X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=solid_state_physics%2Ftutorial%2F1_05s.tex;h=d33f033a35945a148a78cdd041f4c2cac0dca391;hp=9c3b7079a6b010d8bb07af956bde370fc9a81b9a;hb=183bd2b78445842ee859e2f10f8ab9dc84cf2776;hpb=4e2fe58f21aef3283a47ab44a8b8250c0bd501cc

diff --git a/solid_state_physics/tutorial/1_05s.tex b/solid_state_physics/tutorial/1_05s.tex
index 9c3b707..d33f033 100644
--- a/solid_state_physics/tutorial/1_05s.tex
+++ b/solid_state_physics/tutorial/1_05s.tex
@@ -55,12 +55,10 @@
 		      \approx 4\pi k^2dk$
 	      \end{itemize}
 	      $\Rightarrow dZ'=\frac{\frac{1}{8}4\pi k^2dk}{(\pi/L)^3}$
-        \item Express $dk$ and $k$ by $dE$ and $E$ and insert it into $dZ$:
-              \begin{itemize}
-               \item $\frac{dE}{dk}=\frac{\hbar^2}{m}k \rightarrow
-	              dk=\frac{m}{\hbar^2k}dE$
-               \item $k=\frac{\sqrt{2m}}{\hbar^2}\sqrt{E}$
-	      \end{itemize}
+        \item Express $dk$ and $k$ by $dE$ and $E$ and insert it into $dZ$:\\
+              $\frac{dE}{dk}=\frac{\hbar^2}{m}k \rightarrow
+	       dk=\frac{m}{\hbar^2k}dE$\\
+              $k=\frac{\sqrt{2m}}{\hbar^2}\sqrt{E}$\\
 	      $\Rightarrow dZ'=\frac{4\pi k^2m}{(\pi/L)^3\hbar^2k} dE=
 	       \frac{4\pi\frac{\sqrt{2m}}{\hbar}\sqrt{E}m}{8(\pi/L)^3\hbar^2}dE
 	       =\frac{(2m)^{3/2}L^3}{4\pi^2\hbar^3}\sqrt{E}dE$\\
@@ -75,7 +73,18 @@
  \item Curvature of the band:\\
        $\frac{d^2E}{dk^2}=\frac{d^2}{dk^2}\frac{\hbar^2k^2}{2m_{eff}}
                          =\frac{\hbar^2}{m_{eff}}$
- \item
+ \item \begin{minipage}{0.5\textwidth}
+         $m_n=m_p$:\\
+         \includegraphics[width=5cm,angle=-90]{dos_is_1.eps}
+         \includegraphics[width=5cm,angle=-90]{fermi_1.eps}
+         \includegraphics[width=5cm,angle=-90]{ccc_1.eps}
+	\end{minipage}
+	\begin{minipage}{0.5\textwidth}
+         $m_n \ne m_p$:\\
+         \includegraphics[width=5cm,angle=-90]{dos_is_2.eps}
+         \includegraphics[width=5cm,angle=-90]{fermi_2.eps}
+         \includegraphics[width=5cm,angle=-90]{ccc_2.eps}
+	\end{minipage}
 \end{enumerate}
 
 \section{'Density of state mass' of holes in silicon}