The University of Sheffield
Impact Ionisation Group

Silicon Carbide Ionisation Coefficients


The figure shows the impact ionization coefficients for the group IV semiconductor material, Silicon Carbide (Si-C), as a function of inverse electric field at room temperature. These ionization coefficients were obtained from photomultiplication measurements undertaken on a range of PIN and NIP diodes of different avalanching widths.

Si ionisation coefficients

The electron (hole) ionization coefficients, α (β) plotted in the diagram above can be expressed as


$$\alpha(\beta)=A\exp{\left({-\frac{B}{F}}\right)^c}$$

where F is electric field strength. The constants A, B and c are tabulated as below.

F (kV/cm)Coefficient TypeA (x105 cm-1)B(x105 cm-1)c
1000-4000α7.0070.001.66
β19.00103.001.01

α(β) can be can be used in simple analytical expressions to determine the avalanche multiplication (or gain) and the breakdown voltage. In thin avalanching structures, α(β) overestimate the multiplication as they ignore "dead-space" effects. They also cannot accurately predict the excess noise due to the impact ionization process. Models to predict the multiplication and excess noise in thin avalanching structure require knowledge of enabled ionization coefficients, α*(β*).

α*(β*) can be approximated from α(β) using1

$$\frac{1}{\alpha^*}=\frac{1}{\alpha}-\frac{2E_{the}}{F}$$ $$\frac{1}{\beta^*}=\frac{1}{\beta}-\frac{2E_{thh}}{F}$$
where Ethe (Ethh) corresponds to the InP electron (hole) threshold energy and is given as 12.0 (8.0) eV2. A full description on model which uses α*(β*) (recursive model) is given by Saleh et. al. 3 and the numerical equivalent model (RPL model) is by Ong et. al.4

The above data is from Cheong et. al.1 Other authors who have published Si-C ionisation coefficients include Loh et al.5 . Details of ionisation coefficients over a wide electric field range can be found in Cheong et. al.1 for Silicon Carbide and other popular semiconductor materials.


References

  1. J. S. Cheong, M. M. Hayat, X. Zhou and J. P. R. David, Relating the Experimental Ionization Coefficients in Semiconductors to the Nonlocal Ionization Coefficients, IEEE Transactions on Electron Devices, 62, no. 6 (2015): 1946-1952. DOI: 10.1109/TED.2015.2422789
  2. B. K. Ng, J. P. R. David, R. C. Tozer, G. J. Rees, Y. Feng, J. H. Zhao, et al., Nonlocal effects in thin 4H-SiC UV avalanche photodiodes, IEEE Transactions on Electron Devices, vol. 50, pp. 1724-1732, 2003. DOI: 10.1109/TED.2003.815144
  3. M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, et al., Impact-ionization and noise characteristics of thin III-V avalanche photodiodes, IEEE Transactions onElectron Devices, vol. 48, pp. 2722-2731, 2001. DOI: 10.1109/16.974696
  4. D. S. Ong, K. F. Li, G. J. Rees, J. P. R. David, and P. N. Robson, A simple model to determine multiplication and noise in avalanche photodiodes, Journal of Applied Physics, vol. 83, pp. 3426-3428, 1998. DOI: 10.1063/1.367111
  5. W. S. Loh, B. K. Ng, J. S. Ng, S. I. Soloviev, H. Y. Cha, P. M. Sandvik, et al., Impact Ionization Coefficients in 4H-SiC, IEEE Transactions on Electron Devices, vol. 55, pp. 1984-1990, 2008. DOI: 10.1109/TED.2008.926679