Introduction | Mathematical Analysis | Applet
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As you know, the physics of MOS capacitor is not simple. I have tried
here to create a tool that may help simplify the 'situation'. But it seems,
after all the effort, that it did not improve the situation much. If at
first the applet appears too busy, it may help hiding the "charge"
profile by cliking on the button.
This applet is to illustrate the equilibrium condition of MOS structure
in the charge profile and the energy band diagram. You can try various
gate metals, oxide thickness, and Si doping type and level.
As with the equilibrium band diagram of PN junction diode, the thermal
equilibrium in MOS is dictated by the constant Fermi level (in metal and
in semiconductor). As the equilibrium band diagram is achieved, an additional
constraint to be met is the charge neutrality.
Sources of space charge are:
- Qox = oxide charge: due to impurities and imperfection,
near the oxide-Si interface. Always positive.
- Qb = depletion charge: as EF of gate metal gets near
EF of Si (for thermal equilibrium), the Si energy band is bent and creates
either depletion or accumulation. If depletion, the ionized donor or acceptor
impurity in Si gives another charge.
- Qch = accumulation charge : if EF of gate metal,
relative to EF of Si, is such as to create accumulation of the majority
carrier charge under the gate, then this accumulation charge.
- Qch = inversion charge: if the (depletion) band bending
of Si is not sufficient to bring EF of the gate metal to the same value
as EF of Si, then the potential drop in the oxide is needed. The threshold
voltage for transition from depletion to inversion is an important device
proterty. The condition for inversion threshold is defined as the condition
where the volume density of channel charge is equal to the volume density
of bulk charge, but has an opposite polarity. (Note that Qch is an areal
density). Any additional band bending is negligibly small beyond this point
because: the inversion charge Qch and the oxide voltage drop
go linearly with each other, where as any additional, incremental band
bending goes logarithmically with them. (because Qch ~ Cox
Vox; where as the change in n ~ EXP[(the change in