Counting k states: one band holds 2 electrons (2 spins) per cell
Nearly-free-electron approximation
metals vs. insulators
What is a semiconductor?
Defined by density of carriers : High enough for
interesting conductivity; Low enough to be controlled by
temperature and other factors
Exponential variation with temperature implies energy gap
See figures in Kittel p 186, 188, table of values on p 190
Qualitative understanding of semiconductors and semimetals from band picture
Semiconductors are insulators with a small gap
This leads to important consequences for conductivity
Note: semimetals have overlapping bands - can be close relatives of
semiconductors
Bands in real semiconductors - Si, Ge, GaAs, ...
All are FCC with 2 atoms per primitive cell
8 valence electrons per primitive cell
Starting point - Nearly free electrons!
Free electrons bands for FCC - (homework)
Work out using our knowledge from before about the Brillouin zone
of any FCC crystal
Actual bands - we only give results here (e.g. Ge shown in
figure in Kittel. p 203)
What is the same - what is different about Si, Ge, GaAs, ...
Optical properties - comparison of Si, Ge, GaAs, ...
Why is your computer chip made of Si,
but the laser in your CD player is made of GaAs
(in the future GaN?)
Direct vs indirect transitions
“Vertical transition”, i.e., Delta k = 0, since
light has k nearly 0
In GaAs the lowest energy possible
is a direct “vertical” transition
In Si the lowest energy possible is “indirect”
non-vertical transition - weak - must involve a phonon
to conserve momentum
Light emission is related
very high efficiency in GaAs for excited electron to emit red light
very low efficiency in Si
Why is GaN interesting?(Also AlAs, InAs, ..)
After decades of attempts, it is now possible to make
efficient blue light emitters and lasers
(Physics Today, October, 2006)
Shorter wavelength light focuses to smaller spot
implies higher density of information on a CD!