The set of atoms which, when placed at
each lattice point, generates the crystal
Crystal Structure s Primitive
structure + basis. Translate the basis
through all possible lattice vectors r =
n1a1+n2a2+n3a3 to get crystal structure or
Diamond & Zincblende Structures
Tetrahedral coordination: Each atom has 4 nearestneighbors (nn). Basis set: 2 atoms. Primitive lattice s
face centered cubic (fcc).
Diamond or Zincblende s
2 atoms per fcc lattice point.
Diamond: 2 atoms are the same. Zincb
ECE-E302 HW #3 Solutions Spring 2015
(a) E F E kT ln
1.04 10 19
(b) E c E F E g E F E
Carrier concentration is the product of the
density of states and the Fermi function
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1. ECEE-302-A - SP 15-16
2. HW Soluti
(a) I 15' = eD.Aunno
0! Is = 3.2x10‘" A
0 ' 32 10‘“ 05 )
1 I = I — =
it = 7.75 M
(ii) it = 3.2110" :5
4 = 0.368 m
(in) iC = 3.2x10'" :5
it =175mA 10.20
. . + . .
For a $111con p n Junctlon.
Is = Aen'.2 i
= (10* 1.6x10“’)(1.5x10‘°)2 - M 7
IS = 39431015 A
[D = 15 exp —” = (3.94x10'ls)exp( )
ID = 9.54x10‘7 A 5x10ls
= (0.0259) lo :1»
En — EF
n=no+6n and p=po+¢§o
Forann—type semiconductor, we canwn‘te
o=eu.("o +é0)+eu,(po “59)
a = euro “311,190 +201. +#,)(¢Sv)
A0 =e(u. +u,)(¢iv)
In steady-state, 6p = g't
M = e(”- +erg’11-O) 6.20
f"l oS eh?nctToR
ENtPcY 13nA/-D IAaRnMJ
Figure 11.3 lThe MOS capacitor with a moderate positive gate bias, showing (a) the electric field and charge flow
(b) the induced space charge region.
Diamond & zincblende crystals: Primitive lattice is fcc.
fcc primitive lattice is generated by
fcc primitive lattice vectors are:
a, = ('/2)a(0,l,0),a2= (%)a(l,0,l), a3= (%)a(l,l,0)
NOTE: The a; s are NOT mutually orthogonal!
Primitive fcc lat
3-D Crystal Structure
General: A crystal structure is defined by
primitive lattice vectors a15 si2, a3.
a1? a2, a3 : Depend on geometry. Once
primitive lattice structure is specified.
Generate lattice by translating through a
Allowed and Forbidden Energy Bands
- allowed energy bands associated with different atomic orbitals
may overlap, as in (a)
- the regions between allowed energy bands are called forbidden
bands or band gaps
Electrical Conductivity and Energy Bands
- in sod