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%TCIDATA{Created=Sat Feb 14 15:34:33 1998}
%TCIDATA{LastRevised=Thu Feb 25 12:53:05 1999}
%TCIDATA{Language=American English}

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\begin{document}


\textbf{1}. Explain why a transient current f\/lows when you touch a piece
of $n$-type semiconductor to a piece of $p$-type semiconductor. What is the
direction of current f\/low? What stops the current after a while? Similar
questions are in \textit{Bloomf\/ield}, p. 439.

\vspace{0.5cm}

\textbf{2}. \textit{Melissinos}, exercise 1.1.

(a) Look up the atomic mass number $A$, and density $\rho$ of $Si$ and $Ge$
and f\/ind the number of atoms per $\mathrm{cm}^3$.

(b) Assuming that the atoms are in a diamond structure ($8$ atoms/unit cell)
f\/ind the lattice spacing.

(c) Find the resistivity of $Ge$ at room temperature if it is doped with $%
10^{15}~\mathrm{atoms/cm^3}$ of $Sb$. Assume a mobility of the donor's
electrons of $\mu_e=1200~\mathrm{Cm^2/ V\cdot s}$.

\vspace{0.5cm}

\textbf{3}. \textit{Melissinos}, exercise 1.3.

Consider germanium doped with $10^{14}/\mathrm{cm^3}$ atoms of arsenic.

(a) Find the conductivity assuming a reasonable value of the mobility of the
impurities.

(b) The energy gap of germanium is $E_g=0.67~\mathrm{eV}$ and the density of
states at the edge of the conduction band can be taken as $N_c=10^{19}/%
\mathrm{cm^3}$. Estimate the intrinsic carrier density for germanium at room
temperature.

(c) Use the result of (b) to f\/ind the density of holes in the doped sample.

\textit{(Note that part (a) is closely related to part (c) of exercise 1.1.)}

\vspace{0.5cm}

\vspace{0.5cm}

\textbf{4}. \textit{Melissinos} exercise 1.4.

Make a plot of the Fermi-Dirac distribution at $T=-78^{\circ}\mathrm{C}$,
room temperature, and a $T=500^{\circ}\mathrm{C}$ when $E_F=1~\mathrm{eV}$.

\textit{(Accurate plots are expected. First plot for $0 < E < 2~\mathrm{eV}$
and then for $0.8~\mathrm{eV}<E<1.2~\mathrm{eV}$.)}

\vspace{0.5cm}

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