Effect of Inversion layer Centroid on MOSFET capacitance

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Effect of Inversion layer Centroid on MOSFET
capacitance
EEL 6935 class project

• Srivatsan Parthasarathy
• SWAMP Group

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Organization

• Introduction
• Scaling Issues in nanometer MOSFETS
• Parasitics the ultimate showstoppers
• Project relevance
• Simulation Approach
• Tools of the trade what we need
• Bandstructure
• Selfconsistent solution
• Computing surface potential
• Capacitance
• Results and Discussion

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Part IIntroduction
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Scaling Issues in nanometer MOSFETS

• Phenomenal scaling in last 40 years
• LGATE from 10 µm to 30 nm !
• Major changes in both technology and materials
• Smart optimizations in device structures
• Timely introduction of new processing techniques
• New materials (eg. Halo, silicides), but not in
  channel
• Issues with scaling
• Parasitics
• Lesser control on Short Channel effects
• Decreasing ION/IOFF (more leakage with thin
  oxide)
• Industry is looking at new vectors
• Strained Si, III-V channel materials, multi-gate
  architectures

Part 1 Introduction
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Parasitics

• Why does gate capacitance reduce?
• Geometric Scaling
• To first order, Cox is proportional to scaling
  factor
• Quantum effects
• Peak of Inversion Charge is not at Si-SiO2
  interface, but instead a few nm inside.

This reduction due to quantum effects cannot be
neglected.
Part 1 Introduction
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Project relevance

• Very important to quantify capacitance
  degradation
• To build better device models and simulators
• To compare how novel channel materials compete
  with existing technology
• Main goal of this project
• To quantify the quantum effects leading to
  reduction in capacitance using techniques taught
  in class

Part 1 Introduction
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What I did in the project

• Simulated capacitance degradation for unstrained,
  planar nMOS
• Bandstructure - sp3d5s TB model with SO coupling
• Self-consistent solution of schroedinger-poisson
  equation
• Surface potential calculation
• Inversion Capacitance d(QINV)/d(FS)
• The TB Hamiltonian can be used 3-5 materials
  also, but GaAs or other materials was not
  simulated ( as initially planned) due to lack of
  time

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Part IISimulation Approach
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Tools of the Trade

• What all do we need?
• Bulk bandstrcture
• EMA, kp, TB which method to choose?
• Trade-offs/Advantages in TB
• Bandstrcture for M-O-S structure
• Different from bulk bandstructure due to
  confinement
• Self-consistent solution of schroedinger-poisson
  equations
• Computing surface potential
• How is FS related to VGATE ?

Part 2 Approach
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Bandstructure

• Many approaches exist in theory
• Single/multi-band Effective Mass Approximation
  (EMA)
• Hartree, Hartree-Fock, Local Density
  Approximation
• kp method - based on the non-degenrate
  perturbation theory
• Empirical and semi-empirical Tight Binding (TB)
• sp3s, sp3d5s etc.
• Density Functional Theory (DFT)
• Which method should I follow?

Part 2 Approach
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Bandstructure (cont.)

• Tight Binding followed in this project
• Main Advantages
• Atomistic representation with localized basis set
• It is a real space approach
• Describes bandstructure over the entire Brillouin
  zone
• Correctly describes band mixinga
• Lower computational cost w.r.t other method

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Tight Binding Method
1983 Vogl et al. Excited s orbital
1954 Slater and Koster Simplified LCAO Method
1998 Jancu et al. Excited d orbitals
2003 NEMO 3D Purdue

• We attempt to solve the one-electron schoredinger
  equation in terms of a Linear Combination of
  Atomic Orbitals (LCAO)

Cia coefficients fia atomic orbitals (s,p,d)
Caution is needed !
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Tight Binding Method (cont.)

• 3 Major assumptions
• Atom-like orbitals
• Two center integrals
• NN interaction

• Choice of basis
• Atleast need sp3 for cubic semiconductors
• of neighboring-atom interactions is a choice
  between computational complexity and accuracy

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Tight Binding Method (cont.)

• The sp3s Hamiltonian Vogl et al. J. Phys. Chem
  Sol. 44, 365 (1983)
• In order to reproduce both valence and conduction
  band of covalently bounded semiconductors a s
  orbital is introduced to account for high energy
  orbitals (d, f etc.)

• The sp3d5s Hamiltonian
• Jancu et al. PRB 57 (1998)
• Many more parameters, but works quite well !

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Tight Binding Method (cont.)
1D chain Hamiltonian is tridiagonal

• Hamiltonian in spds basis

Size of each block is 10 x 10
Size of each block is 1 x 1
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Tight Binding Method (cont.)

• Each of the elements in the above matrix is a 5 x
  5 block

How to treat SO coupling?
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Tight Binding Method (cont.)

• In sp3d5S TB, SO interaction of d orbitals is
  ignored, but SO is present for all other
  orbitals.
• SO interaction happens between orbitals located
  on the same atom (not neighboring atoms).

Size of each block is 10 x 10 ? Hamiltonian size
is 40 x 40
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Calculated bandstructure
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Applying TB to a MOS structure
Application to finite structure
Bulk Hamiltonian
Z
2X2 block matrix
X
Size of each block is 10 x 10
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Applying TB to a MOS structure
Device Hamiltonian
NX X NX block tridiagonal
Block Size (NZ Nb) X (NZ Nb) (Nb 10 for sp3d5)
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Capacitance Calculation

• The schroedinger-poisson equation is solved
  self-consistently using the method described in
  the text.
• The total carrier concentration n(z) is
  calculated as a function of distance by summing
  up the electron concentration in each energy
  level.
• For calculating the capacitance, we need to find
  surface potential at every gate voltage.
• Ronald van Langevelde,"An explicit
  surface-potential-based MOSFET model for circuit
  simulation", Solid-State Electronics V44 (2000)
  P409

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Simulation results

• Characterization of Inversion-Layer Capacitance
  of Holes in Si MOSFETs, Takagi et al,TED, Vol.
  46, no.7, July 1999.

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Summary

• Quantified the effect of inversion layer
  capacitance with a good TB model for the
  Hamiltonian
• Results agreed with existing published values, so
  approach seems to be right.
• Hamiltonian is not 100 accurate passivation of
  surface states at interface, dangling bonds etc.
• Simulation was only for a 15 nm quantum domain,
  but still am able to get good results ?
  effectiveness of sp3d5 hamiltonian

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References and Thanks

• Exploring new channel materials for nanoscale
  CMOS devices A simulation approach, Anisur
  Rahman, PhD Thesis, Purdue University, December
  2005.
• Characterization of Inversion-Layer Capacitance
  of Holes in Si MOSFETs, Takagi et al,TED, Vol.
  46, no.7, July 1999.
• Ronald van Langevelde,"An explicit
  surface-potential-based MOSFET model for circuit
  simulation", Solid-State Electronics V44 (2000)
  P409

• Dr. Yongke Sun, SWAMP Group, ECE UF
• Guangyu Sun, SWAMP Group, ECE UF

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Questions?