Determination of elementary charge e from measurements of shot-effect

Abstract

Probability fluctuations in thermionic emission (shot effect).Schottky first pointed out that if the electrons evaporate independently of each other, probability fluctuations of current are to be expected. These fluctuations were observed and roughly measured by Hartmann. Measurements have now been made, using a much higher frequency (750×103) and a reliable arrangement for measuring the small r.m.s. voltages (od order 10-4) due to the effect. The method involves the measurement of the alternating current excited in a tuned circuit by the probability variations in the electron current through a vacuum tube (radiotron, UV 199), the Schottky equation for the mean square current being J2=i0e2RC where i 0 is the thermionic current, R and C the resistance and capacity of the tuned circuit and e the electronic charge. To measure the current, it is amplified by a known amount (using a special 4 stage amplifier) and is rectified so that its r.m.s. value may be determined with a d.c. meter. It is important that the rectifier be used only in the range in which it gives a current proportional to the square of the impressed voltage. The tuned circuit picks out a narrow band of frequencies present in the fluctuations, and since the amplification is not the same for frequencies slightly different from the resonance frequency, correction is made for this by a factor F, for which a mathematical expression is derived and values are obtained by integration or summation. Calibration of the amplifier is avoided by substituting, after each reading of the amplified and rectified shot-current, a measured pure sine voltage across the terminals of the tuned circuit, which is adjusted to give the same rectified current as the effect. Calling this v1 the actual mean square shot voltage v02=v12F and J2=Cv12LF where L is the inductance of tuned circuit. It was found that with currents limited by space charge, the observed effect might be only 20 per cent of the theoretical; but with currents limited only by temperature, the agreement was within one per cent. The effect may therefore be used to study the effect of space charge on electronic evaporation. Determination of elementary charge e, by the shot effect.Using temperature limited thermionic current, values of e were obtained which lie within two per cent of the mean, and this mean, 4.76×10-10 e.s.u., agrees closely with Millikan's value. The precision of these measurements can be greatly increased, so as perhaps to exceed that of the oil-drop measurements. Study of secondary electronic current from an electrode by means of the shot effect.Using a special tube with an extra grid, conditions were adjusted so that the primary and secondary currents balanced, yet a shot voltage of 79×10-6 volt was observed. This is exactly the value to be expected if both primary and secondary currents gave a full effect independently of each other, as would be the case if secondary electron emission is due, not to reflection or splashing, but to excitation and subsequent evaporation. This effect promises to furnish a powerful instrument for the study of such electronic phenomena. Measurement of microvoltages of radio frequency.A method was developed which enables a voltage of 20×10-6 to be measured within one per cent, and which is capable of extension to much smaller voltages. © 1925 The American Physical Society.