Transcript Document

DEE4521
Semiconductor Device Physics
Lecture 5
G-R Process
Prof. Ming-Jer Chen
Department of Electronics Engineering
National Chiao-Tung University
Nov. 5, 2012
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Optical injection:
A powerful means to address g-r process.
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The electromagnetic spectrum. (The frequencies of acoustic waves are given for comparison although they are
not electromagnetic waves.)
Figure 11.1
Photon Energy (eV)
= 1.24/Wavelength (um)
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Some Concepts on Photons
• Golden Rule:
Ephoton(eV) photon (m) = 1.24
• Photons, being massless entities, carry very little
momentum, and a photon-assisted transition is essentially
vertical on an E-K plot.
(Kphoton = 2/photon. If Ephoton = 1.42 eV, then photon = 0.87
m. Clearly, photon >> a and Kphoton << 2/a)
(see p.228 of the textbook)
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Overlap of Electron E-K Locus and Photon E-K Locus
can determine some of interesting properties and even can be
related to Einstein’s photoelectric effect.
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(a) A photon of energy 2.06 eV is incident on a material of energy gap 2.5 eV. The photon cannot be absorbed.
(b) The band gap is small enough that allowed states separated by 2.06 eV exist, thus the photon can be
absorbed. The photon’s energy is given to the electron. (c) In emission, the electron goes to a lower energy
state, releasing the extra energy in the form of a photon.
Figure 1.19
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1-19
(a) At equilibrium, electrons and holes are generated and destroyed at equal rates, thus maintaining some
constant equilibrium n0 and p0. (b) When light shines on the sample, the photons can be absorbed, producing
extra electron-hole pairs.
Figure 3.13
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3-14
For absorption to occur, K must be conserved as well as E. (a) A direct gap semiconductor; on the left is the
E-K diagram, and on the right the conventional energy band diagram. (b) An indirect gap material (so called
because conduction band minimum and the valence band maximum do not occur at the same value of K).
Figure 3.14
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3-15
Optical emission. The electron loses energy, giving off the excess as a photon of E H hv.
Figure 3.15
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Emission on the E-K diagram. Both K and E must be conserved. (a) A direct gap material; (b) an indirect
semiconductor.
Figure 3.16
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3-17
Phonon E-K
(Phonon = Lattice Vibrations)
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Electron-Hole Pair Separation
For Direct-gap semiconductors,
the upward transition probability for electron-hole pair separation = f1f2f3.
f1: the probability of finding a filled state in valence band
f2: the probability of finding a photon
f3: the probability of finding a final, unfilled state in conductance band
For Indirect-gap semiconductors,
upward transition probability for electron-hole pair separation = f1f2f3f4.
f4: the probability of finding a phonon
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3-20
Illustration of optical absorption in an indirect semiconductor involving an electron, a phonon, and a photon.
The wave vector needed to make the transitions comes almost entirely from the phonon; the phonon
_
contributes a small amount of energy, hw, as well, but most of the energy is supplied by the photon.
Figure S1B.12
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S1B-12
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
Rate: per unit volume per unit time
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3-20
Absorption coefficients of some semiconductor materials. The indirect-gap materials are shown with a broken
line. Based on data from References 1 and 2.
Figure 11.4
Only case of Ephoton > EG is shown
Indirect edge
Direct edge 15
Quasi-Fermi Levels
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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)
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
po no  ni2
Equilibrium
pn  ( po  p)(no  n)
p  n
Quasi-equilibrium
For optical injection (photon absorption) case
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Minority carrier diffusion lengths Ln and Lp as functions of impurity concentration NA or ND in
uncompensated high quality Si.
Figure 3.23
Ln = (Dnn)1/2
Lp = (Dpp)1/2
Diffusion Length:
The critical distance a carrier can move without being annihilated.
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3-24
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 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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3-18
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.
Six Working Examples
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A generic photodiode.
Figure 11.2
Example 1
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A solar cell illuminated from the left.
Figure 11.9
Steady State
Example 2
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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 3
Transient
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3-23
Example 4
The Haynes-Shockley Experiment:
Carrier Transient Behaviors
Light Flash
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Consider a very intense light source which produces an extremely large
number GL (or GOP) of excess carrier pairs per unit volume per unit time,
over an extremely small length , and an extremely short time T (<<
carrier lifetime). The net result is a flash light, producing instantaneously
at t = 0 a plane of excess carrier pairs at x = 0 having Po excess carriers
per unit area:
Po = lim(GLT), GL ,  0, T  0
Then by solving the continuity equation for holes in a uniform n-type
semiconductor rod in the presence of an electric field Eo:
d 2 p
dp p dp
Dp
  p Eo


2
dx  p
dx
dx
One can derive one solution for the excess hole concentration:
t

Po
p
p( x, t ) 
e e
2 D p t
( x Eo t ) 2

4 D pt
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Schematic of a circuit used to measure minority carrier lifetime in semiconductors.
Figure 3.18
Steady State
Example 5
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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 6
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