Debye length + - + - + - + - + - + - + - + - + - +

Debye length2 vV

+

-

+

-

+

-

+

-

+

-

+

-+

-

+

-

+

-

+

V

x

2

2

d V

dx i en n e

eV0TB e

n e1 e

0B e

eV1 1 n e

T

Debye length

+

-

+

-

+

-

+

-

+

-

+

-+

-

+

-

+

-

+

V

x

2

2

d V

dx

0B e

eV1 1 n e

T

20

B e

n e V

T

x

TB e2n e0

0V V e

B eD 2

0

T

n e

Transient sheath in ion acoustic wave experiments in a plasma

02

20

1 expB e

eVn e

Td V

dx

2

2

dVU

dx

d V dU dV dUU

dx dV dx dV

dVE

dx

0

0

1 expB e

eVn e

TUdU dV

0

0

1 expB e

eVn e

TUdU dV

20

10

exp2

B e

B e

n e TU eVV C

e T

01

0

2expB e

B e

n e TdV eVU V C

dx e T

00 1

0

2expx B e

appliedB e

n e T eVV V V C dx

e T

0

0

1 expB e

eVn e

TUdU dV

1applied

B e

eV

T

2

2 20

02 2 B e

dVn e Vdx

T

0

0

1 1B e

eVn e

TUdU dV

20

0 B e

n edVdx

V T

20 0

0

exp

B e

x

V V n e

T

20

0 B e

n ew

T

1applied

B e

eV

T

01

0

2expB e

B e

n e TdV eVU V C

dx e T

0

0

2n eVdVU

dx

00

00

2applied

w

V

n edVdx

V

0

0

2 appliedVw

n e

MATLAB calculation

Basic model

p n

aN

dNhole diffusion

electron diffusion

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

Basic model

p n+-

space charge region

negative chargeaN positive chargedN

Basic model – thermal equilibriumno applied bias voltage

FE

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

cE

cE

vE

vE

FiEbi biE eV

FiEbi biE eV

bi biE eV

FneVFpeV

Reverse biased PN junction- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

bias RV Vtotal bi RV V V

WW

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

2 s bi R a d

a d

V V N NW

e N N

bi Rmax

2 V VE

W

Reverse biased PN junctionenergy diagram

cE

cEvE

vE

FiE

FiE

FnE

FpE

ReV

totaleV

Forward biased PN junction- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

W

bias FV V

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

W

- +

Forward biased PN junctionenergy diagram

cEcE

vEvE

FnEFpE bi Fe V V

-

+

Schottky barrier junctionThermal equilibrium

cE

vE

FiE

FE

nx

W

bi biE eVSchottky barriermetal surface

FE -

Schottky barrier junction

cE

vE

FiEFE

nx

FE

bias RV V

cE

vE

FiEFE

nx

FEcE

vE

FiEFE

nx

FE

biasV 0bias FV V

Characteristics of a Schottky diode and a PN junction diode

VDVT

D sI I e 1

reverse

saturation current

thermal potential

BT

TV

e

Basic assumptions

p n

aN

dNhole diffusion

electron diffusion

Maxwell Boltzmann distributions

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n+-

acceptor density in p regionp0 ap N

donor density in n regionn0 dn N

sharp boundaries

Basic assumptions

px nx0

hole concentration in n region2i

n0d

np N

electron concentration in p region2i

p0a

nn N

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

Basic assumptions

px nx0

total minority carrier hole densitynp total minority electron densitypn

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

Basic assumptions

excess minority carrier hole densityn n n0p p - p

-

excess minority electron density

p p p0n n n

px nx0

total minority carrier hole densitynp total minority electron densitypn

excess minority carrier hole densityn n n0p p - p

-

excess minority electron density

p p p0n n n

acceptor density in p regionp0 ap N donor density in n regionn0 dn N

hole concentration in n region2i

n0d

np N

electron concentration in p region2i

p0a

nn N

Electron energy profile- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

px nx0

where a d Bbi T T2

i

N N TV V ln V

en

Charge concentration- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

px nx0

where a d Bbi T T2

i

N N TV V ln V

en

VbiVa d T

2i

N Ne

n

eVbiTBe

n0 dn N

2i

p0a

nn

N

eVbiTB

p0 n0n n e

Charge concentration- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

px nx0eVbi

TBp0 n0n n e

n0 dn N

2i

p0a

nn

N


- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

W

bias FV V

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

W

due to space chargeE

due to applied potentialE


- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

bias FV V

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

W

e V Vbi appliedTB

p n0n n e

eVappliedTB

p0n e


- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

bias FV V

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

W

eVappliedTB

p p0n n e

eVappliedTB

n n0p p e

Evolution of the density perturbations

n

2n n nn

p p2p0

x x

p p ppD E g'

x tx

2p p p0L D

2n n

2 2p

d p p0

dx L

Drift due to the electric field

Diffusion of the perturbation

Generation of additional perturbationCollision lifetimeSteady-stateNeglect drift and generation


2

n nn2 2

p

d p p0 x x

dx L

eVappliedT nB

n n0p

x xp p e 1 exp

L

2p p p0L D


eVappliedT pB

p p0n

x xn n e 1 exp

L

2

p pp2 2

n

d n n0 x x

dx L

2

n n n0L D

Currents – sum of hole and electron diffusion currents

eVappliedT pB

p p0n

x xn n e 1 exp

L

np n p

x xn

dpJ x eD

dx

eVappliedT nB

n n0p

x xp p e 1 exp

L

pn p n

x xp

dnJ x eD

dx

Currents – sum of hole and electron diffusion currents

np n p

x xn

dpJ x eD

dx

pn p n

x xp

dnJ x eD

dx

The Cowasaki gets excellent gas mileage.

Simple three-dimensional unit cell

a

b

c

Debye length + - + - + - + - + - + - + - + - + - +

Documents

Transcript of Debye length + - + - + - + - + - + - + - + - + - +