Beam Alignment and Image Metrology for Scanning Beam Interference Lithography–Fabricating Gratings with Nanometer Phase Accuracy by Carl Gang Chen B.A., Swarthmore College (1995) S.M., Massachusetts Institute of Technology (2000) Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2003 c Massachusetts Institute of Technology 2003. All rights reserved. ° Author .............................................................. Department of Electrical Engineering and Computer Science May 23, 2003 Certified by.......................................................... Mark L. Schattenburg Principal Research Scientist, MIT Center for Space Research Thesis Supervisor Accepted by ......................................................... Arthur C. Smith Chairman, Department Committee on Graduate Students Beam Alignment and Image Metrology for Scanning Beam Interference Lithography–Fabricating Gratings with Nanometer Phase Accuracy by Carl Gang Chen Submitted to the Department of Electrical Engineering and Computer Science on May 23, 2003, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract We are developing a scanning beam interference lithography (SBIL) system. SBIL is capable of producing large-area linear diffraction gratings that are phase-accurate to the nanometer level. Such gratings may enable new paradigms in fields such as semi- conductor pattern placement metrology and grating-based displacement measuring interferometry. With our prototype tool nicknamed “Nanoruler”, I have successfully patterned, for the first time, a 400 nm period grating over a 300 mm-diam. wafer, the largest that the tool can currently accommodate. ByinterferingtwosmalldiameterGaussianlaserbeamstoproducealow-distortion grating image, SBIL produces large gratings by step-and-scanning the photoresist- covered substrate underneath the image. To implement SBIL, two main questions need to be answered: First, how does one lock the interference image to a fast-moving substrate with nanometer accuracy? Secondly, how does one produce an interference image with minimum phase nonlinearities while setting and holding its period to the part-per-million (ppm) level? My thesis work solves the latter problem, which can be further categorized into two parts: period control and wavefront metrology. Period control concerns SBIL’s ability to set, stabilize and measure the image grating period. Our goal is to achieve control at the ppm level in order to reduce any related phase nonlinearity in the exposed grating to subnanometers. A grating beamsplitter is used to stabilize the period. I demonstrate experimental results where the period stabilization is at the 1 ppm level. An automated beam alignment system is built. The system can overlap the beam centroids to around 10 µm and equalize the mean beam angles to better than 2 µrad (0.4 arcsec), which translates into a period adjustability of 4 ppm at 400 nm. Image period is measured in-situ via an interferometric technique. The measurement repeatability is demonstrated at 2.8 ppm, three-sigma. Modeling shows that such small period measurement error does not accumulate as growing phase nonlinearities in the patterned resist grating; rather, the resist grating has an averaged period that equals the measured period. Any phase nonlinearity is periodic and subnanometer in magnitude. SBILwavefrontmetrologyreferstotheprocessofmappingthephaseofthegrating imageand adjusting the collimating opticssothat minimumimage phase nonlinearity can be achieved. The current SBIL wavefront metrology system employs phase shift- ing interferometry and determines the image nonlinearity through a moir´e technique. The system has an established measurement repeatability of 3.2 nm, three-sigma. I am able to minimize the nonlinearity to 12 nm across a 2 mm-diam. image. Mod- eling shows that despite an image phase nonlinearity at the dozen nanometer level, printed phase error in the resist can be reduced to subnanometers by overlapping scans appropriately. From the point of view of period control and wavefront metrology, I conclude that SBIL is capable of producing gratings with subnanometer phase nonlinearities. Thesis Supervisor: Mark L. Schattenburg Title: Principal Research Scientist, MIT Center for Space Research To dad, mom and Xiaohui Acknowledgments More than half of this dissertation was written in Beijing, China, at my parents’ place over the course of six months, from September 2002 to February 2003. Little did I anticipate that the anti-terrorism campaign would have such a profound impact on my own life, and on the lives of so many other foreign students. Fortunately, given the circumstances, I was stuck at the right place: home. In hindsight, the forced exile might have been one of the best things that happened to me. I am stronger because of it. During those six agonizing months, I had the love and support of my family and friends to count on. To them, I am forever grateful. Special thanks go to Paul Konkola, Ralf Heilmann, Chulmin Joo, Raymond Scuzzarella, Craig Forest, Yanxia Sun, Juan Montoya, Ed Murphy, Bob Fleming and Mark Schattenburg. They man- aged to ship a hundred kilograms of notebooks, data and references to me, without which, there would not have been any thesis. Another special thank-you to Fred Gevalt, the person who braved the bureaucracy and managed to get me back in time so that I can put an appropriate end to my MIT career. I have the honor to be the first student who did both his Master’s and PhD under the guidance of Dr. Schattenburg. Mark is an effective yet easy-going advisor. I can express and argue my ideas freely in front of him. I am very grateful to his continuing financial support during my time in China. His questions and suggestions have significantly enhanced the quality of my work. Paul’s skill in controls and mechanical design is enviable. As the only people working full time on SBIL (until I was held up in China), he and I have collaborated closely over the years. I am honored to call him a dear colleague and a loyal friend. One could only hope that the camaraderie will last a lifetime. Ralf contributedconsiderablytowards SBILresearchby designing andimplement- ing the phase measurement optics used for heterodyne fringe locking. I also deeply appreciate his help in taking some new period measurement data so that I could analyze them in Beijing and report the findings at a conference. Witheverypassingday,Chulminisastepclosertorealizinghisdreamofbecoming a MIT PhD. I wish him the best of luck, and may I remind the man that he still owes me a dinner in Seoul. I am proud to have Craig as a friend. His enthusiasm and warmth are refreshing. Yanxia has been working extremely hard since she joined the team. I wish her some joyful downtime in the coming year. Over the past couple of months, Juan has become a good colleague and friend. He is starting to put his own signature on the SBIL project. Bob’s caring for the lab made it not-too-painful a place to spend 24 hours in. His good sense of humor is most memorable. Captain Ed’s mastery of fab-processes makes him invaluable to my work. He is easily one of the nicest follows that I know. I wish him the best. Not enough thank-you’s can express my gratitude towards Ray, whose help during my time of need can most certainly be counted on. As new members, Chih-Hao Chang and Mireille Akilian have demonstrated their skills convincingly. The future of SNL looks bright because of them. I thank Professors Henry Smith and Cardinal Warde for serving as my thesis readers. I benefitted from their questions. The work documented in this dissertation is done at the MIT Space Nanotechnol- ogy Laboratory, and is supported by grants from NASA and DARPA. Contents 1 Introduction 27 1.1 Mechanically-ruled gratings . . . . . . . . . . . . . . . . . . . . . . . 28 1.2 Interference gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.3 Gratings for new paradigms . . . . . . . . . . . . . . . . . . . . . . . 30 1.4 Scanning beam interference lithography . . . . . . . . . . . . . . . . . 33 1.4.1 Interference lithography at MIT . . . . . . . . . . . . . . . . . 33 1.4.2 SBIL concept . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.4.3 System advantages . . . . . . . . . . . . . . . . . . . . . . . . 39 1.4.4 System overview . . . . . . . . . . . . . . . . . . . . . . . . . 39 1.4.5 Patterned gratings . . . . . . . . . . . . . . . . . . . . . . . . 50 2 SBIL optics 53 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.1.1 Grating beamsplitter . . . . . . . . . . . . . . . . . . . . . . . 54 2.1.2 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.1.3 Thin lens equation for Gaussian beams . . . . . . . . . . . . . 56 2.2 Optical design and layout . . . . . . . . . . . . . . . . . . . . . . . . 58 2.2.1 Lithography interferometer . . . . . . . . . . . . . . . . . . . . 58 2.2.2 Spatial filtering . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.2.3 Beamsplitter mode . . . . . . . . . . . . . . . . . . . . . . . . 66 2.2.4 Lithography mode . . . . . . . . . . . . . . . . . . . . . . . . 68 2.2.5 Grating mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3 Beam alignment 71 3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.1.1 Beam position and angle decoupling . . . . . . . . . . . . . . . 73 3.1.2 Angle PSD placement error . . . . . . . . . . . . . . . . . . . 75 9 10 CONTENTS 3.1.3 Iterative beam alignment . . . . . . . . . . . . . . . . . . . . . 77 3.2 System setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.2.1 Beamsplitter mode . . . . . . . . . . . . . . . . . . . . . . . . 80 3.2.2 Rectangular beamsplitter design, installation and non-ideality 84 3.2.3 Beam overlapping PSD . . . . . . . . . . . . . . . . . . . . . . 89 3.2.4 Grating mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.3 Noise study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.3.1 Digitization noise floor . . . . . . . . . . . . . . . . . . . . . . 92 3.3.2 DAQ system accuracy . . . . . . . . . . . . . . . . . . . . . . 93 3.4 Period stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.4.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . 96 3.4.2 Measurement consistency . . . . . . . . . . . . . . . . . . . . . 97 3.4.3 Angular noise correlation . . . . . . . . . . . . . . . . . . . . . 97 3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.5.1 Beam position and angle instabilities . . . . . . . . . . . . . . 101 3.5.2 Beam alignment performance . . . . . . . . . . . . . . . . . . 104 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4 Period measurement 107 4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.1.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . 110 4.1.2 Point detector without beam diverting mirror . . . . . . . . . 114 4.1.3 Point detector with beam diverting mirror . . . . . . . . . . . 117 4.1.4 Measurement error for a point detector . . . . . . . . . . . . . 123 4.1.5 Wave model for a non-point detector . . . . . . . . . . . . . . 124 4.1.6 Locations of Gaussian beam centroids . . . . . . . . . . . . . . 126 4.1.7 Period measurement with a non-point detector . . . . . . . . . 129 4.1.8 Measurement error for a non-point detector . . . . . . . . . . 133 4.1.9 Period measurement with a pseudo-ideal beamsplitter . . . . . 134 4.1.10 Period measurement with a non-ideal beamsplitter . . . . . . 141 4.1.11 Fringe nonlinearity-induced stitching error . . . . . . . . . . . 150 4.1.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4.2 Error modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.2.1 Fringe counting . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.2.2 Noise sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 156 4.2.3 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 4.2.4 The ideal case . . . . . . . . . . . . . . . . . . . . . . . . . . . 158