xmpl2d61, 61st 'example' data file for CPO2D
Extended Schottky emission, spherical cathode.
Based on test2d13, field emission cathode. Please see the notes in that file about the choice of step lengths. See also xmpl3d16.
This example is of course artificial -real Schottky emission cathodes are sharp points mounted usually on cones. When simulating real cathodes it is important to follow the advice on setting up the ray paramerters. Please also see general information on field emission.
The cathode and anode have radii of 1m and 1cm respectively, the cathode-anode voltage difference is 1000V, the work function of the cathode is 2.7eV, and the temperature is 1800K. A modification of the Richardson-Dushman equation is used, as given by Hawkes and Kasper. The initial velocity components are randomised.
The field at the cathode is 1.0001E7 V/cm and the value of kT is 0.15506 eV, corresponding to T = 1800 K.
Equation 44.42 of Hawkes and Kasper (Principles of Electron Optics, Academic Press, 1989) is used in this program to calculate the current density when the 'extended Schottky emission' option is called. For the present parameters the potential barrier is lowered by delta_w = 1.200 eV, the quantity q is 0.5173 and so the current density is 3.985*10^5 mA/mm^2 (that is, 3.985*10^4 A/cm^2). This can be compared with the more accurate current density calculated numerically by A B El-Kareh, J C Wolfe and J E Wolfe, J Appl Phys, vol 48, 4749 (1977), and reported by J E Wolfe, J Vac Sci Tech, vol 16, 1704 (1979). Reading from Fig 3 of the latter paper, the current density is 9*10^4 A/cm^2, which is more than twice as large as that given by equation 4.42 of Hawkes and Kasper. The agreement would be better for smaller fields or higher temperatures.
The current emitted by the present cathode should be 5.008 mA (according to equation 44.42). In fact in the present example it is 4.999 mA.
It can be noticed in the ray output file that there is a randomised component in the energies.
Please see the footnotes of xmpl3d16 for further information.