Lec. 7

P - Substrate

Field Oxiden+n+

source drainLeff ;

Effective Channel Length

Channel Length ; L

VG

VDVS

VB

Gate

2-terminals MOS Capacitor

4-terminals MOSFET

Gate ElectrodeGate Dielectric

MOS Capacitor

Lec. 7

MOS Capacitor

Silicon dioxide

Modern MOSFET used 1nm SiO2 gate dielectric.

How many layers of Silicon dioxide layer?

25nm gate length MOSFET

Lec. 7

ii) To simplify the case, we assume

i) Real MOS case

sm No difference in work function

This is a Flat Band (FB) condition. Although it is not realistic, this assumptionwill simplify our approach.

MOS Band Diagram

p-

Lec. 7

Now if we apply a voltage, voltage drop occurs both across the oxide (linear drop) and near the surface of the Si (bending).

Hole

+++

---

p-

MOS Band Diagram Under Bias

--

-

-

-+++

++

--

-

-

-

Lec. 7

Hole

+++

---

p-

Accumulation (Negative Bias to Gate)

• Accumulation of majority carriers at Si surface

The energy bands of Si near the surface bend upward.

Increased concentration of holes near the oxide/Si interface.

kTEEip

fienP /)(

sdxd

2

2

Vg<0

p-

Vg=0

sm , do not change with applied voltage.

No current through MOS structure, no change of Ef in semiconductor.

Lec. 7

p-

Depletion (Small Positive Bias to Gate)

--

-

-

-+++

++

Vg=0

Energy bands of Si at the surface bend downward as in Metal-Si contact.At the junction, majority carriers (holes) are depleted.

depletion region

WqN AchargeSpace

s

A

s

qNdxd

2

2

p-

Vg>0

Lec. 7

--

-

--

+++

++

p-

Inversion (Large Positive Bias to Gate)Vg>0

--

---

• The energy bands bend downwardeven further than depletion regime

Ei crosses over the Ef near the surface.

• Near the Si surface, (Ef-Ei)>0

At the surface, np>ni & np>pp.

kTEEip

ifenn /)(

p-

Vg>>0

+++

++

+++

++

• Inverted layer, separated from the underlying p-Si by depletion.

Lec. 7

If a bias is applied MOS, the voltage drop occurs across oxide and the depletion region of Si.

Sig VV

We define the onset of a strong inversion as follows:

region neutral in the )E(E : Si theof surface at the Potential :

ln22)(

fi

F

s

i

aFs n

Nq

kTinv

Thus, threshold voltage required for strong inversion is

i

si C

QV

Fi

dT C

QV 2

Threshold Voltage

Onset of strong inversion, there are negligible inversion charge (Qs=Qd)

Lec. 7

Once inversion condition is reached, e-

concentration near the surface increases very fast by even a small increase in band bending. Thus once an inversion layeris formed, the depletion layer width does not increases any more, that is, saturates at maximum value (Wm).

Charge per unit area in Si (QS):

),()(max

negativeareQQQWqNQQ

ns

mans Depletion layer

Inversion layer

Inversion chargeCharge in metal

(Qm is positive)

A

ias

A

Fs

A

ssm

A

ss

NqnNkT

qNqNinvW

qNW 2

)/ln(22)(2,2

W is same as n+ p junction

Inversion Charge & Depletion Width

21

max )(2 Fasad qNWqNQ )

21112(

/

dNaNqVW bis

ε

Lec. 7

Lec. 7

ionized acceptors

electron concentration

TG VV0 TG VV TG VV

FmE

FmE

CE CE

VE VEFE FEiE iE

FmE

QQ Q

x xxmaxQmaxQQ

dmaxx dmaxx

Threshold Voltage

Lec. 7

Inversion layer is less than 10nm.

Therefore we can neglect width of inversion layer in sketching electric field potential distribution.

nasm QWqNQQ max

Sig VV

i

si C

QV

Inversion

Fi

dT C

QV 2

These results are based on the assumption that Ef of metal and Si are equal.

Lec. 7

So far, we assume that Ef of Si and metal are equal. But this is not true for the most cases.

In addition to work function difference, MOS structure is affected by charges in insulator and interface. So we need to compensate this

assumption.

i

imsFB C

QV

FFsiAii

ms

Fi

d

i

imsT

qNQC

CQ

CQV

2))2(2(1

2

Realistic Threshold Voltage

(b)(a)

Work function difference

Interface charge

- Control of Vth: Gate materials, Ci control (thickness, high K), Threshold adjustment by ion implant (Na)

Lec. 7

Realistic Threshold Voltage

Lec. 7

p-Si

CV Characteristics

High freq.(1MHz)

Low freq. (1-100Hz)

MetalOxide

p-Si

_ MetalOxide

p-Si+ + ++ + - -- -

Ci CiCd

+

_

Capacitance decrease at 2, 3, 4 points means that depletion width is increasing.