Lecture 8

OUTLINE• Metal-Semiconductor Contacts (cont’d)

– Current flow in a Schottky diode– Schottky diode applications– Small-signal capacitance– Practical ohmic contacts

Reading: Pierret 14.2-14.3; Hu 4.17-4.21

Voltage Drop across the M-S Contact

• Under equilibrium conditions (VA = 0), the voltage drop across the semiconductor depletion region is the built-in voltage Vbi.

• If VA 0, the voltage drop across the semiconductor depletion region is Vbi - VA.

EE130/230M Spring 2013 Lecture 8, Slide 2

Depletion Width, W, for VA 0

)(2

D

Abis

qN

VVW

2

02xW

K

qNxV

S

D

At x = 0, V = - (Vbi - VA)

• W increases with increasing –VA

• W decreases with increasing ND

Last time, we found that

EE130/230M Spring 2013 Lecture 8, Slide 3

W for p-type Semiconductor

)(2

A

biAs

qN

VVW

2

02xW

K

qNxV

S

A

At x = 0, V = Vbi + VA

• W increases with increasing VA

• W decreases with increasing NA

EE130/230M Spring 2013 Lecture 8, Slide 4

p-typesemiconductor

• Current is determined by majority-carrier flow across the M-S junction:o Under forward bias, majority-

carrier diffusion from the semiconductor into the metal dominates

o Under reverse bias, majority-carrier diffusion from the metal into the semiconductor dominates

REVERSE BIAS

FORWARD BIAS

EE130/230M Spring 2013 Lecture 8, Slide 5

Current Flow

Thermionic Emission Theory• Electrons can cross the junction into the metal if

• Thus the current for electrons at a given velocity is:

• So, the total current over the barrier is:

Abixx VVqmv 2

2

1K.E.

Abin

x VVm

qvv

*min

2

)(, xxvMs vnqAvIx

min

)(v

xxxMs dvvnvqAI

EE130/230M Spring 2013 Lecture 8, Slide 6

Schottky Diode I - VFor a nondegenerate semiconductor, it can be shown that

We can then obtain

In the reverse direction, the electrons always see the same barrier B, so

Therefore

2/2

0

*/

//23

2*

A/cm 120 where,

4

kTnS

kTqVS

kTqVkTnMS

BA

AB

eTm

mJeAJ

eeATh

kqmI

2* 2//3

2*4xncF vkTmkTEEn

x eeh

kTmvn

0 AMSSM VII

SSkTqV

S AJIeII A where)1( /

EE130/230M Spring 2013 Lecture 8, Slide 7

Applications of Schottky Diodes• IS of a Schottky diode is 103 to 108 times larger than that of a

pn junction diode, depending on B .

Schottky diodes are preferred rectifiers for low-voltage, high-current applications.

EE130/230M Spring 2013 Lecture 8, Slide 8

Block Diagram of a Switching Power Supply

Charge Storage in a Schottky Diode• Charge is “stored” on both sides of the M-S contact.

– The applied bias VA modulates this charge.

EE130/230M Spring 2013 Lecture 8, Slide 9

WAC s

Small-Signal Capacitance• If an a.c. voltage va is applied in series with the d.c. bias VA, the

charge stored in the Schottky contact will be modulated at the frequency of the a.c. voltage

displacement current will flow:dt

dvCi a

EE130/230M Spring 2013 Lecture 8, Slide 10

Once Vbi and ND are known, Bn can be determined:

22

)(21

AqN

VV

C sD

Abi

D

cBnFBFcBnbi ln)(

N

NkTEEqV

Using C-V Data to Determine B

Abi

sD

AbiD

s

ss

VV

qNA

VVqN

AW

AC

22

EE130/230M Spring 2013 Lecture 8, Slide 11

Practical Ohmic Contact• In practice, most M-S contacts are rectifying

• To achieve a contact which conducts easily in both directions, we dope the semiconductor very heavily W is so narrow that carriers can “tunnel” directly through

the barrier

EE130/230M Spring 2013 Lecture 8, Slide 12

DABn NVHnDthxDMS

onns

emkTqNvqPNJ

mmhmH

/)(*

13/2*9*

2/

Vcm /104.5/4 where

D

Bns

qNW

2

DABn NVHeP )(y probabilit tunneling

Tunneling Current Density

Ec, EFS

Ev

EFM

Equilibrium Band Diagram Band Diagram for VA0

Ec, EFS

Ev

EFM

qVbiBnq(Vbi-VA)

EE130/230M Spring 2013 Lecture 8, Slide 13

EE130/230M Spring 2013 Lecture 8, Slide 14

Example: Ohmic Contacts in CMOS

Specific Contact Resistivity, c

• Unit: -cm2

– c is the resistance of a 1 cm2 contact

• For a practical ohmic contact, want small B, large ND for small contact resistance

DB NHc e /

contact

ccontact A

R

EE130/230M Spring 2013 Lecture 8, Slide 15

Approaches to Lowering B

• Image-force barrier lowering

4

aNq

s

N = dopant concentration in surface region

a = width of heavily doped surface region

Bo

EF

Ec

metal n+ Si

A. Kinoshita et al. (Toshiba), 2004 Symp. VLSI Technology Digest, p. 168

• M engineering– Impurity segregation via silicidation

– Dual ( low-M / high-M ) silicide technology

A. Yagishita et al. (UC-Berkeley), 2003 SSDM Extended Abstracts, p. 708

M. C. Ozturk et al. (NCSU), 2002 IEDM Technical Digest, p. 375

• Band-gap reduction– strain – germanium incorporation

Very high active dopant concentration desired

EE130/230M Spring 2013 Lecture 8, Slide 16

Voltage Drop across an Ohmic Contact• Ideally, Rcontact is very small, so little voltage is

dropped across the ohmic contact, i.e. VA 0 Volts equilibrium conditions prevail

EE130/230M Spring 2013 Lecture 8, Slide 17

Summary• Charge is “stored” in a Schottky diode.

– The applied bias VA modulates this charge and thus the voltage drop across the semiconductor depletion region

The flow of majority carriers into the metal depends exponentially on VA

2/2

0

*

/

A/cm 120 where

)1(

kTnS

kTqVS

B

A

eTm

mJ

eAJI

EE130/230M Spring 2013 Lecture 8, Slide 18

WAC s

small-signal capacitance

)(2

D

Abis

qN

VVW

EF

Ec

Ev

EF

Ec

Ev

EFEc

Ev

EF

Since it is difficult to achieve small B in practice, ohmic contacts are achieved with heavy doping, in practice:

EF Ec

Ev

EF

Ec

Ev

Ec

Ev

EE130/230M Spring 2013 Lecture 8, Slide 19

Summary (cont’d)