含义Meaning
光子能量大于带隙才能把电子从价带激发到导带。由此可从吸收边或发光峰估算带隙，并解释半导体的颜色与光伏响应范围。
Photons need energy above the band gap to promote electrons from valence to conduction band; the absorption edge or emission peak therefore gives E_g and explains a semiconductor’s colour and photovoltaic range.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(E_g\) | 带隙band gap | eV |
| \(\alpha\) | 吸收系数absorption coefficient | cm⁻¹ |
| \(h\nu\) | 光子能量photon energy | eV |
推导Derivation
\(E = h\nu = hc/\lambda\)，代入 \(hc = 1239.84\ \mathrm{eV\,nm}\)。
\(E = hc/\lambda\) with hc = 1239.84 eV nm.
吸收边附近，直接带隙材料 \(\alpha \propto (h\nu - E_g)^{1/2}/h\nu\)，间接带隙 \(\alpha \propto (h\nu - E_g)^2/h\nu\)（需声子参与）。
Near the edge α ∝ (hν−E_g)^{1/2} (direct) or (hν−E_g)² (indirect, phonon-assisted).
以 \((\alpha h\nu)^{1/n}\) 对 hν 作图，直线段外推到零即得 E_g。
Extrapolate the linear part of the Tauc plot to zero.
适用条件与局限Assumptions & limitations
激子吸收、缺陷态（乌尔巴赫带尾）、量子尺寸效应会使吸收边偏移或变缓。
Excitons, defect tails (Urbach) and quantum confinement shift or smear the edge.
例题Worked example
Si 1.12 eV → 1107 nm；GaAs 1.42 eV → 873 nm；TiO₂（锐钛矿）3.2 eV → 388 nm（只吸收紫外，故为白色）。
Si 1.12 eV → 1107 nm; GaAs 1.42 eV → 873 nm; anatase TiO₂ 3.2 eV → 388 nm (white).