MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1...

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MOSFET Devices HO #14: ELEN 251 - MOSFET Fundamentals Page 1 S. Saha Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building blocks of modern VLSI circuits with the areas of applications: – microprocessors dynamic memories and so on. In modern VLSI circuits: two types of MOSFET structures are used: nMOSFETs: p-substrate with n+ source-drain pMOSFETs: n-substrate with p+source-drain – nMOSFETs and pMOSFETs are used together and is called the complementary MOSFETs (CMOSFETs).

Transcript of MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1...

Page 1: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

MOSFET Devices

HO #14: ELEN 251 - MOSFET Fundamentals Page 1S. Saha

• Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building blocks of modern VLSI circuits with the areas of applications:– microprocessors– dynamic memories– and so on.

• In modern VLSI circuits:– two types of MOSFET structures are used:

♦ nMOSFETs: p-substrate with n+ source-drain♦ pMOSFETs: n-substrate with p+source-drain

– nMOSFETs and pMOSFETs are used together and is called the complementary MOSFETs (CMOSFETs).

Page 2: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

A. CMOS Device Structure

HO #14: ELEN 251 - MOSFET Fundamentals Page 2S. Saha

MOSFETs are four terminal devices as shown in the CMOS structure below:

Gateoxide

Channel Source-Drain

p-welln-well

STI

n+ Poly p+ Poly

n+ n+ p+ p+

NMOS PMOS

DielectricSpacer

p-substrate

Dual-polyGate

Halo

1 Gate: thermally grown oxide on Si-substrate with conducting electrode on the top.

2 Source-drain: heavily-doped regions at the two ends of the gate contacted with metal interconnects.

3 Body: substrate connected with metal interconnect.

Page 3: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

CMOS Structure: A Typical Layout

HO #14: ELEN 251 - MOSFET Fundamentals Page 3S. Saha

p-substrate

p-well n-well

n+

NMOS PMOS

n+ p+p+STI

Gate oxideHalo

P+ polySpacerN+ poly

Page 4: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

B. A Typical CMOS Fabrication

HO #14: ELEN 251 - MOSFET Fundamentals Page 4S. Saha

1 Shallow trench isolation (STI):– grow oxide and Mask #1– etch oxide– etch silicon– deposit oxide to form STI.

2 Mask #2: N-well/threshold adjust implant:– implant P– drive-in and grow oxide– clean.

3 Mask #3: P-well/threshold adjust implant:– implant B– drive-in B– clean.

P−

P-well N-well

Photoresist

P-well N-well

Photoresist

Page 5: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

CMOS Fabrication

HO #14: ELEN 251 - MOSFET Fundamentals Page 5S. Saha

4 Gate formation:– Clean silicon surface– grow gate oxide– deposit poly-Si gate

electrode.

5 Mask #4: Gate definition– etch poly-Si– etch oxide– grow masking oxide.

6 Mask #5: N+ source / drain extension (SDE) and p-halo:– As SDE implant– B/BF2 halo implant– clean.

Gate oxide Poly-Si

P-well N-well

Photoresist

P-Well N-WellHalo

Page 6: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

CMOS Fabrication

HO #14: ELEN 251 - MOSFET Fundamentals Page 6S. Saha

7 Mask #6: P+ SDE and n-halo:– B/BF2 SDE implant– As/Sb halo implant– clean.

8 Deep s/d (DSD) formation:– spacer deposition and etch– Mask #7 - N+ DSD

♦ As implant– Mask #8 - P+ DSD

♦ B/BF2 implant– dopant activation (RTA).

9 Interconnection:– Mask #9- contact opening– Mask #10: define metal.

Photoresist

P-Well N-Well

P-Well N-Well

NMOS PMOS

Page 7: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C. MOSFET Circuit Symbols

HO #14: ELEN 251 - MOSFET Fundamentals Page 7S. Saha

n+

n+

P Body

D

S

G B

D

S

G

D

S

GB

D

S

G

nMOSFETs

G = gate; D = drain; S = source; B = Bulk/BodypMOSFETs

p+

p+

N Body

D

S

G

D

S

GB

D

S

GB

D

S

G

Page 8: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

D. Basic Features of MOSFETs

HO #14: ELEN 251 - MOSFET Fundamentals Page 8S. Saha

• Non-uniform channel doping profile:– vertically due to threshold implants– laterally due to halo implants

• Parasitic elements:– terminal resistances

♦ source (RS), drain (RD), and gate (RG)

– diodes♦ B → S (BS) and B → D (BD)

– capacitance♦ S → B (CBS) and D → B (CBD) junction capacitances♦ G → S (CGSO) and G → D (CGDO) overlap capacitance♦ G → B (CGBO)

Page 9: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Basic Features of MOSFETs - Capacitances

HO #14: ELEN 251 - MOSFET Fundamentals Page 9S. Saha

Page 10: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

E. Equivalent Circuit: DC Model

HO #14: ELEN 251 - MOSFET Fundamentals Page 10S. Saha

• The simplest dc model for an MOS structure includes:– parasitic resistances RS, RD, and RG– parasitic diodes

♦ BS from B → S♦ BD from B → D.

• IDS = drain current from S → D.

• IG,leakage = gate leakage current through the oxide due to tunneling or due to high field effect.

Page 11: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Equivalent Circuit: Dynamic Model

HO #14: ELEN 251 - MOSFET Fundamentals Page 11S. Saha

• The basic MOSFET model consist of:– junction capacitances CBS

and CBD between S → B and D → B, respectively.

– overlap capacitances CGDO and CGSO due to G → S and G → D overlap, respectively.

– G → B capacitance CGBO– BS and BD diodes.

• ID as a function of VG, VD, and VB models the dc MOS device performance.

Page 12: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

MOSFET Device Modeling Approach

HO #14: ELEN 251 - MOSFET Fundamentals Page 12S. Saha

VD

ID

5

4321

VG −VthID

VGVth

VD = 50 mV

• In MOSFET devices:– IDS = f(VGS, VDS, VBS).– a gate voltage VGS ≡ Vth is required to turn-on (off) the device. Vth

depends on process technology and device dimensions.

• The basic modeling approach is to develop models for:– threshold voltage, Vth with technology and geometry dependence– drain current, IDS as a function of applied biases– capacitances for dynamic response.

Page 13: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

F. MOS Fundamentals: 1. Energy Band Diagram

HO #14: ELEN 251 - MOSFET Fundamentals Page 13S. Saha

• Note:– three materials in contact, EF = constant at equilibrium– currents through SiO2 are very small– holes flow from semiconductor → metal on contact– e− flow from metal → semiconductor on contact– bands will bend downwards in silicon at the interface (ΦM < Φs).

Metal(Al)

Oxide(SiO2)

Semiconductor(p-Si)

E0

qΦM= 4.1eV

EFM

qχox=0.95eV

Eg ≈ 8eV

Ec

Ev

EF

E0

Ec

EFEv

qΦS=5eVqχS= 4.15eV

Eg=1.1eVMOS structure

p-Si

SiO2

Page 14: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

MOS System at Equilibrium

HO #14: ELEN 251 - MOSFET Fundamentals Page 14S. Saha

Note:• Abrupt transition in Ec and Ev levels at

the material interfaces.

• A typical potential drop ~ 0.6 eV across SiO2. This depends on EF in Si. This potential can be supported because no current flows through SiO2.

• Substantial barriers exist to current flow from:

– S → M – M → S.

• Depletion region exists near the surface because EF near the surface is further from Ev than the bulk region.

At equilibrium (V = 0).

Ec

Ev

EF

Al SiO2 p-Si

3.7eV

3.20eV3.15eV

0.6eVEc

Ev

Page 15: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

MOS System - Accumulation

HO #14: ELEN 251 - MOSFET Fundamentals Page 15S. Saha

Applied Bias: negative voltage on Al

qVEFM EcEFEv

Al SiO2 p-Si

− ve

• EF is still constant in the Si since SiO2 prevents any current flow.• EF is closer to Ev at the surface.∴ more holes near the surface. ⇒ ACCUMULATION.

Page 16: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

MOS System - Inversion

HO #14: ELEN 251 - MOSFET Fundamentals Page 16S. Saha

Applied Bias: positive voltage on Al

qVEFM

Ec

EFEv

Al SiO2 p-Si

+ ve

EiφFφs

QG

QdQn

• EF is still constant in the Si (I = 0).• EF is closer to Ec at the surface than it is to Ev.

∴ more e- than holes at the surface. ⇒ INVERSION.

Page 17: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

F. MOS Fundamentals: 2. Surface Carrier Densities

HO #14: ELEN 251 - MOSFET Fundamentals Page 17S. Saha

At any point in silicon, we can calculate the hole and e-concentrations using:

If φs = surface potential and φF = bulk potential so that the potential drop across the depletion region = (φF − φs), Then, the surface concentrations are:

Since we know φF from the bulk doping, if we know φs for a given applied VG, then we can calculate the e- and holesurface concentrations.

ennenp

kTq

i

kTq

φ

=

= − (1)

(2)

eNnn

eNp

kTq

A

is

kTq

As

sF

sF

)(2

)(

φφ

φφ

−−

=

= (3)

(4)

Page 18: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

G. MOS Capacitors: 1. Long Channel Vth Model

HO #14: ELEN 251 - MOSFET Fundamentals Page 18S. Saha

(a) Accumulation: VG > 0

Co

+

n-Si

SiO2

e−↑

VG

− +

Co

V

C

Note:• e- are attracted to the surface.• The small-signal capacitance per unit area is given by:

Co = εox/tox where

εox = dielectric constant in the oxide tox = oxide thickness.

Page 19: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics

HO #14: ELEN 251 - MOSFET Fundamentals Page 19S. Saha

(b) Depletion: VG < 0

n-Si

SiO2

e−

+ + + + + ++ + + + + +

Ionizeddonoratoms Co

Cd − +

Co

V

C

• e- are repelled from the surface resulting in a depletion region.• The small-signal depletion capacitance per unit area is:

Cd = εs/xd

where εs = dielectric constant of silicon xd = width of the depletion layer.

• The total capacitance: C = CoCd/(Co + Cd)

Page 20: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics

HO #14: ELEN 251 - MOSFET Fundamentals Page 20S. Saha

(c) Inversion: VG << 0

− −

n-Si

SiO2

e−

+ + + + + ++ + + + + +

Inversionlayer

holes

xdmax

Co

Cdmin − +

Co

V

C

Cmin

• Minority-carriers pile-up near the SiO2/Si interface.

• In strong INVERSION:– xdmax = maximum width of depletion region is a constant,– Cd = Cdmin is a constant.

• For VG between ACCUMULATION and strong INVERSION: – xd ∝ VG

1/2.

Page 21: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics

HO #14: ELEN 251 - MOSFET Fundamentals Page 21S. Saha

Let us consider the depletion condition (b), then: Q = QG = − Qs = − qNDxd (5)

where, xd = width of the depletion region ND = donor concentration/cm3.

Assuming that ND is independent of distance (uniform substrate doping), then from Poisson’s equation we have:

n-Si

SiO2

+ + + + + ++ + + + + + xd

VG

Qs

potential Surface 2

where

siliconin Potential 1

2

2

2

2

==

=⎟⎟⎠

⎞⎜⎜⎝

⎛−=∴

−=−=

εφ

φφ

εερφ

os

dDs

ds

os

D

os

KxNqxx

KNq

Kxdd (6)

(7)

(8)

Page 22: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics

HO #14: ELEN 251 - MOSFET Fundamentals Page 22S. Saha

n-Si

+ + + + + ++ + + + + + xd

VG

φs

toxVo

Assume, tox = oxide thickness Vo = potential across oxide

Then, the applied voltage is given by:

ε

φ

os

dDoxox

soG

KxNq

Et

VV

2

2

+=

+=

(9)

We know from Gauss’ Law, the electric displacement must be constant across Si/SiO2 interface, so that: KoEox = KsEs (10)

where Ko and Ks are dielectric constants of oxide and Si, respectively Eox & Es are ε-fields in oxide & in Si at the interface, respectively.

Page 23: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics

HO #14: ELEN 251 - MOSFET Fundamentals Page 23S. Saha

From (10) we get: Eox = Es(Ks/Ko) (11)

Substitute for Es in (11) from Gauss’ Law:

Then, from (9) we get:

Using (5) we have:

ε

εε

ooox

osos

ss

KQ

E

KQ

KQ

E

−=⇒

−=−= (12)

εε os

dD

oo

oxG K

xNqK

tQV2

2

+−= (13)

NqKQ

KtQV

Dosoo

oxG

εε 2

2

+−= (14)

Page 24: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics

HO #14: ELEN 251 - MOSFET Fundamentals Page 24S. Saha

From (14) we get:

This is the amount of charge on the metal plate or in the depletion region when the depletion is taking place.

The small signal-capacitance of the structure is given by:

VNqKK

tNqKK

tNqKQ GDoso

oxDs

o

oxDs ε22

+⎟⎟⎠

⎞⎜⎜⎝

⎛±=

VNqKK

tNqK

NqKVd

dQC

GDoso

oxDs

Dos

G

ε

ε

22

+⎟⎠

⎞⎜⎝

⎛==

VtKNq

KCC

GoxsD

ooo2

221

1

ε+

=∴ (15)

(Here, Co = Koεo/tox = Oxide cap/area)

Page 25: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics

HO #14: ELEN 251 - MOSFET Fundamentals Page 25S. Saha

− +

Co

V

C

Cmindepletion, C ∝ 1/√V

Vth

inversion, C is fixed

During depletion, C falls as 1/√(V).

However, when the surface inverts, C reaches a minimum value.

When an inversion layer forms, we have:

φF

φs EFEi

xd

xx dd

Fs

max≅−≅ φφ

⎭⎬⎫

⎩⎨⎧−+

NP,ln2)(@

nN

qkT

VVi

DthGs ±==∴φ (16)

( )φεF

D

osd

NqKxand 22, max = (17)

Page 26: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics − Strong Inversion

HO #14: ELEN 251 - MOSFET Fundamentals Page 26S. Saha

In strong inversion,• φs = 2φF.

• the inversion layer width < 50 A.

• a higher φs or ε-field tends to confine inversion charge closer to the surface.

Generally, inversion-carriers must be treated quantum-mechanically (QM) as a 2-D gas. According to QM model:

• inversion layer carriers occupy discrete energy bands• peak distribution is 10 − 30 A away from the surface.

0.0E+00

2.0E+18

4.0E+18

6.0E+18

8.0E+18

1.0E+19

1.2E+19

0 50 100 150 200

Distance from surface, x (A)

Inve

rsio

n la

yer c

once

ntra

tion

(cm

-3)

N(sub) = 1016 cm-3

φs = 0.88 V

φs = 0.85 V

Page 27: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics − Vth

HO #14: ELEN 251 - MOSFET Fundamentals Page 27S. Saha

When xd reaches xdmax, C reaches a minimum in the C − V plot and we have:

Co

Csmin

Co

VG

C

Cmin

Vth

nN

NKqkTxd

KCs

i

D

Dos

os

ln41

2max

min

ε

ε ==(18)

The threshold voltage is defined as the gate voltage necessary to just reach the inversion (that is, φs = −φF, xd = xdmax):

VV oFth +=∴ φ2

Page 28: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics − Vth

HO #14: ELEN 251 - MOSFET Fundamentals Page 28S. Saha

dxx

KNq

KKt

EtVd

o os

D

o

soxF

oxoxFth

∫+=

+=max

2

2

εφ

φ

[use (11) for Εox and expression for Es]

Now, using the expression for Co and (17) for xdmax we get:

CKNq

Vo

FosDFth

)2(22

φεφ += (19)

In (19), we have assumed that QI ≈ 0 at Vth.

Co

VG

C

− +

Ideal

MeasuredN-typeSubstrate

Comparison of Ideal andthe measured C − V plot

Page 29: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics − Vth

HO #14: ELEN 251 - MOSFET Fundamentals Page 29S. Saha

Actual C - V curves are shifted laterally from the theoretical curve due to:– Work function difference between the metal and silicon – Qf : charge at the Si/SiO2 interface.

CKNq

C

QqV

o

FosDF

o

fMSth

)2(22

φεφφ ±±−= (20)

(assume Qf is rightat Si/SiO2 interface)

+ p-type substrate− n-type substrate

Thus, by measuring a C - V curve for a particular process– tox can be calculated from Co

– ND can be calculated from Cmin

– Qf can be calculated from the difference between the ideal and experimental curves.

Page 30: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

C − V Characteristics − Vth

HO #14: ELEN 251 - MOSFET Fundamentals Page 30S. Saha

If VSub = back bias = voltage between source and body: VSub < 0 for nMOSFETs VSub > 0 for pMOSFETs.

Then,

(21)C

VKNq

C

QqV

o

SubFosDF

o

fMSth

)2(22

±±±−=

φεφφ

FBV=

φφγ FSubFthth VVV 220 −±±=∴ (22)

factorbody2

Where

≡=C

KNq

o

osD εγ (23)

Page 31: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Low-Frequency C − V Characteristics

HO #14: ELEN 251 - MOSFET Fundamentals Page 31S. Saha

Co

VG

C

− +

Highfrequency

N-typeSubstrate

Lowfrequency

Vth

Co

Cmin

Co

Cd CI

(Low freq.)

If the frequency of the applied signal is lower (<< 100 Hz) than the reciprocal of the minority-carrier response time:

– inversion charge (QI) is able to follow the applied signal

– QI varies with φs and Cs depends on QI .

∴ C↑ as |VG|↑.

– At higher |VG|, C increases back to Co.

Page 32: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

G. MOS Capacitors: 2. Polysilicon Gates

HO #14: ELEN 251 - MOSFET Fundamentals Page 32S. Saha

At equilibrium (VG = 0). At Inversion (VG >> 0).

Ec

Ev

EF

n+ poly SiO2 p-Si

Ei

φF

Ec

Ev

EF

n+ poly SiO2 p-Si

EiφS

VG

Ei

Ev

EFφp

Ec

Vox

Work-function difference:n+poly with p-type Si: φMS = − Eg/2 − (kT/q)ln(NA/ni)p+poly with n-type Si: φMS = Eg/2 + (kT/q)ln(ND/ni)

Page 33: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

MOS Capacitors - Polysilicon Depletion Effect

HO #14: ELEN 251 - MOSFET Fundamentals Page 33S. Saha

Note:• Capacitance at inversion, Cinv

does not return to Cox.• Cinv shows a maximum value,

Cmax < Cox.• Cmax↑ as the polysilicon

doping concentration, Np↑.• As Np↑, depletion width↓

∴ Cmax → Cox for higher Np.

Total capacitance at strong inversion is given by: 1/C = 1/Cox + 1/Csilicon + 1/Cpoly

As VG↑, Csilicon↑ but xd(poly)↑ ⇒ Cpoly↓. ∴Low frequency C − V shows a local maximum at a certain VG.

Page 34: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

G. MOS Capacitors: 3. Inversion Layer Quantization

HO #14: ELEN 251 - MOSFET Fundamentals Page 34S. Saha

• Typically, near the silicon surface, the inversion layer chargesare confined to a potential well formed by:– oxide barrier– bend Si-conduction band at the surface due to the applied gate

potential, VG.

• Due to the confinement of inversion layer e− (in p-Si): – e- energy levels are grouped in discrete sub-bands of energy, Ej

– each Ej corresponds to a quantized level for e− motion in the normal direction.

E2E1E0

Edge of EC

Distance from the surfaceBottom ofthe well

E

Page 35: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Inversion Layer Quantization

HO #14: ELEN 251 - MOSFET Fundamentals Page 35S. Saha

• Due to Quantum Mechanical (QM) effect, the inversion layer concentration:– peaks below the SiO2/Si interface− ≈ 0 at the interface determined by the boundary condition of

the e- wave function.

• Solve Schrodinger and Poisson Eq self-consistently with the boundary conditions for wave function equal to:– 0 for x < 0 in oxide– 0 at x = ∞.

QM

Classical

Depth

n (c

m-3

)

Page 36: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

QM Effect on Device Performance

HO #14: ELEN 251 - MOSFET Fundamentals Page 36S. Saha

• At high fields, Vth↑ since more band bending is required to populate the lowest sub-band, which is some energy above the bottom of EC.

• Once the inversion layer forms below the surface, a higher VGover-drive is required to produce a given level of inversion charge density. That is, the effective gate oxide thickness, tOX

eff↑ by: ∆tOX = (εox/εsi)∆z (24)

• Inversion layer quantization can be treated as bandgap widening due to an increase in the effective bandgap by ∆Eg given by:

Here, ∆Eg = EgQM − EgCL. (25) ⇒ ni↓ and n↓ due to QM effect.

kTE

CLi

QMi

g

enn 2∆

−= (25)

Page 37: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

H. Geometry Effect on Vth: 1. Short Channel Effect

HO #14: ELEN 251 - MOSFET Fundamentals Page 37S. Saha

For short channel devices, Vth↓ as L↓. Many researchers have attempted to analyze this 2-D problem.

We will consider only the simplest approach (by Yau) to understand the basic idea of short channel effect.

Assume: – VD = 0 = VS− φs = 2φF @ VG = Vth and φs

is unaffected by short channel effect.

– xd = xdj

From charge conservation: QG + Qox + QI + QB = 0 (26)

Also,

whereo

BFFBth C

QVV ++= φ2 (27)

)2(2 SubFAosB VNqKQ +−= φε (28)

n+

P

L

rj n+L′

VG VDVS

xd

VSub

xdj

Page 38: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Short Channel Effect (SCE)

HO #14: ELEN 251 - MOSFET Fundamentals Page 38S. Saha

From first order MOS theory:

Now, let us assume that only the charge inside the trapezoid is supported by the gate, i.e. the junctions support the remaining charge. (This implies that QB is smaller than the long channel device and therefore, for a given VG, QI is larger to maintain charge neutrality. And, Vth↓).

The total charge in the trapezoid is:

QB′L = qNAxd[(L + L′)/2] (30)

where, QB′ < QB because L′ < L.

∴In Eq (27), QB is replaced by QB′.

( )SubFA

osd V

NqKx += φε 22

(29)

n+

P

L

rj n+L′

VG VDVS

xd

VB

xdj

Page 39: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Short Channel Effect

HO #14: ELEN 251 - MOSFET Fundamentals Page 39S. Saha

From Fig. on the right, we get: (L−L′)/2

xdxd

rj

rj

(31)

( )

( )

( )

Lr

rx

LLL

rrxrrxrLLor

xxrrLLor

xrxrLL

j

j

d

jj

djjdj

ddjj

djdj

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−+−=′+

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−+=−+=′−

−+=+′−

+=+⎟⎠⎞

⎜⎝⎛ +

′−

12112

12122

,

2,

222

222

⎥⎥⎦

⎢⎢⎣

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−+−=Lr

rx

QQ j

j

dBB 1211' (32)

Using (29) and (31) in (30), we can show that:

Page 40: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Short Channel Effect

HO #14: ELEN 251 - MOSFET Fundamentals Page 40S. Saha

Thus, if we assume that the effect of non-uniform QBdistribution can be averaged over L, then:

This is the desired result that predicts Vth as a function of L, rj and xd (or NA) for VD = 0.

Note: 1) ∆Vth ∝ 1/L. 2) As rj↓, ∆Vth↓, shallow junctions are preferred. 3) For large L↑, ∆Vth → 0 and the long channel form applies. 4) NA shows up in xd and QB. ∴ NA affects both Vth and ∆Vth

5) VSub is included in xd as well.

⎥⎥⎦

⎢⎢⎣

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−+−++=Lr

rx

CQVV j

j

d

o

BFFBth 12112φ (33)

Page 41: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

H2. Drain Induced Barrier Lowering (DIBL)

HO #14: ELEN 251 - MOSFET Fundamentals Page 41S. Saha

To this point we have modeled the effect of the drain voltage in short channel devices as a reduction in Vth.

n+

P

L

rj n+xd L4L3

( )DS

A

sDSbis

eff

VqN

VVL

LLLL

∝−+

=

−−=

φε24

43

Currents in the device (sub-threshold as well as “normal” high currents) are then increased because Leff↓ and Vth↓.

An alternative explanation of these effects is called drain-induced barrier lowering (DIBL). This phenomenon, in essence, is identical to ∆Vth modeling or SCE we discussed before.

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Drain Induced Barrier Lowering (DIBL)

HO #14: ELEN 251 - MOSFET Fundamentals Page 42S. Saha

The drain bias lowers the potential barrier between source and channel and hence increases the current.

In principle, it seems possible to derive an analytical model to estimate ∆φs as a function of ∆L and VD. However, such models do not exist. Thus, only analytical models for SCE are based on charge sharing approaches.

In reality, 2-D computer simulations have to be used to analyze DIBL. If the surface region is implanted to shift Vth, then DIBL may occur

beneath the surface where the doping is lighter. Therefore, often a deep heavily doped channel implant is used to

prevent the drain potential from “punching through” to the source.

Page 43: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

H. Geometry Effect on Vth: 3. Narrow Channel Effect

HO #14: ELEN 251 - MOSFET Fundamentals Page 43S. Saha

In addition to channel length effects on Vth, small channel widths, also, affect Vth. These effects can be understood physically as follows:

Figure shows the MOS cross-section along the channel width direction.

The depletion layer cannot abruptly change from deep to shallow.Therefore, the transition region and some spreading of field lines from gate outside W.

Thus, QG supports some charge outside W. As a result, QI↓ and Vth↑.

P

QI QB

W

Page 44: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Narrow Channel Effect

HO #14: ELEN 251 - MOSFET Fundamentals Page 44S. Saha

Consider the uniformly doped substrate with VD = 0.

P

xd

W

αxd

QBW = triangle area charge under thick oxide that is supported by gate.

n+

P

L

rj n+xd

QBL = trapezoidal area charge supported by gate (Yau).

The parameter α depends on oxide thickness, shape of field oxide edge, substrate doping, field threshold adjustment implant, and so on.

It is likely that α has to be experimentally determined.

Page 45: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Narrow Channel Effect

HO #14: ELEN 251 - MOSFET Fundamentals Page 45S. Saha

The charge inside the volume is (1/2)QBW. The shape is rectangular on top, the sides are triangular and slope inward.

We know from SCE:

The charge contained in the volume above can be shown to be:

Now, we assume that the narrow width and short channel effects can be simply superimposed so that the total charge supported by the gate is given by: QT = QBL + QBW

⎥⎥⎦

⎢⎢⎣

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−+−=Lr

rxLWxqNQ j

j

ddABL 1211 (34)

⎥⎥⎦

⎢⎢⎣

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−+−=Lr

rxLxqNQ j

j

ddABW 3

212112α (35)

Page 46: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Narrow Channel Effect

HO #14: ELEN 251 - MOSFET Fundamentals Page 46S. Saha

The charge contained in the volume can be shown to be:

The term in front of the brackets can be recognized as the bulk charge which would be present in a long and wide channel device so that:

⎥⎥⎦

⎢⎢⎣

⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟

⎠⎞

⎜⎝⎛ +−+=

⎥⎥⎦

⎢⎢⎣

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−+−+⎟

⎟⎠

⎞⎜⎜⎝

⎛−+−=

+=

1213211

1213211211

j

ddjddA

j

djd

j

djdA

BWBLT

rx

Wx

Lr

WxLWxqN

rx

Lr

Wx

rx

Lr

LWxqN

QQQ

αα

α

(36)

CQ

C

QV

o

TF

o

fMSth ++−= φφ 2

⎥⎥⎦

⎢⎢⎣

⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟

⎠⎞

⎜⎝⎛ +−+++−=∴ 121

32112

j

ddjd

o

BF

o

fMSth r

xWx

Lr

Wx

CQ

CQ

V ααφφ (37)

Page 47: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Narrow Channel Effect

HO #14: ELEN 251 - MOSFET Fundamentals Page 47S. Saha

Note that if L and W → ∞, the normal long channel Vth Eq is obtained.

Summary:♦ L↓ ⇒ Vth↓

♦ W↓ ⇒ Vth↑

♦ xd↑ ⇒ Vth more sensitive to L and W (i.e. lightly doped substrates and/or VSub increase problems).

♦ rj↑ ⇒ Vth more sensitive to L (i.e. deep junctions undesirable).♦ α↓ ⇒ minimizes Vth variation due to narrow W.

⎥⎥⎦

⎢⎢⎣

⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟

⎠⎞

⎜⎝⎛ +−+++−=∴ 121

32112

j

ddjd

o

BF

o

fMSth r

xWx

Lr

Wx

CQ

CQ

V ααφφ (38)

)2(2 where BSFAosB VNqKQ +−= φε

Page 48: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

I. Effect of Channel Doping on Vth

HO #14: ELEN 251 - MOSFET Fundamentals Page 48S. Saha

Assuming Nsub = constant, we showed :

where

In MOSFET devices Nsub varies vertically as well as laterally. Therefore, for accurate modeling of Vth, non-uniform channel doping concentration must be considered.

CKNq

C

QqV

ox

FossubF

ox

fMStho

|2|22

φεφφ ±±−= (40)

( )φφγ FSubFthth VVV 220 −±±=∴ (39)

factorbody2

≡=C

KNq

ox

ossub εγ (41)

Page 49: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Non-uniform Channel Doping Profile

HO #14: ELEN 251 - MOSFET Fundamentals Page 49S. Saha

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I1. Vth Model due to Non-uniform Vertical Profile

HO #14: ELEN 251 - MOSFET Fundamentals Page 50S. Saha

• The doping concentration may be higher or lower at the Si/SiO2interface depending on Vth target.

• Due to the non-uniform body doping, γ = f(VSub).

• Let us model the non-uniform vertical doping profile by a step function shown below:– NCH = uniform shallow doping concentration– NSub = uniform deep doping concentration– Xdx = depletion width @ Vsub = Vbx; NSub= NCH.

• At VSub > Vbx, we can write the general expression:

(VSub and Vbx < 0 for NMOS and > 0 for PMOS).

Depth

Con

cent

ratio

n

Xdx

Model

Actual

( )( ) bxSubbxFSubF

FbxFthth

VVVV

VVV

>−−−+

−−+=

for 22

22

2

10

φφγ

φφγ

(42)

Page 51: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Non-Uniform Vertical Channel Profile

HO #14: ELEN 251 - MOSFET Fundamentals Page 51S. Saha

Here

In general (42) is complex and a unified expression for Vth is used to model the non-uniform vertical channel doping profile:

where ♦ K1 and K2 are the key parameters to model the vertically non-

uniform doping effect.♦ K1 and K2 are determined by fitting (43) to the measured Vth

data♦ VSub < 0 for NMOS ♦ VSub > 0 for PMOS.

( ) SubFSubFthth VKVKVV 210 22 −−−+= φφ (43)

CKNq

CKNq

ox

ossub

ox

osCH εγεγ2

and2

21 ==

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I2. Effect of Non-uniform Lateral Channel Profile

HO #14: ELEN 251 - MOSFET Fundamentals Page 52S. Saha

For sub-micron devices, Vth is found to increase first as L↓and then decrease with further reduction in L.

The anomalous Vth↑ as L↓ is due to non-uniform lateral channel doping concentration caused by: • an enhanced diffusion of channel implant induced by the damage from S-D implant.• boron segregation to the S-D implant regions.

Gate

Std O2poly-reox

injectionof interstitialduring poly-reox.

S D

L

Vth

Page 53: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Non-uniform Lateral Profile due to S/D Processing

HO #14: ELEN 251 - MOSFET Fundamentals Page 53S. Saha

0.35 µm nMOSFETs 1.0 µm nMOSFETs

2-D non-uniform lateral boron channel profile after S-D processing

Page 54: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Non-Uniform Lateral Profile due to Halo Implant

HO #14: ELEN 251 - MOSFET Fundamentals Page 54S. Saha

DSD

Lg = 100 nmHalo

Lg = 250 nm

DSD

Halo

• Halo implant around source-drain extensions (SDE):– significantly increases the channel doping concentration as L↓– causes Vth↑ as L↓ (i.e. RSCE).

Page 55: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

RSCE due to Halo Implant

HO #14: ELEN 251 - MOSFET Fundamentals Page 55S. Saha

0.10

0.15

0.20

0.25

0.30

0.35

0.40

20 60 100 140 180 220 260 300Leff (nm)

Vth (

V)

Strong haloModerate haloLow halo

nMOSFETsTOX(eff) = 2.7 nm

VDS = 50 mV; VBS = 0

• RSCE (i.e. Vth↑ with L↓) for Leff < 200 nm is due to halo implants around SDE.

• RSCE depends on halo doping concentration.

Page 56: MOSFET Devices - SCU€¦ · MOSFET Devices S. Saha HO #14: ELEN 251 - MOSFET Fundamentals Page 1 • Metal-oxide-semiconductor field-effect transistors (MOSFET) are the building

Vth Model for Non-Uniform Lateral Channel Profile

HO #14: ELEN 251 - MOSFET Fundamentals Page 56S. Saha

Similar to the previous case, we model the non-uniform lateral channel doping profile by a step function as shown below:

Let L = channel length LX = length of Halo-region NHalo = uniform concentration in LX

NCH = uniform concentration in L−2LX

If Neff is the average channel doping concentration, then the total charge Q is given by: Q = NeffL = NCH(L − 2LX) + NHalo(2LX)

Position along the channel

LX

N(x)

L

LXNCH

NHalo

⎥⎦⎤

⎢⎣⎡ +≡⎥

⎤⎢⎣

⎡ −+=∴

LNN

LL

NNNNN LX

CHX

CH

CHHaloCHeff 121 (44)

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Vth Model for Non-Uniform Lateral Channel Profile

HO #14: ELEN 251 - MOSFET Fundamentals Page 57S. Saha

Where NLX is a fitting parameter extracted from the measured data and is given by:

Substituting Neff in (40) we get:CH

CHHaloXLX N

NNLN −≡ 2 (45)

φ

φφφφ

φφφ

φεφφ

FLX

th

FLX

FFox

fMS

FLX

Fox

fMS

ox

FoseffF

ox

fMStho

LNKV

LNKK

C

Qq

LNK

C

Qq

CKNq

C

QqV

211

21122

212

|2|22

10

11

1

⎟⎟⎠

⎞⎜⎜⎝

⎛−++=

⎟⎟⎠

⎞⎜⎜⎝

⎛−++++−=

⎟⎟⎠

⎞⎜⎜⎝

⎛+++−=

++−=′

(46)

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Vth Model for Non-Uniform Lateral Channel Profile

HO #14: ELEN 251 - MOSFET Fundamentals Page 58S. Saha

Then from (43), Vth due to non-uniform lateral doping is given by:

Substituting V'tho from (46) we get:

Note:– K1 and K2 models the effect of non-uniform vertical channel

doping profile on Vth

– NLX models the non-uniform lateral profile on Vth:♦ at VSub = 0, as L↓, Vth↑ (RSCE) due to halo-profile.

( ) SubFSubFthth VKVKVV 210 22 −−−+′= φφ (47)

( )φ

φφ

FLX

SubFSubFthth

LNK

VKVKVV

211

22

1

210

⎟⎟⎠

⎞⎜⎜⎝

⎛−++

−−−+=

(48)

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Home Work 5: Due May 19, 2005

HO #14: ELEN 251 - MOSFET Fundamentals Page 59S. Saha

1) MOS capacitors are fabricated on uniformly doped P-substrates with NA = 1x1017 cm−3, physical gate oxide thickness TOX = 6.7 nm, and N+ poly-silicon gate doping concentrations Np = 5x1018, 1x1019, and 5x1019 cm−3 as shown in the following C – V plots. Here C and Cox are the gate and oxide capacitances, respectively.

(a) Explain the observed variation in C/COX vs. Vg plots for each Np in the strong inversion region.

(b) Explain the observed increase in C/COX for Np = 5x1018 cm−3 and Vg ≥ 3.5 V.

(c) Describe the possible reasons for C/COX < 1 even for a heavily doped poly with Np = 5x1019

cm−3 in the accumulation as well as in the strong inversion regions?

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Home Work 5: Due May 19, 2005

HO #14: ELEN 251 - MOSFET Fundamentals Page 60S. Saha

2) A p-type MOS-capacitor with NA = 1x1018 cm-3 and TOX = 3 nm was fabricated to characterize van Dort’s analytical bandgap widening quantum mechanical (QM) model we discussed in class. Due to inversion layer quantization, the increase in the effective bandgap ∆Eg = Eg

QM − EgCL ≅ 104

mV. Here EgQM and Eg

CL represent the QM and classical (CL) values of bandgap (Eg), respectively. Assume Qf = 0, VSUB = 0, and N+ poly gate.

(a) Show that the intrinsic carrier concentration due to QM effect is given by:

(b) Calculate the value of niQM at temperature T = 300oK.

(c) Calculate the value of threshold voltage Vth(CL) using the classical approach.

(d) Calculate the value of threshold voltage Vth(QM) due to QM effects.

(e) Calculate the shift ∆Vth due to QM effects.

kTE

CLi

QMi

g

enn 2∆

−=

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Modeling Project: MOS Model Extraction

HO #14: ELEN 251 - MOSFET Fundamentals Page 61S. Saha

• 90-nm CMOS Technology:– complete models for nMOSFETs and pMOSFETs for logic design over

the temperature range, -55 to 125°C– select a MOS compact model of your choice (BSIM3/BSIM4/HiSIM)– justify why the model of your choice should be adequate for 90-nm

technology node.

• Modeling strategy:– selection of devices (W/L) over the design space– selection of data set for parameter extraction– measurement conditions and bias range– parameter optimization strategy and guidelines– temperature dependent parameters and extraction of temperature

coefficients– test/qualify the model and release to production.

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Modeling Project: Final Report

HO #14: ELEN 251 - MOSFET Fundamentals Page 62S. Saha

The results of your modeling work are to be presented in an extended abstract form (3 to 4 pages maximum). The key points to be emphasized are the following:– selection of devices and reasons for your selection– data selection and how will you use specific data file to extract specific

model parameters of your selected model– measurement conditions for data collection data in tabular form

showing all bias conditions and temperature range you plan to use for your modeling

– a complete step by step strategy to extract model parameters from collected data set

– critical discussions of fitting errors to your data with the model equations.

– a typical model file including both p/n-channel devices. Use of extraction tool is not required. However, your report must be an

aid to device engineers for 90-nm compact model parameter extraction.