Schottky diodes: I-V characteristicscontents.kocw.net/KOCW/document/2014/konkuk/minyosep2/16.pdf ·...

Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 14 - Lec 15-1

Schottky diodes: I-V characteristics

• The general shape of the I-V curve in the MS (n-type) diode

are very similar to that in the p+n diode.

• However the dominant current components are decidedly

different in the two diodes.

p+

n M n

Forward-biased


p+n junction diode v.s. Schottky diode

p+

n

Forward-biased • Under small VA, the dominant

current components arise from

recombination in the depletion

region.

• Under large VA, the dominant

component is the hole injection

(minority carrier injection by

diffusion) from p+ to n-side.

• Under large VA, the electron injection from n to p+-side is

negligible due to the light doping.



M n

• Although the recombination and hole

injection currents still exist, because of

the relatively low potential barrier seen

by electrons in the n-side, the

dominant component is the electron

injection from S to M under the

forward bias.

Reverse-biased

Forward-based

• Under reverse bias, electron

flow from M to S totally

dominates the observed

current.

• So, the MS diode is often

said to be a “majority carrier

device”.


Thermionic emission theory

• The current resulting from majority carrier injection over the

potential barrier in an MS diode is referred to as the

thermionic emission current.

• If an electron entering the depletion

region from the semiconductor bulk

has a velocity vx directed toward the

interface, the kinetic energy in the x-

direction is given by

2*

2

1xnvmxKE

• When KEx ≥ q(Vbi ─ VA), the electron can surmount the

surface barrier and cross into the metal.

)(2

1 2*

Abixn VVqvm


• The velocity required for surmounting the barrier is

)(2

1 2*

Abixn VVqvm

)(2

*min Abi

n

x VVm

qvv

• Assuming there are n(vx) electrons/cm3 in the semiconductor

bulk with a velocity, –vx, which is sufficient to surmount the

barrier.

• The current associated with this set of electrons with –vx will

be )(, xxvMS vnqAvIx

• Summing over all electrons with sufficient energies,

x

v

xxMS dvvnvqAI

min

)(



• For a non-degenerate semiconductor, n(vx) is given by

x

v

xxMS dvvnvqAI

min

)(

2* )2/(/)(

3

2*4)( xnCF vkTmkTEEn

x eeh

kTmvn

• Substituting, integrating, and simplifying the results,

KTqVKT

MSAB eeTAI //2*

A

where


AA

0

*

0*m

mand 22 Kamps/cm 120

3

2

04

h

kπqmA

• The constant A and A* are called Richardson constant and

effective Richardson constant, respectively.



• Electrons crossing the interface from M to S always see the

Schottky barrier height (B). Consequently,

)0()( ASMASM VIVI

• Moreover, under equilibrium, the and currents

across the barrier must precisely balance.

SM MS

KT

AMSASMBeTAVIVI /2*)0()0(

A

• The total current at an arbitrary VA is given by

)0( ASMMSSMMS VIIIII

Combining the equations,

KT

s

KTqV

s

B

A

eTAI

eII

/2

/

*

)1(

A



)1(/

KTqV

sAeII

D

i

p

p

A

i

n

n

N

n

L

D

N

n

L

DqAI

22

0

)1(/

0 kTqVAeII

KT

sBeTAI /2*

A

VA > a few kT/q

KTqV

sAeII /

VA < minus a few kT/q

sII

Is


Deviations from the ideal in Schottky diodes

Forward-biased reverse-biased

series resistance

breakdown

(avalanche) thermal

generation??


Schottky barrier lowering

• Differing from the pn junction diode, the non-saturating

reverse current is primarily attributed to a phenomenon known

as Schottky barrier lowing.

• Even though it is assumed that B is bias-independent in the ideal theory, the Schottky barrier is rather lowered under E-field

(which is also called image force-induced lowering).

BB0B MB0

where B0 is the barrier height when E = 0 and

04 S

S

BK

qq

E

• The electric field at the semiconductor surface (ES) can be

computed from when x = 0. xWεK

qNx

S

D 0

)(E


KT

sBeTAI /2*

A)1(

/

KTqV

sAeII

Schottky barrier lowering

04 S

S

BK

qq

E

• Since Is exponentially varies with B, even a small decrease

in B gives rise to a noticeable increase in the reverse-bias

current.

Schottky barrier

lowering


a.c. response in Schottky diode

Abia VVv A small a.c. signal superimposed on a

d.c. reverse bias gives rise to a charge

fluctuation inside the MS diode.

variation in the depletion width

associated change in the depletion

capacitance

W

AKC S 0

Abi

D

S VVqN

εKW 02

Because ,

Abi

D

S

S

VVqN

εK

AKC

0

0

2

The larger reverse

bias, the smaller C.



Taking the reciprocal and then squared,

Abi

D

S

S

VVqN

εK

AKC

0

0

2

Abi

SD

VVAεKqNC

2

0

2

21

• The 1/C2 plot against VA gives a straight line.

• The slope of the straight line gives the doping concentration.

• The extrapolated intercept at 1/C2 = 0 gives the built-in

potential.



Abi

SD

VVAεKqNC

2

0

2

21

Abi

D

S

S

VVqN

εK

AKC

0

0

2


Practical considerations: rectifying contact

• An MS contact is defined to be ideal if the M and S are in

intimate contact on an atomic scale, there is no intermixing of

components, and there is no adsorbed impurities or surface

charges at the MS interface. practically it’s not the case.

Ex) According to the Schottky-Mott model,

But…..

Regardless of the metal employed in a Ge MS diode, nearly all

metals form a significant Schottky contact to n-type Ge and an

ohmic contact to p-type Ge.

The EV of Ge is strongly pinned to the EFM.

MB

Fermi level pinning due to surface states


Fermi level pinning

EC

EV

Ei

intrinsic n-type before equil. n-type after equil.

donor-like or

accepter-like

surface states.

EF EC

EV

Ei Ei = EF EC

EV

ρ

no space charge

ρ

no space charge

ρ

+

-


Practical considerations: ohmic contact

• In ideal cases, for ohmic contact,

M > S M < S (n-type) (p-type)

• However, due to the Fermi level pinning, the deposition of any

metal on n-type GaAs forms a barrier type contact.

• How are ohmic contacts achieved in practice?

by heavily doping the surface region

The depletion depth decreases with doping!!

Tunneling through the narrow W.


Announcements

• Next lecture: p. 563 ~ 575

• Homework: 14.2; 14.3; 14.9

Schottky diodes: I-V characteristicscontents.kocw.net/KOCW/document/2014/konkuk/minyosep2/16.pdf ·...

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