From bac0b6c5a075ad4db1397134c87b922b3c99afc5 Mon Sep 17 00:00:00 2001
From: Kostas Vilkelis <kostasvilkelis@gmail.com>
Date: Mon, 6 Apr 2020 12:06:59 +0000
Subject: [PATCH] fix E_F equation
---
src/13_semiconductors.md | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/src/13_semiconductors.md b/src/13_semiconductors.md
index eb2de5de..f080556c 100644
--- a/src/13_semiconductors.md
+++ b/src/13_semiconductors.md
@@ -227,7 +227,7 @@ $$n_h \approx N_V e^{-E_F/kT} = N_C e^{-(E_G-E_F)/kT} \approx n_e$$
Solving for $E_F$:
-$$E_F = \frac{E_G}{2} - \frac{3}{4}kT\log(m_e/m_h)$$
+$$E_F = \frac{E_C + E_V}{2} - \frac{3}{4}kT\log(m_e/m_h)$$
An extra observation: regardless of where $E_F$ is located, $n_e n_h = N_C N_V e^{-E_G/kT} \equiv n_i^2$.
--
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