| Laser-grating interferometry has the advantages of high accuracy,high thermal inertia,insensitive to air refractive index,and easy to achieve multidegree-of-freedom(multi-DOF)measurement.Therefore,the simultaneous measurement of position and attitude through multiple linear displacement grating interference units is an advantageous solution for ultra-precision six-DOF measurement.It has already been used in the NXT series of deep-ultraviolet immersion lithography machines of ASML Company and has become a core technology of 38 nm to 7 nm process chip lithography.However,this technology has only been owned by ASML and other companies and the technical details are strictly kept secret.On the other hand,public researches on this technology has not form a complete six-DOF grating interferometry research system.There are problems such as incomplete analysis method of alignment tolerance,lack of global measurement model,and imperfect decoupling algorithm.The abovementioned problems lead to large errors in the six-DOF decoupling results and hinder the practical application of six-DOF grating interferometry in ultraprecision manufacturing equipment.Therefore,aiming at high-precision and wide-range six-DOF measurement requirements proposed by the deep-ultraviolet immersion lithography machine and other high-end equipment manufacturing fields,this article conducts in-depth theoretical exploration and technical research on the six-DOF measurement method based on high-tolerance grating interferometric sensing in the view of the key problems mentioned above in the six-DOF grating interferometry technology:(1)A multi-probe laser-grating interferometry six-DOF measurement method is proposed,combining the advantages of short z-axis measurement of heterodyne laser interferometric beam and small influence of airflow disturbance on ranging accuracy,z-axis displacement is measured by dual-frequency laser interferometry beam;on the horizontal plane grating surface,4-probe z-axis heterodyne laser interferometry beams are arranged on the horizontal plane grating,which can be measured to solve the angle of the plane grating along the x-and y-axes;the zaxis measurement beams are also used as the light source for the diffraction measurement of the plane grating.The x-and y-axes displacements are measured according to the changes in the diffraction fringes on the x-and y-axes,and the angle around the z-axis is calculated according to the change measurement of the four sets of diffraction fringes;the influence of airflow disturbances caused by the high speed and high acceleration of the workpiece table can be effectively avoided;the resolution forces of the x-,y-,and z-axes displacements are 0.244 nm,0.244 nm and 0.171 nm after 1 024 electronic interpolation factors;the angle resolution along the x-,y-,and z-axes is 4.88 nrad and 4.88 when the probe spacing is 50 mm nrad and 3.42 nrad.(2)Aiming at the problems that the multi-probe laser-grating interferometric six-DOF measurement model has not yet been established,and the six-DOF decoupling algorithm only considers local solution,its six-DOF measurement model and decoupling algorithm are established.According to the benchmark for x-and y-axis measurement are changing with the grating,but the laser benchmark of z-axis measurement always remains unchanged,a direct geometric model between the six DOFs of the grating and the interferometric phase of each axis is established,and the analytical expression of the accurate solution of the grating six DOFs is derived;the grating benchmark directions are corrected by the grating angle,which can effectively compensate for the cosine error and the Abbe error in the multi-probe structure.The simulation results show that the three-axis displacement decouping error obtained by the proposed algorithm is consistent with the error of probes,and the influence of the decoupling algorithm can be controlled below 0.1%,which effectively avoids the micron-scale decoupling error introduced by the existing algorithm.(3)Aiming at the problem that the displacement measurement of each axis of the laser grating interferometric probe is affected by the grating rotation,resulting in the mutual restriction and difficulty of taking into account the measurement needs of a wide range and high precision,a grating rotation error compensation method based on laser-grating interferometric optical path tracing is proposed.According to the normal vector and the benchmark vector of the grating,the diffraction direction could solved by the vectorial diffractive equation,and the beam mismatch and optical path change of the interfering beam affected by the rotation of the grating can be obtained;the interference signal intensity attenuation degree caused by the beam mismatch can be measured,the structural parameters of the interferometer group can be optimized,and the grating rotation error can be compensated according to the relationship between the grating attitude and the optical path change.Experimental results show that in the range of grating deflection ±2 mrad,the proposed method not only realizes the accuracy measurement of the two-dimensional line displacement both in-plane and out-ofplane,but also ensures that the measurement accuracy of each single-axis grating reaches 5 nm,which provides an effective probe scheme for six-DOF measurement that takes into account both high precision and large range.In summary,this thesis studies the six-DOF measurement method based on laser-grating interferometry.It provides a theoretical and technical foundation for the field of ultra-precision six-DOF grating interferometry,and has important application value in the field of domestic high-end equipment manufacturing such as deep-ultraviolet immersion lithography machine. |
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