Physics of Semiconductor Devices

Effective mass

In a semiconductor where the bottom of the conduction band is at k = 0, an electron moves with a wavenumber k = 10⁹ m^-1.

(a) If the effective mass of electrons in the conduction band is 0.5 m_e, what is the energy of this electron measured from the bottom of the conduction band?

(b) Electrons in the conduction band will occupy some states up until about k_BT above the bottom of the conduction band. What is the maximum value of k that electrons would have from thermal fluctuations at room temperature? What consequences does this have for a light emitting diode?