Integrated Circuit Devices

Professor Ali Javey

Summer 2009

MOS CapacitorsReading: Chapter 16

EE143 – Ali Javey

MOS: Metal-Oxide-Semiconductor

SiO2

metalgate

Si body

Vg

SiO2

gate

P-body

Vg

N+N+

MOS capacitor MOS transistor

MOS Capacitors

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 CapacitorAt Equilibrium:

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 = – q VG

– 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 conditionIf 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.

Ideal MOS Capacitor – n-type Si

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]

)]((bulk)[1

)( ii xEEq

x

(surface)](bulk)[1

iiS EEq

](bulk)[1

FiF EEq

Potential at any point x

Surface potential

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

| F | related to doping concentration

Electrostatic potential

S = 2F at the depletion-inversion

transition point (threshold voltage)

S is positive if the bands bend\ …….?

Charge Density - Accumulation

p-type silicon accumulation condition

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

close to the surface and fall-offrapidly as x increases.

One can assume that the free carrier concentration at the oxide-semiconductor

interface is a -function.

M O S

VG < 0

p-Si

Accumulation of holes

Charge on metal = QM

Charge on semiconductor = (charge on metal)

|QAccumulation| = |QM|

x

Charge Density - Depletionp-type Si,

depletion conditionThe depletion charges in Si are

immobile ions - results in depletionlayer similar to that in pn

junction or Schottky diode.VG > 0

M O S

p-Si

Depletion of holes

wQM|q NA A W| = |QM| () (+)

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

SA

Si2 qN

W

Charge Density - Inversion

VG>>0

M O S

p-Si

Depletion of holes

wQM

Inversion electrons:-function-like

p-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.

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)

C-V: under accumulation

VG < 0

M O S

p-Si

Accumulation of holes

x

Consider p-type Si under accumulation.

VG < 0.Looks similar to parallelplate capacitor.

CG = Cox

where Cox = (ox A) / xox

CG is constant as a function of VG

C-V: under depletionDepletion condition: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)

sA

Si2

qNW

where s is surface potential

VG > 0

M O S

p-type Si

Depletion of holes

WQM

Cox Cs

CG decreases with increasing VG

C-V: under inversion (high frequency)

VG >>0

M O S

p-Si

Depletion of holes

WQM

Inversion electrons- function

Cox Cs

VG = VT and VG > VT

Inversion condition s = 2 F

FA

SiT 2

2

NqWW

At high frequency, inversionelectrons are not able to respondto ac voltage.

Cox=ox A / xox

Cs = Si A / WT

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

CG will be constant for VG VT

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

Ideal MOSC (p-type Si)

C-V: under inversion (low frequency)

CG increases for VG VT until it reaches Cox

CCox

accumulation depletion inversionVgVfb Vt

high frequency

low frequency