CND-09

Hall coefficient

R_H = 1 / (n e) for a single carrier of charge +e. Sign flips for electrons.

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Electrons in solidsHall

Governing equation

R_H=1/(ne)

$n \in \left[0.001, 20\right]$

where

n: Carrier density (10²⁸/m³)
R_H: Hall coefficient (10⁻¹⁰ m³/C)

The figure, part by part

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①

Governing law — red

R_H=1/(ne)

$n \in \left[0.001, 20\right]$

$n = 0.001$ $R_H = 6241.5$

Along the curve

②

Domain of the variable — blue

n_{\min} = 0.001,\quad n_{\max} = 20

$n \in \left[0.001, 20\right]$

$n = 0.001$ $n = 0.001$

Along the curve

③

Response curve — green

R_H=1/(ne)

$n \in \left[0.001, 20\right]$

$n = 0.001$ $R_H = 6241.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R_H}{\mathrm{d}n}

$n \in \left[0.001, 20\right]$

$n = 0.127$ $R_H^{\prime} = -24713$

Along the curve

Lecture brief

Historical brief

Drude electrons, Bloch waves, BCS pairing (1957) and Wiedemann–Franz heat are the first solids-and-metals laws. The lab is conductivity, gap and phonon heat in closed form. This sheet (CND-09 — Hall coefficient) is the form associated with Hall. Working symbols: $n$ $\rightarrow$ $R_H$ . V_H = R_H I B / t. A map of carrier density and sign in metals and semiconductors.

Purpose

Purpose: compute

R_H

from

n

in Condensed matter via

R_H=1/(ne)

R_H = 1 / (n e) for a single carrier of charge +e. Sign flips for electrons. Use it when a real condensed matter question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

n = 8.500\,\mathrm{10^{2}⁸/m^{3}}

, the governing relation

R_H=1/(ne)

yields

R_H = 0.734\,\mathrm{10⁻¹⁰ m^{3}/C}

. A bar, a B field, a transverse voltage. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Carrier density n8.5 10²⁸/m³

Outputs

Hall coefficient R_H0.734 10⁻¹⁰ m³/C

Reading speed

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Narration of this film

A bar, a B field, a transverse voltage.

V_H = R_H I B / t. A map of carrier density and sign in metals and semiconductors.

Reading speed

Watch on YouTube