add the first semiconductor lecture

README.md

@@ -26,7 +26,7 @@
   (based on chapters 15–16)  
   Exercises 15.1, 15.3, 15.4, 16.1, 16.2
 
-* Week 7: Semiconductors  
+* Week 7: [Semiconductors](lecture_7.md)  
   (based on chapters 17–18)
 
 * Week 8: Magnetism  

SUMMARY.md

@@ -6,5 +6,5 @@
 * [Electrons and phonons in 1D](lecture_4.md)
 * [Crystal structure and diffraction](lecture_5.md)
 * [Tight binding and nearly free electrons](lecture_6.md)
-* Semiconductors
+* [Semiconductors](lecture_7.md)
 * Magnetism

lecture_2.md

@@ -186,3 +186,21 @@ $$
 ![](figures/transport.svg)
 
 The orange circle represents the Fermi surface at finite current $\rightarrow$ this circle will shift only slightly before the electrons reach terminal velocity $\rightarrow$ all transport takes place near the Fermi surface.
+
+## Useful trick: scaling of $C_V$
+
+Behavior of $C_V$ can be very quickly memorized or understood using the following mnemonic rule
+
+> Particles with energy $E \leq kT$ are thermally excited, and each carries extra energy $kT$.
+
+#### Example 1: electrons
+
+$g(E_F)$ roughly constant ⇒ total energy in the thermal state is $T \times [T\times g(E_F)]$ ⇒ $C_V \propto T$.
+
+#### Example 2: graphene with $E_F=0$ (midterm 2018)
+
+$g(E) \propto E$ ⇒ total energy is $T \times T^2$ ⇒ $C_V \propto T^2$.
+
+#### Example 3: phonons in 3D at low temperatures.
+
+$g(E) \propto E^2$ ⇒ total energy is $T \times T^3$ ⇒ $C_V \propto T^3$.
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