Let's talk about the recombining electrons for a minute. When
the electron falls down from the conduction band and fills in a
hole in the valence band, there is an obvious loss of energy.
The question is; where does that energy go? In silicon, the
answer is not very interesting. Silicon is what is known as an
indirect band-gap material. What this means is
that as an electron goes from the bottom of the conduction band
to the top of the valence band, it must also undergo a
significant change in momentum. This all comes about from the
details of the band structure for the material, which we will
not concern ourselves with here. As we all know, whenever
something changes state, we must still conserve not only energy,
but also momentum. In the case of an electron going from the
conduction band to the valence band in silicon, both of these
things can only be conserved if the transition also creates a
quantized set of lattice vibrations, called
phonons. Phonons posses both
energy and momentum, and their creation upon the recombination
of an electron and hole allows for complete conservation of both
energy and momentum. All of the energy which the electron gives
up in going from the conduction band to the valence band (1.1
eV) ends up in phonons, which is another way of saying that the
electron heats up the crystal.
In some other semiconductors, something else occurs. In a class
of materials called direct band-gap semiconductors,
the transition from conduction band to valence band involves
essentially no change in momentum. Photons, it turns out,
posses a fair amount of energy (several eV/photon in some cases)
but they have very little momentum associated with them. Thus,
for a direct band gap material, the excess energy of the
electron-hole recombination can be taken away as heat, or more
likely, as a photon of light. This, radiative
transition, then conserves energy and momentum by giving
off light whenever an electron and hole recombine. This gives
rise to (for us) a new type of device, the light emitting diode
(LED). Emission of a photon in an LED is shown schematically
in Figure 1.
It was Planck who postulated that the energy of a photon was
related to its frequency by a constant, which was later named
after him. If the frequency of oscillation is given by the
Greek letter "nu" (
νν), then the
energy of the photon is just
hν
h
ν
, where
hh is Planck's
constant, which has a value of
4.14×10-15eVseconds
4.14
10
-15
eV
seconds
.
E=hν
E
h
ν
(1)
When we talk about light it is conventional to specify its
wavelength,
λλ, instead of
its frequency. Visible light has a wavelength on the order of
nanometers (Red is about 600 nm, green about 500 nm and blue is
in the 450 nm region.) A handy "rule of thumb" can be derived
from the fact that
λ=cv
λ
c
v
, where
cc is the speed of
light. Since
c=3×103msec
c
3
10
3
m
sec
or
c=3×1017nmsec
c
3
10
17
nm
sec
λnm=hcEeV=1242EeV
λ
nm
h
c
E
eV
1242
E
eV
(2)
Thus, a semiconductor with a 2 eV band-gap should
give off light at about 620 nm in the red. A 3 eV band-gap
material would emit at 414 nm, in the violet. The human eye, of
course, is not equally responsive to all colors. We can show
this in
Figure 2, where we have also included the
materials which are used for important light emitting diodes
(LEDs) for each of the different spectral regions.
As you no doubt notice, a number of the important LEDs are based
on the GaAsP system. GaAs is a direct band-gap semiconductor
with a band gap of 1.42 eV (in the infrared). GaP is an
indirect band-gap material with a band gap of 2.26 eV (550 nm,
or green). Both As and P are group V elements. (Hence the
nomenclature of the materials as
III-V compound
semiconductors.) We can exchange some of the As with P
and make a mixed compound semiconductor
Ga
As
1-x
P
x
Ga
As
1-x
P
x
. When the mole fraction of phosphorous is less than
about 0.45 the band gap is direct, and so we can "engineer" the
desired color of LED that we want by simply growing a crystal
with the proper phosphorus concentration! The properties of the
GaAsP system are shown in the diagram below. It turns out that
for this system, there are actually
two
different band gaps, as shown in the inset in
Figure 3. One is a direct gap (no change in momentum)
and the other is indirect. In GaAs, the direct gap has lower
energy the indirect one (like in the inset) and so the
transition is a radiative one. As we start adding phosphorous
to the system, both the direct and indirect band gaps increase
in energy. However, the direct gap energy increases faster with
phosphorous fraction than does the indirect one. At a mole
fraction xx of about 0.45, they cross over and the material goes
from being a direct gap semiconductor to an indirect gap
semiconductor. At
x=0.35
x
0.35
the band gap is about 1.97 eV (630 nm), and so we
would only expect to get light up to the red using the GaAsP
system for making LED's. (The common helium-neon laser used in
supermarket checkout counters emits at 628 nm.) Fortunately,
people discovered that you could add an impurity (nitrogen) to
the GaAsP system, which introduced a new level in the system.
An electron could go from the indirect conduction band (for a
mixture with a mole fraction greater than 0.45) to the nitrogen
site, changing its momentum, but not its energy. It could then
make a direct transition to the valence band, and light with
colors all the way to the green became possible. The use of a
nitrogen
recombination center is depicted in the
Figure 4.
If we want colors with wavelengths shorter than the green, we
must abandon the GaAsP system and look for more suitable
materials. A compound semiconductor made from the II-VI
elements Zn and Se make up one promising system, and several
research groups have successfully made blue and blue-green LEDs
from ZnSe. SiC is another (weak) blue emitter which is
commercially available on the market. Recently, workers at a
tiny, unknown chemical company stunned the "display world" by
announcing that they had successfully fabricated a blue LED
using the II-V material GaN. A good blue LED has been the "holy
grail" of the display and CD ROM research community for a number
of years now. Obviously, adding blue to the already working
green and red LED's completes the set of 3 primary colors
necessary for a full-color flat panel display (Hang a TV screen
on your wall like a picture?). Using a blue LED or laser in a
CD ROM would more than quadruple its data capacity, as bit
diameter scales as
λ λ, and
hence the area as
λ2
λ
2
.
