Transcript 2014.10.9

DEE4521
Semiconductor Device Physics
Lecture 3b:
Transport: Generation and Recombination (g-r)
Prof. Ming-Jer Chen
Department of Electronics Engineering
National Chiao-Tung University
October 9, 2014
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Textbook pages involved
This lecture accompanies pp. 131–153 of
textbook.
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Energy band diagram of the semiconductor of Figure 3.18, under electrical bias and optical illumination. The
combination rate R, thermal generation rate Gth, and the optical generation rate Gop are illustrated.
Figure 3.19
Bulk Generation or Recombination rate: per unit volume per unit time
Microscopic Picture
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3-20
Optical injection:
A powerful means to address g-r process.
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Quasi-Fermi Levels
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(a) Illustration of minority carrier diffusion in a surface-illuminated p-type semiconductor. The absorption is
assumed to occur at the surface (how to make it real?). (b) Plots of the excess minority carrier concentration
as a function of distance into the bar with increasing time. As the excess carriers are generated at the surface,
they diffuse to regions of lower concentration, where they recombine.
Figure 3.22
Example 1
Transient
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3-23
Illustration of quasi Fermi levels for electrons and holes for the steady-state nonequilibrium case of
Figure 3.22, with external field = 0.
Figure 3.24
Level Split due to Carrier (Optical) Injection
Equilibrium
no = NC exp(-(EC-EF)/kBT) = ni exp((EF-Ei)/kBT)
po = NV exp(-(EF-EV)/kBT) = ni exp((Ei-EF)/kBT)
Quasi-Equilibrium (or non-equilibrium with a small field applied)
n = NC exp(-(EC-EFn)/kBT) = ni exp((EFn-Ei)/kBT)
p = NV exp(-(EFp-EV)/kBT) = ni exp((Ei-EFp)/kBT)
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3-25
Thermal generation rate
R G 
R G 
Net recombination rate
R–G=
p

n-type bulk
p
n
n
p-type bulk
Thermal recombination rate
Principle of detailed balance
Assume trap level Et at midgap
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pn  ni
 p ( n  ni )   n ( p  ni )
Hole lifetime
Electron lifetime
p o no  ni2
Equilibrium
pn  ( p o  p )( no  n)
p  n
Quasi-equilibrium
For optical injection (photon absorption) case
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The geometry for determining the continuity equation. The rate at which carriers accumulate in the
incremental volume depends on the incoming and outgoing currents as well as the recombination and
generation within the region dx.
Figure 3.17
3-18
Then we can write the Continuity Equation according to
the
Conservation of Flux in two channels (one of conduction
band and one of valence band):
For p-type semiconductor:
dn/dt = dFn/dx + (Gn –Rn) = (1/q)(dJn/dx) + (G – R)
= dn/dt = (1/q)(dJn/dx) + (Gop –(n/n))
dp/dt = dFp/dx + (Gp –Rp) = (1/q)(dJp/dx) + (G – R)
= dp/dt = (1/q)(dJp/dx) + (Gop –(n/n))
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The geometry for determining the continuity equation. The rate at which carriers accumulate in the
incremental volume depends on the incoming and outgoing currents as well as the recombination and
generation within the region dx.
Figure 3.17
Then we can write the Continuity Equation according to
Conservation of Flux in two channels (one of conduction
band and one of valance band):
For n-type semiconductor:
dn/dt = dFn/dx + (Gn –Rn) = (1/q)(dJn/dx) + (G – R)
= dn/dt = (1/q)(dJn/dx) + (Gop –(p/p))
dp/dt = dFp/dx + (Gp –Rp) = (1/q)(dJp/dx) + (G – R)
= dp/dt = (1/q)(dJp/dx) + (Gop –(p/p))
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3-18
These expressions may be misleading from the aspect of the
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the conservation of flux.
Schematic of a circuit used to measure minority carrier lifetime in semiconductors.
Figure 3.18
Steady State
Example 2
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3-19
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Valid only for a sample thickness of no more than the reciprocal
of the absorption coefficient .
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Variation of excess carriers in a semiconductor under pulsed illumination. (a) When the light is turned on, the
excess carrier concentration increases exponentially. For the complete pulse, (b) the rise and fall time
constants are equal to the minority carrier lifetimes.
Figure 3.20
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Plot of minority carrier lifetime in uncompensated high quality Si as a function of doping concentration NA or
ND.
Figure 3.21
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Example 3 (average time for a carrier to stay in a band)
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This thought experiment is quite interesting.
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