86 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS
The key difference between electronic states in the perfect crystal and a non-perfect crystal is
related to the wavefunction. In the periodic state, the electron state is extended over the entire
system, as shown in figure 2.38a. This reflects the fact that the electron can propagate from one
region to another. In the case of a defect a bandgap state may be created with an associated
wavefunction that is spatially localized near the defect region, as shown in figure 2.38b. When
an electron is occupying such a localized state its transport (mobility, diffusion) properties are
seriously affected. Localized electrons cannot move across the material as easily.
In figure 2.39 we show a comparison of the density of states in a perfectly periodic and of a
defect-containing material. In the case of the perfect material we have a well-defined bandgap,
while in the presence of defects we have bandgap states. Electrons can be trapped into the
bandgap states (hence these states are also called traps).
2.13 TECHNOLOGY ISSUES..............................
We have examined some of the driving forces behind some of the technologies. The use
of alloys and heterostructures adds a tremendous versatility to the available parameter space to
exploit. Semiconductor alloys are already an integral part of many advanced technology systems.
Consider the following examples.
- The HgCdTe alloy is the most important high-performance imaging material for long
wavelength applications (10 – 14μm). These applications include night vision, seeing
through fog, thermal imaging of the human body parts for medical applications, and a
host of special purpose applications involving thermal tracking. - The AlGaAs alloy is an important ingredient in GaAs/AlGaAs heterostructure devices
which drive a multitude of technologies including microwave circuits operating up to
100 GHz, lasers for local area networks, and compact disc players. - InGaAs and InGaAsP alloy systems are active ingredients of MMICs operating above
100 GHz and long-haul optical communication lasers.
While alloys are important ingredients of many technologies, it must be emphasized again
that alloys are not perfectly periodic structures. This results in random potential fluctuations
which leads to an important scattering mechanism that limits certain performances. For example,
the low temperature low field mobility is severely affected by alloy scattering as is the exciton
line width of optical modulators. The growth and fabrication issues in alloy systems are also
sometimes serious due to miscibility gaps that may be present.
2.14 PROBLEMS
Problem 2.1Plot the conduction band and valence band density of states in Si and GaAs
from the bandedges to 0.5 eV into the bands. Use the units eV−^1 cm−^3. Use the following