Electron concentration in p-type semiconductor

In summary, the electron concentration in a Si semiconductor doped with Phosphorus atoms at 0K can be assumed to be approximately equal to the concentration of donors. At room temperature, the electron concentration can be calculated using the electron mobility of Si, which is 1350 cm2/Vs. The resistivity of the semiconductor can then be calculated based on this electron concentration. It is unclear whether the information about room temperature is relevant to the first part of the question.
  • #1
Philmac
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Electron concentration in n-type semiconductor

Homework Statement



At T = 0 K, what is the electron concentration in a Si semiconductor that is doped with Phosphorus atoms at ND=1017 cm^-3? At room temperature, what is the electron concentration of this semiconductor? The electron mobility of Si is 1350 cm2/Vs, calculate the resistivity of this semiconductor.

Just the bolded part. I'm not sure if the information in the second sentence is relevant to the first part.

Homework Equations



In the course notes I'm given dozens of equations, but I don't see how any of them would be useful for this question.

The Attempt at a Solution



I'm totally clueless, don't even know where to begin.
 
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  • #2
Two things have popped into my head.

1. In a doped semiconductor you can assume that the concentration of carriers is approximately equal tot he concentration of donars (assuming that the donars each produce one carrier) - i.e. Nd = p (approx.)

2. Surely at 0K all of the electrons would be localised to their parent atoms? In order to create holes in the valence band which electrons need to be elevated to the energy level of the Phosphorus, but at 0K with no other excitation there is no energy for the electrons to use to get to the energy level. I can't make my mind up whether this effects the concentration or not.
 
  • #3


I can provide a response to this content by explaining the concept of electron concentration in p-type and n-type semiconductors.

In a p-type semiconductor, the majority charge carriers are holes (positively charged) and the minority charge carriers are electrons (negatively charged). This is achieved by doping the semiconductor with acceptor impurities, such as Boron or Gallium, which have fewer valence electrons than the host semiconductor material. These acceptor impurities create holes in the valence band, making it easier for electrons to move into the conduction band, resulting in a low electron concentration.

On the other hand, in an n-type semiconductor, the majority charge carriers are electrons and the minority charge carriers are holes. This is achieved by doping the semiconductor with donor impurities, such as Phosphorus or Arsenic, which have more valence electrons than the host semiconductor material. These donor impurities create extra electrons in the conduction band, resulting in a high electron concentration.

Now, to answer the first part of the question, at T=0K, the semiconductor will be in its pure form and there will be no donor or acceptor impurities to create extra electrons or holes. Therefore, the electron concentration in a Si semiconductor doped with Phosphorus atoms at ND=1017 cm^-3 will be equal to 0.

At room temperature, the thermal energy will cause some of the electrons in the valence band to jump into the conduction band, creating a small number of electron-hole pairs. However, the majority of the electrons will still be in the valence band and the electron concentration will be very low.

The information about electron mobility and resistivity is relevant to the second part of the question, as it allows us to calculate the resistivity of the semiconductor. The resistivity is a measure of how strongly a material opposes the flow of electric current. It is inversely proportional to the electron concentration, which means that as the electron concentration increases, the resistivity decreases. Using the given electron mobility and the electron concentration at room temperature, we can calculate the resistivity of the semiconductor using the formula ρ= 1/neμ, where n is the electron concentration, e is the electron charge, and μ is the electron mobility.

I hope this response helps to clarify the concept of electron concentration in p-type and n-type semiconductors and how it relates to the given information.
 

1. What is p-type semiconductor?

P-type semiconductor is a type of semiconductor material that has been doped with impurities to create a positive charge carrier concentration. This is achieved by introducing elements such as boron, aluminum, or gallium into the semiconductor crystal lattice.

2. How does p-type semiconductor differ from n-type semiconductor?

P-type semiconductor differs from n-type semiconductor in terms of the majority charge carriers. In p-type semiconductor, the majority charge carriers are holes (positive charge), while in n-type semiconductor, the majority charge carriers are electrons (negative charge).

3. How does the electron concentration in p-type semiconductor affect its conductivity?

The electron concentration in p-type semiconductor is lower compared to n-type semiconductor. This results in lower conductivity in p-type semiconductor because there are fewer charge carriers available to carry the current.

4. What factors can affect the electron concentration in p-type semiconductor?

The electron concentration in p-type semiconductor can be affected by the doping concentration, temperature, and impurity type. Higher doping concentration and lower temperature can increase the electron concentration, while the type of impurity used for doping can also affect it.

5. How is the electron concentration in p-type semiconductor measured?

The electron concentration in p-type semiconductor can be measured using various techniques such as Hall effect, capacitance-voltage measurement, or optical spectroscopy. These techniques involve applying an external magnetic field, voltage, or light to the semiconductor and measuring the resulting changes in properties such as resistance, capacitance, or absorption.

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