Semiconductor Drift & Diffusion Currents: Lecture 7 by Dr. Alan Doolittle at Georgia Tech , Study notes of Electrical and Electronics Engineering

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Lecture 7

Drift and Diffusion Currents

Reading:

Pierret 3.1-3.

Ways Carriers (electrons and holes) can change concentrations•Current Flow:

•Drift: charged particle motion in response to an electric field.•Diffusion: Particles tend to spread out or redistribute from areasof high concentration to areas of lower concentration •Recombination: Local annihilation of electron-hole pairs•Generation: Local creation of electron-hole pairs

Drift

Current Density J[A/cm

2 ]

Electric Field [V/cm]

• ElectronMotion

• HoleMotion

Given current density J (I=J x Area) flowing in a semiconductorblock with face area A under the influence of electric field E, the

component of J due to drift of carriers is:J |^ pDrift

= q p v

d^

and

J^ n^ |^ Drift

= q n v

d

Area A Hole Drift current density

Electron Drift current density

ECE 3040 - Dr. Alan Doolittle

At low electric field values,J = qpp^

μp

E^

and

J^ n^ = qn

μn

E

μ^ is the “mobility” of the semiconductor and measures the ease with whichcarriers can move through the crystal. [

μ]=cm

2 /V-Second

Thus, the drift velocity increases with increasing applied electric field.

More generally, for Silicon and Similar Materials the drift velocity can be

empirically given as:

Drift

  

∞ → →

≅   

  

  

  

=^

E

when v

E

when E

v

E E

v

o sat

o o sat

d

0

1

1

μ

μ μ

β β

where v

sat^

is the saturation velocity

ECE 3040 - Dr. Alan Doolittle

Drift E [V/cm]

Drift Velocity [cm/Sec]

v^ sat

μ~ E^ o

v GaAs and similar materials peak

Designing devices to workhere results in faster operation

Georgia Tech

Mobility

μis the “mobility” of the semiconductor and measures the ease with which

carriers can move through the crystal. [

μ]= cm

2 /V-Second

μn ~1360 cm

2 /V-Second for Silicon @ 300K

μp ~460 cm

2 /V-Second for Silicon @ 300K

μn ~8000 cm

2 /V-Second for GaAs @ 300K

μp ~400 cm

2 /V-Second for GaAs @ 300K

Drift

• ,

,

p n

p n^

q m

τ

μ

=

Where <

τ> is the average time between “particle” collisions in the semiconductor.

Collisions can occur with lattice atoms, charged dopant atoms, or with othercarriers.

Length L [cm]

Area A[cm

2 ]

Do not confuse Resistance and Resistivity or Conductance

and Conductivity

Resistance to current flow along length L (I.e. theelectric field is applied along this samples length).R=

ρL/A or in units, [ohm-cm][cm]/[cm

2 ]=[ohms]

Energy Band Bending under Application of an Electric Field

Energy Band Diagrams represent the energy of an electron.When an electric field is applied, energies become dependent on theirposition in the semiconductor.If only energy E

is added, then all energy would go to generating theg^

electron and hole pair.

Æ

No energy left for electron/hole motion. (I.e the

electron only has potential energy, and no kinetic energy).If energy E>E

is added, then the excess energy would allow electron/holeg^

motion. (Kinetic energy).

KE of electrons = E-E

for E>Ec

c

KE of holes = E

-E for E<Ev

v

Energy Band Bending under Application of an Electric Field

Diffusion

Nature attempts to reduce concentration gradients to zero.

Example: a bad odor in a room.

In semiconductors, this “flow of carriers” from one regionof higher concentration to lower concentration results in a“diffusion current”.

Total Current

n p

n

n

Diffusion n

Drift n n

p

p

Diffusion p

Drift p p

J J andJ

n

qD nE q

J

J andJ

p

qD pE q

J

J SinceJ

=

∇

=

=

∇

−

=

=

μ μ

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