AC. IMPEDANCE OF CON T ACT RECTlinER 433 



Provided tliuL the barrier heiglit, F„ + Va, is as much as several times kT/e,^ 

 the integrand in both integrals is largest near x = and drops rapidly with 

 increase in x. Where the integrand is large we inay write to a sufficient ap- 

 proximation: 



F = F„ + F„. - Fx, (7) 



where /*' is the field in the semiconductor at the interface. The approxima- 

 tion (7) may be used if kT/eF is small compared with the thickness of the 

 barrier layer. The value of d-V/dxdl is nearly constant over the important 

 part of the integration and may be replaced by its value at x = and taken 

 out of the integral. The upper limit .ti may be replaced by x without ap- 

 I)reciable error, so that we get finally: 



where 



and 



/(/) = Im{Q){l - exp [-eVJkT]) + dQ/dt, (8) 



Im{Q) = (4we M Q He/K) cxp [-eVJkT] (9) 



Q = kF/4w (10) 



is the surface charge density at the metal interface. 



The current Im{Q) has a simple interpretation; it is just the conduction 

 current in the semiconductor at the interface resulting from the field F. 

 In equilibrium, this conduction current is balanced by a diffusion current 

 of equal magnitude and opposite sign. A voltage Va applied in the reverse 

 direction reduces the diffusion current at the interface as compared with 

 the conduction current by the factor exp [—eVa/kJ]. The current dQ/dl 

 is the displacement current at the interface. 



Actually, the diffusion theory as given above is not complete. The Schottky 

 effect, the lowering of the barrier by the image force, has been neglected. 

 There may be appreciable tunneling through the barrier. There may be a 

 patch field resulting from nonuniformity of the barrier. If the variations 

 in the patch fields are not too large, the modification of current resulting 

 from these factors depends only on the field at the metal and not on the 

 form of the barrier at some distance from the metal. Thus we may expect 

 the form (8) to be generally valid if /„ (Q) is considered to be a general 

 function of Q. Equation (10) is also of the form to be expected from the diode 

 theory.^ In the latter case, I,„{Q) is the thermionic emission current from 

 metal to semiconductor. 



If the current is varying in time it is the instantaneous value of Q at 



' The value of kT/e at room temperature is .025 volts. 



