Silicon is doped an acceptor of 10^18/cm^3. Find the electron and hole concentration, the electron and hole mobilities, and the resistivity of this silicon material at 300 K. Is this n-type or p-type?

You might find the equation you need at

http://pvcdrom.pveducation.org/SEMICON/NI.HTM

The previous reference I provided won't help you. It is for intrinsic silicon only.

There is a discussion of doped semiconductor electron and hole concentrations at
http://ecee.colorado.edu/~bart/book/book/chapter2/ch2_6.htm?pagewanted=all

Good luck. This is not my field of expertise

To find the electron and hole concentrations, we need to understand the concept of doping. Doping is the process of intentionally adding impurities to a semiconductor material, such as silicon, to modify its electrical properties. In this case, silicon is doped as an acceptor.

Given that silicon is doped as an acceptor with a concentration of 10^18/cm^3, it means that each acceptor atom introduces one extra hole in the crystal lattice. Therefore, the hole concentration (p) is equal to the acceptor concentration:

p = 10^18/cm^3

To determine whether the material is n-type or p-type, we compare the electron and hole concentrations. If the electron concentration (n) is larger than the hole concentration (p), the material is n-type. Otherwise, if p is larger than n, the material is p-type.

The electron concentration depends on the temperature and the intrinsic carrier concentration (ni) of silicon. At room temperature (300 K), the intrinsic carrier concentration for silicon is approximately:

ni ≈ 1.5 × 10^10/cm^3

To find the electron concentration, we'll use the equation for an intrinsic semiconductor:

n × p = ni^2

Since we know the hole concentration (p) and the intrinsic carrier concentration (ni), we can solve for the electron concentration (n):

n = ni^2 / p

n = (1.5 × 10^10/cm^3)^2 / (10^18/cm^3)
n ≈ 2.25 × 10^2/cm^3

So, the electron concentration (n) is approximately 2.25 × 10^2/cm^3.

Now, let's move on to the electron and hole mobilities. The mobility of charge carriers represents their ability to move through the semiconductor material under the influence of an electric field. The electron mobility (μn) and hole mobility (μp) depend on various factors and can vary significantly. As an approximation, we'll use typical values for silicon at 300 K:

Electron mobility (μn) ≈ 1350 cm^2/Vs
Hole mobility (μp) ≈ 450 cm^2/Vs

Finally, we can calculate the resistivity (ρ) of the silicon material using the following formula:

ρ = 1 / (q × (μn × n + μp × p))

where q is the elementary charge (1.6 × 10^-19 C).

ρ = 1 / (1.6 × 10^-19 C × (1350 cm^2/Vs × 2.25 × 10^2/cm^3 + 450 cm^2/Vs × 10^18/cm^3))

Calculating this expression gives us the resistivity of the silicon material.

Upon knowing the resistivity value, we can determine whether the material is n-type or p-type. If the resistivity is relatively low, it is an indication of high electron conductivity, making it n-type material. In contrast, if the resistivity is high, it implies higher hole conductivity, making it p-type material.

In conclusion, to determine if the silicon material is n-type or p-type, we compare the electron and hole concentrations. If n is greater than p, it is n-type. Otherwise, if p is greater than n, it is p-type.