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Advanced

Semiconductor

Devices

Lecture 8

Advanced

Semiconductor

Devices

Lecture 8

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V. Ariel 2013 Advanced Semiconductor Devices Lecture 8

Lecture outline

Review

Three-terminal MOS structure

Quasi-Fermi potential

Regions of operation

Accurate modeling of three-terminal MOS capacitor

Surface potential

Inversion charge

Pinchoff voltage

MOSFET transistor

Charge-sheet model

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Three-terminal MOS structure

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Three-terminal MOS structure energy bands

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Three-terminal MOS structure - charges

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Three-terminal MOS structure regionsof operation

Depletion:

Weak inversion:

Moderate and strong inversion:

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Three-terminal MOS structure basic equations in depletion and inversion

From charge and potential balance

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Three-terminal MOS structure basic equations in depletion and inversion

Define

Then

Depletion weak inversion:


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Surface potential in moderate and stronginversion

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Approximation for surface potential inmoderate and strong inversion

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Approximation for MOS capacitance inmoderate and strong inversion

MOS capacitance in general

MOS capacitance in moderate and strong inversion

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Depletion

Condition for depletion

Approximation for gate voltage in depletion

(similar to two-terminal MOS structure)

Can neglect inversion charge!!!

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MOS Capacitor in depletion

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Weak inversionWeak inversion is defined as

Consequently

Need to pay attention to terms of the order of

Note that inversion charge contribution is mostly importanton the border with moderate inversion

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On the border of moderate inversion

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Charges in depletion and weakinversion

Obtained approximation where the first term is the regular

contribution of the depletion charge while the second term

is due to the inversion charge on the border of moderate

inversion

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Surface potentialin depletion and weak inversion

Approximating for gate voltage for small

Re-arranging

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Depletion and linear approximations of the surface potential

MOS capacitance in depletion andweak inversion

Linear approximation

Depletion approximation

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Need to account for both depletion charge and inversion

charge in weak inversion

MOS Capacitor in depletion andweak inversion

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Using approximations for the surface potential


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Depletion and weak inversion

MOS capacitance in all regions of operation

Moderate and strong inversion

The model is fully analytic with explicit dependence on applied

voltages

The model is physics based, all parameters have physical

meaning and can be determined from experimental MOS capacitor

measurements

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The new approximation of MOS capacitor is accurate!!!


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MOS capacitance at different VCB

terminal biases

VCB

= 0V

VCB

= 0.5V

VCB

= 1V

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MOS surface potential in all regionsof operation


The model is fully analytic with explicit dependence on applied

voltages

The model is physics based and accurate since surface potential

is an integral function of MOS capacitance

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Surface potential at different VCB

terminal biases

VCB

= 0V

VCB

= 0.5V

VCB = 1V

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Semiconductor charges in allregions of operation

Since we have a model of surface potential in all regions of

operation, we can easily calculate semiconductor charges

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Inversion charge at different VCB

terminal biases

VCB

= 0V

VCB = 0.5V

VCB

= 1V

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Increasing bulk potential reduces inversion charge

Body effect

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Inversion disappears for large VCB

Pinchoff voltage

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Assume large L and W

Also assume IG

= 0 and IB

= 0

Long-channel MOS transistor (MOSFET)

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Regions of inversion are determined by the most heavily

inverted terminal (usually source)

MOSFET regions of inversion

Depletion weak inversion:


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Drain current in different regions of inversion

MOSFET regions of inversion

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All voltages measured with respect to bulk

Body reference

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All voltages measured with respect to source terminal

Convenient because measure drain voltage vs source voltage

Source reference

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Basic equations along MOSFET channel

All equations depend on the gate voltage, channel voltage,

and surface potential

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Surface potential along MOSFET channel



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Basic assumptions for current calculation

DC operation

Horizontal electric field is much smaller than the vertical

electric field Gradual channel approximation

Channel length is much larger than pn-junction depeletionregions around source and drain

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Charge-sheet model

Inversion layer charge is approximated as a layer of charge

of zero thickness at semiconductor surface

Current consists of drift and diffusion components

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Charge-sheet model: basics

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Charge-sheet model: constant mobility

Assume that mobility is constant along the channel (???)

Use

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Charge-sheet model comparison

Lines: charge-sheet model

Dots: full semiconductor equation solution

We have an approximate analytical model of surface potential

which should lead to similar accuracy as charge-sheet model

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