Lecture #33
OUTLINE
The MOS Capacitor:
• C-V examples
• Impact of oxide charges
Reading: Chapter 18.1, 18.2
Spring 2007
EE130 Lecture 33, Slide 1
Examples: C-V Characteristics
C
QS
Cox
HF-Capacitor
VFB
VT
VG
Does the QS or the HF-capacitor C-V characteristic apply?
(1) MOS capacitor, f=10kHz.
(2) MOS transistor, f=1MHz.
(3) MOS capacitor, slow VG ramp.
(4) MOS transistor, slow VG ramp.
Spring 2007
EE130 Lecture 33, Slide 2
Example: Effect of Doping
C/Cox
1
VFB
VT
VG
• How would C-V characteristic change if substrate
doping NA were increased?
– VFB
– VT
– Cmin
Spring 2007
EE130 Lecture 33, Slide 3
Example: Effect of Oxide Thickness
C/Cox
1
VFB
VT
VG
• How would C-V characteristic change if oxide
thickness xo were decreased?
– VFB
– VT
– Cmin
Spring 2007
EE130 Lecture 33, Slide 4
Oxide Charges
In real MOS devices, there is
always some charge in the oxide
and at the Si/oxide interface.
• In 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
Spring 2007
EE130 Lecture 33, Slide 5
Effect of Oxide Charges
• In general, charges in the oxide cause a shift
in the gate voltage required to reach the
threshold condition:
VT  
xo
1
 SiO
2
 x
ox
( x)dx
0
(x 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
Spring 2007
EE130 Lecture 33, Slide 6
Fixed Oxide Charge QF
M
3.1 eV
O
S
qQF / Cox
Ec= EFM
|qVFB |
Ev
Ec
EFS
Ev
4.8 eV
Spring 2007
EE130 Lecture 33, Slide 7
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 that the gate-electrode material is
heavily doped n-type poly-Si (FM=4.05eV), and that the
gate dielectric is SiO2 (r=3.9):
– From Cmax = Cox we determine the oxide thickness xo
– From Cmin and Cox we determine substrate doping (by iteration)
– From substrate doping and Cox we calculate the flat-band
capacitance CFB
– From the C-V curve, we can find VFB  VG
C  C FB
– From FM, FS, Cox, and VFB we can determine Qf
Spring 2007
EE130 Lecture 33, Slide 8
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

Spring 2007
 SiO
2

–0.3V
xo

EE130 Lecture 33, Slide 9
QF
Mobile Ions
• Odd shifts in C-V characteristics were once a mystery:
VFB
QM

Cox
• Source of problem: Mobile charge moving to/away from
interface, changing charge centroid
Spring 2007
EE130 Lecture 33, Slide 10
Interface Traps
Traps cause “sloppy” C-V and also
greatly degrade mobility in channel
QIT (S )
VG  
Cox
Spring 2007
EE130 Lecture 33, Slide 11