Physics 365 Introduction
Semiconductor Device Physics Quantum mechanics in everyday life Quantum engineering is now routine Common Examples: Quantum well lasers: CD players, telecom lasers, laser poin
Energy band picture of electrons and holes
Oversimplified (and misleading) 2-d picture of Si lattice:
Pure Si: all bonding electrons are paired as shown above. Electrons are not actually localized a
Each relation holds whether the material is intrinsic, ntype, or p-type For intrinsic semiconductor, we have ni = pi . Equating [1] and [2]:
N C e - ( E c - E F ) / kT = N V e - ( E F - EV ) / kT
N C
For finite T, if we substitute E=E F we obtain f(E) = 1/2 i.e. electron level at the Fermi energy has a 50% chance of being occupied. Fermi level for intrinsic semiconductors Intrinsic=> no donor or
Transport: Conduction of electrical charge -Charges move in response applied electric field: F=-eE. -Without frictional effects, electrons (holes) would continue to accelerate indefinitely. -Frictiona
Bloch Functions and crystal momentum Free Electrons:
( x, t ) = e j ( k x x -t ) = ( x )e - jt
jk x where ( x ) = Ae x In 3-d a plane wave is described by
( x ) = Ae jk x x e
jk y y
e jkz z = Ae jkr
SWE Solution for particle in an infinite potential well (1-d) Previous solution for free particle similar to free travelling wave solution of classical wave equation for infinite wire. Energy E and wa
Molecular Beam Epitaxy (MBE) High purity technique for growing very thin layers of compound semiconductors Start with thin wafer of binary semiconductor such as GaAs. Heat wafer to growth temperature
Zincblende vs Wurtzite Structures
GaAs, GaP, InP crystallize in Zincblende Structure GaN, InN, AlN usually crystallize in Wurtzite structure. These are closely related as indicated in figure below
([
Multielectron Systems Hydrogen atom: single electron system, exactly solvable by the SWE. In general, multielectron systems (atoms with Z>1) are much more complicated: numerical solutions must be used
d ( t ) jE + (t ) = 0 dt h
[4]
h 2 d 2 ( x ) - + V ( x) ( x ) = E ( x ) 2 2m dx
[5]
E = "separation constant" . Eq. 5 is time independent SWE, since it depends only on x.
Exercise: Show that solution