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. m o 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 3 excitons 6 shallow donors 5 4 Deep donors Deep acceptors 2 shallow acceptors Others: Donor to conduction band, acceptor to valence band

Slide # 2

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 Peak of the emission spectrum  

hc/E g

Direct bandgap: a (

E

) =

A

0 (

E

-

E

g ) 1/2 Indirect bandgap: a E p a = absorption coefficient, =

A

(

E

exp -

E g

  

E KT p

  

E

-

p

) 1 2 is the phonon energy. Intensity proportional to a +ve and –ve signs are for absorption and emission Direct K Indirect

Slide # 3

Other radiative transitions

Process 3: Excitonic transitions For free excitons:

hv

= E g - E ex bind For bound excitons:

hv

= E g - E ex bind – E b E b is the energy binding the exciton to the donor or acceptor Process 4 and 5: Free-bound transitions 1 excitons For D o

h : hv

= E g - E D For A o

e

:

hv

= E g - E A 3 6 shallow donors shallow acceptors 4 5 Deep donors Deep acceptors 2 Process 6: Donor-acceptor pair transitions

hv

(

r

) =

E g

(

E A



E D

) 

e

2 4 

r

where

r

is the distance between the donor and acceptor

Slide # 4