How can we calculate the impurity (dopant) carrier (electrons and holes) concentration in the host material at 0K by DFT calculations and at room temperature by using semi-classical theory or some alternative method?
Is there anyway to calculate the impurity carrier concentration with BoltzTraP code?
I am vasp user.
Dear Muhammad,
welcome,
As for the calculation of the carrier concentration in doped crystalline semiconductors one uses the following rules:
The material is known in the sense, its effective density of states in the conduction band Nc and valence band Nv,its energy gap , and the intrinsic concentration ni.
The doping concentration and the energy level of the dopant in the energy gap, that is the ionization energies. Also the temperature is assumed.
- The mass action law is valid such that n0p0=ni^2. n0,p0 are electron and and hole concentration,
- The neutrality equation is valid such that Nd+ + p0= Na- +n0, where Nd+ and N- are ionized impurities concentration,
- The final and third rule is that the fermi statistics is valid: f(E)= 1/( 1+ exp ( E-Ef)/kT,
These three rules are used to calculate n0, and p0.
There are many simplification assumptions to estimate n0 and p0..
The DFT may be used to determine the donor and acceptor levels as well as the density function of states. instead of determining them on experimental basis.
Best wishes
∆E (q) f = E (q) tot − 1 2 (nAl + nSb) µ bulk AlSb − 1 2 (nAl − nSb) µ bulk Al − µ bulk Sb + ∆µ + q (EVBM + µe).
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