PRINCIPLES OF TRANSISTOR ACTION 263 



and the differential resistance about 5 X 10^ ohms. The ratio of the for- 

 ward to the reverse current at one volt bias is about 500. At a reverse 

 voltage of about 160 the differential resistance drops to zero, and with 

 further increase in current the voltage across the unit drops. The nature 

 of this negative resistance portion of the curv-e is not completely under- 

 stood, but it is believed to be associated with thermal effects. Successive 

 l)oints along the curve correspond to increasingly higher temperatures of 

 the contact. The peak value of the reverse voltage varies among different 

 units. Values of more than 100 volts are not difficult to obtain. 



Theories of rectification as developed by Mott,='*' Schottky," and others^ 

 have not been successful in explaining the high-back-voltage characteristic 

 in a quantitative way. In the following we give an outline of the theory 

 and its application to germanium. It is believed that the high forward 

 currents can now be explained in terms of a flow of holes. The type of 

 barrier which gives a flow of carriers of conductivity type opposite to that 

 of the base material is discussed. It is possible that a hole current also 

 plays an important role in the reverse direction. 



The Space-Charge L.4.yer 



According to the Mott-Schottky theor>^ rectification results from a 

 potential barrier at the contact which impedes the flow of electrons between 

 the metal and the semi-conductor. A schematic energy level diagram of 

 the barrier region, drawn roughly to scale for germanium, is given in Fig. 

 15. There is a rise in the electrostatic potential energy of an electron at the 

 surface relative to the interior which results from a space charge layer in 

 the serai-conductor next to the metal contact. The space charge arises 

 from positively ionized donors, that is from the same impurity centers 

 which give the conduction electrons in the body of the semi-conductor. 

 In the interior, the space-charge of the donors is neutralized by the space 

 charge of the conduction electrons which are present in equal numbers. 

 Electrons are drained out of the space-charge layer near the surface, leaving 

 the immobile donor ions. 



The space charge layer may be a result of the metal-semi-conductor con- 

 tact, in which case the positive charge in the layer is compensated by an 

 induced charge of opposite sign on the metal surface. Alternatively, the 

 charge in the layer may be compensated by a surface cliarge density of 

 electrons trapped in surface states on the semi-conductor.* It is believed, 

 for reasons to be discussed below, that the latter situation applies to high- 

 back-voltage germanium, and that a space-charge layer exists at the free 

 surface, independent of the metal contact. The height of the conduction 

 band above the Fermi level at the surface, <ps, is then determined by the 

 distribution in energ>' of the surface states. 



