Thermionic Emission Constants and Band Overlap

A general treatment is given of the effect of band overlap on thermionic emission. The results are applied to nickel, for which the experimental value of the current constant A of 1380 amp. cm^-2 deg^-2 differs markedly from the standard value of 120 amp. cm^-2 deg^-2. The case of nickel has recently been discussed by Sun Nien T'ai and Band (1946), who derive an expression for the variation of A with temperature. It is shown that their relation strictly applies only to "holes" in an isolated d-band and is reliable only over a temperature range such that kT/_0d is considerably less than unity, _0d being the unoccupied width of the d-band. With an overlapping s-band, as in nickel, there is an increasing transfer of electrons from the d-band as the temperature rises. The effect is strongly dependent on the ratio r₀ = ₀₈/_0d' where ₀₈ is the occupied width of the s-band. Expressions are derived and precise calculations carried out for the transfer effect and the variation of A over a range 0.0 ⩽ kT/_0d ⩽ 1.0 (including temperatures up to about 2000° K.), and for r₀ values of 10, 20 and ∞. The last corresponds in effect to an isolated d-band. The results of the calculations are shown in figures 2 and 3. A comparison with the experimental value of A is made using a value of _0d estimated from thermal and magnetic data. The satisfactory agreement previously obtained is due to the adoption of a value of the bandwidth which is incompatible with the experimental evidence, and it is shown that the calculated and observed values of A actually differ by a factor of about 6. Various reasons for this discrepancy are discussed, especially the effect of surface impurities.