Transcript Slide 1

Mechanical Stress Effect on Gate
Tunneling Leakage of Ge MOS Capacitor
Younsung Choi
Electrical Engineering
University of Florida
1
Outline
1.
2.
3.
4.
Background
Ge MOS Device
Gate Tunneling Current
Summary
2
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
3
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, 073509,2006
4
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
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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
6
L valley of Ge Conduction Band
For electrons in Ge, the conduction band minima are located at L valley
[001]
s[110]
Uniaxial Tension along <110> direction
[111]
[111],[11-1]
∆EHydro
[111]
[111]
∆EShear
[010]
[1-11],[-111]
Unstrained
[111]
[100]
s[110]
Hydrostatic
Strain
Shear
Strain
Four-fold degenerate L-valleys
in the Ge conduction band.
7
How to calculate?
1-D Effective Mass Hamiltonian
2


d2
  * 2  H strain  qV ( x)   n ( x)  En  n ( x),
 2mn dx

mn* : the effective mass associated the electron motion perpendicular to the interface
H strain : the strain Hamiltonian
Electron Concentration along quantum box
n( x)  
n
md* kBT

2
ln[1  exp( EF  En / kBT )]   n ( x) ,
2
Electro static potential with Poisson equation
d2
 2 V ( x)  q /  Si [ N ( x)  n( x)  N D ( x)],
dz
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Ge MOS Electrostatics
Conduction Band Edge vs Distance
18
HfO2 Ge Sub.
10
Vg = 1V
electron density (/cm3) --->
1.5
Energy (eV) --->
1
0.5
0
-0.5
-1
0
5
10
z (nm)--->
15
4
2
12
electron density (/cm3) --->
Energy (eV) --->
6
Vg = 0.5V
0.5
0
5
10
z (nm)--->
5
13
1
-0.5
0
Vg = 1V
8
0
0
20
2
1.5
x 10
15
20
10
z (nm) --->
15
20
x 10
Vg = 0.5V
10
8
6
4
2
0
0
5
10
z (nm) --->
15
20
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Stress Effect on Ge Quantization
EChydro  ( d 
Electron
Repopulation
Lowest Energy Level (eV) --->
3
x 10
ECshear  
1
S 44  us
x 10
6
3.615
12
Electron Density (/cm2) --->
Band Splitting
-3
[111],[11-1]
2
1
0
[-111],[1-11]
-1
-2
0
5
Uniaxial Tension (Pa) --->
7
x 10
[111],[11-1]
0.136
0.134
0.132
0.13
[-111],[1-11]
0
5
Uniaxial Tension (Pa) --->
10
7
x 10
[-111],[1-11]
3.605
10
0.14
0.138
3.61
relative change of electron density (%) --->
Conduction Band Edge Splitting (eV) --->
1. Energy Band Splitting
2. Electron Repopulation
1
 u )( xx   yy   zz )
3
[111],[11-1]
3.6
0
5
10
7
Uniaxial Tension (Pa) --->
x 10
0.2
[-111],[1-11]
0.1
0
-0.1
[111],[11-1]
-0.2
-0.3
0
5
10
7
Uniaxial Tension (Pa) --->
x 10
10
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)
EL(σ)
Direct
Tunneling
Current
EC
EV
J   N n /  n ( En )
n
1

 n (E)
T (E)

tox
0
Metal
Gate
HfO2
Ge
Substrate
2mn /[ En  EC ( z )]dz
Y.T. Hou et al., Direct tunneling hole currents
through ulrtathin gate oxides in MOS devices,
JAP, 91, 258
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Tunneling Probability Calculation with a
modified WKB approximation
T  TRTWKB
TWKB : the usual WKB tunneling probability valid for smoothly varying potentials
TR : the correction factor for reflections from boundaries of the oxide
tox
TWKB  exp(2 k ( E, z )dz)
0
K(E) : the imaginary wave number within the oxide gap energy
4vGe ( E )vOX ( EOXi ) 4vGe ( E  qVOX )vOX ( EOXo )
TR  2
 2
2
2
vGe ( E )  vOX ( EOXi ) vGe ( E  qVOX )  vOX
( EOXo )
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
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3
0.7
0.6
Line
Model
Symbol Exp.Data
2
∆n/n & ∆τ/τ (%)
∆ФB(σ)<0
E(σ)[111],[11-1]
0.5
E(σ)[1-11],[-111]
0.4
Vg=0.6V
0.3
0.2
Vg=0.8V
Vg=1V
0.1
VG=0.6V
∆n[-111],[1-11]
4
6
Uniaxial Tension (Pa)
8
10
x 10
7
Relative Change of Tunneling Current
with Uniaxial Tension along (110) direction
Barrier Lowering of [111],[11-1] valleys
=> Tunneling Current Enhancement
~-3%
∆n[111],[11-1]
-1
∆τ[111],[11-1]
-2
-3
1
2
~+2%
0
-1%
2
1.5
0
0
∆τ[-111],[1-11]
1
-4
0
∆n/n & ∆τ/τ (%)
Tunneling Current Enhancement (%)
Stress Effect on Gate Tunneling Current
VG=1V
4
6
Uniaxial Tension (Pa)
8
10
x 10
7
∆τ[-111],[1-11]
∆n[-111],[1-11]
0.5
~+1.3%
0
∆n[111],[11-1]
-0.5
-1
-1.5
~-2%
∆τ[111],[11-1]
-2
-2.5
0
-0.7%
2
4
6
Uniaxial Tension (Pa)
8
10
x 10
7
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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.
=> Barrier Height Lowering leads to Enhancement of Tunneling
Current
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Thank You !!!
Q&A
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