Richardson-Dushman Equation¶

The Richardson-Dushman equation relates the current density of thermionic emission to the work function (W) and temperature (T) of the emitting material:

$j_s = A T^2 exp(-W/kT)$

where

$j_s$ is the current density of the emission (mA/mm^2)
$A$ is Richardson’s constant. $A = 4 p m e k^2/h^3 \approx 1202 \, mA/mm^2K^2$ , where $m$ is the mass of electron, $e$ is elementary charge, and $h$ is Plank’s constant. In practice, $A$ is emperical and 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) [*]

Table 1: Work functions and Richardson’s constants for various materials [1,2] (b is material correction factor).

Material	W (eV)	A*b (A cm-2 K-2)
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)


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Richardson-Dushman Equation¶

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