ond method uses
the results for the Liouville equation for the independent atoms. We will show why the
development works for the semiconductor laser with vertical transitions.
The two approaches share important common features. Fermis golden rule
requires matrix elements involving the electromagnetic interaction. The matrix elements
use the energy basis set of wave functions. For semiconductors, the electron basis set
consists of the Bloch functions. The Liouville equation implicitly incorporates the Bloch
functions by considering only vertical transitions. Both approaches, Fermis golden rule
and the Liouville equation, require the density of states. Fermis golden rule provides the
transition rate from a single initial state to a range of final states. For the semiconductor,
we must develop the reduced density of states. The reduced density of states applies to
all semiconductor lasers including the quantum diode, well, wire and dot lasers.
The chapter shows how the parts of the emitter and detector fit together. It shows
how to compute the gain required for lasing and the range of useful wavelengths for
detectors. Reverse biasing a device can emphasize effects not normally important for the
forward biased regions. Changing the bias applied to a homojunction device necessarily
changes the internal electric field and the shape of the band edge. Forward biased
devices tend to have flat bands at least for high levels of injection. Reversed biased
quantum well devices do not have flat bands; the wells become triangular shape.