1

Notes For 25 February

Electron and Hole Concentrations in Extrinsic Semiconductor

,expexpexp

)()(expexp0

kTEEn

kTEE

kTEEN

kTEEEEN

kTEENn

FiFi

FiFcFic

FiFFicc

cFc

,expexpexp

)()(expexp0

kTEEp

kTEE

kTEEN

kTEEEEN

kTEENp

FFii

FFiFivv

FFiFivc

Fvv

200 exp i

gvc n

kTE

NNpn

For both undoped material and doped

material under equilibrium condition

2

Position of Fermi Energy in Extrinsic Semiconductors

iFi

vv

iFi

ccF

np

kTENp

kTE

nn

kTENn

kTEE

00

00

lnln

lnln

,expexp0

kTEE

nkTEE

Nn FiFi

cFc

,expexp0

kTEEp

kTEENp FFi

iFv

v

Position of Fermi-level:

3

Position of Fermi Energy in Extrinsic Semiconductors

iFi

vv

iFi

ccF

np

kTENp

kTE

nn

kTENn

kTEE

00

00

lnln

lnln

,expexp0

kTEE

nkTEE

Nn FiFi

cFc

,expexp0

kTEEp

kTEENp FFi

iFv

v

Position of Fermi-level:

44

Variation of Fermi-Energy with Doping Concentration

55

Variation of Fermi-Energy with Temperature

66

Chapter 5 Carrier Transport Phenomena

Charged carriers in semiconductor: electrons and holes

Carrier transport: movement of electrons and holes

Mechanisms of carrier transport

Drift:

Diffusion:

charge movement due to electric field

charge movement due to density gradient

88

Carrier DriftObserve that the text uses “e” instead of “q” as a symbol for a unit of charge

Drift current densityddrift vJ

Current density due to the holesep

Drift velocity of holes Ev pdp

EenJ ntdrifn

Current density due to the holes

Current density due to the electrons

EepJ ptdrifp

Drift velocity of electrons Ev ndn

Total drift current density EnpeJ npdrift )(

Charge density:

Charge density: en

99

Definition of Carrier Mobility

Ev pdp Drift velocity of holes

Drift velocity of electrons Ev ndn

p : mobility of holes

n : mobility of electrons

Mobility: relates the average drift velocity of a carrier to the electric field

1010

Conductivity

EEnpeJ npdrift )(

)( np npe Conductivity:

Resistivity:

Unit: (Ω.m)-1

)(11

np npe

Unit: (Ω.m)

N-type semiconductor:ndnnp eNennpe )(

P-type semiconductor:papnp eNepnpe )(

Intrinsic semiconductor: )()( npinp ennpe

1414

Resistance

AIJ

LVE

EJ

LV

AI RII

ALI

ALV

AL

ALR