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, NY

Depts. of 2Materials and 3ECE, University of
California, Santa Barbara, CA
24th International Conference on Indium Phosphide
and Related Materials Santa Barbara, CA
2
Ohmic Contacts Critical for nm THz Devices
Scaling laws to double bandwidth
FET parameter change
gate length decrease 21
current density (mA/mm), gm (mS/mm) increase 21
transport effective mass constant
channel 2DEG electron density increase 21
gate-channel capacitance density increase 21
dielectric equivalent thickness decrease 21
channel thickness decrease 21
channel density of states increase 21
source drain contact resistivities decrease 41
gt 0.5 O-µm2 resistivity for 10 nm III-V MOSFET gt 0.5 O-µm2 resistivity for 10 nm III-V MOSFET
Ls/d
Lg
Intel 32 nm HKMG IEDM 2009
HBT parameter change
emitter collector junction widths decrease 41
current density (mA/mm2) increase 41
current density (mA/mm) constant
collector depletion thickness decrease 21
base thickness decrease 1.41
emitter base contact resistivities decrease 41
gt 2 O-µm2 resistivity for 2 THz fmax gt 2 O-µm2 resistivity for 2 THz fmax
THz HBT Lobisser ISCS 2012
3
Ohmic Contacts Critical for nm THz Devices
Scaling laws to double bandwidth
FET parameter change
gate length decrease 21
current density (mA/mm), gm (mS/mm) increase 21
transport effective mass constant
channel 2DEG electron density increase 21
gate-channel capacitance density increase 21
dielectric equivalent thickness decrease 21
channel thickness decrease 21
channel density of states increase 21
source drain contact resistivities decrease 41
gt 0.5 O-µm2 resistivity for 10 nm III-V MOSFET gt 0.5 O-µm2 resistivity for 10 nm III-V MOSFET
Ls/d
Lg
Intel 32 nm HKMG IEDM 2009
HBT parameter change
emitter collector junction widths decrease 41
current density (mA/mm2) increase 41
current density (mA/mm) constant
collector depletion thickness decrease 21
base thickness decrease 1.41
emitter base contact resistivities decrease 41
gt 2 O-µm2 resistivity for 2 THz fmax gt 2 O-µm2 resistivity for 2 THz fmax
THz HBT Lobisser ISCS 2012
4
Ultra Low-Resistivity Refractory Contacts
Schottky Barrier is about one lattice constant
what is setting contact resistivity ?
what resistivity should we expect ?
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Landauer (State-Density Limited) Contact
Resistivity
momentum
velocity
density
current
conductivity
G valley
L, X, D valleys
6
Landauer (State-Density Limited) Contact
Resistivity
momentum
velocity
density
current
conductivity
G valley
L, X, D valleys
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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

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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

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Calculation of Contact Resistivity
Current density, J
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
Contact Resistivity, ?c
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Results Zero Barrier Contacts, Landauer Contacts
Step potential energy profile
Step Potential Barrier interface quantum
reflectivity, resistivity gtLandauer Parabolic
vs. non-parabolic bands differing Efs-Ecs ?
differing interface reflectivity Landauer
resistivity lower in Si than in G-valley
semiconductorfs multiple minima, anisotropic
bands
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Results InGaAs
Assumes parabolic bands At n 51019 cm-3
doping, FB0.2 eV measured resistivity 2.31
higher than theory Theory is 3.91 higher than
Landauer
In-situ contacts

• References
• Jain et. al., IPRM, 2009
• Baraskar et al., JVST B, 2009
• Yeh et al., JJAP, 1996
• Stareev et al., JAP, 1993

12
Results N-InAs
n-InAs
Assumes parabolic bands At n 1020 cm-3
doping, FB0.0 eV measured resistivity 1.91
higher than theory Theory is 3.61 higher than
Landauer
In-situ contacts

• References
• Baraskar et al., IPRM, 2010
• Stareev et al., JAP, 1993
• Shiraishi et al., JAP, 1994
• Singisetti et al., APL, 2008
• Lee et al., SSE, 1998

13
Results P-InGaAs
p-In0.53Ga0.47As
Assumes parabolic bands Theory and experiment
agree well. At n 2.21020 cm-3 doping, FB0.6
eV theory is 131 higher than Landauer ?
Tunneling probability remains low.
In-situ contacts

• References
• Chor et al., JAP, 2000
• Baraskar et al., ICMBE, 2010
• Stareev et al., JAP, 1993
• Katz et al., APL, 1993
• Jain et al., DRC, 2010
• Jian et al., Matl. Eng., 1996

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Conclusions
Correlation of experimental Contact resistivities
with theory excellent for P-InGaAs 41
discrepancy for N-InGaAs, N-InAs N-contacts are
approaching Landauer Limits theory vs.
Landauer 41 discrepancy tunneling
probability is high
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Transmission Probability, T
Potential energy in various regions
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(15)
Transmission Probability, T
Solutions of Schrodinger equation in various
regions
and
are the Airy functions
Transmission probability is given by
.