976 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



root of the applied voltage. The magnitude, voltage dependence, and 

 temperature dependence of the reverse currents can be explained as due 

 to space-charge generated current- with a trapping level 0.5 eV from 

 either the conduction or valence band. These effects will bo discussed 

 in Section II. 



In Section III the breakdown \'oItage and its dependence on the re- 

 sistivity and width of the high resistivity region of the rectifier will be 

 considered. 



In the next section the forAvard current is discussed and explained by 

 considering both a space-charge region generated current and a diffu- 

 sion current that takes into account high levels of minority carrier in- 

 jection.^ 



Device processing information is given in Section V, together with an 

 evaluation of different sources of high resistivity silicon. The devices 

 to be discussed in this paper have been processed with high resistivity 

 p-type material, although some devices have been made with ?i-type ma- 

 terial. 



Finally, a discussion of some surface problems associated with high 

 voltage rectifiers is given in Section VI. 



Although this paper is entitled "High-Voltage Conductivity-Modu- 

 lated Silicon Rectifier", the theoretical arguments are applicable to all 

 semiconductor diodes. However, the experimental results have been 

 limited by considering only high A'oltage diodes. 



II REVERSE CURRENT-VOLTAGE CHARACTERISTIC 



2.1 Theory 



The simple theory* for a p-n junction yields an expression for the re- 

 verse saturation current density (Id) which is: 



h = q 



(2-1) 



where q is the electron charge, np is the equilibrium electron density in 

 p-type material, pn is the equilibrium hole density in /i-type material, 

 D„ and Dp are the diffusion constants for electrons and holes, and r„ 

 and Tp are the minority carrier lifetimes for electrons and holes. 



When reasonable numbers are substituted into (2-1), h at room tem- 

 perature is of the order of 10"^" amperes per square centimeter. This 

 quantity doubles with every increase of 4° C. The theory also contains 

 no voltage dependence of this current. Even when breakdown multi- 

 plication^ is taken into account, there is essentially no voltage dependence 



