EE105 Fall 2011Lecture 3, Slide 1Prof. Salahuddin, UC Berkeley Lecture 3 OUTLINE Semiconductor...

EE105 Fall 2011 Lecture 3, Slide 1 Prof. Salahuddin, UC Berkeley

Lecture 3

OUTLINE• Semiconductor Basics (cont’d)

– Carrier drift and diffusion

• PN Junction Diodes– Electrostatics– Capacitance

Reading: Chapter 2.1-2.2


Recap: Drift Current• Drift current is proportional to the carrier velocity

and carrier concentration:

Hole current per unit area (i.e. current density) Jp,drift = q p vh

Total current Jp,drift= Q/t

Q= total charge contained in the volume shown to the rightt= time taken by Q to cross the volume

Q=qp(in cm3)X Volume=qpAL=qpAvht


Recap: Conductivity and Resistivity• In a semiconductor, both electrons and holes

conduct current:

• The conductivity of a semiconductor is– Unit: mho/cm

• The resistivity of a semiconductor is– Unit: ohm-cm

EEnpqJ

EqnEqpJJJ

EqnJEqpJ

npdrifttot

npdriftndriftpdrifttot

ndriftnpdriftp

)(

)(

,

,,,

,,

np qnqp

1


Electrical Resistance

where is the resistivity

Resistance Wt

L

I

VR (Unit: ohms)

V

+_

L

tW

I

homogeneously doped sample


Resistivity Example


A Second Mechanism of Current Flow is Diffusion


Carrier Diffusion• Due to thermally induced random motion, mobile

particles tend to move from a region of high concentration to a region of low concentration. – Analogy: ink droplet in water


Carrier Diffusion• Current flow due to mobile charge diffusion is

proportional to the carrier concentration gradient.– The proportionality constant is the diffusion constant.

dx

dpqDJ pp

Notation:Dp hole diffusion constant (cm2/s)Dn electron diffusion constant (cm2/s)


Diffusion Examples• Non-linear concentration profile varying diffusion current

L

NqD

dx

dpqDJ

p

pdiffp

,

dd

p

pdiffp

L

x

L

NqDdx

dpqDJ

exp

,

• Linear concentration profile constant diffusion current

dL

xNp

exp

L

xNp 1


Diffusion Current• Diffusion current within a semiconductor consists of

hole and electron components:

• The total current flowing in a semiconductor is the sum of drift current and diffusion current:

)(

,

,,

dx

dpD

dx

dnDqJ

dx

dnqDJ

dx

dpqDJ

pndifftot

ndiffnpdiffp

diffndiffpdriftndriftptot JJJJJ ,,,,


The Einstein Relation• The characteristic constants for drift and diffusion are

related:

• Note that at room temperature (300K)

– This is often referred to as the “thermal voltage”.

q

kTD

mV26q

kT


The PN Junction Diode• When a P-type semiconductor region and an N-type

semiconductor region are in contact, a PN junction diode is formed. VD

ID

+–


Diode Operating Regions • In order to understand the operation of a diode, it is

necessary to study its behavior in three operation regions: equilibrium, reverse bias, and forward bias.

VD = 0 VD > 0VD < 0


Carrier Diffusion across the Junction• Because of the differences in hole and electron concentrations on

each side of the junction, carriers diffuse across the junction:

Notation:nn electron concentration on N-type side (cm-3)pn hole concentration on N-type side (cm-3)pp hole concentration on P-type side (cm-3)np electron concentration on P-type side (cm-3)


Depletion Region• As conduction electrons and holes diffuse across the

junction, they leave behind ionized dopants. Thus, a region that is depleted of mobile carriers is formed.– The charge density in the depletion region is not zero.– The carriers which diffuse across the junction recombine

with majority carriers, i.e. they are annihilated.

width=Wdep

quasi-neutral region

quasi-neutral region


Some Important Relations

dE

dx

E dV

dx

Energy=-qV


The Depletion Approximation

In the depletion region on the N side:

bxqN

E

qN

dx

dE

si

D

si

D

si

(x)

x-qNA

qND

In the depletion region on the P side:

xaqN

E

qN

dx

dE

si

A

si

A

si

DA bNaN

a

-b

Because charge density ≠ 0 in the depletion region, a large E-field exists in this region:


Carrier Drift across the Junction


PN Junction in Equilibrium• In equilibrium, the drift and diffusion components of

current are balanced; therefore the net current flowing across the junction is zero.

diffndriftn

diffpdriftp

JJ

JJ

,,

,,

0,,,, diffndiffpdriftndriftptot JJJJJ


Built-in Potential, V0

• Because there is a large electric field in the depletion region, there is a significant potential drop across this region:

qppE qDpdp

dx pp

dV

dx

Dp

dp

dx

p dV x1

x2

Dpdp

ppn

p p

V (x2) V (x1) Dpp

lnpppn

kT

qln

NAni

2 /ND

ln 20

i

DA

n

NN

q

kTV (Unit: Volts)


Built-In Potential Example• Estimate the built-in potential for PN junction below.

– Note that

N P

ND = 1018 cm-3 NA = 1015 cm-3

mV603.2mV26)10ln( q

kT


• A forward bias decreases the potential drop across the junction. As a result, the magnitude of the electric field decreases and the width of the depletion region narrows.

PN Junction under Forward Bias

(x)

x-qNA

qND

a

-b

V(x)

xa-b

V0

ID

0

EE105 Fall 2011Lecture 3, Slide 1Prof. Salahuddin, UC Berkeley Lecture 3 OUTLINE Semiconductor...

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