Lower Limits To Specific Contact Resistivity

1

Lower Limits To Specific Contact Resistivity

Ashish Baraskar1, Arthur C. Gossard2,3, Mark J. W. Rodwell3

1GLOBALFOUNDRIES, Yorktown Heights, NYDepts. of 2Materials and 3ECE,

University of California, Santa Barbara, CA

24th International Conference on Indium Phosphide and Related Materials

Santa Barbara, CA

FET parameter change

gate length decrease 2:1

current density (mA/m), gm (mS/m) increase 2:1

transport effective mass constant

channel 2DEG electron density increase 2:1

gate-channel capacitance density increase 2:1

dielectric equivalent thickness decrease 2:1

channel thickness decrease 2:1

channel density of states increase 2:1

source & drain contact resistivities decrease 4:1

> 0.5 Ω-µm2 resistivity for 10 nm III-V MOSFET

Ohmic Contacts: Critical for nm & THz Devices

HBT parameter change

emitter & collector junction widths decrease 4:1

current density (mA/m2) increase 4:1

current density (mA/m) constant

collector depletion thickness decrease 2:1

base thickness decrease 1.4:1

emitter & base contact resistivities decrease 4:1

> 2 Ω-µm2 resistivity for 2 THz fmaxTHz HBT: Lobisser ISCS 2012

Intel 32 nm HKMG IEDM 2009

Ls/d Lg

Scaling laws to double bandwidth

Ultra Low-Resistivity Refractory Contacts

10-9

10-8

10-7

10-6

1018 1019 1020 1021

N-InAsC

on

tac

t R

es

isti

vit

y (c

m2)

concentration (cm-3)1017 1018 1019 1020

N-InGaAs

concentration (cm-3)1018 1019 1020 1021

P-InGaAs

IrWMo

concentration (cm-3)

Schottky Barrier is about one lattice constantwhat is setting contact resistivity ?what resistivity should we expect ?

Landauer (State-Density Limited) Contact Resistivity

momentum

velocity

density2/32/33

ff Emkn

2/12/1ff Emk

2/12/1 // mEmkv fff

current21fEmJ

conductivity 3/2011 nmEmE

Jf

f

3/23/22

8

3n

qc

valley

3/2valley

6/1

2

3/22

8

3n

m

mmq

z

yxc

valley

L, X, valleys

7

About this work

Scope• Analytical calculation of minimum feasible contact

resistivities to n-type and p-type InAs and In0.53Ga0.47As.

Assumptions• Conservation of transverse momentum and total energy

across the interface • Metal E-k relationship treated as a single parabolic band• Band gap narrowing due to heavy doping neglected for

the semiconductor

8

Potential Energy Profile

• Schottky barrier modified by image forces

• Modeled potential barrier: piecewise linear approximation

• introduced to facilitate use of Airy functions for calculating transmission probability

Bnq

9

Calculation of Contact ResistivityCurrent density, J

Contact Resistivity, ρc

sx

sx

sy

sy

sz

sz

k

k

k

k

k

k

szsysxmssz dkdkdkTffvπ)(

qJ

03

)(2

2

0

1

Vc dV

dJ

ρ

z : transport direction

ksx, ksy ksz : wave vectors in the semiconductor

vsz : electron group velocity in z direction

T : interface transmission probability

fs and fm : Fermi functions in the semiconductor and the metal

10

10-10

10-9

10-8

1018 1019 1020 1021Co

ntac

t R

esi

stiv

ity,

-cm

2

Electron Concentration, cm-3

Landauer limit, [100] Si

Landauer limit, InAsone isotropic band

InAs, step potential.non-parabolic

parabolic

Results: Zero Barrier Contacts, Landauer Contacts

Step potential energy profile

Step Potential Barrier:

interface quantum reflectivity, resistivity >Landauer

Parabolic vs. non-parabolic bands:

differing Efs-Ecs → differing interface reflectivity

Landauer resistivity lower in Si than in Γ-valley semiconductorfs

multiple minima, anisotropic bands

11

10-10

10-9

10-8

10-7

10-6

10-5

1018 1019 1020 1021

[2]

[3]

[4]

[1]

B=0.6 eV

0.4 eV0.2 eV

0 eV


Co

nta

ct R

esi

stiv

ity

,

cm

2

step-barrierLandauer

In-situ contacts

References:

1. Jain et. al., IPRM, 2009

2. Baraskar et al., JVST B, 2009

3. Yeh et al., JJAP, 1996

4. Stareev et al., JAP, 1993

Assumes parabolic bands

At n = 5×1019 cm-3 doping, ΦB=0.2 eV

measured resistivity 2.3:1 higher than theory

Theory is 3.9:1 higher than Landauer

Results: InGaAs

12

1018 1019 1020 1021

[1]

[3]

[4]

[5]

[2]

10-10

10-9

10-8

10-7

10-6

10-5


0.2 eV

B=0.3 eV

step-barrier

B=0 eV

0.1 eV

LandauerC

on

tact

Res

isti

vity

, c

m2

Results: N-InAsn-InAs

In-situ contacts

References:

1. Baraskar et al., IPRM, 2010


3. Shiraishi et al., JAP, 1994

4. Singisetti et al., APL, 2008

5. Lee et al., SSE, 1998


At n = 1020 cm-3 doping, ΦB=0.0 eV

measured resistivity 1.9:1 higher than theory

Theory is 3.6:1 higher than Landauer

13

1018 1019 1020 1021

[2]

[4]

[1]

[5]

[6]

[3]

10-10

10-9

10-8

10-7

10-6

10-5

Hole Concentration, cm-3

B=0.8 eV

0.6 eV0.4 eV0.2 eV

step-barrierLandauer

Co

nta

ct R

esi

stiv

ity

, c

m2

Results: P-InGaAsp-In0.53Ga0.47As

In-situ contacts

References:

1. Chor et al., JAP, 2000

2. Baraskar et al., ICMBE, 2010


4. Katz et al., APL, 1993

5. Jain et al., DRC, 2010

6. Jian et al., Matl. Eng., 1996


Theory and experiment agree well.

At n = 2.2×1020 cm-3 doping, ΦB=0.6 eV

theory is 13:1 higher than Landauer

→ Tunneling probability remains low.

14

Conclusions

Correlation of experimental Contact resistivities with theory

excellent for P-InGaAs

~4:1 discrepancy for N-InGaAs, N-InAs

N-contacts are approaching Landauer Limits

theory vs. Landauer: 4:1 discrepancy

tunneling probability is high

15

0,0)(1 zzV

112 0,)( dzzsdzV Bnm

2121

12

3 ,)( dzdzsddd

zV Rmm

24 ,)( dzzV R

SBnRm

11 / dds Bn

12

2 dds Rm

Transmission Probability, T

Potential energy in various regions

csfss EE

16

111112 0)],)(([)])(([)( dzEzqVBiDEzqVAiCz zz

2122223 )],)(([)])(([)( dzdEzqVBiGEzqVAiFz zz

24 ),exp()( dzziktz mz

)(zAi )(zBi

3/1

2

1

21 )2

(s

ms

3/1

2

2

22 )2

(s

ms

(15)

and are the Airy functions

0))((2 2

22

zVE

dz

d

m z

s

0),exp()exp()(1 zzikRzikz mzmz

Transmission Probability, TSolutions of Schrodinger equation in various regions

2t

m

m

k

kT

s

m

mz

sz

Transmission probability is given by

Lower Limits To Specific Contact Resistivity

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