PIU.XCN'LKS OF TRAXSLSTOR ACTIOS 267 



of the germanium diode characteristic can be explained by the hole current. 

 While a complete theoretical treatment has not been carried out, we will 

 give an outline of the factors involved and then give separate discussions 

 for the rcA-erse and forward directions. 



The current of holes may be expected to be imj)ortant if the concentra- 

 tion of holes at the semi-conductor boundary of the space charge layer is as 

 large as the concentration of electrons at the metal-semi-conductor inter- 

 face. In equili])rium, with no current tiow, the former is just the hole con- 

 centration in the interior, ;/;,ii, which is given by 



n,,n = Ch r'- exp{-^,o/kT), (4.10) 



where (fho is the energy difference between the Fermi level in the interior 

 and the top of the filled band. The concentration of electrons at the inter- 

 face is given by: 



nr,n = Ce T"'' exp(- ^J kT) . (4.11) 



Since Ch and C, are of the same order, him will be larger than iiem if <Ps is 

 larger than (pi,o. This latter condition is met if the hole concentration at 

 the metal interface is larger than the electron concentration in the interior. 

 The concentrations will, of course, be modified when a current is flowing; 

 but the criterion just given is nevertheless a useful guide. The criterion 

 applies to an inversion barrier layer regardless of whether it is formed by 

 the metal contact or is of the surface states type. In the latter case, as 

 discussed in the Introduction, a lateral flow of holes along the surface layer 

 into the contact may contribute to the carrent. 



Two general theories have been developed for the current in a rectifying 

 junction which apply in different limiting cases. The diffusion theory 

 applies if the current is limited by the resistance of the space charge layer. 

 This will be the case if the mean free path is small compared with the thick- 

 ness of the layer, or, more exactly, small compared with the distance re- 

 quired for the potential energy to drop kT below the value at the contact. 

 The diode theory ai)plies if the current is limited by the thermionic emission 

 current over the barrier. In germanium, the mean free path (10~^ cm) 

 is of the same order as the barrier thickness. Analysis shows, however, 

 that scattering in the barrier is unimportant and that it is the diode theory 

 which should be used.^^ 



Reverse Current 



Different parts of the d-c. current-voltage characteristics require sepa- 

 rate discussion. We deal first with the reverse direction. The applied 

 voltages are assumed large compared with kT/e (.025 volts at room tem- 

 perature), but small compared with the peak reverse voltage, so that ther- 



