Effective mass of electron via energy

In solid state physics, a particle’s effective mass is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass.

Notation:

1. \(\hbar\) (hbar) is hbar.

Links:

1. Technische Universität Kiel, green box.

2. Wikipedia, fifth formula with adjustments.

effective_mass

Effective mass of the electron.

Symbol:

m_eff

Latex:

\(m_\text{eff}\)

Dimension:

mass

angular_wavenumber

angular_wavenumber.

Symbol:

k

Latex:

\(k\)

Dimension:

angle/length

energy

Electron energy as a function of angular wavenumber.

Symbol:

E(k)

Latex:

\(E{\left(k \right)}\)

Dimension:

energy

law

m_eff = hbar^2 / Derivative(E(k), (k, 2))

Latex:

\[m_\text{eff} = \frac{\hbar^{2}}{\frac{d^{2}}{d k^{2}} E{\left(k \right)}}\]