Emission Spectra for p-n Junction Lasers
Under forward bias, an inversion layer can be obtained along the plane of the junction, where a large population of electrons exists at the same location as a large hole population.
Emission Spectra for p-n Junction Lasers:
- An inversion layer indicates that spontaneous emission of photons can occur due to direct recombination of electrons and holes, releasing energies ranging from approximately Fn - Fp to Eg.
That is, an electron can recombine over an energy from Fn to Fp, yielding a photon of energy hv = Fn - Fp , or an electron can recombine from the
bottom of the conduction band to the top of the valence band, releasing a photon with hv = Ec - Ev = Eg.
- These two energies serve as the approximate outside limits of the laser spectra.
- The photon wavelengths which participate in stimulated emission are determined by the length of the resonant cavity.
- Figure illustrates a typical plot of emission intensity vs. photon energy for a semiconductor laser.
- At low current levels (Fig. a), a spontaneous emission spectrum containing energies in the range Eg<hv< (Fn - Fp) is obtained.
- As the current is increased to the point that significant population inversion exists, stimulated emission occurs at frequencies corresponding to the cavity modes as shown in Fig. b.
- These modes correspond to successive numbers of integral half-wavelengths fitted within the cavity.
- Finally, at a still higher current level, a most preferred mode or set of modes will dominate the spectral output (Fig. c).
- This very intense mode represents the main laser output of the device; the output light will be composed of almost monochromatic radiation superimposed on a relatively weak radiation background, due primarily to spontaneous emission.
- The separation of the modes in Fig. b is complicated by the fact that the index of refraction n for GaAs depends on wavelength X.
If m (the number of half-wavelengths in L) is large, we can use the derivative to find its rate of change with λ0:
Now reverting to discrete changes in m and λ0, we can write