8/2/2019 Pn Junctions Introduction

1/9

EEE 531: Semiconductor Device Theory I

EEE 531: Semiconductor Device Theory I

Instructor: Dragica Vasileska(Notes provided by: Prof. Dieter Schroder)

Department of Electrical EngineeringArizona State University

Topic covered: Introduction to some general concepts for PN-

junctions

8/2/2019 Pn Junctions Introduction

2/9

EEE 531: Semiconductor Device Theory I

1. PN-junctions - General Consideration:

PN-junction is a two terminal device. Based on the doping profile, PN-junctions can beseparated into two major categories:

- step junctions

- linearly-graded junctions

p-side n-side

AD NN

p-side n-side

AD NN ax

Step junction Linearly-graded junction

8/2/2019 Pn Junctions Introduction

3/9

EEE 531: Semiconductor Device Theory I

(A) Equilibrium analysis of step junctions

(a) Built-in voltage Vbi:

(b) Majority- minority carrier

relationship:

CE

VE

iE

FE

biqV

W)(

x-qNA

qND

)(xV

x

biV

)(E

xmaxE

px nx

+-

p-side n-side

( ) ( )

( )[ ]

[ ]

=

==

+=

2200

0

0

lnln

exp

exp

i

DAT

i

npBbi

BFiip

BiFin

niFpFibi

nNNV

nnp

qTkV

TkEEnp

TkEEnn

EEEEqV

[ ]

[ ]Tbinp

Tbipn

VVnn

VVpp

/exp

/exp

00

00

=

=

8/2/2019 Pn Junctions Introduction

4/9

EEE 531: Semiconductor Device Theory I

(c) Depletion region width:

Solve 1D Poisson equation using depletion charge

approximation, subject to the following boundary condi-tions:

p-side:

n-side:

Use the continuity of the two solutions at x=0, andcharge neutrality, to obtain the expression for the depletion

region width W:

0)()(,)(,0)( ==== pnbinp xExEVxVxV

( )202

)( ps

Ap xx

k

qNxV +

=

( ) bins

Dn Vxx

k

qNxV +

= 202

)(

DA

biDAs

nDpA

np

pn

NqN

VNNkW

xNxN

VV

Wxx)(2)0()0( 0 +=

=

==+

8/2/2019 Pn Junctions Introduction

5/9

EEE 531: Semiconductor Device Theory I

(d) Maximum electric field:

The maximum electric field, which occurs at the

metallurgical junction, is given by:

(e) Carrier concentration variation:

)(00max

DAs

DA

x NNk

WNqN

dx

dVE

+==

=

105

107

109

1011

1013

1015

0 0.5 1 1.5 2 2.5 3 3.5

n [cm-3

]

p [cm-3

]

Concentration

[cm

-3]

Distance [m]

cmkVE

cmkVE

mW

cmNN

sim

DC

calc

DA

/93.8

/36.9

23.1

10

)max(

)max(

315

=

==

==

8/2/2019 Pn Junctions Introduction

6/9

EEE 531: Semiconductor Device Theory I

cmkVEcmkVEmW

cmNN

simDCcalc

DA

/93.8,/36.9,23.1

10

)max()max(

315

===

==

-1015

-5x1014

0

5x1014

1015

0 0.5 1 1.5 2 2.5 3 3.5

(x)/q

[cm

-3]

Distance [m]

-10

-8

-6

-4

-2

0

0 0.5 1 1.5 2 2.5 3 3.5

Electricfield[kV/cm]

Distance [m]

8/2/2019 Pn Junctions Introduction

7/9

EEE 531: Semiconductor Device Theory I

cmkVEcmkVEmW

cmNcmN

simDCcalc

DA

/67,/53.49,328.0

10,10

)max()max(

318316

===

==

-10

17

-5x1016

0

5x1016

1017

0.6 0.8 1 1.2 1.4

(x)/q

[cm

-

3]

Distance [m]

-70

-60

-50

-40

-30

-20

-10

0

10

0.6 0.8 1 1.2 1.4

Electricfield[k

V/cm]

Distance [m]

8/2/2019 Pn Junctions Introduction

8/9

EEE 531: Semiconductor Device Theory I

(f) Depletion layer capacitance:

Consider a p+n, or one-sided junction, for which:

The depletion layer capacitance is calculated using:

( )

D

bis

qN

VVkW

m02 =

02

0 )(21

)(2 =

=== sDbi

bi

sDDc

kqN

VV

CVV

kqN

dV

dWqN

dV

dQ

C

m

m

VVbi V

21 C

DN

slope1

Forward biasReverse

bias

Measurement setup:

W dW

~

V

vac

8/2/2019 Pn Junctions Introduction

9/9

EEE 531: Semiconductor Device Theory I

(B) Equilibrium analysis of linearly-graded junction:

(a) Depletion layer width:

(c) Maximum electric field:

(d) Depletion layer capacitance:

Based on accurate numerical simulations, the depletion

layer capacitance can be more accurately calculated ifVbiis replaced by the gradient voltage Vg:

( )3/1

012

=qa

VVkW bis

m

( )

3/120

2

12

=

VVqakC

bi

s

m

0

2

max8

=sk

qaWE

=

30

2

8ln

3

2

i

TsTg

qn

VkaVV