DC FIELD IN A ''sWEPT INTRINSIC" SEMICONDUCTOR 669 



and 



E and p are continous at ?/ = L. (10) 



Finally, we choose the reference level for the electric potential in the 

 intrinsic region so that 



^ = f or n = p (11) 



and regard the potential at the interface ?/ = as a prescribed parameter, 



;/, = !^ . [/ at 2/ = 0. (12) 



The two conditions (11) and (12) apply directly to the solutions for 

 the intrinsic region. The conditions (7)-(10) indirectly imply the two 

 additional restraints necessary to determine a unique solution of (1')- 

 (40 inO < y < L. 



NORMALIZED VARIABLES AND EQUATIONS 



It is convenient to introduce dimensionless normalized variables 

 before proceeding further with the mathematical analysis. As reference 

 voltage it is natural to adopt the Boltzmann voltage 



rl^B^—, (13) 



Q 



the voltage equivalent of the mean kinetic energy of an electron at 

 temperature T. (At room temperature the Boltzmann voltage is about 

 1/40 of a volt.) As reference quantity for carrier concentrations we 

 choose the geometric mean of the majority carrier excess concentrations 

 for the two extrinsic regions, i.e., 



reference concentration = (NP)^^l (14) 



The reference voltage and carrier concentration having been so chosen, 

 it is natural to select as reference length the mean Dehye length 



£ = 



kT/q 



2 2 (Arp)i/2 



1/2 



(15) 



K 



This mean Debye length is related by 



£ = {£n£py" (16) 



to the n-region and p-region Debye lengths defined respectively by 



