Lec. 4 1 Excess Carriers • Optical Absorption i) No light, There are thermal generated carriers. ii) Turn Light ON semiconductors We can generate electron-hole pairs (EHPs or excess carriers) depending on the frequency. Excited electrons loses energy to lattice until it reaches the equilibrium with other C.B electrons. Luminescence Photoluminescence: excited by photon Electroluminescence: Cathodoluminescence : cf) fluorescence, phosphorescence ) exp( 0 l I I t : absorption coefficient t I : Transmitted light 0 I : Initial photon beam intensity high energy electron bombardment excited by current Semiconductor device operate by the excess carriers (created by optical excitation, pn forward bias) In chap 4, we study excess carriers’ properties created by optical absorption.
Transcript
Lec. 41
Excess Carriers
• Optical Absorption i) No light,
There are thermal generated carriers.
ii) Turn Light ON semiconductors
We can generate electron-hole pairs (EHPs or excess carriers) depending on the frequency.
Excited electrons loses energy to lattice until it reaches the equilibrium with other C.B electrons.
Luminescence
Photoluminescence: excited by photon
Electroluminescence:
Cathodoluminescence :
cf) fluorescence, phosphorescence
)exp(0 lIIt : absorption coefficient
tI : Transmitted light
0I : Initial photon beam intensity
high energy electron bombardment
excited by current
Semiconductor device operate by the excess carriers (created by optical excitation, pn forward bias) In chap 4, we study excess carriers’ properties created by optical absorption.
Ex) 1017 cm-3 n-type Si has 1014 cm-3 excess carrier
This equation is based on one time exposure.
What if constant light or voltage is applied?
SiS D
G
Lec. 43
)]()()[(
)]()][([)(
200
002
tntnpn
tpptnnndt
tnd
r
rir
)()(0 tnp
dttnd
r
Low level injection
nr ttp nenetn /0)(
:n lifetimeionrecombinat )(1
00 pnrn
Ex) 1017 cm-3 p-type Si has 1014 cm-3 excess carrier
This graph may not be a low level injection. But clearly state n, p decay.
Lec. 44
Quasi-Fermi Level, “ Fn and Fp ”
Ec
EF
Ei
Ev
Ec
Fn
Ei
Ev
Fp
light
(=EF), in case of
low-level injection
under thermal equilibrium nonequilibrium2in0n0 npn
majority carrier
minority carrier
n0nn
2inn
piin
inin
2inn
nnn
injectionlevel-low:npnii)
]kTFEexp[np
]kTEFexp[nn
injectionlevel-high:npni)
]kTFEexp[np pi
in
이면 Fn EF
o Quasi-Fermi Levels
; energy levels used to specify the carrier concentration inside a semiconductor under non-equilibrium conditions.
> n0n
Lec. 45
Steady State Excess Carriers
))(()( 00 ppnnnpgTg rrop
If a steady light is shone on the sample, optical generation rate gop will be added to thermal generation.
Thermal generation
Steady optical generation
Recombination
])[()( 20000 nnpnpngTg rrop
nrop
nnpng )( 00
nopgpn
ex) An p-type Si sample with Na = 3x1016/cm3 is steadily illuminated such that gop= 1021 EHP/cm3-s. If taun= taup =1 µs for the excitation, calculate the separation in the quasi-Fermi levels, (Fn-Fp). Draw a band diagram.
1. n2. Low level injection or high level injection?
3. Fn-Ei=? Ei-Fp=?
4. Fn-Fp=?
Lec. 46
Carrier Transport
• Current Density Equations
Two basic transport mechanisms in semiconductor crystal
( 1 ) Drift
The movement of charge due to electric field
( mobility : collisions with semiconductor atoms and with
ionized dopant atoms. )
(2) Diffusion
The flow of charge due to concentration gradient
( diffusion coefficient )
• Due to thermal energy, e- and h are in constant motion with scattering with lattice. Thus the net movement is “zero” unless there is Drift and Diffusion
velocityThermal :300Kat sec/10 ~
energy) (kinetic 21
04.0 ~ 23 energy Thermal
7
2*
cmv
vm
eVTk
th
thn
B
Lec. 47
Diffusion
Flux of carriers
Different carrier concentration with position (i.e., concentration gradient) generates diffusion of charge carriers. Diffusion current
In practical cases,
Lec. 48
Flux of e- and h
)(
))()(()(
arge).(Flux)x(ch isdiffusion this toduedensity Current
)()( carriers ofFlux
dxxdnqD
qdx
xdnDdiffJ
dxxdnDx
n
nn
nn
Lec. 49
tly.significan contributecan carrier minority current,diffusion for Thus,
.dxdpor
dxdn toalproportion is J(diff) whilepor n toalproportion is J(drift)
)(
)(
pntotal
ppp
nnn
JJJdx
xdpqDpqJ
dxxdnqDnqJ
Diffusion and DriftIf E field is present in addition to carrier gradient, the current densities will be
Electric field
Fig 4-14
+ -
Lec. 410
Current Flow in Non-uniformly Doped Semiconductor under Equilibrium.
Under equilibrium conditions the total current is identically “zero”.The electron and hole current density, and , must also independently “zero”.
“A nonzero electric field is established inside nonuniformly doped semiconductors under equilibrium conditions.”
And “a nonuniform doping” gives rise to carrier concentration gradients,
Jn|drift and Jn|diff have same magnitude but opposite direction.
0dxdpqDpqJJ
0dxdnqDnqJJ
ppdiffpdriftp
nndiffndriftn
εμ
εμ
0J driftn
0J diffn
0)J(J diffndriftn
nJ pJ
n+ ni
Diff
Drift
0dx
dEF
Fermi level at equilibrium must be constant throughout materials. (Chap. 3.5)
(Until Equilibrium)
Lec. 411
Einstein Relationship
Insert (2) into (1)
Same for hole
Einstein Relationship for electrons
Einstein Relationship for holes
ε
ε
εμ
nkTq
dxdE)/kT]Eexp[(EnkT
1dxdn
)/kT]Eexp[(EnndxdE
q1
0dxdnqDnqJJ
iiFi
iFi
i
nndiffndriftn
nn DkTq)(qn)(qn εμε
qkT
μD
n
n
qkT
μD
p
p
------- (1)
------- (2)
= 1014 /cm3, RT
= 0.0259 1358 cm2/V sec
= 35.2 cm2/sec ( in Si )
Nd
DkT
qn n ( )
ex)
Lec. 412
Continuity Equation
The overall rate of hole increase
(1) the number of holes flowing into the slab (+ )
(2) the number of holes flowing out ( - )
(3) the rate at which holes are generated ( + )
(4) the rate at which they recombine ( - )
1
2
3
4
For one dimensional case,
1 2
3 4Jp(x) G R Jp(x+dx)
Assumption of steady state injection,
1. No generation
2. No build-up carriers.
pLxpepxp /0)(
Lec. 413
(Current is carried by diffusion (negligible drift))
No generation
(no build-up)
Negligible drift
Lec. 414
Minority Carrier Diffusion Length
nnn
ppp
DLDLτ
τ
; the average distance minority carriers can diffuse into a sea of majority carriers before being annihilated.
