CARRIER TRANSPORTPHENOMENA

Topics 2

Carrier Transport Phenomenon

Carrier drift: mobility, conductivity and velocity saturation

Carrier Diffusion: diffusion current density, total current density

The Einstein relation

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Densities of charged particles are important to understand the electrical

properties of a semiconductor material and device.

Net flow of the electrons and holes in a semiconductor generate currents.The process by which these charged particles move is called transport.

Two basic transport mechanisms in a semiconductor crystal are:•Drift:- the movement of charge due to electric fields,•Diffusion:-the flow of charge due to density gradients.

Carrier transport determines the current-voltage characteristicsof semiconductor devices.

Carrier Transport Phenomenon

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2th

*B vm

2

1Tk

2

3holeorelectronofenergythermal.Av

The carriers undergo collision with vibrating atoms and charged dopant ions after travelling a distance resulting in scattering of the carriers.

nm10m1010x10sosec,10

vpathfreemean

collisionsbetweentimeaverage

813513

c

cth

c

Carrier Drift

sec/m10x3.2m

Tk3v,velocityThermal 5

*B

th

Electric field applied produces a force on electrons and holes, so that they are accelerated.This net movement of charge due to an electric field is called drift, which give rise to drift current.

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fielddrifttoduecarrierofvelocitynetAveragev,velocityDrift d

Carrier DriftOn application of an electric field, E, and a , = qE/m* acts on the carrier between collisions.

tm

q)t(v

p,n

t

v(t)

vd

p,n

p,n

p,n

p,n

dm

q

m

qv

,smallFor

.iscollisionbetweentimeAverage p,n

When the charged particle collides with anatom in the crystal, the particle loses most ofits energy. The particle will again begin toaccelerate and gain energy until it is againinvolved in a scattering process. Thiscontinues over and over again. Throughoutthis process, the particle will gain an averagedrift velocity which, for low electric fields, isdirectly proportional to the electric field.

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VelocitySaturation

p,n

p,n

p,n

dm

qv

,0For

E

v d

Drift velocity saturates at high fields

p

p

ppdp

n

nnndn

m

q,v,holesFor

m

q,v,electronsFor

Mobility:

mobilitym

q

p,n

p,n

p,n

vsat

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0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

1E+19 1E+21 1E+23 1E+25 1E+27

at/m3

m2/V

-se

c

µn

µp

Electron & hole mobilities:

• At low doping levels, the mobility is limited by collision with lattice, i.e., phonons

• At high doping levels, mobility is limited by scattering by dopant ions

• µn > µp for same doping level, since holes have higher effective mass than electrons.

For Silicon

Ge Si GaAs

μn,, m2/V-sec

(cm2/V-Sec)

0.39

(3900)

0.14

(1400)

0.85

(8500)

μp, m2/V-sec

(cm2/Vsec)

0.19

(1900)

0.047

(470)

0.04

(400)

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Drift Current :

ndndriftn qnqnvJdensitycurrentdriftElectron

)pn(qJJJ pndriftp

driftn

drift

Current due to drift of carriers in presence of an electric field then will be given by:

)pn(q1

tyconductiviwhereJ

pn

drift

pdpdriftp qpqpvJdensitycurrentdriftHole

driftnJ

driftpJ

vdn

Electron Drift Flow

vdp

Hole Drift Flow

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Resistivity of Silicon :

Mobility of carriers is affected by scattering mechanisms.Scattering mechanism is of two types – phonon and impurity[A] Electrons move freely and unperturbed in a perfect periodic

potential in a solid.•But the thermal vibrations cause a disruption of the potentialfunction, resulting in an interaction between the electrons orholes and the vibrating lattice atoms.•This affect the velocity and mobility of the carriers which iscalled to as phonon scattering.[B]Impurity atoms are added to the semiconductor to control oralter its characteristics.•These impurities are ionized at room temperature so that acoulomb interaction exists between the electrons or holes andthe ionized impurities.•This coulomb interaction produces scattering or collisions andalso alters the velocity of the charge carrier:- impurity scattering.

Scattering Mechanisms:

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IPTpnIPT

111111

,

• Phonon scattering increases with temperaturep = collision time of carriers due to phonon scattering p 1/(phonon density x thermal velocity) 1/(T*T

1/2) T-3/2

• Impurity scattering increases with concentration of impurityatoms and defects.

• As temp. increases, carriers posses high thermal vel., so easily pass by the impuritiesI = coll. time of electron due to impurities and defects • Total Scattering effect =

Scattering Mechanisms:

pn

Tpn m

q,

,

)N(N

T

da

3/2

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Mobility vs. Temperature

Mobility is determined by• Lattice scattering (dominant

at high T)At small dopant conc., μ decreases with increasing T, Indicating the dominance of phonon scattering

• Impurity scattering (dominant at low T)

At very high dopant conc.,and low temperature, impurity Scattering dominate, so μ increases with increasing T

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Microelectronics I

Carrier diffusion

Diffusion; process whereby particles from a region of high concentration toward a region of low concentration.

dividerCarrier

Ele

ctr

on c

oncentr

ation,

n

Position x

Electron diffusion

current density

Electron flux

dx

dneDJ

dx

dnDeJ

ndifnx

ndifnx

=

−−=

|

| )(

Dn; electron diffusion coefficient

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Microelectronics I

Hole

centr

ation,

p

Hole diffusion

current density

Hole flux

dx

dpeDJ

dx

dpeDJ

pdifpx

pdifpx

−=

−=

|

|H

ole

centr

ation,

p

Position x

current density

Dp; hole diffusion coefficient

Diffusion coefficient; indicates how well carrier move as a result of density gradient.

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Carrier Diffusion

The left hand side particle is likely to move to the right and vice versa: Net flow (L R) per second= nL* v - nR* v

nDdx

dnDF

F

D: diffusion coefficient

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Number of particles change / second = Net number of leaving or entering particles:

nDnDt

n 2

F

Total Current Flow Electron diffusion current:

Hole diffusion current:

Net electron current:

dx

dneDeFxJ nDn

dx

dpeDeFxJ ppDp

dx

dneDxExnexJ nnn

dx

dpeDxExpexJ ppp

Net electron current:

Net hole current:

xJxJxJ np Net current:

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6 Optical Absorption&Generation.pdfOptical properties of semiconductorsSlide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Quasi Fermi levels, definitionsSlide Number 26Slide Number 27Slide Number 28