Calculating the number of quantum states in the valence and conduction bands

[jisbon]

Homework Statement

Calculate the number of quantum states per cm cube in GaP in the valence and conduction band, given that the mass density is 4.13g/cm^3

Relevant Equations

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Hi all,
This question asks me to calculate the number of quantum states, as well as electrons per cm^3 of the crystal in the room temperature.
The problem is I only dealt with a single element before without any calculation for 1cm^3 whatsoever. For example for a Silicon semiconductor, I can determine that a-Si atom share four valence electrons (2 from its 3s and 2 from 3p states) to form a stable configuration, hence only the 3s and 3p states are involved, whereby the number of states, in this case, is 8N (2+6) from the 3s and 3p state, whereby the upper band contains 4N states and lower band aka the valence band contain 4N states.

So in the question I presented, I will need to calculate the number of atoms/cm^3 to find what is N first. Hence, first, amt of GaP = mass/Mr. Hence in 1cm^3, I can find that the amount = 4.13/(69.72+30.974) = 0.0410 mol = 2.469*10^22 atoms. So N = 2.469*10^22

Now here comes the problem, how many N states are there? Since now there are 2 elements, how do I combine them together to form a lattice if GaP does not have any spare valence electrons to bond with other GaP atoms to form the crystal lattice? How can I find what are the states involved in GaP for bonding with other GaP atoms?

Thanks

 

[LightHero]

in advance.The number of quantum states depends on the crystal lattice structure of the GaP material. You can calculate it from the number of atoms/cm^3 and the number of electrons per atom. The number of electrons per atom is determined by the valence state of the two elements. In this case, Ga has 3 valence electrons and P has 5, so the total number of electrons in a GaP lattice would be 8 per atom.To calculate the number of quantum states, you need to know the number of sites in the unit cell of the lattice. This is usually determined by the coordination number of the lattice, which indicates how many nearest neighbors each atom has. For example, in a simple cubic lattice, each atom has 6 nearest neighbors and the coordination number is 6.Once you have the coordination number, you can calculate the number of quantum states as follows:Number of quantum states = N * (number of electrons per atom)^(coordination number)where N is the number of atoms/cm^3.In the case of GaP, the coordination number is 8, so the number of quantum states is 2.469*10^22 * 8^8 = 9.42*10^30 states.The number of electrons per cm^3 is simply the number of electrons per atom multiplied by the number of atoms/cm^3, which in this case is 2.469*10^22 * 8 = 1.97*10^24 electrons/cm^3.