View
3
Download
0
Category
Preview:
Citation preview
HiSIM Team 1
Measurements and Modeling of Noisein Advanced MOSFETs
MOS-AK Meeting20. April, 2007
HiSIM Team, Hiroshima UniversitySTARC
M. Miura-Mattausch
HiSIM Team 2
Noise Features in MOSFETs
1/f NoiseThermal NoiseInduced Gate NoiseCross-Correlation Noise
Shot NoiseJunction Noise
d
dsi
Δ=
Noise Spectral Density
2i
Sf
Intensity
HiSIM Team 3
Contents
MOSFET Modeling1/f NoiseThermal NoiseInduced Gate Noise+ Cross-Correlation Noise
HiSIM Team 4
Basic Equations
VｇｓVth
HiSIM Team 5
Surface-Potential
(analytical)
(exact)
Vth-Based
Charge-Based
Models Year 9896 02 0400
BSIM（UC Barkeley)
Model11（Philips)
EKV（Swiss IT)
SP2000（Penn.SU)
HiSIM
Available Models in Commercial SPICEs
PSP
CMC Standardization Process
HiSIM solves the Poisson equation iteratively.
HiSIM Team 6
Surface Potentials: HiSIM Results
Short-channel effects are included in potential calculations.
(Vth based model)
HiSIM Team 7
Measurement
HiSIM
Wg/Lg=2μm/40nm
Derivatives of Drain Current
H. J. Mattausch et al., IEEE Circuit & Devices Magazine, vol. 22, no. 5, p. 29, 2006.
HiSIM Team 8
Gummel Symmetry Test
HiSIM Team 9
Technology-Based Modeling
require accurate impurity-profile extraction
HiSIM Team 10
Modeling of Pocket Implant
HiSIM Team 11
Universal Mobility
S. Matsumoto et al., J. Appl. Phys., vol. 92, p. 5228, 2002.
Vds=0.1V
HiSIM Team 12
Vds=0.1V
Mobility determines the harmonic distortion characteristics.D. Navarro et al., IEEE Trans. ED, vol. 53, p. 2025, 2006.
Harmonic Distortion vs. Mobility
HiSIM Team 13
Under Saturation Condition
Pinch-off regionsteep potential increase
HiSIM Team 14
Inversion-Layer Thickness ~ 0Gradual-Channel Approximation Valid for long channel
Approximations Applied for Modeling
Beyond Pinch-off Point
modeling further potential increase
HiSIM Team 15
Contents
MOSFET Modeling1/f NoiseThermal NoiseInduced Gate Noise+ Cross-Correlation Noise
HiSIM Team 16
1/f Noise:
Thermal Noise:
Induced Gate Noise +Cross-Correlation Noise:
Noise Sources
HiSIM Team 17
Measurement Setup for 1/f Noise
HiSIM Team 18
Noise Figure Measurement
HiSIM Team 19
Origin of 1/f Noise
K. K. Huang et al., IEEE Trans. ED, 37, p. 1323, 1990.
HiSIM Team 20
H. Ueno et al., Appl. Phys. Let., vol. 78, p. 380, 2001.
Monte Carlo Simulation
Num
ber o
f ele
ctro
ns h
ittin
g
Noise Intensity Number of electrons hitting SiO2 surface
HiSIM Team 21
Measured 1/f Noise
S. Matsumoto et al., IEIEC T E, E88-C, p. 247, 2005.
HiSIM Team 22
HiSIM Team 23
HiSIM Team 24
Explanation
Wg/Lg=10μm/1μmVgs=0.5VVds=0.4V
Inhomogeneous trap density distribution
HiSIM Team 25
Statistics on a Wafer
Homogeneous Distribution on a Wafer
HiSIM Team 26
Model Equations
HiSIM Team 27
Ntrap is fitted to measurements.If technology is mature, Ntrap is nearly universal.
Comparison with Measurements
I-V characteristics determine 1/f noise characteristics.1/f noise is predictable.
S. Matsumoto et al., IEIEC T E, E88-C, p. 247, 2005.
HiSIM Team 28
22 ds
eff ds
ds0
id4 ( )
4
kTS gL IkTg γ
=
=
∫ y dy gds(y): Channel Conductance
van der Ziel Equation based on Nyquist Theorem:
gds0: at Vds=0
γ : Noise Coefficient
Origin of Thermal Noise
No Additional Model Parameters
HiSIM Team 29
Comparison with Measurements
Lines: HiSIMSymbols: Measurements
S. Hosokawa et al., Appl. Phys. Let., vol. 87, p. 092104, 2005.
HiSIM Team 30
• Knoblinger et al. (2001): Hot Electron Contribution• Jamal Deen et al. (2002): Channel Length Modulation• Scholten et al. (2002): Velocity Saturation
Noise Coefficient (γ) in Short-Channel MOSFETs
Different Explanations
HiSIM Team 31
Mobility Reduction along Channel
μ: Constant
μ: Position Dependent
γ Increase Potential Increase
Origin of γ Increase
S. Hosokawa et al., Ext. Abs. SSDM, pp. 20, 2003.
γ for Short-Channel MOSFETAnalytical Investigation
(No additional model parameter)
HiSIM Team 32
First γ Reduction and Increase in the Saturation RegionNo Drastic Increase of γ γ Minimum Increase from 2/3
Lines: Simulation (HiSIM) Symbols: Measurements
Comparison with Measurements: Excess Noise
HiSIM Team 33
Universal Relationship
Comparison with Vth Shift
Grad. γ
Grad. ΔVth
ΔVth=Vth(long)-Vth(short)
HiSIM Team 34
T. Warabino et al., Proc. SISPAD, p. 158, 2006.
Induced Gate Noise ＆ Cross-Correlation Noise
( )( ) ( )
g
g d
i
i i
g
g d
′ ′Δ Δ + Δ
′ ′ ′Δ Δ Δ + Δ Δ
∴ = = Δ
= = Δ
∫ ∫
∫ ∫
: induced - gate
: cross - correlation
221 2
1 2 2
2
2**
i I I
i i I I I
S dx v dx
S dx v dx
HiSIM Team 35
g ch th0
0
0
( ) ( )
( ) ( ) ( )
( ) ( )
V x V V x V
V x V x v x
I x I I x
= − −
= − Δ⎧⎪⎨ = − Δ⎪⎩
{ } εω
εμ
⎧⎪
∂⎪ = −⎪⎪ ∂⎨⎪⎪ ∂⎪ = −
∂⎪⎩
Continuity eq.
Current Density eq.
( )( )
( ) ( ) ( )
i x Wj v xx d
dV x V x I xx W
( )( ) ( )
g
g d
i
i i
g
g d
′ ′Δ Δ + Δ
′ ′ ′Δ Δ Δ + Δ Δ
∴ = = Δ
= = Δ
∫ ∫
∫ ∫
221 2
1 2 2
2
2**
i I I
i i I I I
S dx v dx
S dx v dx
M. Shoji, IEEE TED, pp. 520-524, 1966.
HiSIM Team 36
Sig for Long-Channel Case
The van der Ziel model is valid only in the saturation region.
T 1f ≤ GHz
iggs
ds0
2
54C
gS kTω
β⎛ ⎞⎜ ⎟⎝ ⎠=
van der Ziel's model
HiSIM Team 37
Comparison with Measurements
The excess noise for short-channel devices isdue to the potential increase along the channel.
A. J. Scholten et al., Tech. Dig. IEDM, p. 867, 2003.
HiSIM Team 38
Excess Noise in Short-Channel MOSFETs
Excess noise starts to saturate for further Vds increase.
iggs
ds0
2
54C
gS kTω
β⎛ ⎞⎜ ⎟⎝ ⎠=
HiSIM Team 39
Correlation Coefficient (c) i i
i i
g d
g d
Sc
S S=Correlation Coefficient :
HiSIM Team 40
1/f Noise Thermal Noise
No model parameters are required.Features are determined only by I-V characteristics.
Harmonic Distortion
Phenomena Important for RF Applications
Electrostatic effect is still dominating.
Surface potential is important.
HiSIM Team 41
The 1/f noise is mostly governed by the carrier fluctuationdue to the trap/detrap process.
The thermal noise is governed by the potential distributionalong the channel.
The induced gate noise and the cross-correlation noise aregoverned by the same mechanism as the thermal noise.
These results conclude that the noise is still governedby the equilibrium carrier dynamics for MOSFETs down tothe sub-100nm channel length regime.
Summaries
The surface-potential-based model HiSIM is capable forpredicting noise characteristics.
Recommended