Carrier Transport Phenomena And MeasurementChapter 5

26 February 2014

22

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

33

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

99

Conductivity

EEnpeJ npdrift )(

)( np npe Conductivity:

Resistivity: (Ω-cm)-1

)(

11

np npe

N-type semiconductor:ndnnp eNennpe )(

P-type semiconductor:papnp eNepnpe )(

Intrinsic semiconductor: )()( npinp ennpe

(Ω-cm)-1

1111

Resistance

A

IJ

L

VE

EJ

L

V

A

I RIIA

LI

A

LV

A

L

A

LR

1414

Non-equilibrium Excess Carriers in Semiconductors (Chapter 6)

When external field (electric, thermal, optical) is applied on the semiconductor, the semiconductor is operating under non-equilibrium conditions

Excess electrons in the conduction band and excess holes in the valence band may exist in addition to the thermal equilibrium condition

Excess carriers’ movements: generation, recombination, drift, and diffusion

1515

Total Diffusion Current

dx

dneDJ ndifnx ,

Electron diffusion current

Hole diffusion current

dx

dpeDJ pdifpx ,

Total diffusion current

)(dx

dpD

dx

dnDeJ pndif

Dn: electron diffusion coefficient (m2/s)

Dp: hole diffusion coefficient (m2/s)

1616

Low-Level Injection and High-Level Injection

Low-level injection: excess carrier concentration is much less than thermal equilibrium majority carrier concentrations

• n-type material: no>>po, δn(t) << no

• p-type material: po>>no, δn(t)<<po

High-level injection: excess carrier concentration is comparable to or greater than the thermal equilibrium majority carrier concentrations

• n-type material: no >> po, δn(t) >= no

• p-type material: po >>no, δn(t)>= po

1818

Carrier Generation and Recombination

Mechanisms of generation and recombination: band-to-band, traps (recombination centers)

19

Excess Carrier Generation and Recombination

When external force (electric, optical, thermal) is applied, excess electrons and holes are create in pairs

pn RR

With generation of excess carriers, concentration of electrons and holes are increased

pn gg

Electrons and holes are recombined at the same time of generation are equal

nnn 0 ppp 0

2020

Carrier Generation and Recombination in Equilibrium (Band-to-Band)

For direct band-to-band generation, the electrons and holes are created in pairs

00 pn RR

For direct band-to-band recombination, the electrons and holes are combined in pairs

00 pn GG

In thermal equilibrium, the generation and recombination rates are equal

0000 pnpn RRGG