266 BELL SYSTEM TECHNICAL JOURNAL 



the space charge of the conduction electrons. Thus, if no is the normal 

 concentration of electrons/^ 



P = eno (4.5) 



Integration of the space charge equations gives a parabolic variation of 

 potential with distance, and the potential rise, (fb, is given in terms of the 

 thickness of the space charge layer, /', by the equation 



(Ph = 2irep(r/K = lire-nof/^/K (4.6) 



For 



(Pb = (fs — <Peo '^ 0.5 e.v. '^ 8 X 10~^^ ergs 



and 



Wo ~' W^/cm^ 



the barrier thickness, ^, is about 10^^ cm. The dielectric constant, k, 

 is about 18 in germanium. 



When a voltage, Va, is applied to a rectifying contact, there will be a 

 drop, Vb, across the space charge layer itself and an additional drop, IR^, 

 in the body of the germanium which results from the spreading resistance, 

 Rs, so that 



Va= Vb + IRs. . (4.7) 



The potential energy drop, —eVb, is superimposed on the drop cpb which 

 exists under equilibrium conditions. For this case Eq. (4.6) becomes 



^, _ eVb = 2TehioP/K (4.8) 



The potential Vb is positive in the forward direction, negative in the re- 

 verse. A reverse voltage increases the thickness of the layer, a forward 

 voltage decreases the thickness of the layer. The barrier disappears when 

 eVb = <Pb, and the current is then limited entirely by the spreading resist- 

 ance in the body of the semi-conductor. 

 The electrostatic field at the contact is 



F = 4Teno^/K = {STnio(fb-eVb)/Ky'^ (4.9) 



For Ho ~ W\ I ^ 10"^ and k ~ 18, the field F is about 30 e.s.u. or 10,000 

 volts/ cm. The field increases the current flow in much the way the current 

 from a thermionic emitter is enhanced by an external field. 



Previous theories of rectification have been based on the flow of only one 

 type of carrier, i.e. electrons in an n-type or holes in a p-type semi-conduc- 

 tor. If the barrier layer has an inversion region, it is necessary to consider 

 the flow of both types of carriers. Some of the hitherto puzzlmg features 



