Calculating Hole & Electron Concentrations at 343K

Your Name]In summary, the problem involves a silicon semiconductor with an area of 4mm2 and a temperature of 343K. The concentration of holes is given as 1.47*1015 cm-3 and the mobilities of carriers are 390 cm2/Vs and 970 cm2/Vs. To solve this problem, you will need to calculate the intrinsic carrier concentration (ni) at 343K using the formula ni(T) = A*T^(3/2)*e^(-Eg(T)/2kT), where A and Eg(T) are constants that can be found in a reference book or online. From there, you can use the formula n(343K) = ni^2
  • #1
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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)=ni2/p
But I need to calculate intrinsic ni for 343K temperature, right? If I use this formula ni(T) = A*T3/2*e(-Eg(T)/2kT) I might calculate A for 300K but I still need Eg, the forbidden zone energy level to calculate ni at 343K. Help!
 
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  • #2


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!
 

1. What is the formula for calculating hole concentration at 343K?

The formula for calculating hole concentration at 343K is: p = ni²/n, where p is the hole concentration, ni is the intrinsic carrier concentration, and n is the number of acceptor impurities.

2. How do I calculate electron concentration at 343K?

The formula for calculating electron concentration at 343K is: n = ni²/p, where n is the electron concentration, ni is the intrinsic carrier concentration, and p is the number of donor impurities.

3. What is the intrinsic carrier concentration at 343K?

The intrinsic carrier concentration at 343K can be calculated using the formula: ni = (n₀p₀)^(1/2) * exp(-Eg/2kT), where n₀ and p₀ are the effective density of states for electrons and holes, Eg is the band gap energy, k is the Boltzmann constant, and T is the temperature in Kelvin.

4. How does temperature affect hole and electron concentrations?

As temperature increases, the number of thermally generated carriers (electrons and holes) also increases. This results in an increase in both hole and electron concentrations. However, the effect is more pronounced for electrons due to their lower effective density of states compared to holes.

5. Can the hole and electron concentrations be calculated at any temperature?

No, the formulas for calculating hole and electron concentrations at 343K assume that the material is in thermal equilibrium. This means that the temperature must not be too high to cause significant carrier recombination or too low to significantly affect the effective density of states. In most cases, the formula is applicable for temperatures between 0K to 300K.

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