Institute of Metals Division - Analysis of a GaAs Laser

An analysis of the semiconductor injection laser is presented which is based on a phenomenological model using device and material parameters. The intent of the laser threshold analysis is not to predict from theory the actual threshold current density but rather to provide a logical means of interpreting experimental results. The device and material parameters have been selected such that they describe both the threshold conditions and quantum efficiency of the lasev. A technique is proposed whereby the current required to obtain a population inversion is predicted from device 1-V characteristics. Experimental data are presented which support the analysis. THIS investigation is concerned with the characteristics of GaAs lasers fabricated in this laboratory. However, the assumptions used in these calculations should not limit their application to GaAs alone. It is felt that the analysis is sufficiently general to be useful in describing the operation of other semiconductor-laser materials. ANALYSIS heavily doped semiconductors to be considered. The absorption and/or generation of optical radiation may be completely specified in terms of q(E) and the probability functions f,,(E) and f,(E) which define the occupancy of the valence-band and conduction-band levels, respectively. The symbols used in this analysis are listed at the end. Following the approach of all' it can be shown that the effective gain coefficient, g, in the plane of a forward-biased P -N junction is g(E)=-ai@)[1-fv(E)-fc(E)] [1I In particular Eq. [I] holds for the photon energy at which lasing occurs, Ep. Throughout the following discussion Eq. [I] is considered only for the lasing transition E = Ep. For simplicity the functional energy dependence of the various factors is omitted in subsequent equations. Unless otherwise stated the symbols used represent the values at Ep. If the analysis is limited to the P-type side of the laser junction, the function q(l -f,,) is recognized as the band-to-band absorption in the P-type material at thermal equilibrium. Under forward-bias conditions the function f, is determined by the electron quasi Fermi level in P-type material. For sufficiently large forward bias the second term in Eq. [3] will become dominant and net gain will result; i.e., g will become positive. In order to simplify the subsequent analysis several assumptions are in order at this point. a) No conductivity modulation occurs. /„ is independent of f, and therefore go is a constant. b) The P-type material is heavily doped such that the degeneracy of the valence band permits popu-