1. Mechanical Stress Effect on Gate Tunneling Leakage of Ge MOS Capacitor
Younsung Choi
Electrical Engineering
University of Florida

2. Gate Tunneling Current Summary
Outline
Background
Ge MOS Device
Gate Tunneling Current
Summary

3. 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)
Hydrostatic strain
Shear strain

4. 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, 731,2004 Lim et al., Measurement of conduction band deformation potential constants using gate direct tunneling current in n MOSFET under mechanical stress, APL, 89, ,2006

5. 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? => 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 MOSFET =>direct electron tunneling through very thin SiO2

6. 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

7. L valley of Ge Conduction Band
For electrons in Ge, the conduction band minima are located at L valley
Uniaxial Tension along <110> direction
[111],[11-1]
[1-11],[-111]
Shear
Strain
∆EShear
Hydrostatic
Strain
∆EHydro
Unstrained
Four-fold degenerate L-valleys
in the Ge conduction band.

8. How to calculate? 1-D Effective Mass Hamiltonian
: the strain Hamiltonian
: the effective mass associated the electron motion perpendicular to the interface
Electron Concentration along quantum box
Electro static potential with Poisson equation

9. Ge MOS Electrostatics Vg = 1V Vg = 1V Vg = 0.5V Vg = 0.5V HfO2 Ge Sub.
Conduction Band Edge vs Distance
HfO2
Ge Sub.
Vg = 1V
Vg = 0.5V
Vg = 1V
Vg = 0.5V

10. Stress Effect on Ge Quantization
Energy Band Splitting
Electron Repopulation
[111],[11-1]
[-111],[1-11]
Band Splitting
Electron
Repopulation

11. 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

12. 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)
EL(σ) EC
Direct
Tunneling
Current
Y.T. Hou et al., Direct tunneling hole currents
through ulrtathin gate oxides in MOS devices,
JAP, 91, 258 EV
Metal
Gate Ge
Substrate
HfO2

13. 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(E+qVOX) : 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

14. Stress Effect on Gate Tunneling Current
∆τ[111],[11-1]
∆τ[-111],[1-11]
∆n/n & ∆τ/τ (%)
VG=0.6V
VG=1V
~+2%
~-3%
-1%
~+1.3%
~-2%
-0.7%
Line Model
Symbol Exp.Data
∆ФB(σ)<0
E(σ)[111],[11-1]
E(σ)[1-11],[-111]
Relative Change of Tunneling Current
with Uniaxial Tension along (110) direction
Barrier Lowering of [111],[11-1] valleys
=> Tunneling Current Enhancement

15. 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. => Barrier Height Lowering leads to Enhancement of Tunneling Current

16. Thank You !!!
Q & A