Integrated Circuit Devices. Professor Ali Javey Summer 2009. MOS Capacitors Reading: Chapter 16. MOS Capacitors. MOS: M etal- O xide- S emiconductor. MOS transistor. MOS capacitor. Ideal MOS Capacitor. Oxide has zero charge, and no current can pass through it.
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Professor Ali Javey
Reading: Chapter 16
EE143 – Ali Javey
If we continue to increase the positive gate voltage, the bands at the semiconductor bends more strongly. At sufficiently high voltage, Ei can be below EF indicating large concentration of electrons in the conduction band.
We say the material near the surface is “inverted”. The “inverted” layer is not gotten by chemical doping, but by applying E-field. Where did we get the electrons from?
When Ei(surface) – Ei(bulk) = 2 [EF – Ei(bulk)], the condition is start of “inversion”, and the voltage VG applied to gate is called VT(threshold voltage). For VG > VT, the Si surface is inverted.
Define a new term, (x) taken to be the potential inside the semiconductor at a given point x. [The symbol instead of V used in MOS work to avoid confusion with externally applied voltage, V]
Potential at any point x
| F | related to doping
F > 0 means p-type F < 0 means n-type
S is positive if the
bands bend\ …….?
S = 2F at the
transition point (threshold voltage)
VG < 0
Accumulation of holesCharge Density - Accumulation
M O S
The accumulation charges in the semiconductor are ……. , and appear
close to the surface and fall-off
rapidly as x increases.
One can assume that the free carrier concentration at the oxide-semiconductor interface is a -function.
Charge on metal = QM
Charge on semiconductor = (charge on metal)
|QAccumulation| = |QM|
VG > 0
holesCharge Density - Depletion
The depletion charges in Si are immobile ions - results in depletion
layer similar to that in pn
junction or Schottky diode.
|q NA A W| = |QM|
If surface potential is s, then the depletion layer width W will be
VG>>0Charge Density - Inversion
Once inversion charges
appear, they remain close to the surface since they are
…….. Any additional voltage to the gate results in extra QM in gate and get compensated by extra inversion electrons in
So, the depletion width does not change during inversion. Electrons appear as -function near the surface. Maximum depletion layer width W = WT
- functionC-V: under inversion (high frequency)
VG = VT and VG > VT
Inversion condition s = 2 F
At high frequency, inversion
electrons are not able to respond
to ac voltage.
Cox=ox A / xox
Cs = Si A / WT
CG ( ) = Cox Cs / (Cox + CS)
CG will be constant for VG VT
At low frequency, the inversion electrons will be able to respond to the ac voltage. So, the gate capacitance will be equal to the “oxide capacitance” (similar to a parallel plate capacitance).
CG ( 0) = Cox
= ox A / xox
Ideal MOSC (p-type Si)
CG increases for VG VT until it reaches Cox