Lecture 19 - Metal-Semiconductor Junction (cont.) March 19, 2007 ...

6720J343J - Integrated Microelectronic Devices - Spring 2007 Lecture 19-1

Lecture 19 - Metal-Semiconductor Junction(cont)

March 19 2007

Contents

1 Schottky diode

2 Ohmic contact

Reading assignment

del Alamo Ch 7 sectsect73-75

Cite as Jesuacutes del Alamo course materials for 6720J Integrated Microelectronic Devices Spring 2007 MIT OpenCourseWare (httpocwmitedu) Massachusetts Institute of Technology Downloaded on [DD Month YYYY]


Key questions

bull What is the basic structure of a Schottky diode What are its

most important parasitics

bull What are key technological constraints in the design and fabrishy

cation of Schottky diodes

bull How are Schottky diodes modeled for circuit design

bull How do Schottky diodes switch What sets their time response

bull What does one have to do for a metal-semiconductor junction to

become an ohmic contact

bull Why do ohmic contacts look as S = infin for minority carriers



1 Schottky diode

Key uniqueness fast switching from ON to OFF and back

Widely used

bull in analog circuits in track and hold circuits in AD converters

pin drivers of IC test equipment

bull in communications and radar applications as detectors and mixshy

ers also as varactors

Technological constraint Schottky diodes engineered using process

modules developed for other circuit elements rarr demands resourceshy

fulness and imagination from device designer

Typical implementations

n+

n+ nSchottky metal

n+ n

Schottky junction ohmic contactohmic contact

semi-insulating GaAs

p



Parasitics

Series resistance due to QNR ohmic drop

Voltage across junction is reduced and I-V characteristics modified

q(V minus IRs)I = IS[exp minus 1]

kT

ideal

with series resistance

I log |I|

IRs

1Rs

0 0 V 0 V

linear scale semilogarithmic scale

Rs bad because

bull for given forward current V increased and harder to control

bull it degrades dynamic response of diode



Substrate capacitance

Is C n+

n Rs

n+

p

parasitic substrate p-n diode

Also degrades dynamics of diode



Equivalent circuit models

Rs Rs

=

CIs Q rd

a) general b) small-signal

General model

rdquoIdeal dioderdquo in parallel with capacitor and in series with resistor

Ideal diode is element with exponential I-V characteristics

qV I = IS(exp minus 1)

kT

and no capacitance



Small-signal model

In many analog and communications circuits Schottky diode is bishy

ased in some way and then a rdquosmall signalrdquo is applied on top of bias

rarr interested in response to small signal

Linearize general model

q(V + v)I + i = IS [exp minus 1]

kT qV qv q(I + IS)

IS [exp (1 + ) minus 1] = I + v kT kT kT

For small signal diode looks like resistor of dynamic resistance

kT rd =

q(I + IS)

In forward bias rd only a function of I

kT rd

qI

In reverse bias rd rarr infin



Circuit CAD model (such as SPICE)

In general no specific Schottky diode model exists p-n diode model

is used

Different models exist with different topologies All of them described

by model parameters (determined by device engineers)

Current in simplest model

qVjID = ISA(exp minus 1)

NkT

with

A equiv relative area of modeled device and characterized device

and

⎛ ⎞XTI T minusqEG 1 1 ⎝ ⎠IS = IS exp[ ( minus )] TM k T TM

Capacitance

CJO C = A Vj(1 minus VJ)M

Additional models exist for breakdown noise additional leakage curshy

rents other temperature effects etc

Cite as Jesuacutes del Alamo course materials for 6720J Integrated Microelectronic Devices Spring 2007 MIT OpenCourseWare (httpocwmitedu) Massachusetts Institute of Technology Downloaded on [DD Month YYYY]Cite as Jesuacutes del Alamo course materials for 6720J Integrated Microelectronic Devices Spring 2007 MIT OpenCourseWare (httpocwmitedu) Massachusetts Institute of Technology Downloaded on [DD Month YYYY]



Summary of model parameters in simplest model

name parameter description

IS saturation current

N ideality factor

EG Schottky barrier height

RS series resistance

CJO zero bias depletion capacitance

VJ built-in potential

M grading coefficient

XTI saturation current temperature exponent

TT transit time

BV breakdown voltage

units ideal value

A -

- 1

V -

Ω -

F -

V -

- 05

- 2

s 0

V -

All models should account for parasitic substrate pn diode

p

n+

n+

n Rs

CIs



Breakdown


In reverse bias as |V | uarrrarr |Emax| uarr

At a high-enough voltage avalanche breakdown takes placerarr breakshy

down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18

-3doping level (cm )

Computation of BV

bull Triggering current IS (all electron current for SBD on n-type

semiconductor)

bull Computation difficulty E non-uniform in SCR

bull For moderate doping levels BV function of ND alone

(independent of ϕBn)



Technology layout and design considerations

Often no special metal is available rarr ohmic metal must be used

Premature breakdown may occur at edges of diodes

Premature breakdown mitigation requires rdquoedge engineeringrdquo

high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n

If p guard ring used must make sure that p-n junction never turns

on

In essence this is a 2D or 3D problem



Design issues log |I|

VVfBV 0

If

IS

bull Metal selection

ϕBn uarr rarr Vf (for fixed If ) uarr

rarr IS darr

rarr more T sensitivity

bull Doping level selection

ND uarr rarr Rs darr

rarr C uarr

rarr BV darr

bull Vertical extension of QNR

minimum value of t required to deliver BV (beyond that Rs uarr)

bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr

rarr Vf (for fixed If) darr

rarr more expensive



Dynamics

Uniqueness of Schottky diodes they switch fast

Large-signal example

V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC

-switch-off transient C charges up through Rs

time constant sim RsC

-switch-on transient C discharges through Rs


for fast switching rArr minimize Rs and C



Switch-off transient

Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+

I(0minus) = If (Vf ) I(0+) = minus( Vf minus Vr

minus If )Rs

note in this notation Vr is negative



Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+

I(0minus) = minusIs I(0+) = Vf minus Vr

Rs



HSPICE example of large-signal switching

SPICE Exercise Vf = 045 V Vr = 3 V

Diode model parameters IS= 55e minus 13 N= 103 EG= 089

RS= 11 CJO= 324e minus 13 VJ= 05 M= 0339 XTI= 2 and

TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)

parameter SPICE hand calculation

τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact

bull Ohmic contacts means of electrical communication with outside

world

bull Key requirement very small resistance to carrier flow back and

forth between metal and semiconductor

bull Ohmic contact = MS junction with large JS

bull V small rarr linearize I-V characteristics

J A lowast T 2 exp minusqϕBn qV

= V

kT kT ρc

Figure of merit for ohmic contacts

ρc equiv ohmic contact resistivity (Ω middot cm2)

Good values ρc le 10minus7 Ω middot cm2



How does one make a good ohmic contact

bull Classically use metal that yields small qϕBn

bull Increase ND until carrier tunneling is possible

Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec

ohmic contact to n-type semiconductor ohmic contact to p-type semiconductor



Experimental measurements in n-Si

Ohmic contact resistance

Rc = ρc

Ac

Ac uarr rArr Rc darr


Image removed due to copyright restrictions Specific contact resistivity versus Nd graphSwirhun Stanley Edward Characterization of Majority and Minority Carrier Transportin Heavily Doped Silicon PhD diss Stanford University 1987 340 pages


Justify two assumptions made earlier about ohmic contacts

1) Through a good ohmic contact outside battery rdquograbsrdquo mashy

jority carrier quasi-Fermi level

In rdquogoodrdquo ohmic contact Rc is very small rArr V very small rArr

negligible difference in Ef across M-S interface

2) S = infin at ohmic contact

Strong electric field at M-S interface rdquosucksrdquo minority carriers

towards it where they recombine

In vicinity of ohmic contact negligible concentration of excess

minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions

bull Main parasitics of Schottky diode series resistance and subshy

strate capacitance

bull Ideal BV of Schottky diode entirely set by doping level

bull Junction edge effects in Schottky diode may cause premature

reverse breakdown

bull No minority carrier storage in Schottky diode rArr fast switching

bull Dominant time constant of Schottky diode RsC

bull Typical design goals for Schottky diode small time constant

high forward conduction low reverse conduction high breakshy

down voltage and small area All without a dedicated process

bull Good ohmic contacts fabricated by increasing doping level rArr

carrier tunneling

bull ρc specific contact resistance (in Ωmiddotcm2) proper figure of merit

for ohmic contact

bull Order of magnitude of key parameters in Si at 300K

ndash Desired specific contact resistance ρc lt 10minus7 Ω middot cm2 (deshy

pends on metal and doping level)



Self study

bull Small-signal dynamics of Schottky diode



Key questions

bull What is the basic structure of a Schottky diode What are its

most important parasitics

bull What are key technological constraints in the design and fabrishy

cation of Schottky diodes

bull How are Schottky diodes modeled for circuit design

bull How do Schottky diodes switch What sets their time response

bull What does one have to do for a metal-semiconductor junction to

become an ohmic contact

bull Why do ohmic contacts look as S = infin for minority carriers



1 Schottky diode


Widely used









n+

n+ nSchottky metal

n+ n



p



Parasitics




kT

ideal


I log |I|

IRs

1Rs

0 0 V 0 V


Rs bad because






Is C n+

n Rs

n+

p






Rs Rs

=

CIs Q rd


General model




kT

and no capacitance



Small-signal model






kT qV qv q(I + IS)



kT rd =

q(I + IS)


kT rd

qI






is used





NkT

with


and


Capacitance










N ideality factor







TT transit time


units ideal value

A -

- 1

V -

Ω -

F -

V -

- 05

- 2

s 0

V -


p

n+

n+

n Rs

CIs



Breakdown




down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18


Computation of BV


semiconductor)










high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study




1 Schottky diode


Widely used









n+

n+ nSchottky metal

n+ n



p



Parasitics




kT

ideal


I log |I|

IRs

1Rs

0 0 V 0 V


Rs bad because






Is C n+

n Rs

n+

p






Rs Rs

=

CIs Q rd


General model




kT

and no capacitance



Small-signal model






kT qV qv q(I + IS)



kT rd =

q(I + IS)


kT rd

qI






is used





NkT

with


and


Capacitance










N ideality factor







TT transit time


units ideal value

A -

- 1

V -

Ω -

F -

V -

- 05

- 2

s 0

V -


p

n+

n+

n Rs

CIs



Breakdown




down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18


Computation of BV


semiconductor)










high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study




Parasitics




kT

ideal


I log |I|

IRs

1Rs

0 0 V 0 V


Rs bad because






Is C n+

n Rs

n+

p






Rs Rs

=

CIs Q rd


General model




kT

and no capacitance



Small-signal model






kT qV qv q(I + IS)



kT rd =

q(I + IS)


kT rd

qI






is used





NkT

with


and


Capacitance










N ideality factor







TT transit time


units ideal value

A -

- 1

V -

Ω -

F -

V -

- 05

- 2

s 0

V -


p

n+

n+

n Rs

CIs



Breakdown




down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18


Computation of BV


semiconductor)










high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study





Is C n+

n Rs

n+

p






Rs Rs

=

CIs Q rd


General model




kT

and no capacitance



Small-signal model






kT qV qv q(I + IS)



kT rd =

q(I + IS)


kT rd

qI






is used





NkT

with


and


Capacitance










N ideality factor







TT transit time


units ideal value

A -

- 1

V -

Ω -

F -

V -

- 05

- 2

s 0

V -


p

n+

n+

n Rs

CIs



Breakdown




down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18


Computation of BV


semiconductor)










high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study





Rs Rs

=

CIs Q rd


General model




kT

and no capacitance



Small-signal model






kT qV qv q(I + IS)



kT rd =

q(I + IS)


kT rd

qI






is used





NkT

with


and


Capacitance










N ideality factor







TT transit time


units ideal value

A -

- 1

V -

Ω -

F -

V -

- 05

- 2

s 0

V -


p

n+

n+

n Rs

CIs



Breakdown




down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18


Computation of BV


semiconductor)










high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study




Small-signal model






kT qV qv q(I + IS)



kT rd =

q(I + IS)


kT rd

qI






is used





NkT

with


and


Capacitance










N ideality factor







TT transit time


units ideal value

A -

- 1

V -

Ω -

F -

V -

- 05

- 2

s 0

V -


p

n+

n+

n Rs

CIs



Breakdown




down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18


Computation of BV


semiconductor)










high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study






is used





NkT

with


and


Capacitance










N ideality factor







TT transit time


units ideal value

A -

- 1

V -

Ω -

F -

V -

- 05

- 2

s 0

V -


p

n+

n+

n Rs

CIs



Breakdown




down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18


Computation of BV


semiconductor)










high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study







N ideality factor







TT transit time


units ideal value

A -

- 1

V -

Ω -

F -

V -

- 05

- 2

s 0

V -


p

n+

n+

n Rs

CIs



Breakdown




down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18


Computation of BV


semiconductor)










high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study



Breakdown




down voltage

I 1000

BV

V bre

akd

ow

n v

olt

ag

e (

V)

100

Si

300 K

10

1E+15 1E+16 1E+17 1E+18


Computation of BV


semiconductor)










high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study








high field at edge

direct edge contact

n

metal overlap

n

moat

n

guard ring p p

n


on





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study





VVfBV 0

If

IS



rarr IS darr




rarr C uarr

rarr BV darr



bull Diode area

Aj uarr rarr C uarr

rarr IS uarr

rarr Rs darr


rarr more expensive



Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study




Dynamics



V

Vf 0

tI

+ Vr

I V Vf Vr

RsC

-

0 t

RsC









Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study





Vf

Rs

+

-

Vf-IfRs

If(Vf)

C

I

Vr

Rs

+

+

-

-

Vf-IfRs

Vf-IfRs -Vr

C

I

t=0- t=0+


minus If )Rs




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study




Switch-on transient

Vf

Rs

+

-

C

I

VrVr

Rs

+

+

-

-

Vr

Vf-Vr

C

I

t=0- t=0+


Rs







TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study








TT= 0

-04

-03

-02

-01

00

01

02

03

04

cu

rren

t (A

)

4 ps

2 ps

00E+00 50E-12 10E-11 15E-11 20E-11 25E-11

time (s)


τoff 4 ps 78 ps

τon 2 ps 19 ps

Ir(pk) 031 A 031 A

If (pk) 030 A 031 A



2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study




2 Ohmic contact


world






= V

kT kT ρc









Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study







Ec

Ev EF EF

Efe Efh

Ev

Ec

Efh

Ev

Efe

Ec






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study






Rc = ρc

Ac














minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study













minority carriers

Ef

Ec

Ev

Efe

Efh


Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study



Key


conclusions


strate capacitance



reverse breakdown







carrier tunneling


for ohmic contact






Self study




Self study



Lecture 19 - Metal-Semiconductor Junction (cont.) March 19, 2007 ...

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Transcript of Lecture 19 - Metal-Semiconductor Junction (cont.) March 19, 2007 ...