\[V_H = \frac{IB}{nqt},\qquad R_H = \frac{1}{nq},\qquad \mu = \frac{|R_H|}{\rho}\]
含义Meaning
通电导体置于垂直磁场中，洛伦兹力使载流子偏向一侧，形成横向霍尔电压。其符号给出载流子类型（电子或空穴），大小给出载流子浓度，结合电阻率得到迁移率。
In a perpendicular magnetic field the Lorentz force pushes carriers sideways, producing a transverse Hall voltage whose sign gives the carrier type and whose size gives the carrier density; with resistivity it gives mobility.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(V_H\) | 霍尔电压Hall voltage | V |
| \(I\) | 电流current | A |
| \(B\) | 磁感应强度magnetic field | T |
| \(t\) | 样品厚度sample thickness | m |
| \(n\) | 载流子浓度carrier density | m⁻³ |
| \(\mu\) | 迁移率mobility | m²·V⁻¹·s⁻¹ |
推导Derivation
稳态时横向电场力平衡洛伦兹力：\(qE_H = qvB\)。
At steady state the transverse field balances the Lorentz force: \(qE_H = qvB\).
电流 \(I = nqvwt\)（w 为宽度），\(V_H = E_Hw\)。
Current \(I = nqvwt\) and \(V_H = E_Hw\).
消去 v 得 \(V_H = IB/(nqt)\)；电导率 \(\sigma = nq\mu\) 给出 \(\mu = \sigma R_H\)。
Eliminate v; with σ = nqμ, μ = σR_H.
适用条件与局限Assumptions & limitations
单一载流子模型；两种载流子共存时需加权（双极霍尔）。范德堡法要求样品均匀、接触点在边缘。
Single-carrier model; mixed conduction needs a two-band analysis; van der Pauw needs uniform samples.