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For MOS Cap curve, does the depletion region in MOS when VFB < VGB < 0?

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mpig09

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Hi all:

Many books explain the MOS Cap value is Cox(oxide cap) serial Cdep(depletion cap) when VFB < VGB < VTH,
I have a questions: is there a depletion region in MOS when VFB < VGB < 0?

If Yes, could you help me to understand it.

Thanks.

mpig
 

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erikl

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is there a depletion region in MOS when VFB < VGB < 0?

Yes, there is, because for VFB < VGB
the positive charge on the gate (compared to VFB) pushes the mobile holes into the substrate. Therefore, the semiconductor is depleted of mobile carriers at the interface and a negative charge, due to the ionized acceptor ions, is left in the space charge region.
The capacitance of this space charge region is in series with the oxide capacitance, thus correspondingly reduces the total MOS capacitance, s. e.g. the explanation from this book, where I took the above quote from.
 

mpig09

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Hi erikl :

When VFB < VGB < VTH(MOS Cap in depletion region) : Cox(oxide cap) serial Cdep(depletion cap)
But I don't know where is the Cdep(depletion cap) ?

Please reference the attached file.

mpig Cdep.png
 

mpig09

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Hi erikl :

I know the depletion region is light green.
Could you help me to know the depletion cap structure? like Cox.

I wish to know the two plates of Cdep.

I think the Ctol = Cox serial Cdep in the depletion region that means the structure is:
one plate is gate
other plate is bulk
The distance between the gate and the bulk is tox (the width of the oxide) + Wdep (the width of the depletion region).
==>The distance is increased, so the cap value is decrease.

If I am wrong, please correct me.

Thanks.
mpig
 

erikl

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Could you help me to know the depletion cap structure? like Cox.
I wish to know the two plates of Cdep.
Hi mpig :

I'd suggest you first read the chapter 6 explanation of MOS capacitors - which I stated above - once more, especially this sub-chapter
6.2.3. Depletion

As a more positive voltage than the flatband voltage is applied, a negative charge builds up in the semiconductor. Initially this charge is due to the depletion of the semiconductor starting from the oxide-semiconductor interface. The depletion layer width further increases with increasing gate voltage.

P-type silicon usually is doped by Boron - a triad atom, missing one electron compared to the silicon atoms around it, so playing a hole for electrons, which can hop from one Boron atom to another one by diffusion or drift, which means the same as moving a positive charge into the opposite direction: p-type (hole) conductivity (hole mobility being substantially lower than the electron mobility).

Now what does depletion - here in p-type material - really mean? A positive voltage VFB < VGB < VTH at the gate attracts mobile electrons from the p-substrate in direction to the substrate-oxide interface, there filling the available Boron holes, which so constitute a fixed (immobile) negative anti-charge to the positive charge on the gate metal.

A layer of p-type substrate by this is depleted of mobile (positive) holes, which now are replaced by immobile negatively charged Boron atoms. The width of the depletion layer (Wdep) depends on VGB-VFB and the substrate doping concentration (available number of doping atoms (holes) per volume).

Hope, this is clearer now. If you still have concrete questions, you're welcome!


The distance between the gate and the bulk is tox (the width of the oxide) + Wdep (the width of the depletion region).
==>The distance is increased, so the cap value is decrease.
If I am wrong, please correct me.
No, you are right!
 

mpig09

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Hi erikl :

Thanks for your help, I have more clearly.
I have two issues:

Now what does depletion - here in p-type material - really mean? A positive voltage VFB < VGB < VTH at the gate attracts mobile electrons from the p-substrate in direction to the substrate-oxide interface, there filling the available Boron holes, which so constitute a fixed (immobile) negative anti-charge to the positive charge on the gate metal.
==>Does it mean the hole repel by VGB (when VGB > VFB)?

A layer of p-type substrate by this is depleted of mobile (positive) holes, which now are replaced by immobile negatively charged Boron atoms.
==>The depletion in the p-type substrate(when VGB > VFB) is formed by the recombination of electrons and holes in the Boron atoms, so this condition cause the Boron atoms is negative charge?

mpig
 

erikl

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Now what does depletion - here in p-type material - really mean? A positive voltage VFB < VGB < VTH at the gate attracts mobile electrons from the p-substrate in direction to the substrate-oxide interface, there filling the available Boron holes, which so constitute a fixed (immobile) negative anti-charge to the positive charge on the gate metal.
==>Does it mean the hole repel by VGB (when VGB > VFB)?
No, s. above text! Holes cannot be repelled, they are fixed, immobile (Boron) atoms in the (Silicon) lattice. VGB attracts mobile electrons from the p-substrate in direction to the substrate-oxide interface, there filling the available Boron holes ...

A layer of p-type substrate by this is depleted of mobile (positive) holes, which now are replaced by immobile negatively charged Boron atoms.
==>The depletion in the p-type substrate(when VGB > VFB) is formed by the recombination of electrons and holes in the Boron atoms, so this condition cause the Boron atoms is negative charge?
Alike. A recombination means a transformation of a charged atom (an ion) into a neutral one; in this case it's the other way round: the neutral Boron atom (the hole) traps an electron and keeps it - now it has the same number of electrons as its Silicon neighbors and so holds a good equilibrium state in the lattice - however is negatively charged now: a charged atom - an ion, but a fixed & immobile charge.
 
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timof

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Re: For MOS Cap curve, does the depletion region in MOS when VFB &lt; VGB &lt; 0?

Hi erikl :

I know the depletion region is light green.
Could you help me to know the depletion cap structure? like Cox.

I wish to know the two plates of Cdep.

I think the Ctol = Cox serial Cdep in the depletion region that means the structure is:
one plate is gate
other plate is bulk
The distance between the gate and the bulk is tox (the width of the oxide) + Wdep (the width of the depletion region).
==>The distance is increased, so the cap value is decrease.

If I am wrong, please correct me.

Thanks.
mpig

You are very close, but not right there.
The total thickness - Tox plus Tdep - contains two distinctively different materials (dielectric/oxide, and depleted Si) - that have different dielectric constants (eps~4.2 in SiO2, and eps ~11.9 in Si).
That's why it is meaningful to treat these two regions as two capacitors connected in series, rather than one capacitor.

- - - Updated - - -

Erikl - you are confusing hole with an energy state in atom.
The holes are mobile (as mobile as electrons - with somewhat different mobility), atoms are fixed and not moving (after device is formed).
Hole is kind of a missing electron in the valence band.
Mobile electrons are in the conduction band.

Electrons normally do not hop from one acceptor atom to another (unless acceptor concentration is so high that they form a, energy band where electrons can move - this normally does not happen in semiconductor devices).

Your explanation of depletion region is wrong.

In neutral p-type semiconductor, concentration of (free) holes is equal to concentration of ionized (negatively charged - by capturing electrons from the valence band) acceptors - that's why it is electrically neutral, charge density is zero.
When positive voltage is applied to the gate, the holes are pushed away from the dielectric/semiconductor interface, and depletion regions is formed - which contains no holes, but contains negatively charged acceptors.

There is no mobile electrons in p-type neutral region (it is extremely low).
Electrons can appear in the depletion region due to thermal generation (electron excitation from the valence band, across band gap, into conduction band).

Holes are not fixed, they are mobile!!!
 
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erikl

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Re: For MOS Cap curve, does the depletion region in MOS when VFB &lt; VGB &lt; 0?

Holes are not fixed, they are mobile!!!

Thanks for your explanation and correction, Max!
 

mpig09

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Hi timof and erikl:

Thanks for your explanation,
I have more clearly the MOS cap structure that in the depletion region.

mpig
 

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