Lecture 18

OUTLINE• The MOS Capacitor (cont’d)

– Effect of oxide charges– Poly-Si gate depletion effect

– VT adjustment

Reading: Pierret 18.2-18.3; Hu 5.7-5.9

Oxide ChargesIn real MOS devices, there is always some charge within the oxide and at the Si/oxide interface.

EE130/230M Spring 2013 Lecture 17, Slide 2

• Within the oxide:– Trapped charge Qot

• High-energy electrons and/or holes injected into oxide

– Mobile charge QM• Alkali-metal ions, which have

sufficient mobility to drift in oxide under an applied electric field

• At the interface:– Fixed charge QF

• Excess Si (?)– Trapped charge QIT

• Dangling bonds

Effect of Oxide Charges• In general, charges in the oxide cause a shift in the

gate voltage required to reach threshold condition:

(x is defined to be 0 at metal-oxide interface)

For example, positive charge in the oxide near to the p-type Si substrate (for an NMOS device) helps to deplete the surface of holes, so that the gate voltage that must be applied to invert the surface (to become n-type) is reduced, i.e. VT is reduced VT is negative.

• In addition, oxide charge can affect the field-effect mobility of mobile carriers (in a MOSFET) due to Coulombic scattering.

ox

oxSiO

T dxxxV0

)(1

2

EE130/230M Spring 2013 Lecture 17, Slide 3

Fixed Oxide Charge, QF

ox

FMSFB C

QV Ec

EFS

Ev

Ec= EFM

Ev

M O S

3.1 eV

4.8 eV

|qVFB |

qQF / Cox

EE130/230M Spring 2013 Lecture 17, Slide 4

Parameter Extraction from C-VFrom a single C-V measurement, we can extract muchinformation about the MOS device:• Suppose we know the gate material is heavily doped n-type

poly-Si (M= 4.1 eV), and the gate dielectric is SiO2 (r = 3.9):

1. From Cmax = Cox we can determine oxide thickness xo

2. From Cmin and Cox we can determine substrate doping (by iteration)

3. From substrate doping and Cox we can find flat-band capacitance CFB

4. From the C-V curve, we can find

5. From M, S, Cox, and VFB we can determine Qf

FBCCGFB VV

EE130/230M Spring 2013 Lecture 17, Slide 5

Determination of M and QF

FSiO

oMSFB Q

xV

2

0

–0.15V

–0.3V

xo

VFB10nm 20nm 30nm

Measure C-V characteristics of capacitors with different oxide thicknesses. Plot VFB as a function of xo:

EE130/230M Spring 2013 Lecture 17, Slide 6

Mobile Ions• Odd shifts in C-V characteristics once were a mystery:

• Source of problem: Mobile charge moving to/away from interface, changing charge centroid

ox

MFB C

QV

EE130/230M Spring 2013 Lecture 17, Slide 7

Interface Traps

Traps result in a “sloppy” C-V curve and also greatly degrade mobility in channel

ox

SITG C

QV

)(

EE130/230M Spring 2013 Lecture 17, Slide 8

Poly-Si Gate Depletion • A heavily doped film of polycrystalline silicon (poly-Si) is often

employed as the gate-electrode material in MOS devices.

– There are practical limits to the electrically active dopant concentration (usually less than 1x1020 cm-3)

The gate must be considered as a semiconductor, rather than a metal

p-type Si

n+ poly-Si

n-type Si

p+ poly-Si

NMOS PMOS

EE130/230M Spring 2013 Lecture 17, Slide 9

MOS Band Diagram w/ Gate Depletion

)( TpolyGoxinv VVVCQ

How can gate depletion be minimized?

VG is effectively reduced:Ec

EFSEv

Ev

qVG

qS

WT

p-type Sin+ poly-Si gate

Ec

qVpoly

Wpoly

Si biased to inversion:

poly

polySipoly qN

VW

2

EE130/230M Spring 2013 Lecture 17, Slide 10

Gate Depletion Effect

n+ poly-Si

Gauss’s Law dictates that Wpoly = oxEox / qNpoly

)3/(

11

2

2

11

polyo

SiO

Si

poly

SiO

o

polyox

Wx

Wx

CCC

xo is effectively increased:

)3/()( 2

polyo

SiOTGinv Wx

VVQ

p-type Si

-- - - --

+ + + + + +

N+

+ +

-- -

Cpoly

Cox

EE130/230M Spring 2013 Lecture 17, Slide 11

Example: Gate Depletion EffectThe voltage across a 2 nm oxide is Vox = 1 V. The active dopant concentration within the n+ poly-Si gate is Npoly = 8 1019 cm-3 and the Si substrate doping concentration NA is 1017 cm-3.

Find (a) Wpoly , (b) Vpoly , and (c) VT .

Solution:

(a)

EE130/230M Spring 2013 Lecture 17, Slide 12

Wpoly = oxEox / qNpoly = oxVox / xoqNpoly

cm103.1

]cm[108]C[106.1]cm[102

)V][1F/cm][1085.89.3

7

3-19197

14

(b) poly

polySipoly qN

VW

2

V 11.02/2 Sipolypolypoly WqNV

(c)

V 97.0V 11.0V 1V 84.0V 98.0

V 98.0ln2

2

T

i

AGFB

polyoxFFBT

V

n

N

q

kT

q

EV

VVVV

EE130/230M Spring 2013 Lecture 17, Slide 13

Inversion-Layer Thickness, Tinv

The average inversion-layer location below the Si/SiO2 interface is called the inversion-layer thickness, Tinv .

EE130/230M Spring 2013 Lecture 17, Slide 14

Effective Oxide Thickness, Toxe

33invpoly

ooxe

TWxT

(VG + VT)/Toxe can be shown to be the average electric field in the inversion layer.

Tinv of holes is larger than that of electrons due to difference in effective masses.EE130/230M Spring 2013 Lecture 17, Slide 15

Effective Oxide Capacitance, Coxe

33invpoly

ooxe

TWxT

dVVVCQ T

V

V oxeinv

G

T

)(

EE130/230M Spring 2013 Lecture 17, Slide 16

VT Adjustment• In modern IC fabrication processes, the threshold voltages of

MOS transistors are adjusted by adding dopants to the Si by a process called “ion implantation”:– A relatively small dose NI (units: ions/cm2) of dopant atoms is

implanted into the near-surface region of the semiconductor– When the MOS device is biased in depletion or inversion, the

implanted dopants add to (or substract from) the depletion charge near the oxide-semiconductor interface.

ox

IT C

qNV

atomsacceptor for 0

atomsdonor for 0

I

I

N

N

EE130/230M Spring 2013 Lecture 17, Slide 17