Measurement Method for Numerical Aperture of Projection Lens Based on Ronchi Lateral Shearing Interferometry

Objective The wavefront aberration and the numerical aperture (NA) of projection lens directly determine the critical dimension and resolution in lithography. Hence, high -accuracy wavefront and NA measurement is crucial in lithography systems. With the advantages of a common optical path, null testing, and no need for extra ideal reference, double -grating Ronchi lateral shearing interferometry (LSI) has great potential for high -accuracy and high -dynamic -range wavefront measurement, which is suitable for online wavefront aberration measurement of the projection lens in lithography. In Ronchi LSI, NA is also a basic parameter for wavefront measurement. Traditional method of NA measurement needs to measure the focal length and the exit pupil diameter. Although there are many ways to measure the focal length, the diameter of exit pupil cannot be measured, unless the aperture of the system is that of the last element. The method which uses the commercial Abbe apertometer (Zeiss) is relatively mature, however, this method requires manual adjustment of the vernier and surveyors have to observe at the exit pupil plane, which increases the complexity of the measurement process. In the present study, we report a new method of NA measurement in the double -grating Ronchi LSI system. With theoretical derivation of the geometric optical path difference introduced in the shearing wavefront, by measuring the shearing wavefront and calculating the tilt coefficient (the coefficient of Zernike Z2 in X -direction shearing wavefront or Z3 in Y -direction shearing wavefront) at two different axial positions, NA is calculated by using the distance between the two axial positions and the differential value of the tilt coefficients. This method can be integrated easily into the current double -grating Ronchi LSI system, which can achieve the online measurement of the NA and wavefront simultaneously.Methods The image -plane grating is moved along the axial direction (Z direction) in the study. Taking the X -direction shearing interferogram for example. The projection lens under test is placed in the double -grating Ronchi LSI system, and the object -plane grating and the image -plane grating are placed at the corresponding focal planes of the projection lens under test, respectively. The image -plane grating is moved to the first position, and then moved along the X direction according to the phase shifts mentioned in the (3N+1) -frame algorithm, where N is a positive integer. A total of 3N+1 interferograms are obtained. Firstly, the shearing wavefront phi 1 at the first position is calculated using the (3N+1) -frame algorithm. Then, the image -plane grating is moved along the axial direction with distance delta z to the second position, and the shearing wavefront phi 2 at the second position is measured and calculated again with the same method. Thirdly, the X -tilt coefficients of Zernike terms (Z2) of phi 1 and phi 2 are calculated, which are recorded as c21 and c22, respectively. The differential value Delta c2 between c21 and c22 is obtained. Substituting the delta z and Delta c2 values into Eq. (12), the NA of the projection lens under test is calculated. The method using Y -direction shearing interferogram has the similar process. The NA of the projection lens under test is calculated by substituting the delta z and Delta c3 (differential value of Z3 coefficients between the first position and the second position) values into Eq. (13). The image -plane grating can be moved n times, then an average value of the n-1 groups of Delta c2 and Delta c3 will be obtained to eliminate the random error during the measurement.Results and Discussions The projection lens under test used in the experiment has a magnification of 5x and an NA of 0.3. Overall, with the equally spaced movement of image -plane grating along the axial direction, i. e., all the intervals between two adjacent positions are equal, the measured tilt coefficients of c2 of Z2 (X direction) and c3 of Z3 (Y direction) change linearly with the position variation along the axial direction, as shown in Fig. 13. We can see that both c2 and c3 have nearly the same value at the same positions, which is consistent with the information shown in Eqs. (12) and (13). An average value of the 12 groups of Delta c2 and Delta c3 is 216.4 nm, and the distance delta z between any two adjacent positions is 10 mu m, then the NA of the projection lens under test is calculated to be 0.292.Conclusions In this paper, a new method which can be used for the online measurement of the NA of projection lens in the double grating Ronchi LSI system is proposed. The geometric optical path difference in the shearing wavefront introduced by the defocusing of image -plane grating is theoretically derived, and the mathematical model of the relationship between NA and the tilt coefficients of the shearing wavefront (Z2 in X -direction shearing wavefront and Z3 in Y -direction shearing wavefront) is established. By moving the image -plane grating along the axial direction, the shearing wavefront is measured and the tilt coefficients are calculated at each position. The NA of the projection lens under test is calculated using the corresponding mathematical model. A microscope with a designed NA value of 0.3 is used to carry out the experiment, and the experimental measurement result is 0.292. The result of NA measurement by using geometric optical method is 0.294, which verifies the effectiveness of the proposed method. Compared with the traditional geometric optical method, the NA value can be obtained by small defocusing near the focal plane using the proposed method and only the shearing wavefronts at two different positions along the axial direction are needed to measure. This method is also the premise of high -accuracy and high -NA wavefront measurement in Ronchi LSI system, and it provides a convenient method for the measurement of wavefront and NA in Ronchi LSI system simultaneously, without any need of other devices.