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7.4.1 Free carrier reflectivity and absorption
Assume the system is lightly damped,  ïƒ 0,  ïƒ 0, r
ïƒ 1, zero reflectivity occurs at a frequency given by:
2 
 opt
 opt  1
processes with a single frequency-independent
scattering time  deduced from the DC conductivity.
2p
By fitting this formula to the data, the effective mass of
InSb can be determined.
By splitting the r into its real and imaginary parts:

2p  2 

1   opt 1 
 1  2  2 


 opt2p 
2 
(1  2  2 )
A free carrier transition in a doped semiconductor.
p-type semiconductors show another effect, this is called
intervalence band absorption, in addition to those related
with the free carriers.
In a typical semiconductor, with  ~ 10-13 s at RT,  >> 1
in near-infrared. Free carrier term in r is small, therefore,
1 opt and 2 << 1 , n= (opt )1/2 and  = 2/ 2n. The
absorption coefficient:
 opt2p
Ne2 1
N
 free carrier 


.
nc2  m 0 nc 2 2
Experimentally,  free carrier   ,  is in the range 23. The departure from the predicted value of 2 is caused
by the failure of the assumption that  is independent of
. The mechanism that can contribute to the momentum
conservation process include phonon scattering and
scattering from their ionized impurities. It is
oversimplification to characterize all the possible
scattering
The figure shows the valence band of a p-type III-V
semiconductor. The unfilled states near k=0 is due to the
p-type doping. EF is the Fermi energy determined by the
doping density. The arrow indicate: (1) transition from the
light hole (lh) band to the heavy hole (hh) band; (2)
transition from the spilt-off (SO) band to the lh band; and
(3) transitions from the SO band to the hh band. The
absorption occurs in the infrared, and can be a strong
process because no scattering events are required to
conserve momentum.