176 BELL SYSTEM TECHNICAL JOURNAL 



are Kelvin degrees or centigrade degrees; it plays the same role in equation 

 (1) as does the work function in Richardson's equation for thermionic 

 emission. For Material No. \, B — 392()C°. This corresponds to an elec- 

 tron energy equivalent to 3920 11600 or 0.34 volt. 



While the curves in Fig. 3 are approximately straight, a more careful 

 investigation shows that the slope increases linearly as the temperature 

 increases. From this it follows that a more precise expression for p is: 



, T — c PIT 



p = A 1 6 or 



log p = log .1 - r log T + D/2.303r (2) 



The constant c is a small positive or negative number or zero. For Ma- 

 terial No. 1, log A = 5.563, < = 2.73 and D = 3100. For a particular 

 form of Material No. 2 log .1 = 11.514, c = 4.83 and D = 2064. 

 If we define temperature coefilicient of resistance, a, by the equation 



a = {\/R) {(IR/dT) (3) 



it follows from equation (1) that 



a = -B/r. (4) 



For Material No. 1 and T - 300°K, a - -3920/90,000 = -0.044. For 

 platinum, a — +0.0037 or roughly ten times smaller than for semiconduc- 

 tors and of the opposite sign. From equation (2) it follows that 



«= -{D/D- (c/T). (5) 



From equation (3) it follows that 



a = (1 2.303) {(flogR'dT). (6) 



For a discussion of the nature of the conductivit}^ in semiconductors, 

 it is simpler and more convenient to consider the conductivity, a, rather 

 than the resistivity, p. 



a = \/p and logo- = —log p. (7) 



The characteristics of semiconductors are brought out more clearly if the 

 conductivity or its logarithm are plotted as a function of \/T over a wide 

 temj:;erature range. Figure 4 is such a j)lot for a number of silicon sam- 

 ples containing increasing amounts of impurity. At high temperatures 

 all the samples have nearly the same conductivity. This is called the 

 intrinsic conductivity since it seems to be an intrinsic properly of silicon. 

 At low temperatures the conductivity of different sami:)les varies by large 

 factors. Tn this region silicon is said to be an impurity semiconductor. 

 For extremely i)ure silicon only intrinsic conductivity is present and the 



