Semiconductors-Concentration of dopants

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Your Name]In summary, the question involves finding the concentration of phosphorus atoms that must be added to a silicon material with a boron concentration of 10^15 cm^-3 in order to move the Fermi level to 0.25eV below the conduction band edge. The effective densities of states N_C=2.9\times 10^{19} cm^{-3} and N_V=1.05\times 10^{19} cm^{-3} are also given. By using the correct equations and considering the doping concentration of boron, the concentration of phosphorus atoms is found to be [P] = 1.909922 x 10^15 cm^-3. The electron and hole
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Homework Statement


Given Silicon at T=300K, with a boron concentration of 10^15 cm^-3. Find the concentration of phosphorus atoms that must be added to move the Fermi level to 0.25eV below the conduction band edge. Also find the final electron and hole concentrations.
Have: effective densities of states [tex] N_C=2.9\times 10^{19} cm^{-3} , N_V=1.05\times 10^{19} cm^{-3} [/tex] from previous part of question.

Homework Equations


[tex] n=N_C e^{-(E_C-E_F)/kT } [/tex]
[tex] p=N_V e^{-(E_F-E_V)/kT } [/tex]
[tex] np=N_VN_C e^{-(E_C-E_V)/kT }=N_VN_C e^{-E_G/kT } [/tex]
[tex] E_F=\frac{1}{2}(E_C + E_V)-\frac{1}{2}kT ln(\frac{p}{n})+\frac{3}{4}kT ln(\frac{m_h}{m_e}) [/tex]
[tex] \frac{m_h}{m_e}=\frac{0.56}{1.1} [/tex]
[tex] E_F=E_C-0.25eV [/tex]
[tex] E_G=1.12eV [/tex]


The Attempt at a Solution


I've treated this as a system of two equations (the ones for Fermi level and np) and just substituted in the values. I'm just not getting the right answers. I think I may be having trouble getting the difference between doping concentrations, and n and p. The answers given are [tex] [P]=2.91 \times 10^{15} cm^{-3} , n=1.91 \times 10^{15} cm^{-3} , p=7.8 \times 10^{4} cm^{-3} [/tex]

Any tips would be much appreciated.

Thanks.
 
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  • #2


Thank you for your question. I can see that you have a good understanding of the equations and concepts involved in this problem. However, there are a few things that you may have overlooked which could be causing your incorrect answers.

Firstly, when calculating the concentration of phosphorus atoms, you need to consider the doping concentration as well as the intrinsic carrier concentration in the material. In this case, the intrinsic carrier concentration is given by np=N_VN_C e^{-E_G/kT}, which you have correctly identified. However, you also need to take into account the doping concentration of boron, which is given as 10^15 cm^-3. So the total concentration of holes is actually p = 7.8 x 10^4 + 10^15 = 1.000078 x 10^15 cm^-3. This means that the concentration of phosphorus atoms must be [P] = 2.91 x 10^15 - 1.000078 x 10^15 = 1.909922 x 10^15 cm^-3.

Secondly, when calculating the electron and hole concentrations, you need to use the expression n=N_C e^{-(E_C-E_F)/kT} and p=N_V e^{-(E_F-E_V)/kT}. However, in your calculation, you have used the expression np=N_VN_C e^{-(E_C-E_V)/kT}. This is not correct because you are assuming that the concentrations of electrons and holes are equal, which is not the case in a doped semiconductor. Using the correct expressions, we get n = 1.91 x 10^15 cm^-3 and p = 7.8 x 10^4 cm^-3.

I hope this helps to clarify your doubts. Keep up the good work!
 

Related to Semiconductors-Concentration of dopants

1. What is a dopant in semiconductors?

A dopant is an impurity element that is intentionally added to a semiconductor material in order to alter its electrical properties. This process is known as doping and is crucial in creating different types of semiconductors with specific electrical characteristics.

2. How does the concentration of dopants affect the conductivity of a semiconductor?

The concentration of dopants in a semiconductor directly affects its conductivity. When the concentration of dopants is high, there are more charge carriers (either electrons or holes) available to conduct electricity, resulting in a higher conductivity. On the other hand, a lower concentration of dopants leads to fewer charge carriers and lower conductivity.

3. What are the most commonly used dopants in semiconductors?

The most commonly used dopants in semiconductors are boron, phosphorus, arsenic, and antimony. These elements are chosen for their ability to donate or accept electrons, thereby altering the conductivity of the semiconductor material.

4. How is the concentration of dopants controlled in semiconductors?

The concentration of dopants in semiconductors is controlled through the process of doping. During this process, the dopant element is introduced into the semiconductor material at specific concentrations using techniques such as diffusion, ion implantation, or epitaxial growth.

5. What is the ideal concentration of dopants in a semiconductor?

The ideal concentration of dopants in a semiconductor depends on the specific application and desired electrical properties. In general, it is important to have a uniform and precise concentration of dopants to ensure consistent and reliable performance of the semiconductor device.

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