Basic MOS structure question

calculating ef-ei at bend

I want to ask, in a MOS structure. Why thereis a band-bending in the interface of Oxide and Semicondutor.

In the meanwhile,why the fermi level remain straight across all the three material.
Just like the picture below

Dear pal,

Of course your energy bands will be bent because, for a uniformly doped junction(which is formed by the channel and the substrate), the energy is obtained by doubly integrating the carrier concentration in the depletion region. Once it crosses the depletion region into the substrate, then the energy levels are constant because there are no free carriers in the substrate.

Coming to the Fermi Level,Fermi level a measure of the energy of the least tightly held electrons within a solid and is the measure of an electron occupying an available state. It depends on the concentration of the donor and acceptor impurities in the semiconductor junction......Hence, it is independent of the electric fields and the energies. So, it will be a straight line.......

I hope that I am right. Kindly correct me if I am not.....

vamsimocherla,

I thought that Fermi level is the energy level where the probability of finding an electron(or hole) is half. If that is the definition, then according to the definition, Fermi level should also bend.,I am not sure why it does not.,

Hi,
Fermi level is the energy level where the Fermi function f(E)=1/2. Fermi function is the probability desinity distribution of electrons across the whole energy band. When an electron jumps from the valence band to conductance band, the distribution will change, however, the energy position where f(E)=1/2 will never change. This is the symmetrical point of the distribution. That why Fermi level remains constant regardless the bend of valence and conductance band. This could also be used to explain the constant Fermi level across different material connected together.
Ei refers to instrinsic Fermi level. It is located around the center of the band gap. generally, Ei = (Ec+Ev)/2. So, when the energy band bends, it bends also. To my understanding, it has no significant physical meaning here, simply to keep the following formula valid.
n = ni exp[(Ef-Ei)/kT], and
p = ni exp[-(Ef-Ei)/kT]

Hope this helps

ceyjey

The Fermi level constant through out the three device layers shows the thermal equiliburium reached by the whole device in total.
Fermi level represent the probability of occupancy of an energy level by an electron and at thermal equiliburium the constant fermi level reflects the fact that the flow of carriers in both directions is same.
try to understand this concept by drawing the energy band diagrams for three layers separately and then join them to get to thermal equiliburium and visualise the effect on the enery band diagram representation.
this will clear your doubt regarding the bending of bands also.
hope it helps
else you can refer the books by
1).Ben G. Streetman and Sanjay Banerjee.
2).Physics of semconductor devices by Mullar Kamines
regards

Many thanks to the above guys
I will still try to read some books to enhance my understanding on this issue

Well, Femi level is an enegy level, so it is strait, like the sea level. Do you think
the sea level will bend in a local erea? the same reason.

The enegy band is bent near the surface of semiconductor, because of the surface
effects of semiconductor. Electons tend to accumulate on the surface because of the surface effects, and a surface electry field is built near the surface. Please check any book about surface effects of semi-conductor for details.

now the picture u have shown is for the case of accumulation.the reason for this is simple.when u apply a negative gate voltage i.e when the gate is made negative wrt to the source then u have a case where holes will accumulate beneath the gate oxide and the surface beneath the gate oxide becomes more p type than initially.so in order to indicate that phenomenon the EF or the fermi level bends towards the valence band,this is just a concept to indicate the greater presence of holes than electrons beneath the gate oxide.so just to use a measure to indicate whether a surface is more p-type or n-type we bend the fermi level in the direction of the valence or the conduction band respectively.

regards
amarnath