Calibration method for rotating-analyzer ellipsometers

One of the main sources of errors in ellipsometry is inaccurate calibration; if the plane of incidence is not known correctly, all azimuthal angles of the optical components involved, such as the polarizer, the analyzer, and sometimes the compensator, contain errors. Thus calibration errors proliferate, leading ultimately to errors in the measured quantities A and *. Not withstanding the fact that the final errors in A and I can be eliminated in first order in a twozone measurement,1' 2 it is obvious that an accurate method of calibration is desirable. With the introduction of the rotating-analyzer ellipsometer (REA), an appropriate measuring technique for this type of ellipsometer was developed.35 First, the plane of incidence is determined by a technique that we shall call residue calibration, a method similar to the calibration methods used earlier in nulling ellipsometers.6 Second, once the plane of incidence is known, the signal-detection system can be calibrated. Finally, A and 'I can be obtained from a single measurement and the previously determined calibration parameters. In this way, the complete measurement consists of two parts, a calibration and the actual measurement. That other methods are possible as well was shown recently by Kawabata, who presented a method for a RAE to measure A and I without previous calibration (a kind of an integral method).7 In Kawabata's method, four quantities are measured, all of them with a finite accuracy, from which A and I as well as the calibration parameters are obtained. Obviously, errors can cause a strong mixing of these four quantities, and one should be alert to statistical and systematic errors. The first method has the advantage that, in principle, statistical errors are eliminated from the calibration and thus do not contribute to the errors in the two measured quantities, A and T. In practice it has been shown that residue calibration works well on metals in general. However, when applied to semiconductors in the visible-wavelength region or to nonabsorbing substrates, residue calibration is less useful, yielding poor results. In what follows we show that residue calibration becomes highly inaccurate with A approaching either 0 or 7r rad. Under these circumstances, one could perform the calibration on another sample or at another wavelength; however, a complementary method for a direct approach should be desirable. In this paper we present such a complementary method, which looks much like residue calibration and which we call phase calibration. 8 This paper is organized as follows. In Section 2 we present a general description of the measuring technique and the data handling used in the RAE. In Section 3 we treat residue calibration, for which we derive an expression offering the opportunity to calculate the accuracy of the calibration directly from the calibration itself. Phase calibration is presented in Section 4. It is shown that the two methods are complementary; phase calibration is most suited for cases of A near 0 or 7r rad, and residue calibration for A near 7r/2. The paper concludes with a short discussion on the work presented. An example is included, clearly illustrating the usefulness of each method under specific circumstances.