Chap 8 Semiconductor

1
Chap 8 Semiconductor
8.1 Overview

• Semiconductor
• A crystal with small band gap filled valence
  band, empty conduction band
• (electrons can be excited by thermal energy kBT)

• Energy gap
• Si 1.17 eV
• Ge 0.74 eV
• GaAs 1.52 eV
• Diamond 5.4 eV

-Tetrahedral covalent bond - Diamond or
Zincblend structure

• Conduction becomes possible due to
• 1. Thermal excitation (intrinsic carrier)
• 2. Impurity doping (extrinsic carrirer)

• Electrical resistivity

r 10-2109 ohm-cm
Insulator r 10141022 ohm-cm Conductor
r lt 10-6 ohm-cm
2

• Measurement of band gap

1) Optical Absorption Transition of electron
from the occupied valence band state to the empty
conduction band orbital by photon absorption
Conduction band
Valence band
hn
direct
Direct band gap
ex GaAs Indirect band gap
ex Silicon
Absorption
Phonon assisted
Absorption
Eg
n
n
Eg
3
8.2 Hole
If there are vacant orbitals in an otherwise
filled band, the current can flow due to these
vacant orbitals which are called as HOLES.

• Filled band is inert Completely filled band
  carries no current (inversion symmetry)

4
The current produced by occupying with electrons
a specified set of levels is precisely the same
as the current that would be produced if the
specified levels were unoccupied and all other
levels in the band were occupied but with
particles of charge e
Properties of holes
5
5. me - mh
6
Perspective plot of the energy band structure
of silicon
Perspective plot of the energy band structure
of GaAs
http//www.utdallas.edu/dept/ee/frensley/technical
/hetphys/node5.html
7
Constant energy surface
electron
hole
http//www.utdallas.edu/dept/ee/frensley/technical
/hetphys/node5.html
8
8.3 Intrinsic Semiconductor

• Density of State

of state in EEdE De(E)dE
9
Fermi-Dirac Distribution
m chemical potential m 0Eg
Exact position of m depends on the impurity level
and temperature
Assume that Eg gtgt kBT Ec- mgtgt kBT, m- Ev gtgt
kBT
10
Close to Maxwell-Boltzmann distribution

• Electron and hole concentration

A) Electron Concentration
Pv(T)
B) Hole Concentration
11

• Intrinsic Semiconductor number of electron
  number of hole

12

• Law of mass action

B(T)
n p photon
Black body radiation
A(T)

• Intrinsic Mobility

13

• The hole mobility is typically smaller than the
  electron
• mobility band degeneracy at the valence band
  edge
• interband scattering

• Small band gap -gt light effective mass -gt high
  mobility

8.4 Extrinsic (Impurity) Semiconductor
Donor State
Group V element (As, P, Sb..)
14

• Donor State Give one extra valence electron
  with positive ion left (Donor state)

The binding energy of the extra electron can be
calculated with hydrogen-like orbital model, but
with dielectric constant e and effective mass m
10meV
15
The radius of the first Bohr orbit is,

• Acceptor State needs one more electron to
  satisfy the tetrahedral bonds of host materials

(B, Al, Ge, In)
Accepts one electron from the band leaving one
hole state in the band with negative ion at the
impurity state
e
-
Group V element (As, P, Sb..)
16
10meV
Both donor and acceptor state lie close to the
band edge (separation are comparable to kBT)
Thermal ionization of these levels are easier
than the intrinsic case
Dominant contributions for electrical conductivity
N-type donors present --gt electrons P-type
acceptors present --gt holes

• Thermal equilbrium carrier density of impure
  semiconductor

Nd of donor impurities Na of acceptor
impurities nc of conduction electrons nd
of occupied donor level pv of holes pa
of occupied acceptor level
17
(No Transcript)
18
Note major carrier density is much larger than
minor carrier density

• Population of a impurity level in thermal
  equilibrium
• Impurity level no electron
• one electron with spin
  up
• one electron with spin
  down
• two electron with spin
  up down
• (negligible due to the column
  interaction )

e
ee
e
19
(No Transcript)
20
As T decreases,
21
8.5 P-N junction
Two semiconductor one p-type and the other n-type
are in contact
P-type
N-type
e
e
e
e
m
Diffusion of holes and electrons into each
other gt The flow continues until the chemical
potential m becomes equal equilibrium condition
22
conduction band
chemical potential
electrostatic potential
valence band
Electrostatic potential develops due to the
charged depletion layer
carrier density
Under electric potential j(x)
23
Far away from the junction, nND, pNA
24

• Concept of electrochemical potential

• Calculation of electrostatic potential in the
  depletion layer

25
Potential should be continuous at X0
26
Carrier density
p
n

Charge density
Electric potential
27

• Elementary picture of Rectification by p-n
  junction

n
p
e e e e e e e e e e e e
h h h h h h h h h h h h h h
Majority carrirer hole
electron
Hole current 1. Generation Current thermal
excitation of e-h pair at the depletion layer -gt
immediately swept away toward p-side 2.
Recombination Current Hole current over the
potential barrier
28
Under Bias voltage V
I
p
n
Forward bias
Reverse bias
V
29

• Sollar Cells (Photo-diode)

Photon creates electron-hole pairs Diffuse into
the junction Built in electric filed separates
them Produce forward voltage
n
p
hn
h
e
e-h

• Light Emitting Diode

Direct band gap Semiconductor GaAs
hn
n
p
e
h
e
h
e
30
8.6 Excitons
Electron-hole pairs bounded by Coulomb attraction
between them

• Mott-Wannier Excitions Weakly bound excitons
• ? size larger than many lattice spacings
• Frenkel Excitions - Localized on or near a single
  atoms

• Mott-Wanniers
• bound state of electron near the conduction band
  minimum with
• effective mass me, and hole near the valence
  band maximum with effective mass mh.

Coulomb attraction between them can be described
by hydrogenic model
31
C. B
Eg
Excitonic level
hn
V. B
32
Binding energy of Excitions can be measured 1.
Optical Absorption 2. Recombination
luminescence 3. Photo-ionization of excitations
Exciton absorption
Absorption coefficient
Free electron-hole pair absorption
Photon energy

• Frenkel Excitions
• Dielectric constant is small and the Bohr
  radius is small
• ? Warnier picture breaks down tight bound
  excitions ? Frenkel Excitions

Excited state of a single atom but the
excitation can move through atoms due to the
interaction between neighbors ex
Alkali Halides, Molecular crystals
33
Binding Energy of order eV
Eigenfunction
34
E
k

• Exciton Life time (Si, Ge)
• photon ? generate free electron-hole pair
• ? combine to form an exciton (1 ns)
• ? decay with annihilation of e-h pair ( 8 ms)

Electron-Hole Drops condensed excitons (40
ms)