Mechanical Stress Effect on Gate Tunneling Leakage of Ge MOS Capacitor

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Mechanical Stress Effect on Gate Tunneling
Leakage of Ge MOS Capacitor

• Younsung Choi
• Electrical Engineering
• University of Florida

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Outline

1. Background
2. Ge MOS Device
3. Gate Tunneling Current
4. Summary

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Background

• What is strain?
• Strain is differential deformation in
  response to an applied
• stress.
• Uniaxial one directional (1D) deformation
• Biaxial two directional (2D) deformation
• Hydrostatic volume deformation of a solid
  (average energy level shift in the conduction and
  valence bands)
• Shear twisted deformation of a solid (subband
  splitting in the conduction and valence bands
  without changing the average energy level)

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Background
Why is strain important?

• Strain increases carrier mobility in MOSFETs,
  resulting in faster speed of a MOSFET operation.
  Thompson et al., Uniaxial-Process-Induced
  Strained-Si Extending the CMOS Roadmap, IEEE
  Trans. On Electron Devices, 53, 1010, 2006
• Strain affects a MOSFET operation characteristics
  such as its threshold voltage, gate tunneling
  current.Lim et al., Comparison of threshold
  voltage shifts for Uniaxial and Biaxial
  Tensile-stressed n-MOSFETs, IEEE Elec. Device
  Letters, 25, 731,2004Lim et al., Measurement of
  conduction band deformation potential constants
  using gate direct tunneling current in n MOSFET
  under mechanical stress, APL, 89, 073509,2006

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Background
Why do we need Ge?

• Promising as an alternative channel material due
  to its high carrier mobility
• Why have we used Si for a long time?gt based on
  the synergy between the silicon itself and its
  thermal oxide, SiO2. For decades, thermal SiO2
  has provided the best possible surface
  passivation and it is a superb gate insulator.
• Non-SiO2 Gate Insulator with Ge MOSFETgtdirect
  electron tunneling through very thin SiO2

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Ge MOS Device

• L valley of Ge Conduction Band
• How to calculate Ge MOS Electrostatics
• Ge MOS Electrostatics with solving
  self-consistently the Schrodinger and Poisson
  equations
• Stress Effect on Ge Quantization

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L valley of Ge Conduction Band
For electrons in Ge, the conduction band minima
are located at L valley
Uniaxial Tension along lt110gt direction
Unstrained
Four-fold degenerate L-valleys in the Ge
conduction band.
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How to calculate?
1-D Effective Mass Hamiltonian
Electron Concentration along quantum box
Electro static potential with Poisson equation
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Ge MOS Electrostatics
Conduction Band Edge vs Distance
Ge Sub.
HfO2
Vg 1V
Vg 0.5V
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Stress Effect on Ge Quantization

1. Energy Band Splitting
2. Electron Repopulation

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Gate Tunneling Current

• What is Gate Tunneling Current?
• Tunneling Probability Calculation with a modified
  Wentzel-Kramers-Brillouin (WKB) approximation
• Stress Effect on Gate Tunneling Current

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What is Gate Tunneling Current?

• Gate tunneling is a phenomenon in which
  channel charge carriers tunnel into the oxide
  layer when the gate bias is applied.

Z (001)
EC
EL(s)
EV
Ge Substrate
Metal Gate
HfO2
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Tunneling Probability Calculation with a modified
WKB approximation
TWKB the usual WKB tunneling probability valid
for smoothly varying potentials TR the
correction factor for reflections from boundaries
of the oxide
K(E) the imaginary wave number within the oxide
gap energy
vGe(E) vGe(EqVOX) the group velocities of
carrier incident and leaving the Oxide
layers vOX(EOXi) vOX(EOXo) the magnitude of
the imaginary group velocities of Carriers
tunneling in and out of the oxide layer
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Stress Effect on Gate Tunneling Current
Line Model Symbol Exp.Data
??B(s)lt0
E(s)111,11-1
E(s)1-11,-111
Relative Change of Tunneling Current with
Uniaxial Tension along (110) direction
Barrier Lowering of 111,11-1 valleys gt
Tunneling Current Enhancement
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Summary

• Ge Electrostatics with solving self-consistently
  the Schrodinger and Poisson equations

• Tunneling Probability with the modifeied WKB
  approximation

• Gate Tunneling Leakage Current Change with
  Uniaxial Stress was obsereved.gt Barrier Height
  Lowering leads to Enhancement of Tunneling
  Current

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