# Fraction of ionized atoms in an intrinsic semiconductor

• theBEAST
In summary, the conversation discusses the concept of intrinsic semiconductors and their behavior in regards to donors and acceptors. The solution presented defines the fraction of donors and acceptors to be ni/(5*1022), but there is a question about whether it should be 2*ni/(5*1022) since there are both donors and acceptors present. The conversation also brings up the point that intrinsic silicon should not have any donors or acceptors, but the solution explains that some silicon atoms can become ionized by thermal energy, creating an electron-donor pair and leaving a positive ion behind.
theBEAST

## Homework Statement

Here is the problem in the book:

Here is the solution:

What I don't get is why the solution defines the fraction to be ni/(5*1022). Shouldn't it be 2*ni/(5*1022) since we have both donors and acceptors, so there are actually twice the number of atoms.

Also, intrinsic means that the silicon is not doped right? If that is the case why are there even donors and acceptors, shouldn't the concentrations be zero?

theBEAST said:
What I don't get is why the solution defines the fraction to be ni/(5*1022). Shouldn't it be 2*ni/(5*1022) since we have both donors and acceptors, so there are actually twice the number of atoms.

Also, intrinsic means that the silicon is not doped right? If that is the case why are there even donors and acceptors, shouldn't the concentrations be zero?

There are no donors, no acceptors in an intrinsic semiconductor. Some silicon atoms get ionized by thermal energy. One of the electrons of a silicon atom gains enough energy to escape from its ion, which means leaving the valence band and becoming a "free" electron in the conduction band. The escaped electron leaves a positive ion behind, which means lack of an electron, a "hole" in the valence band.

So excitation of a silicon atom produces an electron-donor pair and leaves one positive ion behind.

ehild

## 1. What is an intrinsic semiconductor?

An intrinsic semiconductor is a type of material that has a natural ability to conduct electricity. It is made up of pure elements, such as silicon or germanium, and has a balanced number of electrons and holes, making it electrically neutral.

## 2. How is the fraction of ionized atoms calculated in an intrinsic semiconductor?

The fraction of ionized atoms in an intrinsic semiconductor is calculated by dividing the number of ionized atoms by the total number of atoms in the material. This can be expressed as a percentage or decimal value.

## 3. What factors affect the fraction of ionized atoms in an intrinsic semiconductor?

The fraction of ionized atoms in an intrinsic semiconductor is affected by temperature, impurities, and the band gap of the material. As temperature increases, more atoms become ionized. Impurities can also increase the number of ionized atoms. The band gap determines the energy required for an atom to become ionized.

## 4. How does the fraction of ionized atoms affect the conductivity of an intrinsic semiconductor?

The fraction of ionized atoms directly impacts the conductivity of an intrinsic semiconductor. As more atoms become ionized, more charge carriers are available for conduction, increasing the material's conductivity. Conversely, a lower fraction of ionized atoms will lead to lower conductivity.

## 5. How is the fraction of ionized atoms different from the doping concentration in an intrinsic semiconductor?

The fraction of ionized atoms refers to the percentage or number of atoms that have lost or gained an electron, while the doping concentration refers to the number of impurities added to the material to alter its electrical properties. In an intrinsic semiconductor, the fraction of ionized atoms is equal to the doping concentration, as there are no intentional impurities added to the material.

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