Experimental and Theoretical Analysis of the Hall-Mobility in N-Type Bulk 6H- and 4H-SiC
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r the cubic modification (3C-SiC) [9]. Similtar co thiis worx tie monbility-analysis of n-type 6H- and 4H-SiC bulk crystals grown by the Lely- or modified Lely-method presented in this study is based an extended version of the Rode-Nag iteration method [2], but modified to account for the specific conductivity-anisotropy [10] of these hexagonal polytypes. EXPERIMENT The investigated nitrogen doped n-type 611- and 4H-SiC samples (typical dimensions: 5 x .5x 0.5 mm 3 with the orientation of the basal plane perpendicular to the cristallographic c-axis) were cut from crystals grown by the Lely- (L) or modified Lely-method (ML). Further details of the SiC sublimation growth at the Materials Science Institute VI (Erlangen, Germany) can be found in [11]. Ohmic contacts at the four corners of the samples were prepared by vaporization of titanium, followed by an annealing step at 900°C for 10 min in vacuum. For the measurement of the electrical conductivity 0, and the Hall-constant RH at an magnetic field B of 0.42 T the van der Pauw [12] method was used. The electron density n = rH/(eIRHI) and the Hall-mobility PH = a'(B = 0)1RHI were calculated with the simplified assumption of the Hall-scattering factor rg = 1. Based on the number of hexagonal and cubic lattice sites the donor concentration ratios NVD(h) : ND(k) for 411- and 6H-SiC are 1 : 1 and 1 : 2, respectively. Hereby the energetic difference of the two cubic sites (kI k2 ) in 6H-SiC is too small to be seperated by Hall-measurement. The donor concentration ND = ND(h) + ND(k), the compensating acceptor concentration Ncomp and the ionization energies (AE(h), AE(k)) were determined by direct numerical fitting of the neutrality equation to the n(T) data. In the neutrality equation the temperature dependence of the effective density of states mass [1] was considered and the valley-orbit splitting of the 275 Mat. Res. Soc. Symp. Proc. Vol. 572 ©1999Materials Research Society
nitrogen ground-state [13. 14. 15] was taken into account by modifying the spin degeneracy factor accordingly [16]. The numerical fitting results for the samples of Fig.1 and Fig.2 are summarized in the following table: polytype
611
sample ML1 LI L2 ML4 ML5
ND [cm- 3]
Nc,,mp [cm-3]
2.3 x I0'V
2.9 x 10' 4.0 x 10 17 1.4 x 10"5 6.7 x 1016 11. x 10"'
3.2 x 10" 7.8 x 10' 1.5 x i017 3.8 x I0'
AE(k) [meY] 119 112 101 109 98
AE(h) [meV] 94 77 72 51 53
The dependency of the activation energies from the doping concentrations can be understood within the theory of the formation and broadening of a donor impurity band [17]. Due to the comparatively high donor binding energies in SiC the mechanism of Hopping-conductivity
[17] becomes important at relatively high temperatures of 40-75K, depending on doping and compensation. Connected to this is the high temperature dependence of PH (Fig.1 and Fig.2) in this temperature regime [18], where the theoretical interpretation within the formalism of the Boltzmann-equation used in the following chapter is not valid. From the Hall-analysis of a series of n-type bu
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