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3D Integration and Device Lab. (http://tidlab.sogang.ac.kr)

EEE2120: Physical Electronics I – Woo Young Choi Dept. EE, Sogang Univ.

Lecture 8: SemiconductorFundamentals VIII

Woo Young Choi

Dept. Electronic Eng.

Sogang Univ.



Contents

• Reading: pp. 110 ~ 143

• Generation and recombination

• Excess carrier concentrations

• Minority carrier lifetime

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Generation andRecombination

• Generation: a process by which electrons and

holes are created in pairs

• Recombination: a process by which electrons

and holes are annihilated in pairs

• Generation and recombination processes act tochange the carrier concentrations, and thereby

indirectly affect current flow



Generation Processes

Band-to-Band R-G Center (dominant in Si and Ge)

(trap-assisted)

Impact Ionization(only occurs when

large E is present)

Traps are created

due to impurities or defects.

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Recombination Processes

Direct(occurs in GaAs, GaN

and GaP)

Auger (occurs in heavily-

doped material)

Recombination in Si is primarily via R-G centers

R-G Center (dominant in Si and Ge)

(trap-assisted)

Rate is limited by minority

carrier trapping.



Direct v s . Indirect Band GapMaterials

Little change in momentumis required for recombination

momentum is conserved by

photon emission

Large change in momentumis required for recombination

momentum is conserved by

phonon + photon emission

E-k Diagrams

GaAs, GaN Si, Ge

Photon-small

momentum

-significant

energy

Phonon-small

energy

-significant

momentum

2

*. . where p is momentum

pK E

m

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Excess CarrierConcentrations

0nnn

0 p p p

Charge neutrality condition:

pn

equilibrium values



“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:

– For a p-type material:

• However, the minority carrier concentration can be

significantly affected

so |||| 00 nnn pn

so |||| 00 p p p pn

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Indirect RecombinationRate

Suppose excess carriers are introduced into an n-typeSi sample (e.g. by temporarily shining light onto it) attime t = 0. How does p vary with time t > 0?

1. Consider the rate of hole recombination via traps:

2. Under low-level injection conditions, the hole

generation rate is not significantly affected:

p N c T p Rt

p

0 p N c T pmequilibriu Rt

p

mequilibriuGt

p

Gt

p

cp: capture coefficient



3. The net rate of change in p is therefore

0 p N c p N c T pT pGt

p

Rt

p

G Rt

p

0

1

( )

where (unit: s)

p

p T

p p

p T p T t R G

p c N

c N p p c N p

cp: capture coefficient

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Relaxation to EquilibriumState

n

n

t

n

p

pt

p

for electrons in p-type material

for holes in n-type material

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:



Minority Carrier(Recombination) Lifetime

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 orholes to facilitate recombination and are called

recombination-generation centers.

T nT p N cn N c p11

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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.)

16 30

4 30

10

10

p cm

n cm

2010 Ln

nG

20 6 14 310 10 10 Ln p G cm



What are p and n ?

What is the np product ?

Note: The np product can be very different from n i2.

16 14 16 30

4 14 14 30

10 10 10

10 10 10

p p p cm

n n n cm

30 3 210i

np cm n

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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:

kT E E

i

kT E E

i

n p

i

T iiT en penn

p pnn

n pn

t

p

t

n

/)(1

/)(1

11

2

and where

)()(



Summary

• Generation and recombination (R-G) processes affect

carrier concentrations as a function of t ime, 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:

• Generally, the net recombination rate is proportional

to

material)type-(p material)type-(n 11

T nT p N cn N c p

2innp

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