Page 278 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Electron-Photon
loss process in the intensity rate equation is due to the finite reflectivity of
the mirrors that make up the boundary conditions. In addition, this loss
term allows the laser mode intensity to leave the cavity and to be used as
a strong coherent light source. Omitting the boundary conditions would
clearly lead to all emission processes going into spontaneous emission
out of phase with each other. This in turn is how a light emitting diode
would operate.

Let us now think of the carriers as electron densities in the conduction
band n and in the valence band n . Where the electron density in the
ec ev
valence band is 1 minus the hole density n . Therefore, we may write
h
–
D = n – n = n – ( 1 n ) = n + n – 1 (7.91)
ec ev e h e h
In a semiconductor these densities depend on the wavevector k of the
electron or hole. From Chapter 5 we know that these electrons and holes
follow the respective distribution functions f kx t,,( ) and f ( kx t) .
,,
e h
Both distribution functions do have an equation of motion namely the
Boltzmann transport equation. In this context it becomes clear that also
the dipole moment becomes dependent of the wave vectors of electrons
and holes. It will have an equation of motion too, with a relaxation term,
and transport term and a coupling to the inversion. It is not the place to
explain these processes in detail here, since the classical interpretation is
only half of the truth and for an accurate description a full quantum
mechanical treatment is needed. To explain the phenomena some simple
considerations about p-n diodes will be enough as they are given in Sec-
tion 7.6.4. The holes are transported from the one side to the active
region, while the electrons arrive from the opposite side. Since both
charge carriers have different transport properties all the requirements for
carrier transport apply. A whole lot of phenomena may arise due to these
differences which, at first glance, may be neglected. Nevertheless in spe-
cial applications, e.g., in high frequency modulation of lasers they will
have to be accounted for.

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