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## Homework Statement

In silicon, E_g = 1.12 eV and the effective mass of the n-carriers is m* = 0.31*m_e, where m_e is the electron mass. Find the number densities of n-carriers at 100 K and at 300 K.

ans = _____ (n-carriers/cm^3)

## Homework Equations

n = N_c * e^-(E_c - E_f)/(kT)

or

n = N_c * e^-E_g/(2kT) (is this ok to use?)

N_c = 2 * ((m* * k * T)/(2*Pi*h-bar^2)) ^ (3/2)

not a typo here, it's m-star times k times T, etc.

## The Attempt at a Solution

I can get the answer at 300 K, because the energy gap E_g given works for room temperature, ie 300 K. what I can't get is the answer for when T = 100 K, where in my understanding the value of E_g is slightly larger. I've researched and found a Varshni empirical formula, three constants which are material properties specific to silicon. but this didn't end up helping, that is, my slightly larger value for E_g did not yield the correct answer.

my question is, am I right in thinking the central part of my mistake in the T = 100 K case is how E_g changes with temperature? or does it not change in this problem? Or is there another thing going on here that i'm ignoring/misinterpreting?

Tips or suggestions are very much appreciated on this one.

Thanks.

,Yroyathon