Transcript Slide 1

Hydrogenic model of doping impurities
The simple model for a hydrogen atom can be used to describe the behavior of
an impurity in a semiconductor. Thus, the formula for the ionization energy of a
hydrogen atom,
and the radius of the lowest orbit of the electron around the hydrogen nucleus
can be applied in modified form to calculate how an electron or hole will interact
with its parent impurity atom. mo and o are replaced by m* (effective mass) and
s respectively, since we are now concern with charge embedded in a
semiconductor and not in vacuum (or free space).
Source: http://web.eng.gla.ac.uk/groups/sim_centre/courses/hydrogenic/hydro_1.html
Slide #
1
Radiative transitions in semiconductors
1
• Process 1: Intraband transition
• Process 2: Band-to-band
transition
• Process 3: Excitonic transition
• Process 4: Valence band to
donor transition
• Process 5: Conduction band to
acceptor transition
• Process 6: Shallow donor to
shallow acceptor transition
excitons
shallow donors
5
3
6
4
Deep donors
2
Deep acceptors
shallow acceptors
Others: Donor to conduction
band, acceptor to valence band
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Intraband and interband transitions
Process 1: Intraband transitions
Hot electrons relax their energy mainly by
emitting phonons, but sometimes under
phonon’s or/and other electron’s assistance
can also emit photons. This mechanism is
truly rare as many particles are involved
Process 2: Band-to-band transitions
K
Direct
Indirect
Peak of the emission spectrum   hc/Eg
Direct bandgap: a ( E ) = A0 ( E - Eg )1/2
A( E - E g  E p ) 2
Indirect bandgap: a E  =
  Ep 
 - 1
exp 
a = absorption coefficient,
KT


Ep is the phonon energy. Intensity proportional to a
+ve and –ve signs are for absorption and emission
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Other radiative transitions
Process 3: Excitonic transitions
For free excitons: hv = Eg - Eexbind
1
For bound excitons: hv = Eg - Eexbind – Eb
Eb is the energy binding the exciton to the
donor or acceptor
excitons
Process 4 and 5: Free-bound transitions
For Doh: hv = Eg - ED
3
For Aoe: hv = Eg - EA
shallow donors
5
6
4
Deep donors
2
Deep acceptors
shallow acceptors
Process 6: Donor-acceptor pair
transitions
2
hv ( r ) = E g - ( E A  E D ) 
e
4r
where r is the distance between the donor and acceptor
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