Question

10. Use the MATLAB command taylor to compute Taylor expansions of the Fermi-Dirac function: $f(E) = \frac{1}{e^{(E-E_F)/(k_BT)} + 1}$ where $k_B$ is Boltzmann's constant, $T$ is temperature, and $E_F$ is the Fermi energy. Take $E_F = 0$ and $k_BT$ to be 0.026 eV (its value at $T$=300 K). Taylor expand this function about $E = 0$ to different orders (from 1 to say, 10 terms). Plot the approximation of $f(E)$ for different orders of the Taylor expansion. Overlap this plot on top of the Fermi-Dirac func- tion. Show that as more terms are used in the Taylor expansion, the more accurate is the approximation to the Fermi function by Taylor expansion. (Include plot and MATLAB code with your homework.)

          10. Use the MATLAB command taylor to compute Taylor expansions of the Fermi-Dirac
function:
$f(E) = \frac{1}{e^{(E-E_F)/(k_BT)} + 1}$
where $k_B$ is Boltzmann's constant, $T$ is temperature, and $E_F$ is the Fermi energy. Take
$E_F = 0$ and $k_BT$ to be 0.026 eV (its value at $T$=300 K). Taylor expand this function about
$E = 0$ to different orders (from 1 to say, 10 terms). Plot the approximation of $f(E)$ for
different orders of the Taylor expansion. Overlap this plot on top of the Fermi-Dirac func-
tion. Show that as more terms are used in the Taylor expansion, the more accurate is the
approximation to the Fermi function by Taylor expansion. (Include plot and MATLAB code
with your homework.)

10. Use the MATLAB command taylor to compute Taylor expansions of the Fermi-Dirac
function:
f(E) = (1)/(e^(E-EF)/(kBT) + 1)
where kB is Boltzmann's constant, T is temperature, and EF is the Fermi energy. Take
EF = 0 and kBT to be 0.026 eV (its value at T=300 K). Taylor expand this function about
E = 0 to different orders (from 1 to say, 10 terms). Plot the approximation of f(E) for
different orders of the Taylor expansion. Overlap this plot on top of the Fermi-Dirac func-
tion. Show that as more terms are used in the Taylor expansion, the more accurate is the
approximation to the Fermi function by Taylor expansion. (Include plot and MATLAB code
with your homework.)

Added by Thomas O.

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