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

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Contents

MOSFET Modeling1/f NoiseThermal NoiseInduced Gate Noise+ Cross-Correlation Noise

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Basic Equations

VｇｓVth

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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.

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Surface Potentials: HiSIM Results

Short-channel effects are included in potential calculations.

(Vth based model)

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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.

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Gummel Symmetry Test

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Technology-Based Modeling

require accurate impurity-profile extraction

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Modeling of Pocket Implant

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Universal Mobility

S. Matsumoto et al., J. Appl. Phys., vol. 92, p. 5228, 2002.

Vds=0.1V

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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

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Under Saturation Condition

Pinch-off regionsteep potential increase

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Inversion-Layer Thickness ~ 0Gradual-Channel Approximation Valid for long channel

Approximations Applied for Modeling

Beyond Pinch-off Point

modeling further potential increase

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Contents

MOSFET Modeling1/f NoiseThermal NoiseInduced Gate Noise+ Cross-Correlation Noise

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1/f Noise:

Thermal Noise:

Induced Gate Noise +Cross-Correlation Noise:

Noise Sources

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Measurement Setup for 1/f Noise

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Noise Figure Measurement

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Origin of 1/f Noise

K. K. Huang et al., IEEE Trans. ED, 37, p. 1323, 1990.

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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

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Measured 1/f Noise

S. Matsumoto et al., IEIEC T E, E88-C, p. 247, 2005.

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Explanation

Wg/Lg=10μm/1μmVgs=0.5VVds=0.4V

Inhomogeneous trap density distribution

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Statistics on a Wafer

Homogeneous Distribution on a Wafer

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Model Equations

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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.

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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

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Comparison with Measurements

Lines: HiSIMSymbols: Measurements

S. Hosokawa et al., Appl. Phys. Let., vol. 87, p. 092104, 2005.

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• 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

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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)

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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

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Universal Relationship

Comparison with Vth Shift

Grad. γ

Grad. ΔVth

ΔVth=Vth(long)-Vth(short)

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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

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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.

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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

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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.

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Excess Noise in Short-Channel MOSFETs

Excess noise starts to saturate for further Vds increase.

iggs

ds0

2

54C

gS kTω

β⎛ ⎞⎜ ⎟⎝ ⎠=

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Correlation Coefficient (c) i i

i i

g d

g d

Sc

S S=Correlation Coefficient :

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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.

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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.