Electronics -1, Lecture 05

8/13/2019 Electronics -1, Lecture 05

1/19

Dr. Nasim Zafar

Electronics 1

EEE 231 BS Electrical EngineeringFall Semester 2012

COMSATS Institute of Information Technology

Virtual campus

Islamabad


2/19

Semiconductor device lab.Kwangwoon

U n i v e r s i t y

Semiconductor Devices.

Carrier Transport in Semiconductors

Lecture No: 5

Diffusion of Carriers

Diffusion Processes

Diffusion and Recombination

Continuity Equations

Einstein Relation

Nasim Zafar


3/19

Carrier Diffusion:

Introduction: When excess carriers are created non-uniformly in a semiconductor,

a concentration gradientresults due to this non-uniformity of the carrier

densities in the sample. This concentration gradient, for electrons and holes, will

cause a net motion of the charge carriers from the regions of high density to theregions of low carrier density. This type of carrier motion is called Diffusion and

represents an important charge transport process in semiconductors.

Thus, the charge carriers in a semiconductor diffuse, due to the concentration

gradient by random thermal motion and under going scattering from: The lattice vibrations and

Ionized Impurity atoms.


4/19

Carrier Diffusion:

Introduction:

When excess carriers are created non-uniformly in a semiconductor,

a concentration gradient results due to this non-uniformity of the carrier

densities in the sample. This concentration gradient, for electrons and holes,

will cause a net motion of the charge carriers from the regions of high density

to the regions of low carrier density.

This type of carrier motion is called Diffusion and represents an important

charge transport process in semiconductors.


5/19

Carrier Diffusion:

Introduction:

Thus, the charge carriers in a semiconductor diffuse, due to

the concentration gradient by random thermal motion and

under going scattering from:

The lattice vibrations and

Ionized Impurity atoms.


6/19

Carrier Diffusion:

How can we produce a concentr ation gradient in a semiconductor?

By making a semiconductor or metal contact.

By illuminating a portion of the semiconductor with light, (next slide).

As the carriers diffuse, a diffusion current flows. The force behind the

diffusion current is due to the random thermal motion of the carr iers.

1dn dP

dx kT dx


7/19


8/19

Photo Generation and Diffusion:

By shining light, electron-hole pairscan be produced when the photon

energy>Eg.

The increased number of electron-hole pairs will move toward the lower

concentration region, until they reach their equilibrium values.

So there is a net number of the charge carriers crossing per unit area per

uni t time, which is called flux.

Units: [Flux]= m-2S-1


9/19

Diffusion Flux :

Ficksfirst law

Dif fusion Flux Concentration Gradient dn/dx

ndnFlux Ddx

[Flux]= m-2S-1 D = vthl ,[ D]= m2/S

D measures the ease of carrier diffusion in

response to a concentration gradient.

D limited by vibrations of lattice atoms and

ionized dopant impurities.


10/19

Diffusion Flux :

For Electrons:

Fn= - Dn dn/dx

For Holes:

Fp= - Dp dp/dx

Dn= electron diffusion coefficient

Dp = hole diffusion coefficient


11/19

Einstein Relationship:

Einstein relation relates the two independent current mechanicms of

mobility with diffusion D.

mn= qtn/mn*Dn= kTtn/mn* m*v2= kTDn= v2tn= l2/tn


12/19

Einstein Relation:pn

n p

DD kT kT and for electrons and holes

q qm m

Constant value at a fixed temperature

2

2

/sec

sec

J K Kcm kT volt volt

cm V q C

25kT

mV at room temperatureq


13/19

Diffusion Current Density: J

Diffusion cur rent density = chargexcarr ier flux


14/19

Total Current:

Diffusion Current within a semiconductor consists of:

i . hole component and

i i . electron component

Total Current flowing in a semiconductor is the sum of:

i . dri f t cur rent andi i . diff usion current:


15/19

Diffusion Current Densities:

2 1

2

2

,

,th

n n n

p p p

n p

Flux m s

D l D m s

The current densities for electrons and holes

dn dnJ q D qD for electronsdx dx

dp dpJ q D qD for holesdx dx

J A m


16/19

Total Current Density:

When both electric field and the concentration gradient are

present, the total current density, for the electron, is given as:

n n n

p p p

total n p

dnJ q nE qD

dx

dpJ q pE qD

dx

J J J

m

m


17/19


18/19

Summary

Current flowing in a semiconductor consists of driftand

diffusioncomponents:

Mobility and Conductivity are highly temperature dependent.

Generation and Recombination processes were discussed.

Nasim Zafar 18

dx

dpqD

dx

dnqDEqnEqpJ

pnnptot

mm

Electronics -1, Lecture 05

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