Snew 17

LECTURE 17
GENERATION/RECOMBINATION
Generation of Electrons and Holes
Generation: The movement of an electron from the valence
band to the conduction band. This results in the
creation of an electron-hole pair.
We have talked about the thermal generation of holes and
electrons but they can also be generated by light
(Photogeneration).
Photogeneration
Remember that E-k diagrams of real crystals (whose structure is
still periodic but more complex than a simple chain of atoms)
are not simple parabolas.
The previous figure shows the E-k relationship for real solids (a)
Silicon (which has an indirect bandgap) and (b) gallium arsenide
(which has a direct bandgap).
Lecture 17: Generation/Recombination September, 2000 1
One point that arises is that the maximum of the valence band
does not always occur at the same k value as the minimum of the
conduction band. We speak of a direct bandgap semiconductor
when they do and an indirect bandgap semiconductor when they
do not.
Analyzing the two cases:
a) Direct gap material (e.g. GaAs) –(min of conduction band at same k
as max of valence band)
E
ω - photon frequency
!ω
EG
k
-π/a π/a
(∆k = 0) Change of electron momentum is zero

A photon (a “particle of light”) with energy E = !ω can be
absorbed by promoting a valence band electron to the
conduction band, creating an electron-hole pair. This is a two
body collision (electron, photon).
Direct bandgap materials have strong light absorption and are
modeled by an absorption parameter.
Model for light absorption: I(x) = Ioe-αx
Where α - absorption coefficient [cm-1], Io – incident intensity

b) Indirect gap material (e.g. Si) –(min of conduction band not! at same
k as max of valence band)
∆k
!ω
EG
k
-π/a π/a
(∆k != 0) Change of electron momentum is non zero.

A photon carries little momentum, for a transition we need ∆k (a
momentum change) and this can not be provided by the photon
itself.
Promotion of valence band electron to conduction band requires

momentum transfer from crystal lattice (interaction with a
“phonon”); this is a relatively unlikely event as it is a three body
collision (electron, photon, phonon).
“phonon” = quantized lattice vibration (“particle” of heat)

∴ light absorption is relatively weak.
Note: all semiconductors are effectively - transparent for light

with hv < EG (no possible transition).
- absorb for hv > EG (transitions allowed)
Recombination of Electrons and Holes
Recombination: The movement of an electron from the

conduction band to the valence band. This results in
the destruction of and electron-hole pair.
Once created holes and electrons can recombine and be

eliminated, in doing so, the energy released in the recombination
is given up as light (radiative recombination) or heat (non-
radiative recombination).
•
!ω
a) Direct radiative recombination (e.g. GaAs)

The conduction band electron fills valence band hole,
releasing a photon with the energy Ephoton ~ EG.

This is the basis of semiconductor LEDs and lasers, and is a
very unlikely process in indirect gap materials (need a phonon
for momentum).
Therefore can not make Si LEDs or lasers easily, without

modifying material properties.
b) Recombination through Midgap Energy levels (traps) (two

stage process).
Defect centers or traps are energy levels (ET) in the forbidden

gap which are associated with defect states caused by the
presence of impurities or lattice imperfections.
•
EC EC
• ET
... process repeats
EV ο EV
1) trap captures conduction band 2) trap transfers electron to valence band

electron (capture hole)
• In silicon, midgap defect centers generally associated with

transition metal contamination: Cu, Fe, etc like dopant.
• Traps are generally undesirable as we want long carrier

lifetimes (elapsed time before recombination) in most devices.
• Traps shorten lifetime, produce multiple frequencies and

energy pathways (contribute to non-radiative recombination).

Thermal Generation (trap aided)
• heat (phonon) gives energy to electron.

• usually enabled by midgap energy levels (smaller energy).
EC EC
• ET • ET
... process repeats
ο EV ο EV
1) trap captures valence band 2) trap emits electron to conduction

electron (create hole) band

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LECTURE 17

(∆k = 0) Change of electron momentum is zero

Model for light absorption: I(x) = Ioe-αx

Where α - absorption coefficient [cm-1], Io – incident intensity

Lecture 17: Generation/Recombination September, 2000 2

(∆k != 0) Change of electron momentum is non zero.

Promotion of valence band electron to conduction band requires

Lecture 17: Generation/Recombination September, 2000 3

Note: all semiconductors are effectively - transparent for light

Recombination of Electrons and Holes

Recombination: The movement of an electron from the

Once created holes and electrons can recombine and be

a) Direct radiative recombination (e.g. GaAs)

Lecture 17: Generation/Recombination September, 2000 4

Therefore can not make Si LEDs or lasers easily, without

b) Recombination through Midgap Energy levels (traps) (two

Defect centers or traps are energy levels (ET) in the forbidden

1) trap captures conduction band 2) trap transfers electron to valence band

• In silicon, midgap defect centers generally associated with

• Traps are generally undesirable as we want long carrier

• Traps shorten lifetime, produce multiple frequencies and

Lecture 17: Generation/Recombination September, 2000 5

• heat (phonon) gives energy to electron.

1) trap captures valence band 2) trap emits electron to conduction

Lecture 17: Generation/Recombination September, 2000 6

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