Transcript Lecture #8 OUTLINE • Generation and recombination • Excess carrier concentrations • Minority carrier lifetime Read: Section 3.3

Lecture #8
OUTLINE
• Generation and recombination
• Excess carrier concentrations
• Minority carrier lifetime
Read: Section 3.3
Generation and Recombination
• Generation:
• Recombination:
• Generation and recombination processes act to
change the carrier concentrations, and thereby
indirectly affect current flow
Spring 2007
EE130 Lecture 8, Slide 2
Generation Processes
Band-to-Band
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R-G Center
EE130 Lecture 8, Slide 3
Impact Ionization
Recombination Processes
Direct
R-G Center
Auger
Recombination in Si is primarily via R-G centers
Spring 2007
EE130 Lecture 8, Slide 4
Direct vs. Indirect Band Gap Materials
E-k Diagrams
Little change in momentum
is required for recombination
Large change in momentum
is required for recombination
 momentum is conserved by
photon emission
 momentum is conserved by
phonon + photon emission
Spring 2007
EE130 Lecture 8, Slide 5
Excess Carrier Concentrations
equilibrium values
n  n  n0
p  p  p0
Charge neutrality condition:
n  p
Spring 2007
EE130 Lecture 8, Slide 6
“Low-Level Injection”
• Often the disturbance from equilibrium is small, such
that the majority-carrier concentration is not affected
significantly:
– For an n-type material:
| n || p | n0 so n  n0
– For a p-type material:
| n || p | p0 so p  p0
• However, the minority carrier concentration can be
significantly affected
Spring 2007
EE130 Lecture 8, Slide 7
Indirect Recombination Rate
Suppose excess carriers are introduced into an n-type
Si sample (e.g. by temporarily shining light onto it) at
time t = 0. How does p vary with time t > 0?
1.
Consider the rate of hole recombination via traps:
p
t R
2.
 c p N T p
Under low-level injection conditions, the hole
generation rate is not significantly affected:
p
t G
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
p
t G equilibrium

p
t R equilibrium
EE130 Lecture 8, Slide 8
 c p NT p0
3.
The net rate of change in p is therefore
p
t R G
p
t R G

p
t R

p
t G
 c p NT p  c p NT p0
p
 c p NT ( p  p0 )    p
where  p  c p1NT
Spring 2007
EE130 Lecture 8, Slide 9
Relaxation to Equilibrium State
Consider a semiconductor with no current flow in which
thermal equilibrium is disturbed by the sudden creation
of excess holes and electrons. The system will relax
back to the equilibrium state via the R-G mechanism:
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n
n

t
n
for electrons in p-type material
p
p

t
p
for holes in n-type material
EE130 Lecture 8, Slide 10
Minority Carrier (Recombination) Lifetime
 p  c 1N
p
T
 n  c 1N
n
T
The minority carrier lifetime  is the average time
an excess minority carrier “survives” in a sea of
majority carriers
 ranges from 1 ns to 1 ms in Si and depends on
the density of metallic impurities (contaminants)
such as Au and Pt, and the density of crystalline
defects. These deep traps capture electrons or
holes to facilitate recombination and are called
recombination-generation centers.
Spring 2007
EE130 Lecture 8, Slide 11
Example: Photoconductor
Consider a sample of Si doped with 1016 cm-3 boron,
with recombination lifetime 1 s. It is exposed
continuously to light, such that electron-hole pairs are
generated throughout the sample at the rate of 1020 per
cm3 per second, i.e. the generation rate GL = 1020/cm3/s
What are p0 and n0 ?
What are n and p ?
(Note: In steady-state, generation rate equals recombination rate.)
Spring 2007
EE130 Lecture 8, Slide 12
What are p and n ?
What is the np product ?
Note: The np product can be very different from ni2.
Spring 2007
EE130 Lecture 8, Slide 13
Net Recombination Rate (General Case)
• For arbitrary injection levels and both carrier types in
a non-degenerate semiconductor, the net rate of
carrier recombination is:
pn  n
n
p



t
t
 p (n  n1 )   n ( p  p1 )
2
i
where n1  ni e
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( ET  Ei ) / kT
and p1  ni e
EE130 Lecture 8, Slide 14
( Ei  ET ) / kT
Summary
• Generation and recombination (R-G) processes affect
carrier concentrations as a function of time, and
thereby current flow
– Generation rate is enhanced by deep (near midgap)
states associated with defects or impurities, and also
by high electric field
– Recombination in Si is primarily via R-G centers
• The characteristic constant for (indirect) R-G is the
minority carrier lifetime:
 p  c 1N
p
T
(n - typematerial)
 n  c 1N
n
(p - typematerial)
T
• Generally, the net recombination rate is proportional
to np  ni2
Spring 2007
EE130 Lecture 8, Slide 15