Coherent fourier scatterometry

Abstract

The electronics which makes our lives easier like mobiles, computers, digital cameras contain chips with very small semiconductor components like transistors. When transistors can be made even smaller, the chip can accommodate a larger number of components, which gives more processing capacity, resulting in a faster device with an increased functionality. Industrial lithography, the art of making structures on wafers, follows Moore’s law (1970’s), which states that “the processor speed, or overall processing power for computers would double almost every two years”, i.e., the number of transistors in an integrated circuit would double almost every two years. The implications of this law is clearly seen in the evolution of electronic devices where smaller, lighter and faster computers, high resolution imaging sensors, increased storage capacity are continuously being introduced in the market. But this also sets stringent requirements on lithography processes. The critical dimension printed on a wafer these days are in order of a few tens of nano-meters which in perspective is approximately 1000 times smaller than a strand of human hair. The technology nodes and the uniformity of the line-width or critical dimension (CD) over the wafer as produced by lithographic scanners must be improved in future for an optimal yield and performance of the electronic components. Now, the question is how to design a measurement method that is able to quantify the printing quality of these small features in a fast, stable and non destructive way which can also be incorporated into the machine which makes these chips? When you can measure something and express it in numbers, you know something about it. Lord Kelvin's statement is frequently paraphrased as ``if you can measure something, you can make it better". The research work presented in the thesis is a step forward in that direction, regarding wafer inspection. In the semiconductor industry, a robust, reliable and repeatable in-line control process is required to obtain the intended line shapes and sizes. This is achieved by printing special targets on the wafer, typically gratings, which are successively measured in order to adjust dose, exposure time, overlay/alignment and other relevant process parameters of the photo-lithographic machine. As the specifications get tighter, the measuring technique has to be more accurate. This is the primary reason for the continuous development of increasingly complex, advanced and improved quantitative metrology techniques over the years. Currently, in the semiconductor industry, incoherent optical scatterometry (IOS) is the standard workhorse. Any degree of improvement in the present technique is worthwhile of scientific and technological interest. In this thesis we develop, study, design and implement coherent Fourier scatterometry (CFS). The scatterometer is based on a coherent source of illumination, where a focused spot interacts with the sample. The performance of CFS is compared with IOS in terms of sensitivity to the change in grating shape parameters. The studies are done on grating as samples for the performance comparison. The grating reconstruction is proved with the experimental implementation of a CF scatterometer. Applications and improvements in CFS are also discussed in the thesis. The thesis starts with an introduction to the research goals and scope of CFS in chapter 1. The grating diffraction formula, which predicts the angle of diffraction for a given incidence angle on the grating is explained and the relevance of rigorous coupled wave analysis popularly known as RCWA as a rigorous Maxwell’s solver for periodic structure are highlighted. A brief introduction to principle of the Shack-Hartmann sensor used in experiments is also mentioned. This chapter also contains a summarized description of the work done within the PhD period but are not in the scope of the description in the thesis. In chapter 2 of the thesis, a framework to study the increment in sensitivity of CFS with respect to the IOS and the benefits of using a focused spot from a spatially coherent source (laser) is investigated on a theoretical viewpoint. A specific model of the grating and the illumination is presented, where the grating is defined in terms of a finite number of geometrical shape parameters (such as height, side-wall angles, midCD). The focused spot is scanned over the grating, and for each scan position, a far-field diffraction pattern is recorded. Through sensitivity analysis, we show that the use of coherence and multiple scanning makes CFS more sensitive than IOS under special circumstances. The role of the incident and output polarization, the position of the focused spot w.r.t. the grating and the effect of the number of scanning positions on the sensitivity analysis is also studied. There is an optimum number of scanning positions, which depends on the number of diffracted orders in the exit pupil. Owing to the coherent illumination, the far field in CFS comprise phase information concealed in the complex reflection matrix of interaction. Intensity data with phase between scattered orders is the maximum information that can be extracted in CFS. Unravelling the complex reflection matrix in CFS requires the knowledge of the amplitude and phase of the individual components of the matrix. Intensity measurements provide the amplitude information but the phase information is absent. In chapter 3 of the thesis, we present a non interferometric partial phase retrieval method from the intensity measurements in CFS. The applicability of the principle of temporal phase shifting interferometry (TPSI) in CFS with a scanning spot is presented. An analytical relation is derived and illustrated for the phase difference between two overlapping orders in the exit pupil. The analytic results are compared with the simulations from RCWA. Also, the polarization dependent phase sensitivity of grating parameters is studied for the overlap region of diffracted orders in the exit pupil. In chapter 4, the implementation of an operational CFS instrument in the laboratory environment is reported for grating reconstruction. The setup is capable of illuminating and measuring the response of the sample simultaneously over a broad range of incident and reflected angles and for two orthogonal incident polarizations. The measurement for all radial and azimuthal angles can be performed within a few ms. The system, although currently operating at a relatively low numerical aperture (NA = 0.4) at wavelength 633 nm allows the reconstruction of the grating shape parameters with nano-meter accuracy, which is comparable to that of measured by atomic force microscopy (AFM) and scanning electron microscope (SEM) as the reference measurements. Additionally, nano-meter accuracy in lateral positioning is proven, which in the present used case corresponds to only 0.08% of the period of the grating. In semiconductor lithography, the desired pattern on the wafer is written layer by layer in several steps to realize the finished structure. The positional accuracy of new patterns on the existing ones decides the performance of the circuitry. Deviation of the consecutive layers is called overlay. The allowed deviation is