How to find energy levels in doped silicon

• zje
In summary, the person is struggling with drawing an energy band diagram for doped silicon and finding the energy levels (E_c, E_v, E_f, and E_i) with only concentrations known. They have attempted to use the equation E_f - E_i = kT ln(N_D/n_i) but are unsure of the values for E_i and E_f. They also mention that E_g = 1.12eV and that E_c - E_i = 0.56eV, but are unsure of what to do next. They apologize for any formatting issues and acknowledge that perhaps they just need more sleep.
zje

Homework Statement

This is part of a much larger problem, but I'm stuck on trying to draw an energy band diagram for doped silicon and I'm wondering if it is possible for me to find the energy levels ( E_c, E_v, E_f, and E_i ) in a doped semiconductor knowing only the concentrations? This seems really basic to me, but I'm not getting anywhere. I've tried searching places and I can't seem to find anything.

Homework Equations

I've been looking at this:

E_f - E_i = kT ln(N_D/n_i)

But I don't seem to know E_i or E_f

The Attempt at a Solution

I think that E_g = 1.12eV, so E_c - E_i = 0.56eV, but where can I go from here?

Thank you very much for your help and sorry if this post is a little off, it's my first one

P.S.
Sorry for the poor formatting on the formula, I kept running into problems with the LaTeX formatting

It seems that I can get E_f - E_i rather easily and if my assumption for E_c - E_i is correct, then E_c - E_f = (E_c - E_i) - (E_f - E_i), which is what I think I'm looking for. However, I'm somewhat hesitant to believe it's that simple.

Maybe the trick is to get more sleep :-)

1. How is doping used to change the energy levels in silicon?

Doping is the process of intentionally introducing impurities into a material, such as silicon, to alter its electrical properties. In doped silicon, the impurities create additional energy levels within the band gap of the material, allowing for more efficient electron movement and conductivity.

2. What types of impurities are commonly used for doping silicon?

The most commonly used impurities for doping silicon are boron, phosphorus, and arsenic. Boron is a group III element and is used for p-type doping, while phosphorus and arsenic are group V elements and are used for n-type doping.

3. How do energy levels in doped silicon affect its conductivity?

The added energy levels in doped silicon allow for more efficient electron movement, increasing the material's conductivity. In p-type doped silicon, the energy levels attract electrons, creating a surplus of positively charged holes, while in n-type doped silicon, the energy levels provide extra electrons for conduction.

4. Can the energy levels in doped silicon be controlled?

Yes, the energy levels in doped silicon can be controlled by adjusting the amount and type of impurities added to the material. The concentration and distribution of impurities can be precisely controlled during the manufacturing process to achieve specific energy levels and desired electrical properties.

5. What methods are commonly used to measure the energy levels in doped silicon?

There are several methods for measuring the energy levels in doped silicon, including capacitance-voltage (CV) measurements, deep level transient spectroscopy (DLTS), and photoluminescence spectroscopy. These techniques involve applying an external voltage or light source to the material and then measuring changes in its electrical and optical properties, providing information about the energy levels present in the doped silicon.

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