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 Charges
In real MOS devices, there is always some charge within the
oxide and at the Si/oxide interface.
• 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
EE130/230M Spring 2013
Lecture 17, Slide 2
Effect of Oxide Charges
• In general, charges in the oxide cause a shift in the
gate voltage required to reach threshold condition:
VT  
xo
1
 SiO
2
 x
ox
( x)dx
0
(x is defined to be 0 at metal-oxide interface)
• In addition, they may alter the field-effect mobility of
mobile carriers (in a MOSFET) due to Coulombic
scattering.
EE130/230M Spring 2013
Lecture 17, Slide 3
Fixed Oxide Charge, QF
M
3.1 eV
O
S
qQF / Cox
Ec= EFM
|qVFB |
Ev
Ec
EFS
Ev
4.8 eV
EE130/230M Spring 2013
Lecture 17, Slide 4
VFB   MS
QF

Cox
Parameter Extraction from C-V
From a single C-V measurement, we can extract much
information about the MOS device:
• Suppose we know the gate material is heavily doped n-type
poly-Si (FM= 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 VFB  VG
5.
From FM, FS, Cox, and VFB we can determine Qf
EE130/230M Spring 2013
Lecture 17, Slide 5
C  C FB
Determination of FM and QF
Measure C-V characteristics of capacitors with different oxide
thicknesses. Plot VFB as a function of xo:
VFB
10nm
20nm
30nm
xo
0
VFB  MS 
–0.15V

EE130/230M Spring 2013
 SiO
2

–0.3V
xo

Lecture 17, Slide 6
QF
Mobile Ions
• Odd shifts in C-V characteristics once were a mystery:
VFB
QM

Cox
• Source of problem: Mobile charge moving to/away from
interface, changing charge centroid
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
QIT (S )
VG  
Cox
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.
NMOS
PMOS
n+ poly-Si
p+ poly-Si
p-type Si
n-type Si
– 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
EE130/230M Spring 2013
Lecture 17, Slide 9
MOS Band Diagram w/ Gate Depletion
Si biased to inversion:
WT
Ec
qVpoly
qS
EFS
Ev
Qinv  Cox (VG  V poly  VT )
qVG
Ec
Ev
VG is effectively reduced:
W poly 
2 SiV poly
qN poly
Wpoly
n+ poly-Si gate
EE130/230M Spring 2013
How can gate depletion
be minimized?
p-type Si
Lecture 17, Slide 10
Gate Depletion Effect
Gauss’s Law dictates that Wpoly = oxEox / qNpoly
xo is effectively increased:
1
n+ poly-Si
Cpoly
+ + + + + + + +
Cox
N+
- - - - - - - - -
p-type Si
 xo
 1

W poly 
1


 
C 


C

  SiO

C

ox
poly
Si


2



 SiO
2
xo  (W poly / 3)
Qinv  (VG  VT ) 
EE130/230M Spring 2013
Lecture 17, Slide 11
 SiO
2
xo  (W poly / 3)
1
Example: Gate Depletion Effect
The 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) Wpoly = oxEox / qNpoly = oxVox / xoqNpoly
3.9  8.85 10 14[F/cm] 1[V])

2 10 7 [cm] 1.6 10 19[C]  8  1019[cm -3 ]
 1.3  10 7 cm
EE130/230M Spring 2013
Lecture 17, Slide 12
(b)
W poly 
2 SiV poly
qN poly
2
Vpoly  qN polyWpoly
/ 2 Si  0.11 V
(c)
VT  VFB  2F  Vox  V poly
 EG kT  N A 
  0.98 V
VFB   

ln 
 2q q  ni 
VT  0.98 V  0.84 V  1 V  0.11 V  0.97 V
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
Toxe
W poly
Tinv
 xo 

3
3
(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
Tox  xo  W poly / 3  Tinv / 3
Qinv 
EE130/230M Spring 2013
 ox
Toxe
(VG  VT )  Coxe (VG  VT )
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.
qN I
VT  
Cox
EE130/230M Spring 2013
N I  0 for donor atoms
N I  0 for acceptor atoms
Lecture 17, Slide 17