Page 332 - Electrical Properties of Materials

314 Lasers

In lasers without two-dimensional confinement, the low energy states near
to the bottom of the band play no role. When the probability of occupation is
taken into account, maximum inversion (which defines the centre frequency
of the laser) occurs at an energy higher than the gap energy. These low lying
states are wasted, hence their elimination in MQW lasers is beneficial. Con-
sequently, when the injected current is increased above its threshold, better use
is made of the available electrons. There is, therefore, a much higher increase
of output power with current. This also implies a faster reaction to the increase
or decrease of current, hence MQW lasers may be electronically modulated up
to higher frequencies.
O.K., you might argue, MQW lasers are superior in performance, but surely
they are much more expensive. Oddly enough they are not. When they are pro-
duced by one of the new techniques (MBE or MOCVD) they hardly cost more
than ordinary semiconductor lasers. With GaAs comprising the active region, it
is possible to produce lasers in the wavelength region 650–850 nm by varying
the thickness of the quantum wells, although they are commercially available
only at a few of these wavelengths. If it is possible to confine carriers in one
dimension then, surely, it is possible to confine them in two dimensions. The
resulting structures are called quantum wires. We can determine the density
of states for that configuration by following the arguments used for quantum
wells. Assuming a wire of square cross-section with side d which is of the
order of 100 nm, we can take in Eqn (12.40),

L x = L y = d and L z = , where d . (12.48)

Now the variations in n x and n y lead to sudden discrete changes in energy
whereas the variation in n z can be regarded as smooth continuous change, so
we can still talk about the density of states. The calculation is left to the reader.
The result for the n x = n y = 1 case is

–1/2
1 " #
Z(E)= E 0 (E –2E 0 ) . (12.49)
2 d
There is a singularity at E =2E 0 which means a discrete state. And there are
of course singularities for all integral values of n x and n y .
Is there any interest in producing devices using quantum wires? There are
a few laboratories interested but, on the whole, it has not been a success. It is
a kind of halfway house. If we want to do more carrier confinement, why not
go the whole hog and confine them in all three dimensions? This leads us to
∗
∗ That raises the question of how the quantum dot in which all dimensions are small. All the energy states, both
many dimensions quantum dots have. If for electrons and holes, are now discrete. What are the advantages of quantum
quantum wells are two-dimensional and dot lasers? Higher spectral purity, lower threshold current, and ability to work
quantum wires one-dimensional, then
quantum dots, which confine the elec- at high temperatures, all because the energy levels are discrete and there is a
trons in one fewer dimension, cannot be much more efficient use of the available electrons. It is also easy to design a
anything but zero-dimensional. It is an quantum dot laser to work at a given wavelength. The energy levels depend
odd terminology but one can get used
to it. only on the size of the dot. The problems are mainly technological; how to
make them of the same size, how to control their spatial distribution, and how
to incorporate them in the active layer.