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).
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