1. Lecture 17 OUTLINE The MOS Capacitor (cont’d) Small-signal capacitance
(C-V characteristics)
Reading: Pierret 16.4; Hu 5.6

2. MOS Capacitance Measurement
VG is scanned slowly
Capacitive current due
to vac is measured
C-V Meter
MOS Capacitor
iac
GATE
Semiconductor
vac
EE130/230A Fall 2013
Lecture 17, Slide 2

3. MOS C-V Characteristics (p-type Si)
accumulation
depletion
inversion VG
VFB VT
Qinv C
slope = -Cox
Cox
Ideal C-V curve: VG
VFB VT
accumulation
depletion
inversion
EE130/230A Fall 2013
Lecture 17, Slide 3

4. Capacitance in Accumulation (p-type Si)
As the gate voltage is varied, incremental charge is added (or subtracted) to (or from) the gate and substrate.
The incremental charges are separated by the gate oxide.
M O S DQ Q -Q
-DQ
Cox
EE130/230A Fall 2013
Lecture 17, Slide 4

5. Flat-Band Capacitance (p-type Si)
At the flat-band condition, variations in VG give rise to the addition/subtraction of incremental charge in the substrate, at a depth LD
LD is the “extrinsic Debye Length,” a characteristic screening distance, or the distance where the electric field emanating from a perturbing charge falls off by a factor of 1/e
Cox
CDebye
EE130/230A Fall 2013
Lecture 17, Slide 5

6. Capacitance in Depletion (p-type Si)
As the gate voltage is varied, the depletion width varies.
Incremental charge is effectively added/subtracted at a depth W in the substrate.
M O S DQ Q W
-DQ -Q
Cox
Cdep
EE130/230A Fall 2013
Lecture 17, Slide 6

7. Capacitance in Inversion (p-type Si)
CASE 1: Inversion-layer charge can be supplied/removed quickly enough to respond to changes in gate voltage.
Incremental charge is effectively added/subtracted at the
surface of the substrate. DQ
M O S
Time required to build inversion-layer
charge = 2NAto/ni , where
to = minority-carrier lifetime at surface WT
-DQ
Cox
EE130/230A Fall 2013
Lecture 17, Slide 7

8. Capacitance in Inversion (p-type Si)
CASE 2: Inversion-layer charge cannot be supplied/removed quickly enough to respond to changes in gate voltage.
Incremental charge is effectively added/subtracted at a
depth WT in the substrate. DQ
M O S WT
-DQ
Cox
Cdep
EE130/230A Fall 2013
Lecture 17, Slide 8

9. Supply of Substrate Charge (p-type Si)
Accumulation:
Depletion:
Inversion:
Case 1
Case 2
C. C. Hu, Modern Semiconductor Devices for ICs, Figure 5-17
EE130/230A Fall 2013
Lecture 17, Slide 9

10. MOS Capacitor vs. MOS Transistor C-V (p-type Si)
MOS transistor at any f,
MOS capacitor at low f, or
quasi-static C-V
Cmax=Cox
CFB
MOS capacitor at high f
Cmin VG
accumulation
depletion
inversion
VFB VT
EE130/230A Fall 2013
Lecture 17, Slide 10

11. Quasi-Static C-V Measurement (p-type Si)
Cmax=Cox
CFB
Cmin VG
accumulation
depletion
inversion
VFB VT
The quasi-static C-V characteristic is obtained by slowly ramping the gate voltage (< 0.1V/s), while measuring the gate current IG with a very sensitive DC ammeter. C is calculated from IG = C·(dVG/dt)
EE130/230A Fall 2013
Lecture 17, Slide 11

12. Deep Depletion (p-type Si)
If VG is scanned quickly, Qinv cannot respond to the change in VG. Then the increase in substrate charge density Qs must come from an increase in depletion charge density Qdep
depletion depth W increases as VG increases
C decreases as VG increases VG
VFB VT C
Cox
Cmin
EE130/230A Fall 2013
Lecture 17, Slide 12

13. MOS C-V Characteristic for n-type Si
MOS transistor at any f,
MOS capacitor at low f, or
quasi-static C-V
Cmax=Cox
CFB
MOS capacitor at high f
Cmin VG
accumulation
depletion
inversion VT
VFB
EE130/230A Fall 2013
Lecture 17, Slide 13

14. Examples: C-V CharacteristicsVG
VFB VT C
Cox QS
HF-Capacitor
Does the QS or the HF-capacitor C-V characteristic apply?
MOS capacitor, f=10kHz
MOS transistor, f=1MHz
MOS capacitor, slow VG ramp
MOS transistor, slow VG ramp
EE130/230A Fall 2013
Lecture 17, Slide 14

15. Example: Effect of Doping
How would the normalized C-V characteristic below change if the substrate doping NA were increased?
VFB VT
Cmin
C/Cox 1
VFB VT
EE130/230A Fall 2013
Lecture 17, Slide 15

16. Example: Effect of Oxide Thickness
How would the normalized C-V characteristic below change if the oxide thickness xo were decreased?
VFB VT
Cmin
C/Cox 1
VFB VT
EE130/230A Fall 2013
Lecture 17, Slide 16

17. Derivation of Time to Build Inversion-Layer Charge (for an NMOS device, i.e. p-type Si)
The net rate of carrier generation is: (ref. Lecture 5, Slide 24)
where
since trap states that contribute most significantly to G-R have an associated energy level near the middle of the band gap.
Within the depletion region, n and p are negligible, so
where tn  tp  to
Therefore, the rate at which the inversion-layer charge density Qinv (units: C/cm2) increases due to thermal generation within the depletion region (of width W) is
EE130/230A Fall 2013
Lecture 17, Slide 17

18. The solution to this differential equation is
For a fixed value of gate voltage, the total charge in the semiconductor is fixed:
Therefore
The solution to this differential equation is
where
EE130/230A Fall 2013
Lecture 17, Slide 18