Silicon Ionisation Coefficients
The figure shows the impact ionization coefficients for the group IV semiconductor material, silicon (Si), 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.
The electron (hole) ionization coefficients, α (β) plotted in the diagram above can be expressed as
$$\alpha(\beta)=A\exp{\bigg[\left({\frac{B}{F}}\right)^c\bigg]}$$
where F is electric field strength. The constants A, B and c are tabulated as below.
F (kV/cm)  Coefficient Type  A (x10^{5} cm^{1})  B(x10^{5} cm^{1})  c 
175400  α  7.03  12.30  1

 β  15.8  20.40  1

400800  α  7.03  12.3  1

 β  6.71  16.90  1

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 "deadspace" 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) using^{1}
$$\frac{1}{\alpha^*}=\frac{1}{\alpha}\frac{2E_{the}}{F}$$
$$\frac{1}{\beta^*}=\frac{1}{\beta}\frac{2E_{thh}}{F}$$
where E_{the} (E_{thh}) corresponds to the InP electron (hole) threshold energy and is given as 2.8 (3.0) eV^{2}. 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 Overstraeten and Man^{5} Details of ionisation coefficients over a wide electric field range can be found in Cheong et. al.^{1} for silicon and other popular semiconductor materials.
References
 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): 19461952.
DOI: 10.1109/TED.2015.2422789
 C. H. Tan, J. C. Clark, J. P. R. David, G. J. Rees, S. A. Plimmer, R. C. Tozer, et al., Avalanche noise measurement in thin Si p^{+}in^{+} diodes, Applied Physics Letters, vol. 76, pp. 39263928, 2000.
DOI: 10.1063/1.126823
 M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, et al., Impactionization and noise characteristics of thin IIIV avalanche photodiodes, IEEE Transactions onElectron Devices, vol. 48, pp. 27222731, 2001.
DOI: 10.1109/16.974696
 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. 34263428, 1998.
DOI: 10.1063/1.367111
 R. Van Overstraeten and H. De Man, Measurement of the ionization rates in diffused silicon pn junctions, SolidState Electronics, vol. 13, pp. 583608, 1970.
DOI: 10.1016/00381101(70)901395
