270 BELL SYSTEM TECHNICAL JOURNAL 



of /3 may be as low as 10, and in other units are nearly as high as the theo- 

 retical value of 40. The factor h also varies among different units and is 

 of the order 10^" to 10~^ amperes. While both experiment and theory 

 indicate that the forward current at large forward voltages is largely com- 

 posed of holes, the composition of the current at very small forward volt- 

 ages is uncertain. Small areas of low <^.s-, unimportant at large forward 

 voltages, may give most of the current at very small voltages. Currents 

 flowing in these areas will consist largely of electrons. 



Above about 0.5 volts in the forward direction, most of the drop occurs 

 across the spreading resistance, R^, rather than across the barrier. The 

 theoretical expression for R, for a circular contact of diameter d on the 

 surface of a block of uniform resistivity p is: 



R, = p/2d (4.17) 



Taking as typical values for a point contact on high-back-voltage ger- 

 manium, p = 10 ohm cm. and d = .0025 cm, we obtain R, = 2000 ohms, 

 which is the order of ten times the obser\'ed. 



As discussed in the Introduction, Bray and others-'- - have attempted 

 to account for this discrepancy by assuming that the resistivity decreases 

 with increasing field, and Bray has made tests to observe such an effect. 

 The authors have investigated the nature of the forward current by making 

 potential probe measurements in the vicinity of a point contact.- These 

 measurements indicate that there may be two components involved in the 

 excess conductivity. Some surfaces, prepared by oxidation at high tem- 

 peratures, give evidence for excess conductivity in the vicinity of the point 

 in the reverse as well as in the forward direction. This ohmic component 

 has been attributed to a thin p-type layer on the surface. All surfaces 

 investigated exhibit an excess conductivity in the forward direction which 

 increases with increasing forward current. This second component is 

 attributed to an increase in the concentration of carriers, holes and elec- 

 trons, in the vicinity of the point with increase in forward current. Holes 

 flow from the point into the germanium and their space charge is compen- 

 sated by electrons. 



The ohmic component is small, if it exists at all, on surfaces treated in 

 the normal way for high-back- voltage rectifiers (i.e., ground and etched). 

 The nature of the second component on such surfaces has been shown by 

 more recent work of Shockley, Haynes-", and Ryder-^ who have investi- 

 gated the flow of holes under the influence of electric fields. These measure- 

 ments prove that the forward current consists at least in large part of holes 

 flowing into the germanium ffom the contact. 



It is of interest to consider the way the concentrations of holes and elec- 

 trons vary in the vicinity of the point. An exact calculation, including the 



