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Ideal MOS Capacitor

- Oxide has zero charge, and no current can pass through it.
- No charge centers are present in the oxide or at the oxide-semiconductor interface.
- Semiconductor is uniformly doped
- M = S = + (EC – EF)FB

Ideal MOS CapacitorUnder Bias

- Let us ground the semiconductor and start applying different voltages, VG, to the gate
- VG can be positive, negative or zero with respect to the semiconductor
- EF,metal – EF,semiconductor = – qVG
- Since oxide has no charge (it’s an insulator with no available carriers or dopants), d Eoxide / dx = / = 0; meaning that the E-field inside the oxide is constant.

Inversion condition

If we continue to increase the positive gate voltage, the bands at the semiconductor bends more strongly. At sufficiently high voltage, Ei can be below EF indicating large concentration of electrons in the conduction band.

We say the material near the surface is “inverted”. The “inverted” layer is not gotten by chemical doping, but by applying E-field. Where did we get the electrons from?

When Ei(surface) – Ei(bulk) = 2 [EF – Ei(bulk)], the condition is start of “inversion”, and the voltage VG applied to gate is called VT(threshold voltage). For VG > VT, the Si surface is inverted.

Electrostatic potential, (x)

Define a new term, (x) taken to be the potential inside the semiconductor at a given point x. [The symbol instead of V used in MOS work to avoid confusion with externally applied voltage, V]

Potential at any point x

Surface potential

| F | related to doping

concentration

F > 0 means p-type F < 0 means n-type

Electrostatic potential

S is positive if the

bands bend\ …….?

S = 2F at the

depletion-inversion

transition point (threshold voltage)

VG < 0

Accumulation of holes

Charge Density - AccumulationM O S

p-type silicon

accumulation condition

The accumulation charges in the semiconductor are ……. , and appear

close to the surface and fall-off

rapidly as x increases.

One can assume that the free carrier concentration at the oxide-semiconductor interface is a -function.

x

Charge on metal = QM

Charge on semiconductor = (charge on metal)

|QAccumulation| = |QM|

p-Si

VG > 0

QM

w

Depletion of

holes

Charge Density - Depletionp-type Si,

depletion condition

The depletion charges in Si are immobile ions - results in depletion

layer similar to that in pn

junction or Schottky diode.

|q NA A W| = |QM|

() (+)

If surface potential is s, then the depletion layer width W will be

p-Si

VG>>0

Charge Density - Inversionp-type Si,

strong inversion

Once inversion charges

appear, they remain close to the surface since they are

…….. Any additional voltage to the gate results in extra QM in gate and get compensated by extra inversion electrons in

semiconductor.

w

QM

Depletion of

holes

Inversion electrons:

-function-like

So, the depletion width does not change during inversion. Electrons appear as -function near the surface. Maximum depletion layer width W = WT

MOS C-V characteristics

- The measured MOS capacitance (called gate capacitance) varies with the applied gate voltage
- A very powerful diagnostic tool for identifying threshold voltage, oxide thickness, substrate doping concentration, and flat band voltage.
- It also tells you how close to an ideal MOSC your structure is.
- Measurement of C-V characteristics
- Apply any dc bias, and superimpose a small (15 mV) ac signal (typically 1 kHz – 1 MHz)

x

C-V: under accumulationM O S

Consider p-type Si under accumulation.

VG < 0.

Looks similar to parallel

plate capacitor.

CG = Cox

where Cox = (oxA) / xox

p-Si

VG < 0

CG is constant as a function of VG

W

Cox

Cs

Depletion of

holes

C-V: under depletionM O S

Depletion condition:

VG > 0

p-type Si

VG > 0

CG is Cox in series with Cs where Cs can be defined as “semiconductor capacitance”

Cox=ox A / xox

Cs = Si A / W

CG = Cox Cs / (Cox + CS)

where s is surface potential

CG decreases with increasing VG

p-Si

VG >>0

QM

W

Depletion of

holes

Cox

Cs

Inversion electrons

- function

C-V: under inversion (high frequency)VG = VT and VG > VT

Inversion condition s = 2 F

At high frequency, inversion

electrons are not able to respond

to ac voltage.

Cox=ox A / xox

Cs = Si A / WT

CG ( ) = Cox Cs / (Cox + CS)

CG will be constant for VG VT

C-V: under inversion (low frequency)

At low frequency, the inversion electrons will be able to respond to the ac voltage. So, the gate capacitance will be equal to the “oxide capacitance” (similar to a parallel plate capacitance).

CG ( 0) = Cox

= ox A / xox

low frequency

Cox

C

high frequency

Vg

Vfb

Vt

accumulation

depletion

inversion

Ideal MOSC (p-type Si)

CG increases for VG VT until it reaches Cox

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