Commit 9bfea0be by Isidora Araya

### Update 13_semiconductors_solutions.md

parent 6e02a9a4
 ... ... @@ -80,13 +80,17 @@ dispersion(10, 2, 8) ``` ### Subquestion 1 Apply the following to max an min of valence and conduction band, respectively: Apply the following to valence and conduction band, respectively: \$\$v=\hbar^{-1}\partial E(k)/\partial k\$\$ \$\$m_{eff} = \hbar^2\left(d^2 E(k)/dk^2\right)^{-1}\$\$ Be careful with hole calculations. These results assume \$t_{cb}\$ and \$t_{vb}\$ positive. \$\$v_e = \frac{2at_{cb}}{\hbar}sin(ka) \$\$ \$\$m_e = \frac{\hbar^2}{2a^2t_{cb}cos(ka)}\$\$ \$\$v_h = -\frac{2at_{vb}}{\hbar}sin(ka) \$\$ \$\$m_h = \frac{\hbar^2}{2a^2t_{vb}cos(ka)}\$\$ ### Subquestion 2 This approximation indicates the chemical potential is "well bellow" the conduction band and "well above" ... ... @@ -96,12 +100,14 @@ approximate Fermi statistics by Boltzmann's. For electrons, do a taylor expansion around \$k=0\$ (min) of \$E_{cb} = E_G - 2 t_{cb} [\cos(ka)-1],\$. For holes, do a taylor expansion around \$k=0\$ (max) of \$E_{vb} = 2 t_{vb} [\cos(ka)-1]\$. Assume \$t_{cb}\$ and \$t_{vb}\$ positive. ### Subquestion 3 ### Subquestion 4 \$\$n = \int_{E_{cb}}^{E_{cb}+4t_{cb}} f(\varepsilon)g_c(\varepsilon)d\varepsilon\$\$ \$\$p = \int_{-4t_{vb}}^{0} (1-f(\varepsilon))g_h(\varepsilon)d\varepsilon\$\$ \$\$n_e = \int_{E_{cb}}^{E_{cb}+4t_{cb}} f(\varepsilon)g_c(\varepsilon)d\varepsilon\$\$ \$\$n_h = \int_{-4t_{vb}}^{0} (1-f(\varepsilon))g_h(\varepsilon)d\varepsilon\$\$ ### Subquestion 5 For an intrinsic semiconductor the number of electrons excited into the conduction band must be equal ... ...
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