Carrier lifetime and threshold of Pb1-xSnxTe lasers in a magnetic field

It is well known that a magnetic field modifies not only the photon energy, but also the threshold current required by semiconductor lasers. However, the extent to which a given field modifies this threshold current depends very strongly upon temperature and on the lifetimes of the carriers in the valence and conduction bands. Theoretical calculations that predict values of threshold current as a function of magnetic field in mixed-crystal Pb
1-x
Sn
x
Te lasers are presented. The carrier lifetimes in these materials have recently been studied in some detail and turn out to be related to the composition of the material and to its preparation history. Assuming that the carrier Lifetimes are largely determined by the acoustical phonon density or by random distribution of short-range scattering centers, the Kubo formalism can be used to express the individual Landau-level densities of states. From these, the quasi-Fermi levels at any pumping rate can be directly calculated. For
k
-conserving transitions, the optical density of states is then determined by a convolution integral method recently reported elsewhere, and the threshold current is computed numerically by the method of Lasher and Stern. Using some of the measured values of carrier mobilities given by Calawa et al., for compositions with
x = 0.07
and
x = 0.20
, and using the measured values of Butler and Harman for zero magnetic-field threshold to adjust the gain requirement parameter, threshold currents at 77°K are computed for magnetic field strengths up to 250 kG. Curves are obtained that predict a threshold current for the higher mobility material that decreases by a factor of about 3 with increasing magnetic field out to the vicinity of 10 kG, flattens out, and then slowly increases. For the lower mobility material, an overall higher input current is required; however the curve continues to decrease to 25 kG before flattening out and then beginning to rise.