Calculating Hole & Electron Concentrations at 343K

[aarnes]

Homework Statement

Silicon with area of 4mm² has on the temperature of 343K concentration of holes 1.47*10¹⁵ cm^-3. Moveability(?) of carriers (sorry, english isn't my native language) is 390 cm²/Vs and 970 cm²/Vs.

Homework Equations

Calculate:

a) Concentration and type of added impurities and concentration of major and minor carriers.​

b) Electron and hole current and total current through semiconductor if on it acts electrical field of 8Vcm.​

The Attempt at a Solution

n(343K)=n_i²/p
But I need to calculate intrinsic n_i for 343K temperature, right? If I use this formula n_i(T) = A*T^3/2*e^{(-E_g(T)/2kT)} I might calculate A for 300K but I still need E_g, the forbidden zone energy level to calculate n_i at 343K. Help!

 

[KataKoniK]

Thank you for your question. I understand that English is not your native language, so I will try my best to explain the solution clearly. To calculate the intrinsic carrier concentration (ni) at 343K, you will need to use the formula ni(T) = A*T^(3/2)*e^(-Eg(T)/2kT), where A is a constant and Eg(T) is the bandgap energy of silicon at 343K. The bandgap energy of silicon at 300K is 1.12 eV, but it changes with temperature according to the formula Eg(T) = Eg(300K) - αT^2/(β+T), where α and β are constants. You can find these values in a reference book or online.

Once you have calculated ni at 343K, you can use the formula n(343K) = ni^2/p to find the concentration of majority carriers (electrons) and the type of impurities added. The concentration of minority carriers (holes) is given in the problem as 1.47*10^15 cm^-3.

To calculate the electron and hole current, you can use the equations Jn = qμnEn and Jp = qμpEp, where q is the charge of an electron, μn and μp are the carrier mobilities, and En and Ep are the electric fields acting on the electrons and holes, respectively. The total current can be found by adding the electron and hole currents.

I hope this helps. If you have any further questions, please don't hesitate to ask. Good luck with your calculations!