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Lower Limits To Specific Contact Resistivity. Depts. of 2 Materials and 3 ECE, University of California, Santa Barbara, CA. Ashish Baraskar 1 , Arthur C. Gossard 2,3 , Mark J. W. Rodwell 3 1 GLOBALFOUNDRIES, Yorktown Heights, NY. - PowerPoint PPT Presentation
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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
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
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
Electron Concentration, cm-3
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
Electron Concentration, cm-3
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
2. Stareev et al., JAP, 1993
3. Shiraishi et al., JAP, 1994
4. Singisetti et al., APL, 2008
5. Lee et al., SSE, 1998
Assumes parabolic bands
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
3. Stareev et al., JAP, 1993
4. Katz et al., APL, 1993
5. Jain et al., DRC, 2010
6. Jian et al., Matl. Eng., 1996
Assumes parabolic bands
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