For an electron gas generated in the inversion layer of a semiconductor interface, my book gives the conduction band density of states for the two dimensional electron gas as:(adsbygoogle = window.adsbygoogle || []).push({});

##g(E)=\frac{L^2m^*}{\hbar^2 \pi}##

Where m^{*}is the effective mass of the electron. I can't follow how this was exactly derived.

So the density of state is given by

##g(E)=2g(k) \frac{dk}{dE}##

Where

##E=\frac{(\hbar k)^2}{2m} \implies \frac{dE}{dk}= \frac{\hbar^2 k}{m}##

And also the density of states per spin: ##g(k) k dk = 2 \frac{L_x L_y}{\pi} k dk##

Hence substituting I've got:

##g(E) = \frac{2\times 2 L^2 k m}{\pi \hbar^2 k} =\frac{4L^2 m}{\hbar^2 \pi}##

But why do I end up with a "4" on the numerator? Did I make a mistake, or is that a typo in the book?

Any response is greatly appreciated.

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# Band density of states

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