# 2.4.4 Summary to: Conductors - Special Applications

Thermionic emission provides electron beams. The electron beam current (density) is given by the Richardson equation:

$j=A\cdot T^2 \cdot \text{exp}\left(-\frac{E_A}{kT}\right)$

• Atheo = 120 A · cm–2 · K–2 for free electron gas model
Aexp  (20 - 160) A · cm–2 · K–2
• EA = work function  (2 - >6) eV
• Materials of choice: WLaB6 single crystal

High field effects (tunneling, barrier lowering) allow large currents at low T from small (nm) size emitter

Needs UHV!

There are several thermoelectric effects for metal junctions; always encountered in non-equilibrium.

 Seebeck effect:  Thermovoltage develops if a metal A-metal B junction is at a temperature different form the "rest", i.e. if there is a temperature gradeient Essential for measuring (high) temperatures with a "thermoelement" Future use for efficient conversion of heat to electricity ??? Peltier effect: Electrical current I through a metal - metal (or metal - semiconductor) junction induces a temperature gradient ∝I, i.e. one of the junction may "cool down". Used for electrical cooling of (relatively small) devices. Only big effect if electrical heating (∝ I2) is small.