430 BEI.I. SYSTEM TECILXfCAL JOlliNAL 



being occupied by electrons; those below the Fermi level are most likely 

 unoccupied. Holes are depleted from the barrier layer, leaving the negative 

 space charge of the acceptors. This negative space charge, together with 

 the compensating positive charge on the metal, gives the potential energy 

 barrier which impedes the flow of holes from semiconductor to metal. The 

 thickness of the barrier layer may vary from 10^ to 10"^ cm, depending on 

 the materials forming the contact. 



In drawing the diagram of Fig. 2 it has been assumed for simplicity that 

 the concentration of acceptors is uniform over the region of interest. In the 

 main body of the semiconductor only a few of the acceptors are charged. 

 Throughout a large part of the barrier layer practically all acceptors are 

 negatively charged and there are very few holes in the filled band. This 

 part of the barrier layer has been called by Schottky the exhaustion region 

 and is in our case a region of uniform space charge, as shown in the lower 

 diagram of Fig. 2. The transition zone in which the concentration of holes 

 is decreasing and the concentration of charged acceptors is increasing is 

 called the reserve region. 



In thermal equilibrium, with no applied volatge, the potential drop across 

 the barrier layer, Vm, may be a fraction of a volt. If a voltage is applied in 

 such a direction as to make the semiconductor positive relative to the metal, 

 the effective height of the barrier is reduced and holes flow more easily 

 from the semiconductor to the metal. This is the direction of easy flow. If 

 a voltage is applied in the opposite dhection the height of the barrier is 

 increased for holes going from semiconductor to metal and remains un- 

 changed, to a first approximation, for holes going from metal to semiconduc- 

 tor (actually electrons going from the filled band of the semiconductor to 

 the metal). This is the reverse or high resistance direction. 



If a voltage is applied in the reverse direction, and equilibrium is estab- 

 lished, the thickness of the exhaustion layer mcreases. The reserve region 

 keeps the same form but moves outward from the metal. A forward voltage 

 decreases the thickness of the space charge layer. 



The change in charge density corresponding to a small reverse voltage is 

 shown schematically by the curve marked hQ in the lower diagram of 

 Fig. 2. The maximum of 5() occurs where the total charge density is changing 

 most rapidly with distance. If / is the distance from the metal to this maxi- 

 mum, the effective capacitance C, is approximately that of a parallel plate 

 condenser with plate separation I and with the dielectric constant of the 

 medium equal to that of the semiconductor. The capacitance decreases as / 

 increases with a d-c. bias applied in the reverse direction and the capaci- 

 tance increases with forward bias. Schottky'' has shown that information 



* Walter Schottky, Zeitsf. Fliys. 118. 53^ [WAD. 



