Homework Help: Semiconductor Physics - Density of States Calculation Problem?

1. The problem statement, all variables and given/known data

Determine the total number of energy states in silicon from the edge of the conduction band to E_c + kT for T = 300K.

2. Relevant equations

N = [itex]\int[/itex]g(E)dE

3. The attempt at a solution

I'm pretty sure I know how to do this one. The only problem is, when I get to the step where I have to plug in numbers (i.e. the equation becomes N = (2/3)(4[itex]\pi[/itex](2mn^*)^(3/2)*(kT)^(3/2))/h³), I cannot calculate it!

Reason: Obviously Planck's Constant cubed is an INCREDIBLY small number, and my calculator takes exception, just rounding to 0. There must be a way around it, or a rearrangement that helps, but I don't know what to do. Any advice? Sorry if my equation is formatted a little strangely.

 

Update: Realized I could use Google to calculate such a sum, and got the answer! Now I have a new problem.

The second part of that question asks for the same thing, but for the holes. It gives the effective hole mass as 5.10*10^-31. T = 298K this time. When I plug in the values, I get about 1.4*10^19 (in states /cm^3; my answer in m^3 is to the 10^25), but that's not correct. I'm quite confused as I believe I've put it in correctly.

Besides doing the calculation over again, I was wondering if there was a relationship between the electron state density and the hole state density that might allow me to approximate? I know the temperature differs by 2K.