. The Bell System technical journal . uations (27) and (28) follow from equation (19). It is alsoinstructive to compare equation (28) with the corresponding equationwhich is based on classical statistics, namely, iV(Fn)<f Fn = nieyiTrmkT)^ exp. (- Vne/kT)dV„. (29) This is readily derived from equation (8). d. Comparison between classical and quantum-mechanical between equations (28) and (29) is best brought out by agraph such as Fig. 1 which shows log N(Vn) versus Vn for the twocases. It is to be remembered that N{V„)dV„ is the number of elec-trons in the metal which st
. The Bell System technical journal . uations (27) and (28) follow from equation (19). It is alsoinstructive to compare equation (28) with the corresponding equationwhich is based on classical statistics, namely, iV(Fn)<f Fn = nieyiTrmkT)^ exp. (- Vne/kT)dV„. (29) This is readily derived from equation (8). d. Comparison between classical and quantum-mechanical between equations (28) and (29) is best brought out by agraph such as Fig. 1 which shows log N(Vn) versus Vn for the twocases. It is to be remembered that N{V„)dV„ is the number of elec-trons in the metal which strike 1 cm.^ of surface per second whose THERMIONIC ELECTRON EMISSION 423 energy components normal to the surface are in the range (F„, dVn)volts. It has been customary to plot iV(F„) versus F„ for equation(28). At r = 0, N{V,) decreases linearly with F„ from a value of / rv-vne\ FERMI-DIRAC N (Vn) = ^^^i ^ (^H-£~io^j / e2 \!^ Vne CLASSICAL N(Vn)=n(^^^^^^j fyj K= VOLTS (l FREE ELECTRON PERATOM ASSUMED FOR TUNGSTEN). Vn IN VOLTSFig. 1—Classical and Fermi-Dirac distributions. lirGemk/h^ when F„ = 0, to zero when Vn = K/e; for F„ > K/e,^(^n) — 0. For 7 > 0, the function is much the same except in theneighborhood of F„ = K/e and for F„ > K/e; the curve is hereeverywhere higher than the curve for 2 = 0 and decreases exponen-tially. Since only those electrons can escape for which Vn — Pm> (3/2)ir, we are primarily interested in the exponential portion ofthe curve. It is therefore more advantageous to plot log 7V(F„)rather than 7V(F„). In Fig. 1 curves 1 and 2 are for equation (28) at 2 = 0 andT — 1800° K., respectively; while curve 3 is for the classical case orequation (29). For curves 1 and 2, the value of K/e has been takenas volts which is the value appropriate for tungsten assuming one 424 BELL SYSTEM TECHNICAL JOURNAL free electron per atom. For curve 3 the value of n has been so chosenthat this curve is shifted with resp
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