Comparison among modeling approaches for gate current computation in advanced gate stacks

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Comparison among modeling approaches for gate
current computation in advanced gate stacks
ARCES N.Barin, C.Fiegna, E.Sangiorgi BU
P.A.Childs FMNT-CNRS D.Brunel , C.Busseret,
A.Poncet PISA A.Campera, G.Fiori,
G.Iannaccone POLIMI R.Gusmeroli, C. Monzio
Compagnoni, A.L.Lacaita, A.S.Spinelli TUW
M.Karner, H.Kosina, E.Langer UDINE F.Driussi,
P.Palestri, L.Selmi WUT B.Majkusiak, J.Walczak
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• Aim of Task 3 of SINANO Work-Package 4
• Study of the performance and reliability of
  conventional (SiO2) and high-k thin insulator
  gate stacks for sub-50nm MOSFETs)
• To support the understanding of device
  reliability issues and potential limitations of
  device performance related to the gate stack
  architecture of future CMOS technologies.
• The activities foreseen in this context are
• simulation of C/V and I/V for different gate
  stack and device architectures
• investigation of the effects of high-K materials
  and of the related defects, traps, charges, etc..
  on the low-field mobility and carrier transport
  properties of the inversion channel.
• Two main phases
• comparison of gate leakage currents in advanced
  device architectures
• assessment of modeling requirements for
  ultra-thin oxide and high-k, metal gate stacks.

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OUTLINE

• Modeling approaches
• Template devices
• Results
• C/V
• I/V
• Microscopic quantities
• Comparison with experiments
• Conclusions

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Simulation Framework

• Solution of the Schrödinger equation in the
  poly-Si/dielectric/Si stack

Diel.
Si
poly
Poisson Equation

• Boundary conditions ?

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Boundary Conditions
Define quantum boxes
Closed
?0 at both sides of a box
In principle no current !
Ig semiclassical approach
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Boundary Conditions
Open resonance peak
Ei
Inject plane waves and compute transmission/reflec
tion
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Boundary Conditions
Open perfectly-matched-layer
Absorbing boundaries Complex eigenvalues
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Boundary Conditions
The Schrödinger equation is solved two
times, applying Dirichlet and then Neumann
conditions on both sides. This is like
simulating an infinite periodical structure, but
only over one half period
Periodical
T-prob. from the contact to the semiclassical
turning point
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Approaches followed by the partners
Model 1 Model 2 Model 3 Model 4 Model 5 Model
6 Model 7
Different definitions of the quantum boxes in
closed-boundaries
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OUTLINE

• Modeling approaches
• Template devices
• Results
• C/V
• I/V
• Microscopic quantities
• Comparison with experiments
• Conclusions

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Template Devices

• Device A pure SiO2 (tOX1nm) NPOLY1020cm-3
  (n-type) NSUB1018cm-3 (p-type)
• Device B pure SiO2 (tOX3nm) NPOLY5?1019cm-3
  (n-type) NSUB3?1017cm-3 (p-type)
• Device HK 4nm HfO2 1nm ITL NPOLY1020cm-3
  (n-type) NSUB3?1017cm-3 (p-type)
• Device A and B are from C. A. Richter, IEEE EDL,
  vol.22, p.35, 2001.

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Simulation Parameters
Same parameters in all modeling approaches
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OUTLINE

• Modeling approaches
• Template devices
• Results
• C/V
• I/V
• Microscopic quantities
• Comparison with experiments
• Conclusions

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Results C/V curves

• Good overall agreement
• Small problems in accumulation and at beginning
  of inversion (different models for
  poly-quantization)

HK
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Internal quantities affecting C/V
Cond.Band in accumulation
Subbands in inversion
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Results I/V
Errors within a factor of 10 Much larger in
accumulation (not shown)
HK
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Internal quantities affecting IG
Escape-time
HK
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Internal quantities affecting IG
Tunneling probability
HK
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OUTLINE

• Modeling approaches
• Template devices
• Results
• C/V
• I/V
• Microscopic quantities
• Comparison with experiments
• Conclusions

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Comparison with experiments
Data from N.Yang et al., IEEE T-ED, vol.46,
p.1464, 1999. Same physical parameters as in the
template devices.
NPOLY1020cm-3 NSUB5?1017cm-3 (from C/V)
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Conclusions

• Unprecedented comparison effort carried out by
  seven academic groups
• Good agreement between results obtained using
  very different models (open/closed boundaries)
• Approaches based on closed boundaries, coupled
  with the evaluation of the semiclassical
  escape-time provide a good trade-off between
  efficiency and precision
• Results submitted to IEEE T-ED, 2nd review step
  mandatory revisions
• Comparison of Trap-Assisted-Tunneling