## What is a semiconductor? From its name, the definition is given by conductivity, or say resistance, but a better evaluation would be band structure. Some properties may be taken to evaluate & see differences among metal, semiconductors, and insulators, they are 1. Resistivity (and conductivity) This is the original definition, by measuring the resistance, $R$, with given size ($A$, $L$), we have the resistivity, $\rho =R \frac{A}{L}$ and conductivity defined as $\sigma = \rho^{-1}$. metal has large conductivity, insulator has small conductivity, their typical values are listed below. metal: $\sim 10^{14}\ \Omega \cdot \text{cm}$, semiconductor: $10^{-2} \sim 10^9\ \Omega \cdot \text{cm}$, insulator: $\sim 2 \times 10^{-6} \ \Omega \cdot \text{cm}$. >[!Notice] >But for 2D case (like 2DEGs), $\rho$ has the unit $\Omega$. 2. Temperature response of resistivity ![[Drawing 2024-08-31 13.35.33.excalidraw.svg]] For metal, $\rho$ increases due to phonon-$e^-$ scattering; for insulator, the thermal profile possibly caused by increasing number of thermally populated $e^-$. Although specific value/temperature dependence of resistivity also depends on impurity, defects and other parameters. 3. Band structure and optical properties This is a fundamental difference, that insulators and semiconductors have a band gap, separating conduction band and valence band. Band gap (BG) is not common in metal, and $E_f$ for metal lies inside the conduction band (CB). See the band profile. ![[Drawing 2024-08-31 13.44.22.excalidraw.svg]] ![[Drawing 2024-08-31 14.08.47.excalidraw.svg]] This makes the photon absorption response different. For metal, energy is absorbed by $e^-$ of conduction band, getting to higher energy state. While for semiconductor, it's absorbed by valence band, crossing the band gap, so $E_{\text{photon}}$ has to be larger than $E_g$ to make absorption being non-zero. The decreasing behavior of metal for photon absorption $\alpha$ could be caused by a limited number of possible energy levels in a material, or by electron screening. Typical gaps are between $0 \sim 3$ eV, although it could be higher. >[!Note] >Some band gap values to be remember: >Si: 1.1 eV; Ge: 0.7 eV; GaAs: 1.5 eV; AlAs: 2.2 eV; AlN: 6.0 eV; C: 5.5 eV; SiO2: 9 eV. >Also at room temperature, $k_BT \approx 25 \ \text{meV}$, $k_{B}=8.6\times 10^{-5}\ eV/K$.