WAFER TYPE MILLIMETER WAVE RECTIFIERS 1399 



itf Rs , assuming a circular contact area, may be calculated from the for- 

 mula, Rs = p/4ri .* For the above example, Rs = 18 ohms. 



Barrier Resistance 



The approximate operating value of the barrier resistance, /?, may be 

 determined from a knowledge of the intermediate frequency impedance 

 of a typical rectifier. A. B. Cra^^^ord has sho-wn that the optimum inter- 

 mediate frequency output impedance of a crystal mixer rectifier is a 

 function of the exponent of the static characteristic of the rectifier and 

 the impedance presented to the rectifier at the image and signal fre- 

 quencies. This information is presented in Fig. 12.3-6 in G. C. South- 

 worth's book.f In the millimeter wave case it is a good assumption that 

 the impedances for the signal and image frequencies are equal; for this 

 case and for matched conditions, the magnitude of the high frequency 

 impedance is seen to be a simple multiple of the intermediate frequency 

 impedance Rif • 



From numerous measurements on mixer rectifiers operating at differ- 

 ent frequencies it is known that the intermediate frequency impedance 

 of an average rectifier is very nearly 400 ohms. We also know from the 

 DC static characteristics of our millimeter wave type rectifiers that the 

 average exponent is about four. With this information, and the curves 

 in Southworth's book, it is found that R ^ Rif/1.5. Thus, the barrier 

 resistance R is about 250 ohms.| 



Capacitance of Barrier Layer 



From a knowledge of the point contact area, the barrier layer thick- 

 ness, and the dielectric constant of the silicon, the capacitance of the 

 point contact may be calculated. The radius of the contact point area is 

 the same as that used for the calculation of the spreading resistance. The 

 barrier layer thickness, h, for the heat treated silicon used for millimeter 

 waves has been measured by R. S. Ohl to be about 10' meters. The 

 dielectric constant of sihcon is fr = 13. The capacitance is given by the 

 following formula 



^& 



2 



* J. H. Jeans, Mathematical Theory of Electricity and Magnetism, 5th Ed., 

 Cambridge University Press, 1925. 



t G. C. Southworth, Principles and Applications of Waveguide Transmission, 

 New York: D. Van Nostrand Co., Inc., 1950. 



t This resistance cannot be readily measured directly at millimeter waves. 



