Sign of Hall coefficient in nearest-neighbor hopping conduction in heavily Al-doped p-type 4H-SiC

We have observed negative Hall coefficients [RH(T)] in a nearest-neighbor hopping (NNH) conduction region in epilayers of heavily Al-doped or Al–N co-doped p-type 4H-SiC grown on n-type 4H-SiC substrates by CVD or in wafers of heavily Al–N co-doped p-type 4H-SiC fabricated by solution growth. We propose a simple physical model to explain the sign of RH(T) in NNH conduction. According to this model, RH(T) becomes positive when the Fermi level (EF) is higher than the Al acceptor level (EAl), that is, the Fermi–Dirac distribution function f(EAl) is greater than 0.5, whereas RH(T) becomes negative when EF is lower than EAl, which occurs at low temperatures. Because the dominant conduction mechanisms in heavily Al-doped or Al–N co-doped p-type 4H-SiC with Al concentrations on the order of 1019 cm−3 are band and NNH conduction at high and low temperatures, respectively, the proposed model can explain why RH(T) becomes negative at low temperatures.


Introduction
The on-resistance of SiC n-channel insulated-gate bipolar transistors (IGBTs) is considerably lower than that of commercially available SiC n-channel metal-oxide-semiconductor field-effect transistors. To obtain excellent SiC IGBTs, it is crucial to fabricate thick p-type SiC substrates to serve as IGBT collectors with low resistance and high crystalline quality. [1][2][3] Understanding the underlying conduction mechanisms is essential for reducing the resistance of these materials. Electrical transport properties have been reported for thin heavily Al-implanted 4H-SiC layers with Al concentrations (C Al ) of 10 19 -10 21 cm −3 , 4-7) thick Al-doped 6H-SiC wafers with C Al values of ⩽ 1.6 × 10 19 cm −3 , 8,9) and Al-doped 4H-SiC epilayers. 10) We have also investigated the temperature dependence of resistivity [ρ(T)] for thick Al-doped 4H-SiC epilayers with C Al values between 2.4 × 10 19 and 4.7 × 10 20 cm −3 . 11-16) Based on ρ(T) for heavily Al-doped 4H-SiC epilayers, we found that in epilayers with C Al values of ⩽ 1.5 × 10 20 cm −3 , the dominant conduction mechanisms at high and low temperatures were band and nearest-neighbor hopping (NNH) conduction, respectively; 12,13) in an epilayer with C Al of 1.8 × 10 20 cm −3 , the dominant conduction mechanisms at high and low temperatures were band and variable-range hopping (VRH) conduction, respectively; 15) and in epilayers with C Al values of ⩾ 2.4 × 10 20 cm −3 , the dominant conduction mechanism was VRH conduction over the entire range of measurement temperatures examined. 12,13) Krieger et al. 8) reported that in Al-doped 6H-SiC wafers with C Al of 1.6 × 10 19 cm −3 , the temperature dependence of the Hall coefficient [R H (T)] had a maximum at approximately 160 K, which was explained by the two-band model. 17) Although Al-doped SiC is p-type, which usually implies that R H (T) > 0, the sign of R H (T) in the hopping conduction region changed from positive to negative at approximately 75 K. We have investigated R H (T) for approximately 90 μm thick epilayers of Al-doped p-type 4H-SiC with C Al values between 2.4 × 10 19 and 1.8 × 10 20 cm −3 , grown on n-type 4H-SiC substrates by chemical vapor deposition (CVD). 14,16) We found that R H (T) became negative not only in the hopping conduction region, but also in the band conduction region, 14,16) in contrast to the results of Krieger et al. on 6H-SiC. 8) Krieger et al. 8) considered that negative R H (T) in NNH conduction might be explained by the models for amorphous semiconductors proposed by Emin 18) and Grunewald et al. 19) However, Street insisted that the models can be applied to narrow-bandgap materials or materials in which the mobility edge is at the center of the band; however, the conduction in hydrogenated amorphous silicon (a-Si:H) is near the band edge. 20) Sign reversal of R H (T) is observed in a-Si:H, but the correct sign is found in microcrystalline silicon in which the grain size is as small as 3-5 nm. 20) These findings suggest that their models cannot be applied to Aldoped p-type SiC. The Hall effect for hopping conduction has been theoretically considered by Holstein, 21) Németh and Mühlschlegel, 22) and Gal'perin et al. 23) An impurity Hubbard-band model 24) can be used to describe the complicated behavior of R H (T) in group-IV elemental semiconductors of p-type Ge, 25) n-type Ge, 26) and n-type Si, 27) as well as that in III-V compound semiconductors of n-type GaAs 28) and n-type InP. 29) However, the Hall effect for hopping conduction is not yet well understood and the sign inversion of R H (T) in these crystalline semiconductors has not been observed and discussed. The sign inversion of R H (T) has been observed in heavily Al-doped p-type SiC at low temperatures, 8,14,16,30) which might arise from a deep Al acceptor level (E Al ). 31) In this study, we propose a simple physical model to explain negative R H (T) in the NNH conduction region at low temperatures in p-type SiC.

Experimental
A 90 μm thick Al-doped 4H-SiC epilayer and a 7.95 μm thick Al-N co-doped 4H-SiC epilayer were grown using a horizontal hot-wall CVD system (VP508 GFR, Aixtron) at approximately 1620°C on (0001)-oriented 3 inch n-type 4H-SiC substrates (8°off-orientation toward 1120 [¯]). 1,3,11) The depletion layer formed by the pn junction electrically isolates the p-type 4H-SiC epilayer from the n-type 4H-SiC substrate, thus enabling measurement of the electrical properties of the heavily Al-doped or Al-N co-doped epilayer. Thick Al-N codoped 4H-SiC bulk was grown on an on-axis (0001)-oriented 18 mm diameter 4H-SiC substrate at a seed crystal temperature of approximately 2020°C under a He-N 2 atmosphere by solution growth (SG). 32,33) A 368 μm thick wafer was obtained by slicing the bulk. Because this wafer was free-standing ptype 4H-SiC, we could measure its electrical properties. Four Al/Ti/Al contact dots in the van der Pauw configuration 34) were deposited on the four corners of the 5 × 5 mm samples by electron beam evaporation of Al and Ti, and the samples were annealed at 1000°C under a N 2 atmosphere. The Aldoped sample grown by CVD was obtained with C Al of 3.4 × 10 19 cm −3 . The C Al and N concentration (C N ) values of the Al-N co-doped sample grown by CVD were 3.9 × 10 19 and 8.8 × 10 18 , and those of the sample grown by SG were 6.7 × 10 19 and 8.8 × 10 18 cm −3 , respectively. Here, the values of C Al and C N were determined by secondary-ion mass spectrometry. Using a Hall-effect measurement system (ResiTest8400, TOYO Corporation), the ρ(T) values of the samples were measured by the van der Pauw method and their R H (T) values were measured under an AC magnetic field of 0.35 T and 0.05-0.25 Hz, in the temperature range of 60-300 K. The techniques used to obtain reliable ρ(T) and R H (T) values have been described in our previous papers. 13,14) 3. Results and discussion  Figure 2 shows R H (T) for the Al-N co-doped 4H-SiC epilayer grown on the n-type 4H-SiC substrate by CVD with C Al and C N values of 3.9 × 10 19 and 8.8 × 10 18 cm −3 , respectively. The value of T inv is 135 K, and the peak for positive R H (T) is at ∼200 K. Figure 3 shows R H (T) for the Al-N co-doped 4H-SiC wafer grown by SG with C Al and C N values of 6.7 × 10 19 and 8.8 × 10 18 cm −3 , respectively. The value of T inv is 167 K, and the peak for positive R H (T) is at ∼230 K.
We observed the negative R H (T) values at low temperatures for the Al-doped and Al-N co-doped p-type 4H-SiC epilayers grown on n-type 4H-SiC substrates by CVD as well as for the Al-N co-doped p-type 4H-SiC wafer fabricated by SG, indicating that the appearance of negative R H (T) in ptype 4H-SiC, which were also reported in our early papers, [12][13][14][15][16] originated from p-type 4H-SiC epilayers, not from n-type 4H-SiC substrates, and was independent of N codoping. Consequently, we could confirm that the depletion layer formed by the pn junction electrically isolated the ptype 4H-SiC epilayer from the n-type 4H-SiC substrate.    is approximated by two straight lines (shown as broken and solid lines). The temperature at which the two straight lines cross is referred to as T BH .
According to the multiple parallel conduction model, 16 where R HBand (T), R HNNH (T), and R HVRH (T) are the Hall coefficients corresponding to band, NNH, and VRH conduction, respectively. Because the density of localized states   around E F is low owing to the high crystalline quality of the epilayers with C Al values of < 2 × 10 20 cm −3 , ρ VRH (T) is much higher than ρ Band (T) and ρ NNH (T), 12,15) which is consistent with the plots of r -T T ln 1 ( ) in Figs. 4-6. This indicates that ρ(T)/ρ VRH (T) in Eq. (5) is negligibly small in these samples. Consequently Figs. 4-6 reached a peak around T BH and became negative in the NNH conduction region, which can be explained using Eq. (6) if R HNNH (T) is negative. Therefore, we propose and discuss a simple physical model to explain why R T HNNH ( ) becomes negative at low temperatures. Thus, for a force produced by an electric field, it is difficult to distinguish the contribution of holes to I NNH from the contribution of electrons to I NNH .
The inset in Fig. 7(b) shows the direction of the Lorentz force (F) for moving charged carriers in the case of a left-toright flowing current (I) and a magnetic flux density (B) directed toward the back of the plane. The Hall effect for hopping conduction is not well understood. 28) Therefore, assuming that hopping holes and electrons in I NNH are forced into the same direction as the Lorentz force, Fig. 7(b) shows the direction of movement of a hole and an electron in NNH conduction with B directed toward the back of the plane described in a real space. In I NNH , holes as well as electrons are forced to the upper direction under B. Therefore, B makes flowing holes hop to upper nearest-neighbor Al − sites and makes flowing electrons hop to upper nearest-neighbor Al 0 sites, indicating that holes and electrons travel in the same direction. For a force produced by a magnetic field, it is possible to distinguish the contribution of holes to the Hall voltage [V HNNH (T)] produced by I NNH , from the contribution of electrons to V HNNH (T). Figure 8(a) shows the van der Pauw configuration of the Hall-effect measurement system, where W is the thickness of the sample, and four electrodes (Electrodes 1-4) are positioned at the four corners of the sample. I NNH flows from Electrode 1 to Electrode 3, and V HNNH (T) is measured between Electrodes 4 and 2. Analogous to the Hall voltage for band conduction in the van der Pauw configuration, 47) V HNNH (T) is described as HNNH HNNH NNH ( ) ( ) ( ) Figure 8(b) shows the equivalent circuit for the measured V HNNH (T), where V Hh (T) and V He (T) are the Hall voltages due to holes and electrons, respectively, and r NNH (T) is the resistance between Electrodes 2 and 4 due to NNH conduction, and is described as