Lundstrom ECE 305 S15

ECE-305: Spring 2015

MOS Fundamentals

Professor Mark Lundstrom Electrical and Computer Engineering

Purdue University, West Lafayette, IN USA lundstro@purdue.edu

3/29/15

Pierret, Semiconductor Device Fundamentals (SDF) pp. 525-530, 563-571

MOS Fundamentals

2

1)  MOSFET and MOS capacitors 2)  E-bands and workfunctions 3)  Bandbending in ideal MOS-C’s

Lundstrom ECE 305 S15

MOSFETs

3

source drain

SiO

2

silicon

G S D

(Texas Instruments, ~ 2000)

gate oxide EOT ~ 1.1 nm

channel ~ 20 nm

gate

electrode

MOSFET (off)

4

VD

0

L

p-Si

n+-Si n+-Si

VG < VT ID = 0

Lundstrom ECE 305 S15

MOSFET (on)

5

VD

0

L

p-Si

n+-Si n+-Si

VG > VT ID > 0

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MOSFET and MOS C

6

p-Si

n+-Si n+-Si

MOS capacitor

MOS capacitor

7

VG

p-Si or n-Si

metal or

heavily doped “polysilicon”

SiO2

tox ≈1− 2 nm

Lundstrom ECE 305 S15

oxide scaling

8

EC

EV

Ei

SiO2

EG ≈ 8.9eV

χi

e-band diagram

9

EC

EV

Ei

EF

EG = 1.12eV

Si

metal

EFM

ΦM

E0

χS

recall the MS junction

10

EC

EVEFP

Ei

aluminum

EFM

E0

ΦM = 4.08 eVΦS

χS = 4.05 eV

Lundstrom ECE 305 S15

built-in potential

11

EC

EVEFS

Ei

aluminum

EFM

E0

ΦM = 4.08 eVΦS

χS = 4.05 eV

qVbi = EFM − EFS( ) = ΦS −ΦM( ) = − ΦM −ΦS( ) = −ΦMS

potential =VbiVbi =

−ΦMS

q= −φms

example:

12

Aluminum metal and p-type Si

NA = 1016 cm-3

p0 = NVeEV −EFS( )/kBT cm-3

EFS − EV = kBT lnNV

NA

⎛⎝⎜

⎞⎠⎟

NV = 2mp*kBT( )2π!2

⎡

⎣⎢⎢

⎤

⎦⎥⎥

3/2

= 1.83×1019 cm-3

EFS − EVq

= 0.2

ΦM = 4.08 eV

ΦS = χS + EG − EFS − EV( ) q

ΦS = 4.97 eV

φms =ΦM − ΦS( )

q= −0.9 V

Vbi = −φms = +0.9 V

now the band diagram

13

EC

EVEFS

Ei

metal

EFM

E0

ΦM = 4.5 ΦS

Lundstrom ECE 305 S15

the band diagram

14

EC

EVEF

Ei

metal

EF

φM

qVbi

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MOS e-band diagram

15

EC

EV

Ei

SiO2

EG ≈ 8.9eV

EC

EV

Ei

EF

EG = 1.12eV

Si

metal

EFM

ΦM

E0

χS

χi

MOS e-band diagram

16

1) Built-in potential is exactly the same. 2) But part of the voltage drop occurs across the

semiconductor and part across the oxide.

Lundstrom ECE 305 S15

equilibrium e-band diagram

17

EC

EV

Ei

EF

metal

ΔVS

ΔVox

Vbi = −φms φ x( ) = 0 in the bulk

φ x = 0( ) = φS surface potential

V metal( ) = ΔVox +φS

φS

V metal( ) =Vbi

Question 1)

18

EC

EV

Ei

EF

metal

Which of the following statements is true about the electric field in the semiconductor (near the oxide-semiconductor interface). a)  It is 0 V/cm b)  It is > 0 V/cm and constant c)  It is < 0 V/cm and constant d)  It is > 0 V/cm and non-constant e)  It is < 0 V/cm and non-constant

Question 2)

19

EC

EV

Ei

EF

metal

Which of the following statements is true about the electric field in the oxide. a)  It is 0 V/cm b)  It is > 0 V/cm and constant c)  It is < 0 V/cm and constant d)  It is > 0 V/cm and non-constant e)  It is < 0 V/cm and non-constant

equilibrium e-band diagram

20

EC

EV

Ei

EF

metal

constant electric field

monotonically decreasing electric field

dEdx

=ρ x( )ε

V metal( ) =Vbi

equilibrium e-band diagram

21

EC

EV

Ei

EF

metal

ΔVS

ΔVOX

Vbi

E S =E 0+( )

E ox

Koxε0E ox = KSε0E S

E ox =

KS

KOX

E S

E ox ≈ 3E S

Dox = DS

potential vs. position

22

φ x( )

x0−xox

φ = 0

φS > 0V metal( ) =Vbi = −φms = ΔVox + ΔVS

Lundstrom ECE 305 S15

from the e-band diagram: e-field

23

EC

EV

Ei

EF

metal

V metal( ) =Vbi

electric field vs. position

24

x0−xox

φ = 0

E x( )

E S E ox

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from the e-band diagram: charge density

25

EC

EV

Ei

EF

metal Vbi

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space charge density vs. position

26

x0−xox

−qNA

ρ x( )

W

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depletion charge

apply a voltage to the gate

27

EC

EV

Ei

EF

Simetal

ΔVS

ΔVOX

What happens if we apply a voltage to the gate?

V metal( ) =Vbi = ΔVox + ΔVS →

VG +Vbi =VG −φms = ΔVox + ΔVS →V metal( ) =Vbi +VG

e-band under “flat band” conditions

28

EC

EV

Ei

EF

Si

metal

What happens if we apply a negative voltage = ? φms

VG = −Vbi

MOS–C at the flat band voltage.

VG +Vbi = ΔVox + ΔVS →0 = ΔVox + ΔVS

“ideal” MOS structure

29

EC

EV

Ei

SiO2

EG ≈ 8eV

EC

EV

Ei

EF

EG = 1.12eV

Sihypothetical

metal

EFM

ΦM

E0

χS

χi

Vbi = 0

flat band conditions

30

For an ideal MOS structure, flat band occurs for: For a real MOS structure, flat band occurs for:

VG =VFB = 0

VG =VFB = φms

′VG =VG −VFB =VG +Vbi =VG −φms

VFB = φms

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in Chapter 16 of SDF by Pierret

31

VG means V’G; i.e. an ideal MOS structure with NO metal-semiconductor workfunction difference is assumed.

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band banding in an MOS device

32 Fig. 16.6, Semiconductor Device Fundamentals, R.F. Pierret

next: band-bending and depletion approximation

33

1)  V’G < 0: Accumulation (No depletion region)

2)  0 < V’G < VT: Depletion (depletion region)

3)  V’G < VT: Inversion (depletion region + inversion layer)

Lundstrom ECE 305 S15

N-channel MOS (p-type substrate)