- #1
roam
- 1,271
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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:
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
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:
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.
##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.