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Study of Space Charge Limitation of Thermionic Cathodes in Triode Guns

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Study of Space Charge Limitation of Thermionic Cathodes in Triode Guns Scanning Electron Microscopy Volume 3 Number 1 3rd Pfefferkorn Conference Article 17 1984 Study of Space Charge Limitation of Thermionic Cathodes in Triode Guns A. Delâge National Research Council Canada P. B. Sewell National Research Council Canada Follow this and additional works at: https://digitalcommons.usu.edu/electron Part of the Biology Commons Recommended Citation Delâge, A. and Sewell, P. B. (1984) "Study of Space Charge Limitation of Thermionic Cathodes in Triode Guns," Scanning Electron Microscopy: Vol. 3 : No. 1 , Article 17. Available at: https://digitalcommons.usu.edu/electron/vol3/iss1/17 This Article is brought to you for free and open access by the Western Dairy Center at DigitalCommons@USU. It has been accepted for inclusion in Scanning Electron Microscopy by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. Electron Optical Systems (pp. 171-178) SEM Inc., AMF O'Hare (Chicago), IL 60666-0507, U.S.A. STUDY OF SPACE CHARGELIMITATION OF THERMIONIC CATHODESIN TRIODE GUNS A. Delage and P.B. Sewell Division of Elect rical Enginee ring National Research Council Canada Ottawa, Ontario KlA OR6 Canada Abstract Introduction A computer program has been developed to In electron microscopes equipped with compute the emission of cathodes from the fully thermionic sources , the filament is often used in space charge limited diode equation. The the regime of space charge limitation in or der to emission of four different gun arrangements with provide the gun with a higher stability . In this thermionic cathodes of the type used in electron regime the electron emission is in principle microscopes is investigated. Microflat cathodes determined entirely by the cloud of electrons with a small( ~ SOµm in diameter) fixed emitting produced in front of the cathode and is area show several advantages for high brightness independent of the characteristic emission of the possibilities whereas other types of cathodes for cathode itself, provided it can emit a sufficient which the emitting area increases with the number of electrons. The emission is then brightness are usually limited by too great a controlled by the field in front of the cathode total emission. and can be adjusted by varying the Wehnelt potential. Since the life of the cathode is very dependent on its operating temperature, this is generally chosen such that the filament is on the border of the space charge limitation. This regime makes the emission independent of the filament temperature and the nature of the filament itself. The direct replacement of the tungsten filament by a better emitter such as LaB6 would be almost imperceptible if the gun operating parameters remain the same. 1n order to improve the brightness obtained from triode guns a detailed investigation of space-charge limitation is necessary. Thermionic Emission A computer program has been developed to calc ul ate the emission from a cathode taking into account the space charge and th e possible temperature limitation of the cathode. This program follows the technique described by Kirs t ein et al 3 • It is based on the theoretical maximum current that can be drawn from a one ­ dimensional diode. Before discussion of this KEY WORDS: Thermionic emission computation, technique, some basic concepts of thermionic Space-charge simulation, Thermionic cathodes, emission are considered. Microflat cathodes, Triode elect r on gun , Diode electron gun, Low voltage gun The simple model of the free electron gas in a metal 7 describes successfully the thermionic Address for correspondence: emission of solids in terms of only two A. Delage, Division of Electrical Engineering parameters: the temperature T and the work National Research Council Canada, Ottawa, Ontario function </; associated with a particular metal. Canada, KlA OR6 Phone No.: (613) 993-2304. The model predicts a current density given by Richa rdson's equation: 171 A. Dela ge and P.B. Sewell List of Symbols A Constant in the Richardson's equation ve (R,Z) Solution of the potentials exclusively 1 : 120 A. cm- 2 . K- 2 due to the electrode a rran ge ment D Diameter (µm) of the emitting area in Solution of the potentia l s exc lu sively equation (14) due to the space char ge in the gun th E Electric field (vm- 1 if not specified) V at the n iteration SC G (4/9)£ (2e/m)~: 2 . 34 x 10- 6 A.V-l. S 0 z Axial matrix coo rdinat e (integer) in th e G' G/z 0 network method I(r) Current emitted by an annulus on the d Separation cathode-anode in the diode cathode, of mean radius rand a width model t, r th dt Integration step of the traj ec tor y I(r) after the n iter a tion 19 th e Electronic charge (1. 602 x 10- c ) Total current emitted after the n h Mesh size of the grid in the network it e ration method J Current density in Aicm 2 k Boltzmann's constant 1.38 x 10- 23 J .K- 1 J J given by Richardson ' s equation, also 0 m Electronic mass 9.1 x 10- 31 kg called th e temp e rature limitation n(v )dv Density of electrons havin g a speed J(T,E) z z J given by Schottky ' s equation between v and v + dv J Space charge li mit e d J, also called th e z z z SC r The radi a l coordinate space charge limit a ti on Radius of th e small a r ea in the center Jsc for th e diode gun with a limited of the cathode emitting area v v v Electron speeds in the model of el ect ron N x' y' z Number of trajectories issued from eac h gas in metal annulus on the ca thod e z The axial coordinate N Density of e le ctrons in the model of the 0 z Position of th e potential minimum e l ec tron gas in metal m z Axial posi tion where the Child - Langmuir Q( R, Z) 0 The space cha r ge density term for each equation is app li ed mesh of the gr id used in the network f3 Bri ghtn ess in A cm- 2 sr- 1 method y Under-relaxation factor (0 ~ y ~ l; R Radial matrix coordinate (integer) in ideal value 0 . 667 ) th e network method width of an emitting annulus on the s Surface on th e emi ttin g cathode ca thode T Abs olut e temperature (K) !:,vol Volume e lement associated with eac h cell V Pote nti a l minimum (V) m of the me sh in the network method Anode pot en tial co rr espond in g to the VA £ Vac uum permittivity 8 .85 X 10- 12 C/V .m 0 ene r gy of the el ect rons a t the anode (b Work function of th e ca th ode material ( V) (V) V(z ) Axial potential in th e gun (V) J (T,0); A T2 exp(- efb/kT) (1) In the mode of space charge limitation th e 0 barrier Vm produces an emission dens it y simply This equation giv es the thermal limitation given by 4: of th e cathode . In fac t the presence of the electron cloud or the presence of a purely ( 3) attractive field E (without the electron cloud) will influ ence the hei~ht of th e barrier that the As mentioned previously the local field in e l ectrons have to cross at the surface of the front of the cathode will determine the height of so lirl. In the first cas e the space charge gives V . Unfortunately th e relation between this a supplementary barrier (Vm on Fig . lb) that will fTeld (prior to emission) and Vr.i is not known be added t o 0 while in the second case the except for the case of a one -di mension diode. reduction of the hei ght of th e barrier will lead 8 to Schot tk y emission : In a general approach it is possible to compute the emission from this model. It J(T,E) ; J exp {0,4403 /ITT ! (2) 0 consists of evaluating numerically the height of Vm by tr a cin g the trajectories of the el ec tron s (J and J in A/ cm2 , E in V/m and Tin de gree K) . 0 considering a gaussian velocity distribution as 172 Space - charge Limit a ti ons in Triode Gun stated in th e original gas model: V(o,zl V(o,z) This app roach is very t edio us since th e number of tr a jectori es to be calcula t ed is very large a nd only an ins i gnificant port ion succ ee d in going thr ough the barrier to form t he beam9 . It also contains ano th e r difficulty s inc e it d Z assumes th at we have t o r esolve the di s t a nce zm Vm between th e barrier and th e cathode, a distance lbl very small compared to th e l ength of th e beam. lol Fig . la Axi a l potential distribution in a diod e However this procedure can be overcome by (A) prior t o emission and (B ) at the full space ­ usi ng a slightly different ap pr oac h th a t includes charge limitati on . the evaluat i on of the emi ssion fo r the case of Fig .
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