IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-29, NO. 1, MARCH 1980 Contactiess Measurement of Silicon Resistivity in Cylindrical TEoln Mode Cavities STANISIAW DMOWSKI, JERZY KRUPKA, AND ANDRZEJ MILEWSKI Abstract-This paper presents a new contactless method of resistivity measurement of semiconductor plates which is being applied in the production practice with the use of microwave cylindrical TEo 1 nmode resonators The errors of resistivity measure- ment have been shown in the example of silicon plates and the TEol3 mode cavity working in the X band. It has been shown that for the plates of thickness 100-1200 gum and diameters larger than 60 percent of the diameter of the cavity, silicon resistivity can be measured in the range of 10- 6102 Q - m, accurate to several percent. Experimental verification of the present method has been made by comparison of the results of silicon resistivity measured by the conventional four-point probe method. I. INTRODUCTION R ECENTLY MUCH concern has been given to develop- ing new methods of resistivity measurement of semi- conducting materials. On the one hand, it is concerned with higher accuracy of the resistivity measurement, and on the other, with certain imperfections of current measurement methods. Among the imperfections of the most frequently used method-the point probe method-are necessity of special preparation of the sample surface, difficulties in the determination of the resistivity measurement error, and finally, difficulties in resistivity measurement of some mate- A2 2 (2) O A2 co Fig. 1. Cylindrical TEO,. mode cavity with the sample axially placed on its bottom. h is the sample thickness, 2b is the sample diameter, 2a is the cavity diameter. II. THEORETICAL ANALYSIS OF THE PRESENTED METHOD Krupka et al. [7] have used the perturbation method to determine the relation between resistivity of the test sample and the Q-factor and resonant angular frequency of a cylindrical TEO,,, mode cavity (Fig. 1). It is made based on an assumption that the electromagnetic field distribution in a resonant cavity which is filled with a sample of any diameter (Fig. 1) is analogical to the case ofthe cavity which is filled with the sample of a diameter equal to the cavity diameter. Substitution of equivalent distributions of electro- magnetic fields in such a cavity, for a perturbation formula, leads to the following equation: 1 - sin [( zO- P)(L -h)] sin [(kzo + I3z)(L - h)] sin (k h) I (i [ kZ- s z + fs (Lh) 1+ G(b)(sin [Qkz. -fiz)h] -sin [(lC' + I3z)h]sn[zL-h) (1) rials, e.g., Aii,Bv type semiconductors. The contactless method of resistivity measurement has overcome such defects. Among these contactless methods, microwave methods [2]-[8] are of increasing importance. The theoreti- cal basis of the new microwave method [7], [8] has been worked out recently. It allows for the measurement of complex permittivity of cylindrical semiconducting samples with any dimension in the cylindrical TEO,,, mode cavity. This paper gives an analysis of the method and its applica- tion in resistivity measurement of silicon plates. Manuscript received September 29, 1978; revised December 1, 1978, March 15, 1979, and October 12, 1979. The authors are with the Institute of Electron Technology, Warsaw Technical University, Koszykowa 75, Warsaw 00-662, Poland. where G(b) = fJ (Irb) + J2(f b) 2J 0 (#frb)J1 ]r(b) b)2 J(U,1) 1Z = ()C2,60 '(z0 = (@CEoio -_ 2)1/2 fir = U'0P a n7r flZ L Jo, J1 Bessel functions of the first kind of the zero and the first order, 0018-9456/80/0300-0067$00.75 ©) 1980 IEEE 67