# Inversion layer in a MOS

#### Theraven1982

[SOLVED] inversion layer in a MOS

Hello,

I have some questions about MOS devices, and CCD

In a MOS or MIS after applying a voltage on the metal, the valenceband and the conduction band bend downwards (in the usual band diagram) when a positive voltage is applied. (p-type semiconductor).
When the voltage is large enough, the fermi energy (in equilibrium) is above the intrinsic energy level, so that an inversion charge will build up.

The first thing I don't understand is why the electrons make an inversion layer in the first place. I mean, why would the electrons come so close to the oxide/semiconductor boundary in the first place (I understand the electrons are drawn to this boundary by the applied voltage, but why is it such a big deal that the Fermi energy level is larger than the intrinsic level?)

The second thing I don't understand, is what is the use of this inversion layer? Why is the inversion layer necessary in a CCD?

Any help would be greatly appreciated,

Oh, and a bonus 'question': I've seen a useful formula for calculating the dark current, but I can't find a reference. It's about this formula:

amount of dark current generated = $$CT^{1.5}e^{-E_g/2kT}$$

I've seen it in some books, but none of them make a reference to where it is derived, and I don't have a clue how to derive it myself.
(Maybe this question isn't in the right place here, then I'll try a different subforum).

Last edited:
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#### ZapperZ

Staff Emeritus
2018 Award
Oh, and a bonus 'question': I've seen a useful formula for calculating the dark current, but I can't find a reference. It's about this formula:

amount of dark current generated = $$CT^{1.5}e^{-E_g/2kT}$$

I've seen it in some books, but none of them make a reference to where it is derived, and I don't have a clue how to derive it myself.
(Maybe this question isn't in the right place here, then I'll try a different subforum).
Look into the Fowler-Nordheim theory for field emission current. The derivation to get that particular equation isn't trivial and makes many simplifications and assumptions.

Zz.

#### Theraven1982

It is not necessary that I know exactly how it is derived, but just wanted to know where it came from. I've seen the name 'Fowler-Nordheim' before in a paper, and now I at least understand where it comes from.

Any takers for the other questions? ;)

#### chroot

Staff Emeritus
Gold Member
The inversion layer is necessary to establish a conducting channel through which majority carriers can easily move.

- Warren

#### Theraven1982

Thanks.
But why is this conducting channel needed? This inversion layer is above the depletion region which fills up with charge; when the device is clocked (for measuring how much charge is in the well), the charges move from well to well. I don't see the need for this conducting channel.

#### marlon

Thanks.
But why is this conducting channel needed? This inversion layer is above the depletion region which fills up with charge; when the device is clocked (for measuring how much charge is in the well), the charges move from well to well. I don't see the need for this conducting channel.
The inversion layer provides the majority carriers (electrons or protons in nMOS and pMOS case) which make up the current. The inversion layer IS the conducting layer

marlon

#### marlon

The inversion layer provides the MINORITY carriers not the majority carriers.

My mistake.

marlon

#### Theraven1982

I'm sorry for the (very) late reply, but thanks a lot! I now fully understand. Sometimes I need to ripen new information ;).
Thanks again all!

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