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Physical Electronics

Excess Carriers: Steady-state

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Today

Steady-state carrier generation

When semiconductor is under constant light illumination (

..)

Quasi Fermi level

This is not thermal equilibrium any more with excess carriers, and previous

equations for equilibrium are not available. ( equilibrium

, excess carrier,)

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Steady State Carrier Generation

At thermal equilibrium

Thermal generation rate = Thermal recombination rate

00

2)( pnnTg rir ==

Under a steady light shone

Generation rate = Recombination rateThermal generation rate + Optical generation rate

( )

opp

p

rop

r

rrop

gpn

pppng

pnTg

ppnnnpgTg

==

=+=

=)(

=

)+)(+(==+)(

00

00

00

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Example 4.3

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n0=1015 cm-3, Find EF level with respect to Ei using n0 and p0,

respectively.

Fermi level example 1

kTEE

i

kTEE

i

Fi

iF

enp

enn

/)(

0

/)(

0

=

=

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Previous example. And additional excess carriers of 1014 cm-3.

Find EF level with respect to Ei using n and p, respectively.

Fermi level example 2 (Wrong example)

kTEE

i

kTEE

i

Fi

iF

enp

enn

/)(

/)(

=

=

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For steady-state (Non thermal equilibrium)

Steady-state analogues of equilibrium Fermi level ()

Deviation of Fn or Fp from EF

How far the electron and hole populations are from equilibrium values

n0 or p0, when excess carriers are present.

When excessive EHPs

Large shift in the minority carrier quasi-Fermi level

Small shift in the majority carrier quasi-Fermi level

Separation of quasi-Fermi level, Fn-Fp

Direct measure of deviation from equilibrium

At equilibrium, Fn=Fp=EF

Quasi-Fermi Level

kTFE

i

kTEF

i

pi

in

enp

enn/)(

/)(

=

=

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Example 4.4

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If the incident light energy (photon energy, h) is larger than the bandgap, electrons in valence band

absorb the energy and generated into conduction band. ( ( h, chap 2

) band gap, valence band conduction band

generation. solid crystal semiconductor.) If light energy < bandgap, no absorption and just transmitted. ( bandgap

, generation,.)

Optical absorption

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For Si with bandgap of 1.1 eV ( Si, Si

bandgap 1.1eV)

Infrared transmit the Si ( Infrared (). Si.)

Visible light with high energy is absorbed, and Si is not transparent in visible

range. ( bandgap, Si

.)

Band gaps of semiconductors

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Actually, the absorption is not 100% but is determined by the thickness of solid. (

ideal 100%,.

.)

Example of Optical absorption

xeIxI

xIdx

xdI

=

=

0)(

)()( For thickness l

:

,0

l

l eII

=

absorption coeff.

Incident

monochromatic

light

Transmitted

light

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Absorption coeff.

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Luminescence

light emission by cold process

cf) Hot process: incandescence, heated materials

Photoluminescence

radiation from the recombination of the excited carriers by photon

absorption ()

Cathodoluminescence

radiation from the recombination of the created carriers by high-energy

electron bombardment of the materials (CRT TV)

Electroluminescence

radiation from the recombination of the injected carriers by the electrical

current (laser diode or laser pointer, LED)

Luminescience

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Photoluminescence

FluorescenceFast luminescent process

Life time of EHP: ~10-8 sec

PhosphorescenceSlow luminescent process

Life time of EHP: ~10 sec

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Slow luminescent process