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Advanced

Semiconductor

Devices

Lecture 7

Advanced

Semiconductor

Devices

Lecture 7

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V. Ariel 2013 Advanced Semiconductor Devices Lecture 7

Lecture outline

Review

Approximations for regions of operation

Surface potential model in moderate inversion

MOS Capacitor

MOS Capacitor in moderate inversion

Accurate capacitance model in all regions of operation

Surface potential and inversion charge

Three-terminal MOS structure

Quasi-Fermi potential

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Voltage and charge balance

Total charge in semiconductor body

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Flatband

Accumulation

Depletion and inversion

Regions of operation

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Solution for gate voltage

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Accumulation

Condition for charge accumulation

Approximate solution for charge accumulation

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Depletion

Condition for depletion

Approximation for gate voltage in depletion

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Inversion

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Gate voltage and surface potential ininversion

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Weak inversion

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Weak inversion

On the border of moderate inversion

In weak inversion

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Weak inversion

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Strong inversion

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Moderate inversion

Need a simple solution for semiconductor charges and

potentials in moderate inversion !!!

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Moderate and strong inversion

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Moderate inversion

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Approximation for surface potential inmoderate and strong inversion

Obtained explicit approximation for the surface potential as

a function of gate voltage in moderate and strong inversionregions!!!

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Moderate and strong inversion

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MOS Capacitor

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MOS Capacitor

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MOS Capacitor

Need to differentiate a complex expression

Instead, consider different regions of operation

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MOS Capacitor in accumulation

Semiconductor charge capacitance exponentially increasing

for large negative surface potential

Therefore, in accumulation

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MOS Capacitor in depletion

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MOS Capacitor in depletion

MOS C it i d t d

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MOS Capacitor in moderate andstrong inversion

Use surface potential as a function of gate voltage in

moderate and strong inversion regions

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Match with depletion capacitance

MOS Capacitor in moderate andstrong inversion

Match with moderate and strong inversion

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MOS Capacitor in all regions ofoperation

At high frequency measurements observe depletion capacitance

At low frequencies observe both depletion and inversion charges

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MOS Capacitor approximation indepletion and inversion

There seems to be a problem on the border with weak inversion

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Need to account for both depletion charge and inversion

charge in weak inversion

MOS Capacitor in weak inversion

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Obtained approximation that seems to work in all regions of

depletion and inversion

Problem: surface potential as explicit function of gate voltage

MOS Capacitor approximation in allregions of inversion

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Surface potential

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Inversion Charge

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Three-terminal MOS structure

Th t i l MOS t t

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Three-terminal MOS structure energy bands

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Three-terminal MOS structure - charges