Temporally coherent sources

The varieties of exposure sources that have found applications in UV and visible light optical lithography can be broadly divided into two groups (i) high-pressure arc lamp or incoherent sources and (ii) laser sources or temporally coherent sources. In the laser-type sources, we include all techniques and devices for radiation generation that have their basis in stimulated emission of radiation. 

Whereas temporal coherence is important for spectroscopy, spatial coherence is important for imaging. Consider the disturbance at two points Pi and P2 due to a finite sized source S (Fig. 2). If the source is small and distant... 

What Is Interferometry (1.3) Interferometry deals with the physical phenomena which result from the superposition of electromagnetic (e.m.) waves. Practically, interferometry is used throughout the electromagnetic spectrum astronomers use predominantly the spectral regime from radio to the near UV. Essential to interferometry is that the radiation emerges from a single source and travels along different paths to the point where it is detected. The spatio-temporal coherence characteristics of the radiation is studied with the interferometer to obtain information about the physical nature of the source. 

In the hrst case, the degree of self coherence depends on the spectral characteristics of the source. The coherence time Tc represents the time scale over which a held remains correlated this hme is inversely proportional to the spectral bandwidth Au) of the detected light. A more quantitative dehnition of quasi-monochromatic conditions is based on the coherence time all relevant delays within the interferometer should be much shorter than the coherence length CTc. A practical way to measure temporal coherence is to use a Michel-son interferometer. As we shall see, in the second case the spatial coherence depends on the apparent extent of a source. 

The fundamental quantity for interferometry is the source s visibility function. The spatial coherence properties of the source is connected with the two-dimensional Fourier transform of the spatial intensity distribution on the ce-setial sphere by virtue of the van Cittert - Zemike theorem. The measured fringe contrast is given by the source s visibility at a spatial frequency B/X, measured in units line pairs per radian. The temporal coherence properties is determined by the spectral distribution of the detected radiation. The measured fringe contrast therefore also depends on the spectral properties of the source and the instrument. 

Now let us assume that a monochromatic source of flux is placed in the plane of the entrance slit so that there is no constant phase relationship between the fields at any two given points in the slit. This, in itself, is a contradiction, because a perfect source monochromaticity implies both spatial and temporal coherence. By definition of coherence, a constant phase relationship would result. To eliminate the possibility of such a relationship, we must require the source spectrum to have finite breadth. Let us modify the assumption accordingly but specify the source spectrum breadth narrow enough so that its spatial extent when dispersed is negligible compared with the breadth of the slits, diffraction pattern, and so on. Whenever time integrals are required to obtain observable signals from superimposed fields, we evaluate them over time periods that are long compared with the reciprocal of the frequency difference between the fields. We shall call the assumed source a quasi-monochromatic source. 

Conventional sources of electromagnetic radiation are incoherent, which means that the waves associated with any two photons of the same wavelength are, in general, out-of-phase and have a random phase relation with each other. Laser radiation, however, has both spatial and temporal coherence, which gives it special importance for many applications. 

As mentioned in Section 3.1.2, attractive UV sources for lithography are those that produce high power and poor spatial and temporal coherence. Jain and co-workers (13-15) demonstrated that excimer lasers provide excellent quality, speckle-free images with resolution to 0.5 xm in a contact mode. The images were obtained in l- xm-thick diazoquinone photoresists such as AZ2400 with a XeCl laser at 308 nm and a KrF laser at 248 nm... 

Lasers are unique energy sources characterized by their spectral purity, spatial and temporal coherence, and high average peak intensity. Each of these characteristics has led to applications that take advantage of these qualities ... 

Going back to Eq.2.34, the complex visibility or spatial coherence function was defined as the mutual coherence function when r = 0. According to the van-Cittert-Zernike theorem, the normalised spatial coherence funetion is the Fourier transform of the normalised sky brightness distribution (Eq.2.35). The temporal coherence function is defined as the mutual coherence function for b = 0, and according to the Weiner-Khinchin theorem, the normalised value of the temporal coherence function is equal to the Eourier transform of the normalised spectral energy distribution of the source, this is... 

If the phase differences A0 = (pn P, i) -0 (P, 2) at a given point P between two different times t, t2 are nearly the same for all partial waves, the radiation field at P is temporally coherent. The maximum time interval At = t2 —1 for which A0 for all partial waves differ by less than tc is termed the coherence time of the radiation source. The path length Asc = cAt traveled by the wave during the coherence time At is the coherence length. 

Fig. 2.23. Michelson interferometer for measurement of the temporal coherence of radiation from the source S...

Two monochromatic waves having the same amplitude and the same frequency, but with ( ] ((>2, initially are coherent if (j)i - ( )2 is constant during time (monochromaticity or temporal coherence). A phase shift constant during time would also be constant in space (i.e., everywhere in the source there is no local variable intensity—spatial coherence) [22]. 

In contrast the light emitted by a laser is generated by stimulated emission in an optical resonator. As a result the radiation has high spatial and temporal coherence which is not found in light emitted by any other source. In addition, the energy densities of radiation in laser beams... 

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