+ All Categories
Home > Documents > 33 Gate Voltage - nanoHUBGate_Voltage_S16.pdf · Gate voltage and surface potentia l 4 1) Surface...

33 Gate Voltage - nanoHUBGate_Voltage_S16.pdf · Gate voltage and surface potentia l 4 1) Surface...

Date post: 30-Apr-2020
Category:
Upload: others
View: 9 times
Download: 0 times
Share this document with a friend
22
ECE-305: Spring 2016 Gate Voltage Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA [email protected] 3/31/16 Pierret, Semiconductor Device Fundamentals (SDF) pp. 567-584
Transcript

Lundstrom ECE 305 F16

ECE-305: Spring 2016

Gate Voltage

Professor Mark Lundstrom Electrical and Computer Engineering

Purdue University, West Lafayette, IN USA [email protected]

3/31/16

Pierret, Semiconductor Device Fundamentals (SDF) pp. 567-584

band banding in an MOS device

2 Fig. 16.6, Semiconductor Device Fundamentals, R.F. Pierret Flat band Accumulation Depletion Inversion

′VG = 0 ′VG < 0 0 < ′VG <VT ′VG > ′VTφS = 0 φS < 0 0 < φS < 2φF φS > 2φF

Lundstrom ECE 305 F16

depletion approximation

3

E x( )

x

What gate voltage produced this surface potential?

P

E S

W

W = 2κ Sε0φSqNA

cm

E S =

2qNAφSκ sε0

V/cm

QB φS( ) = − 2qκ sε0NAφS C/cm2

QB = −qNAW φS( )C/cm2

0 < φS < 2φF

Gate voltage and surface potential

4

1)  Surface potential à gate voltage 2)  Example

Lundstrom ECE 305 F16

Note: Next week (MOSFET IV), will follow for the most part Lundstrom “Lecture Notes on MOSFETs,” which is posted on the course home page under Week 12.

surface electric field and charge

5

E x( )

x

P E S

dEdx

= − qNA

KSε0

E 0( ) =E S =

qNAWKSε0

Lundstrom ECE 305 F16

E ox

KSε0E S = DS = qNAW( ) = −QB

DS = −QB

Dox = −QB

DS = Dox(no charge at interface)

surface electric field and charge

6 Lundstrom ECE 305 F16

QS > 0 C cm2

D =QS

x

surface electric field and charge

7

E x( )

x

P E S

Lundstrom ECE 305 F16

E ox

QB = −qNAW C/cm2

Dox = −QB DS = −QB

W

gate voltage and surface potential

8

EC

EV

Ei

EF

Si

metal

ΔVS

ΔVOX

EFM

′VG = ΔVOX +φS

0 < φS < 2φF

′VG = ?Given the surface potential, what is the gate voltage?

relation to gate voltage

9

x

E S

W−xo

metal

′VG = ΔVox +φS

′VG

E ox

ΔVox = xoE ox

E x( )

Dox = KOε0E ox = −QB

ΔVox = xoE ox = xo

−QB

KOε0

Volt drop across a capacitor

10

ΔVox

C ≡ QV

= KOε0Axo

= Fxo

+ + + + + +

- - - - - -

CA= KOε0

xo= F/cm2

Cox =KOε0xo

= F/cm2

Lundstrom ECE 305 F16

relation to gate voltage

11

E x( ) E S

W−xo

metal

′VG

E ox

x

′VG = −QB φS( )Cox

+φS

QB φS( ) = −qNAW φS( )

Cox = KOε0 xo

ΔVox = xoE ox = xo

−QB

KOε0

Lundstrom ECE 305 F16

12

E x( )

x

P

E S =

qNA

κ Sε0W

12E SW = φS

E S

W

W = 2κ Sε0φSqNA

cm

QB = − 2qκ sε0NAφS C/cm2

QB = −qNAW φS( )C/cm2

0 < φS < 2φF

′VG = −QB φS( )Cox

+φS

recap (depletion)

MOS electrostatics: inversion

13

EC

EV

Ei

EF

Si

φ x( ) φ 0( )

x

φFφS ≈ 2φF φF

WT

WT =2KSε0qNA

2φF⎡

⎣⎢

⎦⎥

1/2 Maximum depletion region depth

delta-depletion approximation

14

ρ

x

metal

−xo

WT

ρ = −qNA

QB = −qNAWT

Qn

WT =2κ Sε0 2φFqNA

delta-depletion approximation

15

15

E x( )

x

P

WT

E S

E 0+( ) = − QB

KSε0

E 0( ) = − QS

KSε0

Lundstrom ECE 305 F16

MOS electrostatics: inversion

16

EC

EV

Ei

EF

Si

φ x( ) φ 0( )

x

φF

φS ≈ 2φF

φF

WT

WT =2KSε0qNA

2φF⎡

⎣⎢

⎦⎥

1/2

′VG = −QB 2φF( ) +Qn

Cox

+ 2φF

′VT = −QB 2φF( )Cox

+ 2φF

Qn = −Cox ′VG − ′VT( )

′VG = − QS

Cox

+ 2φF

Lundstrom ECE 305 F16

Gate voltage and CV

17

1)  Surface potential à gate voltage 2)  Example

Lundstrom ECE 305 F16

18

example

source drain

SiO

2

silicon

S G DAssume n+ poly Si gate with Φms = -1.0 V NA = 1018 cm-3 channel doping xo = 1.5 nm What is VT? Electric -field in oxide at VG = 1V?

Lundstrom ECE 305 F16

19

example (cont.)

′VG = −QS φS( )Cox

+ φS

′VT = −QB 2φF( )Cox

+ 2φF

VT = φms −QB 2φF( )Cox

+ 2φF

φF =kBTqln NA

ni

⎛⎝⎜

⎞⎠⎟

Cox = KOε0 xo

QB = − 2qκ sε0NA2φF

QB = −qNAW 2φF( )

φms = −1.00 V

φF = 0.48 V

Cox = 2.36 ×10−6 F/cm2

QB = −5.71×10−7 C/cm2

φms = −1.00 VVT = 0.20 V

20

example (cont): electric field in the oxide

Qn = −Cox VG −VT( )

E ox = − QS

Koε0= −

Qn +QB 2φF( )Koε0

Qn = −1.89 ×10−6 C/cm2

E ox = 7.1×106 V/cm

Qn

−q= 1.2 ×1013 /cm2

VG = 1V

VT = 0.2 V

Lundstrom ECE 305 F16

21

example (cont): volt drop in the oxide at VG = 1 V

ΔVox =E oxxo E ox = 7.1×106 V/cm ΔVox = 1.07V

ΔVS = φs φs = 2φF φF = 0.48 V φs = 0.96

VG = ΔVox + ΔVS = 1.07 + 0.96 = 2.03

VG = 1VLundstrom ECE 305 F16

Gate voltage and CV

22

1)  Surface potential à gate voltage 2)  Example

Lundstrom ECE 305 F16


Recommended