drift and diffusion current

7/30/2019 Drift and Diffusion Current

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EE105 Fall 2007 Lecture 2, Slide 1 Prof. Liu, UC Berkeley

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Lecture 1, Slide 1


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Lecture 2

OUTLINE

Basic Semiconductor Physics (contd)

Carrier drift and diffusion

PN Junction Diodes

Electrostatics

Capacitance

Reading: Chapter 2.1-2.2

Lecture 1, Slide 2


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Dopant Compensation

An N-type semiconductor can be converted into P-type material by counter-doping it with acceptors

such that NA > ND.

A compensated semiconductor materialhas both

acceptors and donors.

P-type material

(NA > ND)

DA

i

DA

NN

nn

NNp

2

AD

i

AD

NN

np

NNn

2

N-type material

(ND > NA)


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Types of Charge in a Semiconductor

Negative charges: Conduction electrons (density = n)

Ionized acceptor atoms (density = NA)

Positive charges:

Holes (density =p)

Ionized donor atoms (density = ND)

The net charge density (C/cm3) in a semiconductor is

AD NNnpq


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Carrier Drift

The process in which charged particles move becauseof an electric field is called drift.

Charged particles within a semiconductor move with

an average velocity proportional to the electric field.

The proportionality constant is the carrier mobility.

Ev

Ev

ne

ph

Notation:

p hole mobility (cm2/Vs)n electron mobility (cm2/Vs)

Hole velocity

Electron velocity


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Velocity Saturation

In reality, carrier velocities saturate at an upper limit,called the saturation velocity(vsat).

E

vE

v

bv

bE

sat

sat

0

0

0

0

1

1


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Drift Current

Drift current is proportional to the carrier velocityand carrier concentration:

vhtA = volume from which all holes cross plane in time t

pvhtA = # of holes crossing plane in time t

q pvhtA = charge crossing plane in time t

qpvhA = charge crossing plane per unit time = hole current

Hole current per unit area (i.e. current density) Jp,drift = qpvh


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Conductivity and Resistivity

In a semiconductor, both electrons and holesconduct current:

The conductivityof a semiconductor is Unit: mho/cm

The resistivityof a semiconductor is Unit: ohm-cm

EEnpqJ

EqnEqpJJJ

EqnJEqpJ

npdrifttot

npdriftndriftpdrifttot

ndriftnpdriftp

)(

)(

,

,,,

,,

np qnqp

1


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Resistivity Example

Estimate the resistivity of a Si sample doped withphosphorus to a concentration of 1015 cm-3 andboron to a concentration of 1017 cm-3. The electronmobility and hole mobility are 700 cm2/Vs and 300

cm

2

/Vs, respectively.


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Electrical Resistance

where is the resistivity

ResistanceWt

L

I

VR (Unit: ohms)

V

+ _

L

tW

I

homogeneously doped sample


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Carrier Diffusion

Due to thermally induced random motion, mobileparticles tend to move from a region of highconcentration to a region of low concentration.

Analogy: ink droplet in water

Current flow due to mobile charge diffusion isproportional 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)


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Diffusion Examples

Non-linear concentration profile varying diffusion current

L

NqD

dx

dp

qDJ

p

pdiffp

,

dd

p

pdiffp

L

x

L

NqD

dx

dp

qDJ

exp

,

Linear concentration profile constant diffusion current

dL

xNp

exp

L

xNp 1


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Diffusion Current

Diffusion current within a semiconductor consists ofhole 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 ,,,,


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The Einstein Relation

The characteristic constants for drift and diffusion arerelated:

Note that at room temperature (300K)

This is often referred to as the thermal voltage.

q

kTD

mV26q

kT


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The PN Junction Diode

When a P-type semiconductor region and an N-typesemiconductor region are in contact, a PN junction

diode is formed.VD

ID

+


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Diode Operating Regions

In order to understand the operation of a diode, it isnecessary to study its behavior in three operation

regions: equilibrium, reverse bias, and forward bias.

VD = 0 VD > 0VD < 0


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Carrier Diffusion across the Junction

Because of the difference in hole and electronconcentrations on each side of the junction, carriersdiffuse 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)


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Depletion Region

As conduction electrons and holes diffuse across thejunction, 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 recombinewith majority carriers, i.e. they are annihilated.

width=Wdep

quasi-

neutral

region

quasi-

neutral

region


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Carrier Drift across the Junction

Because charge density 0 in the depletion region,an electric field exists, hence there is drift current.


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PN Junction in Equilibrium

In equilibrium, the drift and diffusion components ofcurrent are balanced; therefore the net current

flowing across the junction is zero.

diffndriftn

diffpdriftp

JJ

JJ

,,

,,

0,,,, diffndiffpdriftndriftptot JJJJJ


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Built-in Potential, V0

Because of the electric field in the depletion region,there exists a potential drop across the junction:

DiA

n

p

p

p

p

p

p

x

x

p

pppp

Nn

N

q

kT

p

pDxVxV

p

dpDdV

dx

dpD

dx

dVp

dx

dpqDEqp

p

n

/

lnln)()(221

2

1

ln20

i

DA

n

NN

q

kTV (Unit: Volts)


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Built-In Potential Example

Estimate the built-in potential for PN junction below.

Note that

N P

ND = 1018 cm-3 NA = 10

15 cm-3

mV603.2mV26)10ln( q

kT


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PN Junction under Reverse Bias

A reverse bias increases the potential drop across thejunction. As a result, the magnitude of the electric fieldincreases and the width of the depletion region widens.

112

0 R

DA

si

dep

VVNNq

W


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Diode Current under Reverse Bias

In equilibrium, the built-in potential effectivelyprevents carriers from diffusing across the junction.

Under reverse bias, the potential drop across the

junction increases; therefore, negligible diffusion

current flows. A very small drift current flows, limitedby the rate at which minority carriers diffuse from the

quasi-neutral regions into the depletion region.


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PN Junction Capacitance

A reverse-biased PN junction can be viewed as acapacitor. The depletion width (Wdep) and hence the

junction capacitance (Cj) varies with VR.

dep

sij

WC


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Voltage-Dependent Capacitance

si 10-12 F/cm is the permittivity of silicon.

0

0

0

0

1

2

1

VNN

NNqC

V

V

CC

DA

DAsij

R

j

j

VD


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Reverse-Biased Diode Application

A very important application of a reverse-biased PNjunction is in a voltage controlled oscillator (VCO),

which uses an LC tank. By changing VR, we can

change C, which changes the oscillation frequency.

LC

fres

1

2

1


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Summary

Current flowing in a semiconductor is comprised of drift

and diffusion components:

A region depleted of mobile charge exists at the junction

between P-type and N-type materials.

A built-in potential drop (V0) across this region is establishedby the charge density profile; it opposes diffusion of carriers

across the junction. A reverse bias voltage serves to enhance

the potential drop across the depletion region, resulting in

very little (drift) current flowing across the junction.

The width of the depletion region (Wdep) is a function of the

bias voltage (VD).

dxdpqD

dxdnqDEqnEqpJ pnnptot

ln20

i

DA

n

NN

q

kTV

112 0 D

DA

sidep VV

NNqW

drift and diffusion current

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