The Richardson-Dushman equation relates the current density of a thermionic emission to the work function (W) and temperature (T) of the emitting material:
js = A T2 exp(-W/kT)
where
js is the current density of the emission
(mA/mm2)
A is Richardson's constant. A =
4*πmek2/h3 ~ 1202
mA/mm2K2, where m is the mass of electron, e is
elementary charge, and h is Plank's constant. In practice, A may be
multiplied by a correction factor that depends on the material (see
Table I below).
Note that A varies from about 32 to 160 A cm-2 K-2
for pure (polycrystalline) metals and over a much greater range
for oxide and composite surfaces.[1]
T is temperature (K)
W is the work
function of the cathode material (J or eV)
k is the Boltzmann constant (1.3806488E-23 J K-1 or 8.6173324E-5 eV K-1) [*]
In Cathode Emissions in CPO, A is treated as an empirical constant. In fact, js may be entered directly.
| Material | W (eV) | A*b (A cm-2 K-2) (b is material correction factor) |
|---|---|---|
| Molybdenum | 4.15 | 55 |
| Nickel | 4.61 | 30 |
| Tantalum | 4.12 | 60 |
| Tungsten | 4.54 | 60 |
| Barium | 2.11 | 60 |
| Cesium | 1.81 | 160 |
| Iriduim | 5.40 | 170 |
| Platinum | 5.32 | 32 |
| Rhenium | 4.85 | 100 |
| Thorium | 3.38 | 70 |
| Ba on W | 1.56 | 1.5 |
| Cs on W | 1.36 | 3.2 |
| Th on W | 2.63 | 3.0 |
| Thoria | 2.54 | 3.0 |
| BaO + SrO | 0.95 | ~10-2 |
| Cs-oxide | 0.75 | ~10-2 |
| TaC | 3.14 | 0.3 |
| LaB6 | 2.70 | 29 |
| theoretical: | 120.2 (b=1) |
References
- [1] Bernhard Wolf. Handbook of ion sources. CRC Press, 1995. ISBN 0849325021, 9780849325021. p.27,11 [*]
- [2] C. J. Smithells, Metals Reference Book, Vol III, Butterworths, London, 1967, 737ff.
- [3] Wikipedia:Thermionic Emission [*]
- [4] CODATA2010 http://physics.nist.gov/cuu/index.html