GaxIn1-xN/GaN interface and is given in terms of Fermi wave vector.
Δ, lateral size of the roughness; Λ, correlation length between fluctuations; JIFR(k), correlation length and the lateral size-dependent integral; n2D, 2D electron density.
x, Ga fraction; Ω0, the volume occupied by one atom; UA, alloy potential.
NDis, dislocation density per unit area which is taken as a fitting parameter; λD, Debye screening length; c, lattice constant of GaxIn1-xN. f, the fraction of filled traps that are assumed fully occupied.
Results and discussions
Modelling of temperature dependence of mobility
In order to understand fully the temperature dependence of electron mobility, we compared the experimental mobility results with analytical theoretical models by taking into account all the possible scattering mechanisms. At low temperatures, the dominant scattering mechanism in bulk semiconductors is ionized impurity scattering that changes with temperature as T3/2. However, this kind of temperature dependence has not been observed in our samples. The samples have metallic-like characteristics, confirming the formation of a high-density 2DEG at both the GaN/GaxIn1-xN interface and on the GaxIn1-xN surface[26, 27]. The dominant momentum relaxation mechanism is the electron-optical phonon scattering in GaxIn1-xN since it is a highly polar material above T > 150 K[34–36].
The values of the parameters used in the calculations
Dislocation density (×1010 cm−2)
1.4 (four monolayer)
3.4 (ten monolayer)
Ga0.52 In0.48 N
3.4 (ten monolayer)
In this paper, we have investigated electronic transport properties of nominally undoped In-rich GaxIn1-xN structures with different Ga concentrations. Hall effect results show that 2DEG mobility in GaxIn1-xN decreases and becomes temperature insensitive with increasing Ga concentrations. The samples are not intentionally doped, but they all have n-type conductivity. Electron density increases with increasing Ga composition. The temperature dependence of electron mobility is determined by taking into account all the major scattering mechanisms. The decrease of the electron mobility with Ga concentration is explained in terms of increased dislocation scattering. The weak temperature dependence of the mobility at high temperatures might be associated with reduced electron-optical phonon scatterings. Alloy and interface roughness scattering mechanisms are dominant at low temperatures. In samples with higher Ga fractions, dislocation scattering becomes more significant, and at high temperatures, phonon scattering is restricted due to increase of dislocation density. At high temperatures, phonon scattering is only pronounced in the samples with low electron densities.
longitudinal optical phonon
longitudinal acoustic phonon
two-dimensional electron gas
transmission electron microscopy
This work was supported by Scientific Projects Coordination Unit of Istanbul University with Project Number BYP 25027. We also acknowledge the partial support from Republic of Turkey, Ministry of Development. (Project Number: 2010 K121050).
- Wu J, Walukiewicz W, Yu KM, Ager JW III, Aller EE, Lu H, Schaff WJ, Saito Y, Nanishi N: Unusual properties of the fundamental band gap of InN. Appl Phys Lett 2002, 80: 3967–3969. 10.1063/1.1482786View Article
- Wu J, Walukiewicz W: Band gaps of InN and group III nitride alloys. Superlattices Microstruct 2003, 34: 63–75. 10.1016/j.spmi.2004.03.069View Article
- Bechstedt F, Furthmüller J, Ferhat M, Teles LK, Scolfaro LMR, Leite JR, Davydov VY, Ambacher O, Goldhahn R: Energy gap and optical properties of InxGa1 –xN. Phys Status Solidi A 2003, 195: 628–633. 10.1002/pssa.200306164View Article
- Monemar B, Paskova PP, Kasic A: Optical properties of InN—the bandgap question. Superlattices Microstruct 2005, 38: 38–56. 10.1016/j.spmi.2005.04.006View Article
- Walukiewicz W, Li SX, Wu J, Yu KM, Ager JW III, Haller EE, Lu H, Schaff WJ: Optical properties and electronic structure of InN and In-rich group III-nitride alloys. J Cryst Growth 2004, 269: 119–127. 10.1016/j.jcrysgro.2004.05.041View Article
- Hsu L, Jones RE, Li SX, Yu KM, Walukiewicz W: Electron mobility in InN and III-N alloys. J Appl Phys 2007, 102: 073705–073710. 10.1063/1.2785005View Article
- Lin SK, Wu KT, Huang CP, Liang CT, Chang YH, Chen YF, Chang PH, Chen NC, Chang CA, Peng HC, Shih CF, Liu KS, Lin TY: Electron transport in In-rich InxGa1 –xN films. J Appl Phys 2005, 97: 046101. 10.1063/1.1847694View Article
- Gunes M, Balkan N, Zanato D, Schaff WJ: A comparative study of electrical and optical properties of InN and In0.48 Ga0.52N. Microelectron J 2009, 40: 872–874. 10.1016/j.mejo.2008.11.020View Article
- Liliental-Weber Z, Zakharov DN, Yu KM, Ager JW III, Walukiewicz W, Haller EE, Lu H, Schaff WJ: Compositional modulation in InxGa1−xN: TEM and X-ray studies. J Electron Microsc 2005, 54: 243–250. 10.1093/jmicro/dfi033View Article
- Tiras E, Gunes M, Balkan N, Schaff WJ: In rich In1−xGaxN: composition dependence of longitudinal optical phonon energy. Phys Status Solidi B 2010, 247: 189–193. 10.1002/pssb.200945144View Article
- Zanato D, Gokden S, Balkan N, Ridley BK, Schaff WJ: The effect of interface-roughness and dislocation scattering on low temperature mobility of 2D electron gas in GaN/AlGaN. Semicond Sci Technol 2004, 19: 427–432. 10.1088/0268-1242/19/3/024View Article
- Veal TD, Piper LFJ, Phillips MR, Zareie MH, Lu H, Schaff WJ, McConville CF: Scanning tunnelling spectroscopy of quantized electron accumulation at InxGa1−xN surfaces. Phys Status Solidi A 2006, 203: 85–92. 10.1002/pssa.200563522View Article
- Morkoc H: Carrier Transport. Handbook of Nitride Semiconductors and Devices. Weinheim: Wiley; 2008:165–395.View Article
- Levinshtein M, Rumyantsev S, Shur M: Properties of Advanced SemiconductorMaterials: GaN, AlN, InN, BN, SiC, SiGe. Canada: Wiley; 2001.
- Ridley BK, Foutz BE, Eastman LF: Mobility of electrons in bulk GaN and AlxGa1 −xN/GaN heterostructures. Phys Rev B 2000, 61: 16862–16869. 10.1103/PhysRevB.61.16862View Article
- Hutson AR: Piezoelectric scattering and phonon drag in ZnO and CdS. J Appl Phys 1961, 32: 2287–2292. 10.1063/1.1777061View Article
- Ridley BK: The electron–phonon interaction in quasi-two-dimensional semiconductor quantum-well structures. J Phys C: Solid State Phys 1982, 15: 5899–5917. 10.1088/0022-3719/15/28/021View Article
- Hirakawa K, Sakaki H: Mobility of the two-dimensional electron gas at selectively doped n -type AlxGa1-xAs/GaAs heterojunctions with controlled electron concentrations. Phy Rev B 1986, 33: 8291–8303. 10.1103/PhysRevB.33.8291View Article
- Sun Y, Balkan N, Aslan M, Lisesivdin SB, Carrere H, Arikan MC, Marie X: Electronic transport in n- and p-type modulation doped GaxIn1−xNyAs1−y/GaAs quantum wells. J Phys Condens Matter 2009, 21: 174210–174217. 10.1088/0953-8984/21/17/174210View Article
- Kearney MJ, Horrell AI: The effect of alloy scattering on the mobility of holes in a quantum well. Semicond Sci Technol 1998, 13: 174–180. 10.1088/0268-1242/13/2/003View Article
- Ng HM, Doppalapudi D, Moustakas TD, Weimann NG, Eastman LF: The role of dislocation scattering in n-type GaN films. Appl Phys Lett 1998, 73: 821–823. 10.1063/1.122012View Article
- Abdel-Motaleb IM, Korotkov RY: Modeling of electron mobility in GaN materials. J Appl Phys 2005, 97: 093715–093721. 10.1063/1.1891278View Article
- Kundu J, Sarkar CK, Mallick PS: Calculation of electron mobility and effect of dislocation scattering in GaN. Semicond Phys, Quantum Elect & Optoelect 2007, 10: 1–3.
- Donmez O, Yilmaz M, Erol A, Ulug B, Arikan MC, Ulug A, Ajagunna AO, Iliopoulos E, Georgakilas A: Influence of high electron concentration on band gap and effective electron mass of InN. Phys Status Solidi B 2011, 248: 1172–1175. 10.1002/pssb.201000780View Article
- Look DC, Lu H, Schaff WJ, Jasinski J, Liliental-Weber Z: Donor and acceptor concentrations in degenerate InN. Appl Phys Lett 2002, 80: 258–261. 10.1063/1.1432742View Article
- Wang CX, Tsubaki K, Kobayashi N, Makimoto T, Maeda N: Electron transport properties in AlGaN/InGaN/GaN double heterostructures grown by metalorganic vapor phase epitaxy. Appl Phys Lett 2004, 84: 2313–2315. 10.1063/1.1690879View Article
- Thakur JS, Naik R, Naik VM, Haddad D, Auner GW, Lu H, Schaff WJ: Electron transport properties in AlGaN/InGaN/GaN double heterostructures grown by metalorganic vapor phase epitaxy. J Appl Phys 2006, 99: 023504–023508. 10.1063/1.2158133View Article
- Donmez O, Gunes M, Erol A, Arikan MC, Balkan N: High carrier concentration induced effects on the bowing parameter and the temperature dependence of the band gap of GaxIn1−xN. J Appl Phys 2011, 110: 103506–103511. 10.1063/1.3660692View Article
- Zanato D, Tiras E, Balkan N, Boland-Thoms A, Wah JY, Hill G: Momentum relaxation of electrons in InN. Phys Status Solidi C 2005, 2: 3077–3081. 10.1002/pssc.200460733View Article
- Ridley BK: Quantum Processes in Semiconductors. New York: Oxford University Press; 1999.
- Sun Y, Vaughan M, Agarwal A, Yilmaz M, Ulug B, Ulug A, Balkan N, Sopanen M, Reentilä O, Mattila M, Fontaine C, Arnoult A: Inhibition of negative differential resistance in modulation-doped n-type GaxIn1−xNyAs1−y/GaAs quantum wells. Phys Rev B 2007, 75: 205306–205316.View Article
- Su Y, Wen Y, Hong Y, Lee HM, Gwo S, Lin YT, Tu LW, Lui HL, Sun CK: Using hole screening effect on hole–phonon interaction to estimate hole density in Mg-doped InN. Appl Phys Lett 2011, 98: 252106–252108. 10.1063/1.3591974View Article
- Kirillov D, Lee H, Harris JS: Raman scattering study of GaN films. J Appl Phys 1996, 80: 4058–4062. 10.1063/1.363367View Article
- Thomsen M, Jönen H, Rossow U, Hangleiter A: Spontaneous polarization field in polar and nonpolar GaInN/GaN quantum well structures. Phys Status Solidi B 2001, 248: 627–631.View Article
- Feneberg M, Thonke K, Wunderer T, Lipski F, Scholz F: Piezoelectric polarization of semipolar and polar GaInN quantum wells grown on strained GaN templates. J Appl Phys 2010, 107: 103517–103522. 10.1063/1.3374704View Article
- Lu CJ, Bendersky LA, Lu H, Schaff WJ: Threading dislocations in epitaxial InN thin films grown on (0001) sapphire with a GaN buffer layer. Appl Phys Lett 2003, 83: 2817–2819. 10.1063/1.1616659View Article
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