Comparison of temperature-dependent resistivity of heavily Al- and N-codoped 4H-SiC grown by physical vapor transport and heavily Al-doped 4H-SiC grown by chemical vapor deposition

The temperature-dependent resistivity of heavily Al- and N-codoped 4H-SiC grown by physical vapor transport (PVT) with Al concentrations (C Al) higher than 1019 cm−3 is investigated to obtain high-growth-rate and low-cost p+-type substrates suitable for the collectors of n-channel insulated-gate bipolar transistors. The resistivity is compared with that of heavily Al-doped 4H-SiC grown by CVD. In the band conduction region, the hole mobility of the PVT-grown codoped samples is slightly lower than that of the CVD-grown sample at the same C Al. At C Al values of around 2 × 1020 cm−3, the temperature range in the variable-range-hopping conduction region for the PVT-grown codoped samples is much wider than that for the CVD-grown samples.

Four Al/Ti/Al contact dots in the van der Pauw configuration 23) were deposited by electron-beam evaporation of Al and Ti.The sample was annealed at 1000 °C under a N 2 atmosphere.
Using a Hall-effect measurement system (ResiTest8400, TOYO), the ρ(T) values of the samples were measured by the van der Pauw method and their temperature-dependent Hallcoefficient [R H (T)] values were measured under an AC magnetic field of 0.35 T and 0.05-0.25 Hz.The techniques used to obtain reliable ρ(T) and R H (T) values have been described in our previous papers. 14,16)The hole concentration in the VB [p(T)] is determined by 24) ( ) ( ) where γ is the Hall scattering factor and is assumed to be 1 here.The hole mobility in the VB [μ h (T)] is estimated by 24) ( ) The X-ray diffraction (XRD) patterns (i.e.θ − 2θ patterns) were measured by using a high-resolution XRD system (SLX-2000, RIGAKU).6][27][28][32][33][34][35][36][37] If the currents due to band, NNH, and VRH conduction flow in parallel in the VB, at an Al acceptor level (E Al ), and around E F , respectively, the overall temperature-dependent resistivity [i.e. ρ(T)] can beexpressed as

Results and discussion
where ρ Band (T), ρ NNH (T), and ρ VRH (T) are the temperaturedependent resistivities for band, NNH, and VRH conduction, respectively; ρ Band0 , ρ NNH0 , and ρ VRH0 are the pre-exponential factors for band, NNH, and VRH conduction, respectively; ΔE Band and ΔE NNH are the activation energies for band and NNH conduction, respectively; T 0 is the constant for VRH conduction; and k B is the Boltzmann constant.Equation (3) shows that the lowest resistivity becomes dominant at a given value of T. In Fig. 2, the ( ) r -T T ln 1 data can be approximated by two straight lines (solid and broken lines).At high temperatures, band conduction is dominant because p(T) becomes very large, whereas at low temperatures hopping conduction becomes dominant because p(T) becomes very low.Thus, from Eqs. ( 4) and ( 8), the dominant conduction mechanisms at high and low temperatures are band and NNH conduction,  respectively.Therefore, at 300 K, the conduction mechanisms of CVD-grown samples and PVT-grown codoped samples with C Al values of around 2 × 10 19 cm −3 are band conduction.
The hole concentration in the VB at 300 K [p(300)] for the PVT-grown codoped sample with C Al of 3.0 × 10 19 cm −3 and C N of 2.9 × 10 18 cm −3 is 1.4 × 10 18 cm −3 , whereas the p(300) values are 1.2 × 10 18 and 2.3 × 10 18 cm −3 for the CVD-grown samples with C Al values of 2.4 × 10 19 and 3.4 × 10 19 cm −3 , respectively.Although the p(300) value of the PVT-grown codoped sample is higher than that of the CVD-grown sample with C Al of 2.4 × 10 19 cm −3 , the ρ(300) value of the PVT-grown codoped sample is not lower than that of the CVD-grown sample.This result indicates that μ h (T) of the PVT-grown codoped sample should be lower than that of the CVD-grown sample.The hole mobility in the VB at 300 K [μ h (300)] for this PVT-grown codoped sample is estimated to be 11 cm 2 /(V•s), whereas the μ h (300) values are evaluated as 20 and 13 cm 2 /(V•s) for the CVD-grown samples with C Al values of 2.4 × 10 19 and 3.4 × 10 19 cm −3 , respectively.
In Fig. 2, the ρ(T) values at low temperatures for the PVT-grown codoped sample are much lower than those for the CVD-grown samples, similar to the values for CVD-grown Al-and N-codoped epilayers. 14)ρ NNH (T) can be expressed as 15,18,21) At low temperatures, E F is located between E Al and E V , 38,39) and then f (E Al ) becomes much less than 1, indicating that The capture of holes emitted from Al acceptors by N donors makes E F larger and shifts it toward E Al , indicating that, at the same C Al , f (E Al ) for the Al-and N-codoped sample becomes much larger than that for the Al-doped sample.According to Eq. ( 8), ρ NNH (T) of the Al-and N-codoped sample becomes much lower than that of the Al-doped samples.Therefore, ρ NNH (T) of the PVT-grown Al-and N-codoped sample with C Al of 3.0 × 10 19 and C N of 2.9 × 10 18 cm −3 is much lower than those of the CVD-grown Al-doped samples with C Al values of 2.4 × 10 19 and 3.4 × 10 19 cm −3 owing to the N codoping [Fig.2].
For SiC power electronic devices, it is important to investigate the resistivity at the operating temperature, that is, around 500 K. Figure 3  The ρ(500) values of the PVT-grown codoped samples as a function of (C Al − C N ) are denoted by ▪.In contrast to ρ(300), the ρ(500) values of the PVT-grown codoped samples are still higher than those of the CVD-grown samples.This is because the hole mobility in the VB at 500 K [μ h (500)] of the PVT-grown codoped sample is lower than that of the CVD-grown sample.The μ h (500) values for the PVT-grown codoped samples with C Al values of 1.7 × 10 20 and 1.8 × 10 20 cm −3 are estimated to be 1.5 and 1.2 cm 2 /(V•s), respectively, whereas the μ h (500) values are evaluated as 4.2 and 2.1 cm 2 /(V•s) for the CVD-grown samples with C Al values of 9.6 × 10 19 and 1.8 × 10 20 cm −3 , respectively.
We discuss the scattering mechanisms in Al-doped samples as well as in the Al-and N-codoped samples.Figure 4 shows the temperature dependence of μ h (T) for the CVD-grown samples with C Al values of 9.6 × 10 19 and 1.8 × 10 20 cm −3 (△ and □, respectively), and for the PVT-grown codoped sample with C Al of 1.7 × 10 20 cm −3 and C N of 1.1 × 10 20 cm −3 (▪).The broken line is a visual guide for the slope of μ h (T) from the interaction with the lattice acoustic phonon [μ ac (T)], which is described as 40) ( ) ( ) m µ - T T .9 ac 3 2 As T increases toward 1000 K, μ h (T) for all the samples approaches μ ac (T).In Fig. 4, the dashed-dotted line is a visual guide for the slope of μ h (T) due to the ionized impurity scattering [μ ii (T)], which is described as 40)     Let us discuss what affects the slope of the Mott plot, namely, T 0 in Eq. ( 6).As C Al increases, the crystallinity of 4H-SiC becomes worse, which probably results in the appearance of VRH conduction. 15)VRH conduction is caused by the hopping of charge carriers around E F , indicating that localized states exist around E F .T 0 in Eq. ( 6) is expressed as 41) ( ) where g(E F ) is the density of localized states at E F , α is the localization radius of localized states around E F , and β is a numerical constant.These localized states could be a bandtail, which probably results from the local disturbance of the periodicity of the lattice. 42)e investigate the disturbance of the (0001) (i.e.c-plane) lattice constant (d c ) using XRD.
Figure 7 shows the dependence of FWHM corresponding to d c for the CVD-grown samples (•) and the PVT-grown  codoped samples (•) on C Al .The FWHM the CVD-grown samples increase with increasing C Al , and increase steeply over C Al of around 1.5 × 10 20 cm −3 .Here, the broken lines in Fig. 7 are visual guides for the C Al dependencies of FWHM.The high level of Al doping disturbs the periodicity of the 4H-SiC lattice because the covalent radius of a substitutional Al atom (0.125 nm) is larger than that of a Si atom (0.117 nm). 2)This difference explains why the values of FWHM increase with increasing C Al for the CVD-grown 4H-SiC, creating the bandtail.Because E F has been reported to be located between E V and E Al in heavily Al-doped 4H-SiC, 38,39) there must be localized states around E F .Therefore, according to Eq. ( 3), above C Al of 1.7 × 10 20 cm −3 , VRH conduction should become dominant at low temperatures.As C Al increases, g(E F ) increases and ρ VRH (T) decreases.Consequently, the highest temperature in the VRH conduction region shifts up to RT, where E F was reported to be located between E V and E Al in heavily Aldoped 4H-SiC even at high temperatures. 38,39)As a result, the FWHM value corresponding to d c is one of the parameters for the appearance of ρ VRH (T) for CVD-grown Al-doped samples.
In Fig. 7, the FWHM values corresponding to d c for the PVT-grown codoped samples are close to those for the CVD-grown samples, suggesting that g(E F ) for the PVT-grown codoped sample might be close to that for the CVD-grown sample.Therefore, according to Eq. ( 11), the slope of the Mott plot in the VRH conduction region for the PVT-grown codoped sample should be close to that for the CVD-grown sample.However, the slope of the Mott plot in the VRH conduction region for the PVT-grown codoped sample with C Al of 1.7 × 10 20 cm −3 is much gentler than that for the CVD-grown sample with C Al of 1.8 × 10 20 cm −3 , whereas the slope is close to that of the CVD-grown sample with C Al of 3.5 × 10 20 cm −3 .This finding suggests that g(E F ) of the PVT-grown Al-and N-codoped sample with C Al of 1.7 × 10 20 cm −3 and C N of 1.1 × 10 20 cm −3 is close to that of the CVD-grown Al-doped sample with C Al of 3.5 × 10 20 cm −3 .

Summary
We investigated the conduction mechanisms in PVT-grown Al-and N-codoped 4H-SiC samples compared with CVD-grown Al-doped samples to obtain low-cost p -type substrates for the collectors of n-channel IGBTs.Here, the codoping of N is necessary to stabilize the 4H-SiC polytype for the heavily Al-doped 4H-SiC grown by PVT.
In the band conduction region at the same C Al , the ρ(T) values of PVT-grown codoped samples were slightly higher than those of CVD-grown samples.This is partially because the density of holes from Al acceptors in the VB decreased owing to the capture of holes by all the N donors, which eventually became positively ionized donors, and partially because the μ h (T) values of the PVT-grown codoped samples became lower than those of the CVD-grown samples owing to the ionized impurity scattering of positively ionized N donors in addition to negatively ionized Al acceptors.
The temperature range in the VRH conduction region for the PVT-grown codoped sample with C Al of 1.7 × 10 20 cm −3 became wider than that for the CVD-grown sample with similar C Al .From the slope of ( ) r -- T T ln 1 4 , the g(E F ) values of PVT-grown codoped samples were much larger than those of CVD-grown samples with similar C Al .

Figure 1
Figure 1 shows the dependence of resistivity at 300 K [ρ(300)] on C Al or (C Al − C N ).The ρ(300) values as a function of C Al of CVD-grown Al-doped samples are denoted by ◯, whereas those of PVT-grown Al-and N-codoped samples are denoted by ▴.The ρ(300) values of the CVD-grown samples decrease with increasing C Al at C Al < 2.5 × 10 20 cm −3 , and then become saturated.The ρ(300) values of the PVT-grown codoped samples with C Al values of around 2 × 10 20 cm −3 are much higher than those of CVD-grown samples with similar C Al , whereas those of the PVT-grown codoped samples with C Al values of around 2 × 10 19 cm −3 are slightly higher than those of the CVDgrown samples.Because the N donors completely capture the holes from the Al acceptors, N codoping decreases p(T) and the Fermi level (E F ) is shifted toward the midgap.The ρ(300) values as a function of (C Al − C N ) of the PVT-grown codoped samples (denoted by ▪) are similar to those of CVD-grown Al-doped samples at approximately 1 × 10 20 cm −3 in Fig. 1.At (C Al − C N ) values of around 2 × 10 19 cm −3 in Fig.1, the ρ(300) values for the PVT-grown codoped samples are still slightly higher than those for the CVD-grown samples.Figure2shows Arrhenius plots of ρ(T) for the CVD-grown samples with C Al values of 2.4 × 10 19 and 3.4 × 10 19 cm −3 (▿ and ◯, respectively), and for the PVT-grown codoped sample with C Al of 3.0 × 10 19 cm −3 and C N of 2.9 × 10 18 cm −3 (•).The well-known conduction mechanisms in semiconductors include band conduction, NNH conduction,9,10,[25][26][27][28][29][30][31][32] and VRH conduction.[26][27][28][32][33][34][35][36][37] I the currents due to band, NNH, and VRH conduction flow in parallel in the VB, at an Al acceptor level (E Al ), and around E F , respectively, the overall temperature-dependent resistivity [i.e. ρ(T)] can beexpressed as

Fig. 1 .
Fig. 1.Dependence of resistivity at 300 K on C Al or (C Al − C N ).The data for the CVD-grown samples are from Ref. 13.
shows the dependence of the resistivity at 500 K [ρ(500)] on C Al or (C Al − C N ).The ρ(500) values of the CVD-grown Al-doped epilayers as a function of C Al are denoted by ◯, whereas those of the PVT-grown Al-and N-codoped samples with C Al values of 1.7 × 10 20 and 1.8 × 10 20 cm −3 are denoted by ▴.The ρ(500) values of the PVT-grown codoped samples are much higher than those of the CVD-grown samples at similar C Al values.

Fig. 3 .
Fig. 3. Dependence of resistivity at 500 K on C Al or (C Al − C N ).

Fig. 4 .
Fig. 4. Hall mobility for 4H-SiC epilayers with C Al values of approximately 1 × 10 20 cm −3 .The broken line is a visual guide for the temperature dependence of μ h (T) due to acoustic phonon scattering.The dashed-dotted line is a visual guide for the temperature dependence of μ h (T) due to ionized impurity scattering.

where
N I is the total density of ionized impurities.As C Al increases, μ ii (T) at the same T value decreases owing to the increase of negatively ionized Al acceptors.μ h (T) of the Al-doped CVD-grown sample with C Al of 1.8 × 10 20 cm −3 is lower than that with C Al of 9.6 × 10 19 cm −3 [Fig.4].Here, μ h (T) of the sample with C Al of 9.6 × 10 19 cm −3 is affected by the ionized impurity scattering, although μ h (T) is plotted above 300 K because anomalous R H (T) values [e.g.negative R H (T)] appear below 300 K.17

, 21 )
Because N I is the sum of the density of negatively ionized Al acceptors and the density of positively ionized N donors, μ h (T) of the Al-and N-codoped PVT-grown sample with C Al of 1.7 × 10 20 cm −3 and C N of 1.1 × 10 20 cm −3 becomes lower than that of the CVD-grown Al-doped sample with C Al of 1.8 × 10 20 cm −3 .Figure 5 shows Arrhenius plots of ρ(T) for the CVD-grown samples with C Al values of 9.6 × 10 19 and 1.8 × 10 20 cm −3 (△ and □, respectively), and for the PVT-grown codoped sample with C Al of 1.7 × 10 20 cm −3 and C N of 1.1 × 10 20 cm −3 (▪).For the CVD-grown sample with C Al of 9.6 × 10 19 cm −3 (△), the ( ) r -T T ln 1 data can be approximated by two straight lines, indicating that the dominant conduction mechanisms at high and low temperatures are band and NNH conduction, respectively.For the CVD-grown sample with C Al of 1.8 × 10 20 cm −3 (□), the ( ) be approximated by a straight line, indicating that the dominant conduction mechanism above 70 K is band conduction.For the PVT-grown codoped sample with C Al of 1.7 × 10 20 cm −3 and C N of 1.1 × 10 20 cm −3 , the ( ) r -T T ln 1 data at ⩾380 K can be approximated by a straight line, suggesting that the dominant conduction mechanism at ⩾380 K is band conduction.In contrasttemperatures for the CVD-grown sample with C Al of 1.8 × 10 20 cm −3 (□) and the PVT-grown codoped sample (▪) cannot be approximated by a straight line [Fig.5]. Figure 6 shows Mott plots of ρ(T) for the CVD-grown samples with C Al values of 1.8 × 10 20 and 3.5 × 10 20 cm −3 (□ and ⋄, respectively), and for the PVT-grown codoped sample with C Al of 1.7 × 10 20 cm −3 and C N of 1.1 × 10 20 cm −3 (▪).The ( ) r -- T T ln 1 4 data at low temperatures can be approximated by a straight line, indicating that the dominant conduction mechanism at those temperatures is VRH conduction.Judging from Figs. 5 and 6, the conduction mechanisms for the CVD-grown samples with C Al of 1.8 × 10 20 cm −3 and the PVT-grown codoped sample with C Al of 1.7 × 10 20 cm −3 are band and VRH conduction at high and low temperatures, respectively.However, the temperature ranges in the VRH conduction regions are different from each other.For the CVD-grown sample with C Al of 1.8 × 10 20 cm −3 , VRH conduction appears below 70 K, whereas VRH conduction appears up to around RT for the PVT-grown codoped sample with C Al of 1.7 × 10 20 cm −3 and C N of 1.1 × 10 20 cm −3 .Moreover, the slopes of the Mott plots are different from each other.In the CVD-grown sample with C Al of 3.5 × 10 20 cm −3 and the PVT-grown codoped sample with C Al of 1.7 × 10 20 cm −3 and C N of 1.1 × 10 20 cm −3 , the temperature ranges in the VRH conduction regions are similar to each other, although the C Al value of the PVT-grown codoped sample is approximately half of that of the CVD-grown sample [Fig.6].

Fig. 7 . 5 ©
Fig. 7. Dependence of FWHM corresponding to d c on Al concentration.The broken lines are visual guides for the C Al dependencies of FWHM.