The four-band Kane Model was used for calculating the gain coefficient of a laser structure with a quantum well [1]. Dependences of the gain coefficient on temperature T, frequency w, quantizated energy levels e_e , e_h, quasi-Fermi levels m_e , m_h and sheet carrier density n_e , n_h of electrons and holes, respectively, were obtained. An expression for the gain coefficient was derived with account for finite relaxation times tin of carriers [2]. Calculated maximum values of the gain coefficient were used for estimating laser threshold characteristics (threshold concentration and threshold current) and laser power characteristic.

Graphical illustrations on the next page of this section show the maximum gain coefficient in the InGaAsP/InP structure versus the carrier concentration n and temperature T as a function of parameters according to your choice: the relaxation time t_in (s) and the width of the quantum well a (A).

Reference

1. Asryan L. V., Gun'ko N. A., Polkovnikov A. S., Zegrya G. G., Suris R. A., Pey-Kee Lau, Makino T. Threshold characteristics of InGaAsP/InP multiple quantum well lasers, Semicond. Sci. Technol., 2000, v. 15, no. 12, 1131-1140.
2. Zegrya G.G., Gunko N.A., Kostko I.A., Dogonkin E.B.
   The effect of carrier relaxation on quantum well laser threshold characteristics, roceedings of 2001 International Semiconductor Conference CAS 24-th Editien, Sinaia, Romania, October 9-13 2001, 169-172.