Abstracts of Technical Articles from Bell System Sources 



The Thermionic Work Function and the Slope and Intercept of 

 Richardson Plots} J. A. Becker and W. H. Brattain. This article 

 is a critical correlation of the slope and intercept of experimental 

 Richardson lines with the quantities appearing in theoretical equations 

 based on thermodynamic and statistical reasoning. The equation 

 for experimental Richardson lines is log i — 2 log T — log A — b/2.3 T; 

 A and b are constants characteristic of the surface, i is the electron 

 emission current in amp./cm.^, T is the temperature in degrees K, log .4 

 is the intercept and —b/2.3 is the slope of experimental lines. Statis- 

 tical theory based on the Fermi-Dirac distribution of electron velocities 

 in the metal shows that i should be given by log i — 2 log T = log 

 f/(l — r) — w/2.3 T, where C/ is a universal constant which has the 

 value 120 amp./cm.^ "K^, r is the reflection coefficient, and w is the 

 work function. A correlation of the experimental and theoretical 

 equations shows that b = w — Tdw/dt, and log A = log U{\ — r) 



— {\l2.3)dwldT. Only when r is and the work function is inde- 

 pendent of the temperature, is it correct to say that the slope is 



— w/2.3 and that the intercept has the universal value log U. But 

 even when w is a function of T, it follows from a thermodynamic 

 argument that the slope is given by —h/2.3, where the heat function h 

 is defined by ^ = {Lp/R) — (5/2) T, Lp is the heat of vaporization per 

 mol at constant pressure. The heat function is related to the work 

 function by the equation h = w — TdwjdT. 



From experimental and theoretical arguments it is deduced that the 

 reflection coefficient is probably negligibly small. Hence we conclude 

 that for most surfaces the work function varies with temperature, since 

 the intercepts of Richardson lines are rarely equal to log 120. This 

 conclusion is to be expected since on Sommerfeld's theory, w depends 

 on the number of free electrons or atoms per cm.\ which in turn varies 

 with temperature due to thermal expansion. 



The photoelectric work function should equal the thermionic work 

 function but should not in general be equal to —2.3 times the slope of 

 the Richardson line. The Volta potential between two surfaces having 

 work functions Wi and Wi should equal {wi — w^ikje rather than 2.3kje 

 times the difference between the slopes of the Richardson lines for the 

 two surfaces. The data from photoelectric and Volta potential meas- 



^Phys. Rev., May 15, 1934. 



516 



