Carrier Transport

8/12/2019 Carrier Transport

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Dr.Dr. VinodVinod PatidarPatidar

Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)

Sir Padampat Singhania University, Udaipur 11

Carrier transport phenomenaCarrier transport phenomena

(i) Drift(i) Drift(ii) Diffusion(ii) Diffusion

Two kinds of charges exist in semiconductors: (i) electronsTwo kinds of charges exist in semiconductors: (i) electronsand (ii) holesand (ii) holes

Drift Current Density:Drift Current Density:

(i) Electron drift current:(i) Electron drift current:

(i) Hole drift current:(i) Hole drift current:

EnenevJ ndndriftn ==)(

EpepevJ pdpdriftp ==)(


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Total drift current:Total drift current:

)()( driftpdriftndrift JJJ +=

EpeEneJ pndrift +=

EpneJ pndrift )( +=

EJdrift =

)( pn pne +=

)(

11

pn pne +

==


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Diffusion current density:Diffusion current density:

(I) Diffusion hole current density:(I) Diffusion hole current density:

(ii) Diffusion electron density(ii) Diffusion electron density

Total diffusion current density:Total diffusion current density:

dx

dpeDJ pdiffusionp =)(

dx

dneDJ ndiffusionn =)(

dx

dpeD

dx

dneDJ pndiffusion =


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Total current density:Total current density:

Epnedx

dpeD

dx

dneD

JJJ

pnpn

diffusiondrift

)( ++=

+=

Epnepn

)( + Epne pn )( +

Induced electric field:Induced electric field:

Consider a semiconductor which is nonConsider a semiconductor which is non--uniformalyuniformaly doped withdoped with

donor impurity atoms. The donor concentration decreases as xdonor impurity atoms. The donor concentration decreases as x

increases. There will be diffusion of electrons from higherincreases. There will be diffusion of electrons from higherconcentration region to the lower concentration region i.e.concentration region to the lower concentration region i.e.

electrons will flow in positive xelectrons will flow in positive x--direction.direction.

The flow of electrons leaves behind a positively charged donorThe flow of electrons leaves behind a positively charged donor

ions.ions.

This separation of positive and negative charge induces anThis separation of positive and negative charge induces an

electric field, which opposes the diffusion process.electric field, which opposes the diffusion process.


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)(xNd

dx

xdN

xNe

kTE d

d

x

)(

)(

1

=

If is the concentration of donor atoms at a particIf is the concentration of donor atoms at a particularular

value of x , then the value of this electric field is given by:value of x , then the value of this electric field is given by:

In general, we can consider for nIn general, we can consider for n--type semiconductortype semiconductor

)()( xNxnorNn dd =

Einstein relation:Einstein relation:

For a non uniformly doped semiconductor in thermalFor a non uniformly doped semiconductor in thermal

equillibriumequillibrium, electron current and hole current should be zero., electron current and hole current should be zero.

0=+=dxdneDEenJ nxnn

)()( xNxn d=usingusing


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And substituting the value of EAnd substituting the value of Exx

e

kTD

n

n=

0==dx

dpeDEepJ pxpp

ekTD

p

p=


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Hall Effect:Hall Effect:

2v

LL

WW

dd

xx

zz yy

BBzz

ee--hh++

EEHHVVHH

IIxxVVxx


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Hall effect is usedHall effect is used

-- to determine that the given semiconductor is nto determine that the given semiconductor is n--type or ptype or p--type.type.

-- measure majority carrier concentration and majority carriermeasure majority carrier concentration and majority carrier

mobility.mobility.

2v

ZxH BqvqE =

The induced electric field in yThe induced electric field in y--direction is known as Hall Field.direction is known as Hall Field.

wEV HH =

wBvV zxH =

Drift velocity of holes:Drift velocity of holes:

)()( wdep

I

Aep

I

ep

Jv xxxdx ===


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2v

z

x

z

x

H Bepd

I

wBepwd

I

V ==

edV

BIp

H

Zx=

Drift velocity of electrons:Drift velocity of electrons:

)()( wden

I

Aen

I

en

Jv xxx

dx

===

zx

zx

H Bend

IwB

enwd

IV ==

edV

BIn

H

Zx=


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2v

xpx

x Epe

A

IJ ==

L

Vpe

wd

IJ xp

xx ==

wdepV

LI

x

xp =

wdenV

LI

x

x

n=

Similarly for nSimilarly for n--type:type:


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The Doping of Semiconductors (Extrinsic Semiconductors)

The addition of a small percentage of foreign atoms in the regularcrystallattice of silicon or germanium produces dramatic changes in theirelectrical properties, producing n-type and p-type semiconductors.

Pentavalent impurities:

Impurity atoms with 5 valence electrons produce n-type semiconductorsby contributing extra electrons.

Trivalent impurities:Impurity atoms with 3 valence electrons produce p-type semiconductorsby producing a "hole" or electron deficiency.


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p- and n- type semiconductors


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p-type semiconductor

The addition of trivalent impurities such as boron, aluminum or gallium to an

intrinsic semiconductor creates deficiencies of valence electrons,called"holes".The addition of acceptor impurities contributes hole levels low in thesemiconductor band gap so that electrons can be easily excited from the

valence band into these levels, leaving mobile holes in the valence band.This shifts the effective Fermi level to a point about halfway between theacceptor levels and the valence band.

Electrons can be elevated from the valence band to the holes in the band gapwith the energy provided by an applied voltage. Since electrons can beexchanged between the holes, the holes are said to be mobile. The holes aresaid to be the "majority carriers" for current flow in a p-type semiconductor.


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0=+=dxdneDEenJ nnn

When the external voltage is zero, the total electron and hole current

will be separately zero.

n

dnDEdx

n

n

=

=

n

p

n

p

n

nn

n

x

x n

dnDEdx

=n

p

n

nn

n

V

V n

dnDdV

2

1

p

n

p

n

n

nB

n

n

e

kT

n

nDVVVV lnln12 ====

=

kT

eVnn Bpn exp

=

kT

eVpp Bnp exp

Similarly, we may prove


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If V=-V2 at x=-xn, then

xxeNxeN

V ndd

+=

2

2DCx

xeNV d ++=

2

2

At x=0, V=0 it gives D=0, hence

22

222

2ndndnd xeNxeNxeNV

=+=

0=dx

dV

ndxeNC=At x=xn, it gives

)(2

22)(

22

22

12

ndpa

pandB

xNxNe

xeNxeNVVVV

+=

+===


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From the charge neutrality, we may say that

the space charge in n-region = space charge in p-region

ndpa xeNxeN =

d

pa

n N

xN

x =

+=

2

2

2 d

pa

dpaBN

xNNxN

eV

2

1

1

2

+

=

d

aa

B

p

N

NeN

V

x

Similarly

a

ndp

N

xNx =

+=

2

2

2 a

ndandB

N

xNNxN

eV

2

1

1

2

+

=

a

dd

Bn

N

NeN

Vx


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The total width of the depletion layer isnp xxx +=

2

1

2

1

1

2

1

2

+

+

+

=

a

dd

B

d

aa

B

N

NeN

V

N

NeN

Vx

2

1

)(2

+=

da

daB

NeN

NNVx

2

1

BVx

Hence the width of the depletion layer is proportional to theBV


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P-n junction diode characteristics

Forward BiasReverse Bias

Various p-n junction diodes:

Zener DiodeZener Breakdown

Avalanche Breakdown

Varactor diode (Reverse biased p-n diode)

Tunnel Diode (very highly doped forward biased p-n junction)

Photo diode (reversed biased p-n diode & exposed to radiation)

Light Emitting Diode (recombination of holes and

electrons in forward bias)

Solar Cell (basically high efficiency photo diodes)


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Carrier Transport