# 2.4.4 Summary to: Conductors - Special Applications

- Page ID
- 2772

[ "article:topic", "Richardson equation" ]

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

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

for free electron gas model*A*_{theo}= 120 A · cm^{–2}· K^{–2}

*A*_{exp}≈ (20 - 160) A · cm^{–2}· K^{–2}work function*E*_{A}=**≈ (2 - >6) eV**- Materials of choice:
**W**,**LaB**single crystal_{6}

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 through a metal - metal (or metal - semiconductor) junction induces a temperature gradient I∝, i.e. one of the junction may "cool down".I |
Used for electrical cooling of (relatively small) devices. Only big effect if electrical heating (∝ ) is small.I^{2} |