Abnormal Sign Behavior of Hall Coefficient in Al Heavily Doped P-Type 4H-SiC +

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Preparing heavily doped p-type substrates with low resistance and high crystal quality is one of the key technical challenges in the process of pursuing SiC N-channel insulated gate bipolar transistors (IGBTs) with lower on resistance. A deep understanding of the internal carrier conduction mechanism is the theoretical basis for optimizing material resistivity. However, in heavily aluminum(Al) doped p-type 4H-SiC, a phenomenon challenging traditional semiconductor physics cognition was observed experimentally: the Hall coefficient RH(T) exhibits negative values at low temperatures. This abnormal behavior not only occurs in the jump conduction region, but even extends to the conduction region that should be dominated by holes, becoming a core issue that must be addressed to understand its electrical transport characteristics. Matsuura et al. systematically analyzed the physical origin of the anomalous Hall coefficient sign behavior in p-type 4H-SiC.

1. Experimental Observation and Phenomena of Hall Coefficient of P-type 4H-SiC

In the 4H-SiC epitaxial layer doped with heavy Al, negative values of RH (T) were observed at low temperatures, not only in the nearest neighbor hopping conduction (NNH) and variable range hopping conduction (VRH) regions, but even in the band conduction region. With the increase of aluminum concentration C_Al, the sign reversal temperature Tinv1 of RH (T) significantly increases, reaching up to 187K. For example, when C_Al=1.8 × 10²⁰cm^-3, RH (T) is negative between 187K and 119K. This phenomenon also exists in Al-N co doped samples, indicating that it is not related to nitrogen co doping.

Fig. 1 Arrhenius of ρ (T) and ∣RH(T)∣ under different C_Al, showing the transition of conduction mechanism and the sign change of RH(T)

2. Physical Model of Negative Hall Coefficient in Conducting Regions

To explain the negative value of RH (T) in the conduction region, researchers proposed the “Allow Microstrip” model. Under heavy Al doping, the excited state wave functions of aluminum acceptors strongly overlap, forming a series of allowed microstrip lines. These microstrip lines have different curvatures in the energy momentum relationship: in the lower part of the microstrip line, ∂²E/∂k²>0, resulting in RH(T)<0; In the upper part of the microstrip and the valence band, ∂²E/∂k²<0, resulting in RH(T)>0. Holes occupy different energy regions at different temperatures, causing changes in RH(T) sign. For example, in the intermediate temperature range, holes mainly occupy the lower part of the first allowed microstrip, resulting in a negative RH(T).

Fig. 2 Schematic diagram of the density of states near the valence band of Al doped 4H-SiC. The density of states N(E) distribution of heavily aluminum doped p-type 4H-SiC near the valence band top (EV) proposed by the theoretical model. This model introduces an allowable microstrip formed by aluminum acceptor excited states and divides it into three regions: region (I) is the valence band with a positive Hall coefficient; Region (II) is the lower part of the first allowed microstrip, with a negative Hall coefficient; Region (III) is the upper part of the first allowed microstrip, with a positive Hall coefficient.

3. Mechanism of P-type SiC Negative Hall Coefficient in Jump Conduction Region

In the NNH conduction region, researchers have proposed a model based on the Fermi Dirac distribution. The Hall coefficient R_HNNH(T) can be expressed as:

Where f(E_A) is the probability of electron occupancy on the aluminum acceptor level E_A. When f (E_A)<0.5, R_HNNH(T)<0， When the Fermi level is lower than E_A, the Hall coefficient is negative. This model successfully explains the negative phenomenon of RH(T) in NNH conduction at low temperatures and is consistent with experimental data.

Fig. 3 Arrhenius of resistivity ρ (T) (circle) and Hall coefficient RH (T) (red square) of heavily doped p-type 4H SiC samples prepared by different methods and doping concentrations

4. Multi Mechanism Parallel Conduction and Hall Coefficient Expression

In actual measurements, conduction, NNH, and VRH mechanisms may coexist. The total resistivity ρ (T) and Hall coefficient RH(T) can be expressed as the weighted sum of contributions from each mechanism:

At low temperatures, if jump conduction dominates and R_HNNH<0, the total RH(T) shows a negative value.

Fig. 4 Schematic diagram of carrier hopping and Hall voltage formation in NNH conduction

By introducing the “Allow Microstrip” model and the jump conduction model based on Fermi level position, researchers have successfully explained the anomalous phenomenon of negative Hall coefficients in the band conduction and jump conduction regions in heavily Al doped p-type 4H SiC. These models not only deepen the understanding of SiC electrical transport mechanism, but also provide theoretical basis for optimizing its application in high-power devices.

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References:

1. Matsuura, H., Hidaka, A., Ji, S., Eto, K., Ishida, Y., & Yoshida, S. (2023). Negative Hall coefficient in band conduction region in heavily Al-doped 4H-SiC. Journal of Applied Physics, 134(11).
2. Matsuura, H., Takeshita, A., Hidaka, A., Ji, S., Eto, K., Mitani, T., … & Okumura, H. (2020). Sign of Hall coefficient in nearest-neighbor hopping conduction in heavily Al-doped p-type 4H-SiC. Japanese Journal of Applied Physics, 59(5), 051004.