Indium Phosphide Ionisation Coefficients
The figure shows the impact ionization coefficients for the IIIV binary semiconductor material, Indium Phosphide (InP), 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 
240380  α  112  31.1  1

 β  47.9  25.5  1

380560  α  29.3  26.4  1

 β  16.2  21.1  1

5601250  α  2.32  8.46  2

 β  2.48  7.89  2 
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
$$\frac{1}{\alpha^*}=\frac{1}{\alpha}\frac{2E_{the}}{F}$$
$$\frac{1}{\beta^*}=\frac{1}{\beta}\frac{2E_{thh}}{F}$$
where E_{the} (E_{thh}) corresponds to the InP electron (hole) threshold energy and is given as 2.8 (3.0) eV^{1}. A full description on model which uses α*(β*) (recursive model) is given by Saleh et. al. ^{2} and the numerical equivalent model (RPL model) is by Ong et. al.^{3}
The above data is from Tan et. al.^{4} Other authors who have published InP ionisation coefficients are Cook^{5}, Umebu^{6} and Armiento et. al.^{7}. Details of ionisation coefficients over a wide electric field range can be found in Cheong et. al. for Indium Phosphide and other popular semiconductor materials^{8}
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
 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
 Tan, L.J.J., J.S. Ng, C.H. Tan, and J.P.R. David. Avalanche Noise Characteristics in Submicron InP Diodes, Quantum Electronics, IEEE Journal of 44, no. 4 (2008): 378382.
DOI: 10.1109/JQE.2007.914771
 L. W. Cook, G. E. Bulman, and G. E. Stillman. Electron and hole impact ionization coefficients in InP determined by photomultiplication measurements, Applied Physics Letters, 40, no. 7 (1982):589591.
DOI: 10.1063/1.93190
 I. Umebu, A. N. M. M. Choudhury, and P. N. Robson. Ionization coefficients measured in abrupt InP junctions, Applied Physics Letters, 36, no. 4 (1980): 302303.
DOI: 10.1063/1.91470
 C. A. Armiento, S. H. Groves and C. E. Hurwitz. Ionization coefficients of electrons and holes in InP, Applied Physics Letters, 35, no. 4 (1979): 333335.
DOI: 10.1063/1.91111
 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
