Finding Free Electrons and Hole Concentration

[asd1249jf]

Homework Statement

Silicon is doped with an Aluminum Concentration of 2 X 10^16 cm^-3

What are the free electron and hole concentrations at room temperature?

What are the electron and hole mobilities at 300K?

What is the majority carrier? What is the minority carrier?

Homework Equations

n_0 * p_0 = (n_i)^2 [[(Concentration of Electrons) * ( Hole Concentration) = (Intrinsic Carrier Concentration)^2]]

n_i = 1.5 X 10^10 cm^-3 [[For Silicon]]

The Attempt at a Solution

This is actually for my electronics class, but this is more of a chemistry type question so I posted here.

I've missed few lectures and I'm already lost. Can anyone just start me off, provide me some hints and equations I should use to find the mobility?

As for the majority/minority carrier part, I understand that if the semiconductor is n-type, electrons are the majority carrier and holes are the minority carriers and the opposite for the p-type. How do you tell which type of material this is?

 

[Astronuc]

Please try not to miss class. Presumably one's textbook contains the necessary information.

For semiconductor like Si, if one adds trivalent atoms (Group 13 (IIIA) e.g. B, Al, Ga) to the Si lattice, the trivalent atoms will tend to accept loosely bound valence electrons from the Si atoms. This will produce a p-type semiconductor. Similarly, if adds pentavalent atoms (Group 15 (VA), e.g. N, P, As, Sb) to the Si lattice, the pentavalent atoms will donate an electron to the lattice, and this produces an n-type material.

See this - http://hyperphysics.phy-astr.gsu.edu/hbase/solids/semcn.html

and http://ece-www.colorado.edu/~bart/book/book/chapter2/ch2_6.htm

http://www-ee.ccny.cuny.edu/www/web/crouse/EE339/Lectures/Charge_Carrier_Statistics.htm

 

[piercas]

To find the free electron and hole concentrations at room temperature, we can use the equation n_0 * p_0 = (n_i)^2 where n_0 is the free electron concentration and p_0 is the hole concentration. The intrinsic carrier concentration, n_i, can be calculated using n_i = 1.5 X 10^10 cm^-3 for silicon. Plugging in the values, we get n_0 * p_0 = (1.5 X 10^10 cm^-3)^2 = 2.25 X 10^20 cm^-6. This means that at room temperature, the free electron concentration and hole concentration are both 2.25 X 10^10 cm^-3.

To find the electron and hole mobilities at 300K, we can use the Einstein relation mu = q * D where mu is the mobility, q is the charge of an electron, and D is the diffusion coefficient. The diffusion coefficient can be calculated using D = k * T / q where k is the Boltzmann constant and T is the temperature in Kelvin. Plugging in the values, we get D = (1.38 X 10^-23 J/K) * (300K) / (1.6 X 10^-19 C) = 2.59 X 10^-3 cm^2/s. Using this value for D, we can then calculate the mobilities for both electrons and holes.

To determine the majority and minority carrier, we need to know the type of material we are dealing with. In this case, the aluminum doping suggests that the silicon is n-type, meaning that the majority carrier is electrons and the minority carrier is holes. If the silicon had been doped with a group III element, such as boron, it would be p-type and the majority carrier would be holes and the minority carrier would be electrons.