CA2086848A1 - Method and apparatus for spatially resolved thickness mapping - Google Patents

Abstract

ABSTRACT

Improved interferometric methods for mapping the variations in the thickness of a thin dielectric film or layer at a large number of sites are described. A scanning optical measurement apparatus is used to obtain the measurements required for the methods of invention. Infrared light is applied to a thin layer, and the interference fringes due to a single wavelength of light are sampled to provide a map of the monochromatic reflectance of the thin layer. The monochromatic reflectance map is analyzed, and a small number of sites are selected according to the methods of the invention for absolute thickness determination by known methods. The interference order is determined for each one of the small number of sites from the determined absolute thickness values. The interference order and monochromatic reflectance are then used to calculate the thickness of the thin layer at other sites. This process allows large numbers of thickness determina-tions to be made quickly. Real data, containing noise and dis-tortions, can be processed by the methods of the invention.

Description

20~6848 BACKGROUND OF THE INVENTION

Field of the Invention This invention relates to optical interferometric methods for determining the thickness of a thin layer or film at a large number of sites. Recent developments in the field of semiconduc-tor device fabrication have created a need for rapid thickness mapping.

Description of tha Prior Art The thickness of a thin transparent layer is commonly deter-10 mined from its reflectance spectrum using a well understoodinterferometric principle which is fully described in standard optics textbooks, such as PRINCIPLES OF OPTICS by M. Born and E.

20~6~48 Wolfe, published by PERGAMON PRESS (1970). There are many de-vices and methods which employ this principle, a few of which are described in U.S. Patents 3,099,579 by Spitzer et al., 4,254,337 by Yasujima et al., 4,645,349 by Tabata, 4,776,6~5 by van Pham et al. and 4,787,749 by Ban et al. The relevant physics will be briefly summarized in the following paragraphs.
Figure 1 presents a cross sectional view of a layered struc-ture consisting of three dielectric materials. There is a thin layer 101 having refractive index nL, in contact with a substrate having refractive index nS on one side and a cover material having refractive index nc on the other side. The cover material is often air. The substrate can have the same refractive index as the cover, but nL cannot equal either nC or ns. The wave-length dependence of the refractive indices must be known to interpret optical interference as thickness. The cover material and the material forming the layer are essentially transparent to light. The thickness of the layer is T.
Light ~of wavelength Lambda in vacuum) that is incident on layer 101 from the side of the cover material will be partially 20 reflected by each of the interfaces between different media. For transparent media in the absence of scattering mechanisms, the Fresnel relations give the amplitude reflectivity and transmit-tivity of an interface. The reflectivity and transmitivity are coefficients that determine the field strength of the reflected ~5 and transmitted waves when they are multiplied by the field strength of an incident wave. An interface between two media, labeled j and k, will have reflectivity rjk when light is inci-203~8 dent from medium j and transmitted into medium k; the order ofthe subscripts gives the direction of incidence on the interface.
Refer to Figure 1 and consider incident light 104. Reflec-tions from the interfaces 100 and 102 result in an infinite S number of emerging electromagnetic fields, each with a different amplitude and phase. The net reflected light from the layer has field strength equal to the sum of these fields. This infinite sum may be evaluated to give the net amplitude reflectivity, r:

r = ( rCL + rLse~i ) I ( 1 + rCLrLSe ) (1) where = (2nLT/Lambda3 2~ cos(eL) (2) and the subscripts C,L and S denote cover, layer and sub-strate.
The total reflectance or intensity reflection factor, R, is equal to the squared modulus of the reflectivity, ¦r¦2, R = [ rCL2 + rLS2 + 2rcLrLscos(~) ] /

[ 1 + rCL2 rLS2 + 2rCLrLscos (~) ]
(3).
The first reflection, 106 in Figure 1, does not travel 20 through the thickness of layer 101, whereas all light reflected from the interface 102 has travelled through the thickness of layer lOl. This results in the phase difference ~ in equations (1) and (2). The interference between light reflected from the two interfaces 100 and 102 i5 thickness dependent. The cosine 25 function in equation ~2) varies from -1 to +1, which causes R to 20~6~48 vary over a range denoted Rmin to Rmax.
Figure 2 shows a reflectance spectrum for the layer 101 of Figure 1, where oscillations are observed in reflectance, R, as the wavelength of light varies. R depends upon the layer thick-ness, T, the refractive indices and wavelength of the incidentlight. With knowledge of the refractive indices, T may be deter-mined from an observed reflectance spectrum either by fitting the spectrum to the functional form given by equation (3), or by using successive maxima. Because it is accurate and non-destructive, this is a commonly used technique for finding thethickness at a single site on a layer.

A suitable prior art apparatus for making spatially resolved thickness determinations using reflective interference, and its mode of operation will now be described. Figure 7 shows a sim-plified schematic diagram of a scanning microreflectometer fromU.S. Patent 4,844,617 by Kelderman et al., adapted to make spec-tral reflectance measurements at vi~ible and ultraviolet wave-lengths. The instrument images a small area of a specimen and then measures the spectral intensity distribution of the light in 20 the image. The thickness of a thin layer can be determined from the spectrum. The imaged small area is varied in a scanning pattern across the specimen. Because of the high spatial resolu-tion of this type of instrument, it is well suited for spatially resolved thickne~s mapping.
Referring to Figure 7, visible light source 706 provides light which is collected by lens 712 and directed toward beam splitter 722. Si~ilarly, a W light source provides light which ~6~48 is collected by lens 710 and directed toward beamsplitter 724.
The beam splitters 722 and 724 are positioned to reflect light from these sources into the objective lens 726, which focuses the light to the spot of illumination 750 on the specimen 728. The specimen 728 is attached to the positioning stage 730, which allows the spot 750 to be scanned and the focus to be adjusted.
Light reflected from the specimen 728 is collected by the objec-tive lens 726 and a portion is focussed through the beamsplitters 722 and 724 onto a small aperture 704. Aperture 704 is imaged by the objective lens 726 to a spot 3 microns by 3 microns in size on the specimen 728. Light emerging from aperture 704 is imaged with concave holographic grating 702 onto a multi-element detec-tor array 700, which is positioned to receive light in the first diffraction order, thereby measuring the reflectance spectrum at 750. Shutters 718 and 720 can be positioned to block the light from either broadband light sources 706 or 708. This system is also equipped with an autofocus light source 732, positioned in the zero order diffraction direction, and control circuitry external to the optical system (not shown) uses a signal produced by 732 to adjust the stage 730 and maintain focus.

The instrument of Figure 7 can be used to determine the thickness of a thin layer at any single site by measuring the reflectance spectrum there. However, it is often necessary to characterize the thickness of a thin layer over the entire sur-~5 face of the specimen, which is called "thickness mapping". Forexample, the specimen could be a gallium arsenide wafer (GaAs) 20868~8 bearing an epitaxially grown layer of aluminum gallium arsenide (AlGaAs). Figure 4A is a perspective representation of such a specimen. For simplicity in the drawing, the layer 404 has been drawn to have a flat interface with the substrate 406, but this need not be the case in general. The variable thickness, T, in Figure 4B, of the AlGaAs layer 404 is to be determined at many sites. Figures 4A and 4C show that these sites are arranged in a rectangular sampling grid 400 on the surface of specimen 490 having the layer 404 and substrate 406. The grid sites are preferably closely spaced in the XY-plane. To accurately charac-terize the surface, the sampling intervals Delta X and Delta Y
must be small compared to the rate of change of the thickness of the layer. The determined thickness values are placed in an array, with position in the array corresponding to position on the grid 400. The resulting array of values is called the "thickness map". It is desired to have about 65,000 thickness determinations in a typical map over the area of a semiconductor wafer.
Obviously, this thickness mapping task can be accomplished by repeated application of the spectral reflectance technique at many sites. This prior art method is briefly described with re~erence to Figures 5, 6 and 7. Each site of sampling grid 400 is positioned under spot of illumination 750 of Figure 7 and the reflectance spectrum is measured there, as described in U.S.
Patent 4,844,617. Figure 5 shows the arrangement of the grid sites and the sequence in which they can be positioned under spot of illumination 750. Figure 6 is a flowchart of the prior art 208~3~8 method for thickness mapping, which involves the steps of 1 selecting a site from the sampling grid, 2 positioning the se-lected site under the spot of illumination, 3 illuminating the site with broadband polychromatic light, 4 measuring the spectral distribution of the light reflected from the site, and 5 analyz-ing the reflectance spectrum to determine the thickness at the site. Step 6 is repeating steps 1 to 5 until the thickness has been determined at every site in the sampling grid 400. A com-puter (not shown in Figure 7) is used to coordinate the operation of the apparatus in steps 1, 2, 3, 4 and 6, and to carry out step 5 to determine thickness. The procedural details for carrying out each of these steps are well known in the art.
Because of its spatial resolution and scanning ability, an instrument such as that depicted in Figure 7 has been the most widely used means of producing detailed thickness maps of thin layers on semiconductor wafers. However, in the case of AlGaAs on GaAs substrate, this instrument would be unable to function because the specimen is not transparent at the wavelengths sup-plied by the visible and W light sources. Infrared light must be used. Even if an infrared light source and detector array replaced the visible light counterparts in Figure 7, this or a similar instrument would still have disadvantages, because of the large number of spectra which must be sampled and analyzed. To be practical, such a system must make many measurements quickly.
Sampling spectra quickly poses difficulties. In general, an apparatus which samples spectra quickly is expensive, complicated and can be inaccurate. Simpler, less expensive systems are too 2~868~8 slow to be useful in mass-production environments.
For example, the detector array 700 of the instrument in Figure 7 samples a spectrum quickly by detecting many wavelengths simultaneously. The array 700 will only sample a fixed set of wavelengths, however, and an inadequate representation of the spectrum may result. Also, photodetector arrays for use at the infrared wavelengths in excess of 1 micron, which are required to study many modern semiconductor materials, are difficult to manufacture and have poor signal-to-noise ratios. An instrument using such an array for infrared measurements will require an extended signal averaging time, thereby reducing overall speed.
The price of detector arrays is high, and they require additional signal reading and processing mechanisms which further add to the co~t.
lS A single element detector is less expensive, is generally more sensitive and has a higher frequency response. However, a wavelength scanning monochromator is required to sequentially scan through a wavelength range for each spectrum again and again, whiCh ta~es a significant amount of time. High speed scanning mirrors and gratings could be used to accelerate the process, such as in the apparatus disclosed in U.S. Patent 4,254,337 to Yasujima et al, but these systems are excessively delicate, prone to wobble during scans, and are expensive.
The process of acquiring a spectrum and making a thickness determination at a site requires from one-half to several sec-onds, using currently available technology of moderate cost.
The time required to produce a detailed thickness map of some 208~8 ~5,000 measurements is in excess of eight hours. This is too slow for production-line wafer processing. Therefore, prior art devices do not function well as high resolution thickness map-pers.
It is frequently desired to combine several optical measure-ment functions within a single instrument, in order to obtain different types of spatially resolved information on the same specimen. An example of this would be a combined thickness and photoluminescence mapping device, which could determine layer thickness and variations in material composition across the layer. Most of the devices using spectral reflectance have been designed with the single purpose of thickness determination, and are therefore unable to provide additional types of spatially resolved information. The instrument of Figure 7 has the poten-tial to combine several functions by replacin~ or adding lightsources, but this is hindered by a disadvantage inherent in its design. There are already two beamsplitters in the image path of system, and to add more light sources, more beamsplitters and shutters must be introduced. Additional beamsplitters in the image path cause loss of light by reflections, which can lead to poor signal-to-noise ratios in the observed data.

SUMMARY OF THE INYENTION

The disadvantages of the prior art techniques for mapping the thickness of thin layers are primarily related to the exces-sive time required to determine absolute layer thicknesses at a 2 ~ 4 ~

.arge number of sites. Detailed layer thickness maps are usefulduring the processing of semiconductor wafers in an industrial production line environment. Accordingly, objects of the present invention are:

a) to determine the thickness of thin layers, which are transparent or partially transparent, at a large number of sites with high spatial resolution;
b) to produce thickness maps in much less time than is possible using prior art methods.
c) to produce thickness maps for layers of semiconductor materials with small band gaps, which are transparent at long infrared wavelengths;
d) to produce thickness maps in an automated manner;
e) to provide methods which compensate for the effects of non-ideal (real-world) reflectance data during the production of thickness maps.

An advantage of the present invention is that it is possible to combine in a single apparatus the thickness mapping function with several other spatially resolved semiconductor characteriza-0 tion functions, such as:photoluminescence measurements, reflectance measurements, and optical beam induced current (OBIC) measurements, without adversely affecting the performance of any optical func-tion. As one preferred means of carrying out the methods of theinvention, a scanning optical measurement apparatus is described .... .

20~3~8 below. This instrument makes spatially resolved thickness deter-minations in addition to spatially and spectrally resolved photo-luminescence measurements. Operating according to the methods of the invention, this instrument is a useful semiconductor analysis tool, because variations in both layer thickness and material composition (from photoluminescence) for epitaxially grown layers of semiconductor material can be studied. The integration of the thickness and photoluminescence functions is economical, since common optical elements are shared.
According to one aspect of the invention, the disclosed instrument operates to carry out the novel method. However, the methods of the invention may be employed by any apparatus which can measure spatially resolved monochromatic reflectance at a large number of sites on a thin layer, and then independently determine the layer thickness at a small number of these sites.
This flexibility is an advantage, since an existing thickness measuring apparatus could be easily adapted to map thickness efficiently.
To achieve these objects and advantages, the present inven-tion exploits the monochromatic interference fringes formed by light reflecting from the thin layer to help determine absolute layer thickness at many sites. These fringes are alternating bands of maximum and minimum reflectance, caused by optical interference. To our knowledge, the use of monochromatic inter-ference fringes has been restricted to applications where theuniformity of optical surfaces or thin layer thickness is to be tested, and their use to map the absolute thickness of a non-4 ~
leformable structure is novel.
Briefly, a method is proposed for mapping the thickness of athin layer, which is essentially described by the steps of deter-mining the reflectance of the layer under illumination with mono-chromatic light at many sites, selecting a small set of siteswhich bracket each fringe extremum, calculating the layer thick-ness at sites in the small set by well known means, determining the half-order number of the interference from these thicknesses, and then calculating the layer thickness at all remaining sites from the value of the monochromatic reflectance and the deter-mined interference orders. The method is preferably carried out by a type of scanning optical measurement apparatus, which is equipped with at least one broadband light source, the light of which is directed along an optical path to a specimen. The opti-cal path is shared by several light sources. The light source isselected, dependent upon the purpose to which the instrument is to be applied. The broadband light directed toward the specimen is focussed to a small spot of illumination by a microscope objective lens, and collected in reflection. Collected light is spectrally resolved by a monochromator with a diffraction grating before impinging on a photodetector, so that either spectral or monochromatic reflectance can be determined. A translating positioning stage provides the means to scan the specimen. The instrument is controlled by a computer, which serves to collect and analyze data in order to map the thickness of a thin layer in an automated fashion.
Other objects, features and advantages of the present inven-20~48 tion will become clear from study of the accompanying descriptionand illustrative drawings.

20~68~8 BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a cross-section of a thin layer and the adjoin-ing materials, showing typical rays of the beams reflected by the layer interfaces.
Figure 2 is a plot of the reflectance, R, as a function of the wavelength of light incident upon a thin layer.
Figure 3 is a plot of the reflectance, R, from a thin layer as a function of layer thickness, T.
Figure 4A is a perspective ~iew of a specimen having a sub-strate and a thin layer.
Figure 4B is a representative cross-sectional view of the specimen from Figure 4A.
Figure 4C is a view of the sampling grid, with the sites for thickness determination distributed across it.
Figure 5 is an illustration of the site-to-site processing scheme for thickness mapping.
Figure 6 is a flowchart which shows the sequence of steps involved in thickness mapping by a prior art method.
Figure 7 is a simplified schematic diagram of a prior art scanning optical measurement apparatus.
Figure 8A is a diagram of thickness contour lines for the thin layer of a specimen depicted in Figure 4A.
Figure 8B is a dot density representation of monochromatic interference fringes which are ohserved in reflectance from the thin layer of a specimen depicted in Figure 4A.
Figure 9A is a plot of the reflectance alonq the path P-Q in Figure 8 for ideal data.

2086~4~

Figure 9B is a plot of the reflectance for non-ideal data.
Figure 9C is a plot of ideal reflectance data at a fringe maximum.
Figure 9D is a plot of non-ideal reflectance data at a fringe maximum.
Figure lO is a diagram which shows the extent of regions of the layer having constant half-order number, H.
Figure 11 is a diagram which shows one of the regions of Figure lO and the sites of the sampling grid that lie within it.
Figure 12 is a flowchart which shows the sequence of steps for thickness mapping by the method of the invention, where the regions of Figure lO are sequentially examined.
Figure 13 is a flowchart which shows the sequence of steps for thickness mapping by the method of the invention, where rows of sites on the sampling grid are sequentially examined.
Figure 14 is a flowchart which shows the sequence of steps for thickness mapping by the method of the invention, where non-ideal reflectance data must be corrected.
Figure 15A is a plot of a reflectance profile which shows extrema and selected bracket sites.
Figure 15B is a plot of the reflectance values near a fringe maximum in Figure 15A.
Figure l5C is a plot of the reflectance values near a minor extremum in Figure 15A.
Figure 15D is a plot of the reflectance values near a fringe minimum in Fi~ure 15A.
Figure 16A is a diagram showing poxtions of three adjacent rows of grid sites.
Figure 16B is a diagram showing the sequence processing for calculating thickness values across a row.
Figure 17 is a series of plots of a reflectance profile during the various steps of processing.
Figure 18 is a diagram which shows the calculated changes in half-order number for the typical row of reflectance data of Figure 17.
Figure 19 is a diagram showing the arrangement of sites for 1~ a portion of the fringe map in the vicinity of a bracket site.
Figure 20A is a plot of a reflectance profile which shows parameters for stretching reflectance data in the simplest case.
Figure 20B is a plot of a reflectance profile which shows parameters for stretching reflectance data in a more complicated case.
Figure 20C is a plot of a reflectance profile which shows important parameters for stretching reflectance data at the end of a row.
Figure 21 is a dot density representation of a monochromatic fringe pattern showing a fringe discontinuity.
Figure 22 is a simplified schematic diagram of the scanning photoluminescence and thickness mapping apparatus.

2086~8 REFERENCE NUMERALS IN DRAWINGS
100 cover/layer interface 101 layer 102 layer/substrate interface 104 incident light 106 light reflected from cover/layer interface 100 400 sampling grid 402 grid site 404 thin layer 406 substrate 408 interface between thin layer and substrate 410 surface of thin layer 490 specimen 700 detector array 702 concave holographic grating 704 aperture 706 broadband visible light source 708 broadband W light source 710 W collecting lens 712 visible collecting lens 718 visible light shutter 720 UV light shutter 722 beamsplitter 724 beamsplitter - 25 726 objective lens 728 specimen 730 xyz positioninq stage 2 Q 8 6 ~ ~ 8 732 autofocus light source 750 site of illumination 700 sampling grid 5 702 site on grid 704 thin layer 706 substrate 802 thickness contour 804 thickness contour 10 806 thickness contour 810 dark fringe minimum 812 bright fringe maximum 814 dark fringe minimum 816 dark fringe minimum 15 818 bright fringe maximum 902 local maximum 920 fringe maximum 922 fringe minimum 924 fringe minimum 20 926 fringe maximum 928 local minimum 930 spike 932 spike 1001 region of constant half-order number 25 1002 region of constant half-order number 10812 contour line along bright fringe maximum 812 10818 contour line along bright fringe maximum 818 .500 bracket site 2 0 8 ~ 8 ~ ~
1501 fringe maximum 1502 bracket site 1503 fringe minimum 5 1504 bracket site 1505 fringe maximum 1506 local minimum 1507 fringe maximum 1508 bracket site 10 1509 fringe minimum 1510 bracket site 1511 fringe maximum 1512 bracket site 1513 fringe maximum 15 1516 bracket site 1517 minor extremum 1620 bracket site 1622 grid site 1624 grid site 20 1626 bracket site 1630 bracket site 1632 grid site 1634 grid site 1636 grid site 25 1691 grid site at fringe extremum 1702 spike 1703 spike ~710 minimum 1711 maximum 208~
1712 minimum 1713 maximum 5 1714 minimum 1715 maximum 1716 minimum 1717 minimum 1718 maximum 10 1719 maximum 1720 bracket site 1722 bracket site 1723 bracket site 1724 bracket site 15 1725 bracket site 1726 bracket site 1727 bracket site 1728 bracket site 1729 bracket site 20 1900 bracket site 1901 column bracket site 1902 fringe extremum site 1904 fringe extremum site 2200 collimated broadband light source 25 2202 white light bulb 2204 aperture 2206 collimating lens 208 laser light source 2 0 8 6 8 4 8 2210 laser light source 2211 movable selecting mirror 2212 mirror position 5 2213 mirror position 2214 mirror position 2216 beam emerging from broadband light source 2220 beam stop 2222 shield wall 10 2223 opening 2226 beam direction 2230 partially reflecting mirror 2232 beam direction 2234 objective lens 15 2236 spot of illumination 2238 beam direction 2239 beam direction 2240 monochromator 2242 diffraction grating 20 2244 beam emerging from monochromator 2246 photodetector 2248 A/~ converter 2250 monochromator stepping motor 2252 computer 25 2254 positioning stage controller 2256 XYZ positioning stage 2270 optical filters 208~848 JETAILED DESCRIPTION OF THE INVENTION

The present invention comprises methods for mapping the thickness of thin layers which exploit measurements of monochro-matic reflectance. This reduces the number of spectral reflect-ance measurements which must be made.
The methods of the invention are described in herein. A
photoluminescence mapper to which has been added a polychromatic light source is capable of carrying out the methods of the inven-tion. This apparatus is also described herein. To facilitate understanding of the present invention, the interference fringes for a thin layer under monochromatic illumination will first be discussed.

MONOCHROMATIC INTERFERENCE FRINGES

Consider the effect when surface 410 of specimen 490 shown in Figure 4A is illuminated with monochromatic light, of wave-length Lambda in vacuum. The variation of reflectance with thickness is shown in Figure 3, as given by equation (3) for representative refractive indices, and it is seen that there are reflectance maxima and minima as thickness varies. A maximum and an adjacent minimum are spaced by the fundamental thickness increment, d, where d = Lambda/4nL (4).

If the whole specimen were illuminated with a parallel beam 2~68`~8 -t- monochromatic light, the surface would appear as in Figure 8B, where the dot density is varied to represent alternating dark and bright bands of continuously varying intensity. Such bands are called fringes of equal thickness. They are formed because sites on the layer of equal thickness reflect the same intensity of light, according to equation (3). Because the reflectance is related to the thickness through the periodic cosine function, any sites differing in thickness by an integral multiple of 2d will also reflect the same intensity. In essence, this interfer-ence pattern is a type of thickness contour map of the layer ofthe specimen. This can be seen by comparing Figure 8B with Figure 8A, which represents thickness contour lines for the specimen. The contour spacing in Figure 8A has been chosen to be 2d to emphasize the similarity between the contours and the fringes.
Although the positions of the contour lines as defined above and the reflectance interference fringes coincide, the absolute value of thickness for the contour lines cannot be directly obtained from the interference fringes because of ambiguity.
In order to demonstrate this ambiguity, equation (3), which relates thickness to reflectance, will be solved for thickness by using the definitions of ~ and d from equations (2) and (4).
The expression for the thickness T as a function of reflectance of the specimen is found to be:

T = d ( 2~N + arccos( F(R) ) I ~ cos( eL ) (5) where, 20~68~8 F(R) = ( R + R rCL2rLS2 ~ rCL ~ rLS
/ [ 2 rcL rLs (l-R) ]
and N is an integer called the fringe order or interference order.

The ambiguity arises because the fringe order, N, is un-known.
For this reason, the monochromatic interference fringes are commonly used only when absolute thickness information is not needed, such as in a test of thickness uniformity.
However, if N can be determined, then the thickness of the layer at a site may be calculated from the monochromatic reflect-ance, R, using equation (5). Since all numerical implementations of the arccosine function return values in the range of O to ~
radians only, it is more useful to consider the fringe half-order number, H. The quantities H and N are related: the truncation of the quotient H/2 is equal to N. The fringe half-order number for a site having thickness T will be given by the truncation of the quotient T/d. For light at normal incidence (eL=o)~ the follow-ing relations replace equation (5):

H even, T = d t H ~ + arccos~ F~R) ) ] / ~ ~6a) H odd, T = d [ ~H~ - arccos~ F(R) ) ] / ~ (6b).

APPARATUS

A preferred apparatus for carrying out the methods of the 20~43 invention will now be described. Refer to Figure 22. Light beam 2216 emitting from collimated broadband light source 2200, is directed toward beam stop 2220. One of the known methods for producing collimated broadband light source 2200 is illustrated S in Figure 22. Incandescent white light bu]b 2202 directs light through field limiting aperture 2204 and collimating lens 2206.
White light bulb 2202 has enhanced infrared emission, and typi-cally emits light with wavelengths in the range from 400 nm (visible) to 2600 nm (infrared). As will be apparent to those skilled in the art, other suitable methods for producing colli-mated broadband light may be utilized.
Movable selecting mirror 2211 in position 2212 reflects the beam 2216 which emerges from collimated broadband source 2200 into beam direction 2226. (With movable selecting mirror 2211 in either position 2213 or 2214, laser light sources 2208 and 2210 are selected. The laser light sources are used to stimulate photoluminescence in specimens for photoluminescence mapping.) With selecting mirror 2211 in position 2214, light beam 2226 passes through opening 2223 in shield wall 2222 and impinges on partially reflecting mirror 2230. Shield wall 2222 blocks stray light in the apparatus.
Partially reflecting mirror 2230 reflects a portion of beam 2226 along beam direction 2232 into objective lens 2234. Beam 2232 underfills objective lens 2234. Objective lens 2234 is a high quality microscope objective with a numerical aperture chosen for the purpose of the invention. A typical value of the numerical aperture suitable for thickness mapping is 0.1.

Objective lens 2234 focuses beam 2232 to spot of illumina-tion 2236 on specimen 490, which is mounted on XYZ positioning stage 2256. Spot of illumination 2236 is the location on speci-men 490 where measurements are made. Under the direction of the apparatus operator or a computer program, computer 2252 directs positioning stage controller 2254 to position stage 2256 to illuminate the sites on specimen 490 at which measurements are to be made. Positioning stage controller 2254 and its interface to computer 2252 are not described, because such systems are well known.
Refer to Figures 4 and 22. The representative specimen on which thickness mapping is performed is shown generally at 490.
Specimen 490 comprises a thin layer 404 of one material overlay-ing a substrate 406 of a material of different refractive index.
The cover material overlaying thin layer 404 in Figures 4 and 22 is air, but this is not a restriction on the invention; thin layer 404 can be overlaid by other materials without impairing the utility of the invention. For thickness mapping, the cover material must be essentially transparent to the ranye of wave-lengths used to make measurements, and have a refractive index that is not equal to the refractive index of layer 404. Refer to Figure 4A. For simplicity, interface 408 between layer 404 and substrate 406 is shown as a plane parallel to the XY plane. In practicing the invention, interface 408 need not be a plane.
Refer to Figure 22. Light reflected from spot of illumina-tion 2236 is collected by objective lens 2234 and directed along beam direction 2238 to partially reflecting mirror 2230. A

2086~8 portion of beam 2238 is transmitted through partially reflecting mirror 2230 toward monochromator 2240 as light beam 2239. Light beam 2239 entering monochromator 2240 is reflected onto grating 2242, where it is separated into its spectral co~ponents by diffraction. Under the control of the apparatus operator or a computer program, computer 2252 directs stepping motor 2250 to select the angular position of grating 2242 and thereby the wavelength of the light exiting from the monochromator as light beam 2244. Such use of a computer-controlled stepping motor and monochromator is well known in the art.
Single wavelength light beam 2244 impinges upon photodetec-tor 2246. Photodetectors suitable for use with broadband light source 2200 include: a normal InGaAs photodiode for detecting infrared wavelengths from 900 nm to 1800 nm; an extended range InGaAs photodiode for detecting wavelength in the range 1300 nm to 2600 nm; and a silicon photodiode for detecting wavelengths in the visible to near infrared range. The output of photodetector 2246 is an electrical signal proportional to the intensity of the light falling on it. This signal is digitized by analog-to-digital (AJD) converter 2248 to produce the detector output valuewhich is stored in computer 2252. A/D data acquisition systems and interfaces are not described here because they are well known in the art.
The apparatus operator executes the methods of the invention by controlling computer 2252, which is pre-programmed to collect and process data. The interface between the operator and computer 2252 is typically a keyboard. Software tools available to the 2~85~8 apparatus operator include routines which display the collected data as digital images on computer monitors, gradient evaluating routines for finding edges in digital images, and smoothing filters for smoothing digital images. These tools, which are useful with the method of the invention, are not described in detail as they are known in the art.

DETERMINATION OF REFLECTANCE WITH APPARATUS

Calibration The manner in which the detector output value is used to determine the reflectivity at the spot of illumination 2236 on specimen 490 will now be described. First, the apparatus cali-bration procedure will be described.
Typically, the calibration specimen comprises only the substrate 406 of specimen 490. Alternatively, a highly reflec-tive front surface mirror i8 used as the calibration specimen.The reflectance of the calibration specimen is determined using a reflectometer or calculated by substiting the refractive indices of the materials comprising the calibration specimen into equa-tion (3) of the BACKGROUND section. The calibration specimen is mounted on positloning s~age 2256 and illuminated at spot of illumination 2236 by broadband light source 2200. It is only necessary to illuminate a single site on the calibration speci-men. Under the control of the apparatus operator and computer 225Z, steppinq motor 22~0 causes monochromator 2240 to scan 2 ~ 8 through the range of wavelengths to be used for thickness map-ping. Typically, for a specimen comprised of GaAs substrate and AlGaAs layer, the wavelength range is 775 nm to 850 nm and the resolution is 0.5 nm. The signal from photodetector 2246 for each wavelength is digitized by A/D converter 2248 and the re-sulting detector output value at each wavelength sent to computer 2252 where it is divided by the previously determined reflectance of the calibration specimen to yield the adjusted detector output value. The adjusted detector output values for each wavelength are stored in the computer in a table called the "reference spectrum".

Reflectance at a Single Site Refer to Figure 22 and Figure 4A. The method for determin-ing the reflectance at a single site on the specimen will now be described. Light from source 2200 incident at spot of illumina-tion 2236 on specimen 490 is partially reflected from surface 410 of thin layer 404 and from interface 408 between layer 404 and substrate 406. The light reflected from the two surfaces recom-bines and is directed towards the monochromator as described under APPARATUS. The apparat~s operator selects the wavelength to be used for the reflectance measurement. ~he detector output value at the selected wavelength which emerges from the A/D
converter is sent to the computer where it is divided by the adjusted detector output value at the same wavelength (obtained from the reference spectrum) to yield the measure of the reflect-ance at the spot of illumination 2236 of specimen 490. The 2~&6~48 reflectance at the spot of illumination 2236 is stored in the computer.

Reflectance at Grid Sites - Fringe Mapping The method of the invention for obtaining reflectances at many sites on a specimen will now be described. This process is called "fringe mapping".
The apparatus operator selects the wavelength of the light to be used for the reflectance measurements so that two or three interference fringes will be present across the width of the typical wafer. The selection of the light wavelength is based on the experience of the operator, or when required, the operator will conduct trials to determine a suitable light wavelength.
For a specific specimen, increasing the light wavelength will de-crease the number of fringes across the specimen and decreasing the light wavelength will increase the number of fringes across the specimen.
~ efer to Figure 4. Measurements of reflectance on a speci-men are made at sites defined by a rectangular sampling grid superposed on the specimen. The number and spacing of the grid lines is selected by the apparatus operator. Typically, there would be 200 to 300 grid lines across a 5 cm wafer. For clarity, the sampling grid 400 shown in Figure 4C has fewer grid lines than would be used in practice. In Figure 4A, grid 400 is shown superposed on specimen 4so. Typical sampling site 402 is shown 2~858~8 ln Figures 4A, 4B, and 4C. Refer to Figure 4C. The X- and Y-directions of Figure 4C correspond to the X- and Y-directions of positioning stage 2256. The position of a grid site can be specified by X and Y grid coordinates.
Refer to Figure 22. After the apparatus operator selects the fringe mapping parameters to be used, computer 2252 begins to collect the monochromatic reflectance data. Under the control of computer 2252 stage 2256 is positioned so that one of the grid sites at which reflectance is to be measured falls under spot of illumination 2236. The reflectance at each grid site is deter-mined in the manner described above and stored in an array called the "fringe map". The storage position in the fringe map corre-sponds to the grid coordinates of the grid site at which the reflectance is measured.

CHARACTERISTICS OF THE FRINGE MAP

Ideal Data The fringe map is a discrete representation of monochromatic interference fringes, and is therefore a digital image.
Refer to Figures 4 and 8B. Figure 8B is a representative plot of the fringe map obtained by the methods of the invention for thin layer 404 of specimen 490 of Figure 4A.
Refe~ to Figures 9A and 8B. Figure 9A is a representative plot of the reflectance values along a typical line P-Q sho~n in Fi~ure 8B, for ideal reflectance data. The reflectance curve in Figure 9A is smoothly varying. Rmin and Rmax are the minimum and 2~863~
maximum possible reflectances for specimen 490, and are calculat-ed using equation (3) of the BACKGROUND section. Extrema, such as 812, 810, 814 and 816 in Figure 9A, with reflectances very close to Rmin or Rmax are labelled fringe extrema. Other extre-ma, such as 902 in Figure 9A, are labelled local extrema. Thereflectance data are discrete, but closely spaced. A larger scale plot of the data in the vicinity of fringe maximum 812 is shown in Figure 9C.
The difference in layer thickness between a fringe maximum and an adjacent fringe minimum is one quarter wave, d, which is defined by equation (4) of MONOCHROMATIC INTERFERENCE FRINGES.

Non-Ideal Data Refer to Figures 9B and 9D, which show representative plots of non-ideal reflectance data. The high frequency features of Figure 9B are random measurement noise. Reflectance values in the vicinity of fringe maximum 920 of Figure 9B are plotted in Fi~ure 9D, to show the effect on a larger scale. Typically, the maximum reflectance value at 920 is not as close to the value Rmax as it is for ideal data. Large narrow s~ikes, which are usually downwardly directed (typically 930 and 932 of Figure 9B) are also present. Spikes are due to imperfections in the layer or dust particles on the surface. The methods of the invention require smoothly varying reflectance data, and it is therefore necessary to remove noise and spikes from non-ideal data before processing. This is accomplished in the manner described in the DATA CONDITIONING section below.

20~8'18 Other non-ideal features which may be found in fringe maps are invalid regions, fringe discontinuities and contrast varia-tion. Each of these will be briefly described.
Invalid regions of the fringe map include areas outside the boundary of the specimen, and near the outer edges of some speci-mens. For example, the edges of a semiconductor wafer bearing an epitaxial layer are known to have highly irregular reflectivi-ty, due to unusual growth conditions for the layer. Invalid regions are excluded from processing.
A typical fringe discontinuity is shown in Figure 21. Such discontinuities are the result of abrupt layer thickness changes in the specimen. Regions of the fringe map separated by fringe discontinuities are processed separately.
Typical contrast variation is shown in Figure 9B. The re-flectances at fringe maxima are not necessarily constant; like-wise reflectances at fringe minima are not necessarily constant.
As a consequence, the fringes show contrast variation across the specimen. For example, difference in reflectance between fringe minima 922 and fringe maximum 920 is not the same as the differ-ence in reflectance between fringe maximum 926 and fringe minimum924 in Figure 9B. The method of the invention compensates for fringe contrast variation.
The treatment of the non-ideal features of the fringe map is described in detail in the section NON-IDEAL DATA PROCESSING
METHoD-2 Q ~

DATA CONDITIONING

The fringe map is a digital image, and well-known digital image processing techniques are utilized to condition the data for further processing. Such techniques are described in DIGITAL
IMAGE PROCESSING by Kenneth R. Castleman published by Prentice-Hall (New Jersey. 1979) and other publications.
The first step in data conditioning is smoothing. Based on experience, the apparatus operator chooses the smoothing filter to be used. Typical smoothing filters include: 5-point averaging window applied along each row of the fringe map; and convolution of the fringe map with square averaging matrices, typically 3x3 or 5x5 in dimension. The smoothing step removes most of the random noise features. Smoothing in this manner does not com-pletely remove large narrow spikes~ The residual spikes in the smoothed data are broader and smaller in amplitude than the spikes in the original data.
Residual spikes are next removed from the fringe map. The apparatus operator chooses one of the known edge-finding or gradient filters stored in computer 2252 to locate residual spikes. The reflectance values at the residual spikes are re-moved from the fringe map and replaced with values interpolated from the surrounding values in the fringe map.
The data condi~ioning procedures described above prepare non-ideal data for further processing.
In some cases, the conditioned fringe map closely approxi-mates the fringe map for ideal data, and the conditioned data are 20~58~
:hen processed by the same methods that are used with ldeal data to obtain the thickness map.

LOCATION OF FRINGE EXTREMA IN THE FRINGE MAP

Based on experience the apparatus operator selects the spatial density of grid sites so that the fringe extrema can be accurately located.
A preferred method for locating fringe extrema in data which are smoothly varying will now be described.
Rmax and Rmin are calculated.
Based either on experience or reflectance data statistics, the apparatus operator specifies values for fa~tors K1 and K2.
The value. of Kl is typically O.O1; the range of values for K2 is typically O.Ol-0.05. The operator also specifies an integer value for the number K3, which is greater than 3 (typically 5).
Parameters used in the determination of fringe extrema are calculated according to the following relations:

Tolerance TOL = Kl~ Rmax - Rmin ) Significance Factor ~R = K2( Rmax - Rmin ) Upper Threshold Rhi = Rmax - TOL
Lower Threshold Rlo = Rmin + TOL

A row in the fringe map is selected for processing.
The column grid coordinate of the first site to be consid-ered in the row is stored in the computer variable START. The column grid coordinate of the final site to be considered in the row is stored in the computer variable STOP. The computer varia-20g6g'1~

ble EXTREME is initially set equal to START. R(EXTREME) is thereflectance value at grid coordinate EXTREME. Value (EXTREME+1) is initially stored in computer variable C.
A straight line is fitted to the first K3 points of the selected row, and the slope of the line is determined. The re-flectances at column grid coordinates are sequentially examined in ascending order commencing with the site at column C. The reflectance at column grid coordinate C is R(C). If the slope of the line is positive, the maximum seeking procedure described below is followed, otherwise the minimum seeking procedure, also described below, is followed.

The maximum seeking procedure will now be described. The follow-ing calculations and decisions are made at each stage:

DIFF = R(EXTREME) - R(C) is calculated;
if DIFF < 0, EXTREME is set equal to C;

if DIFF > ~R, EXTREME is flagged as a maximum and stored;
C is incremented by one to become equal to C~1;

if C > STOP, the process of locating extrema ends;

if EXTREME is flagged as a maximum and stored, the minimum seeking procedure is commenced;

otherwise, the maximum seeking procedure is continued with the incremented value in C.

208~48 The minimum seeking procedure will now be described. The follow-ing calculations and decisions are made at each stage:

DIFF = R(EXTREME) - R(C) is calculated;

if DIFF > O, EXTREME is set equal to C;

if DIFF < ~R, EXTREME is flagged as a minimum and stored;

C is incremented by one to become equal to C+1;

if C > STOP, the process of locating extrema ends;

if EXTREME is flagged as a minimum and stored, the maximum seeking procedure is commenced;
otherwise, the minimum seeking procedure is continued with the incremented value in C.

The maximum and minimum seeking procedures are applied alternately as described until the end of the data (column STOP) is reached. The column grid coordinates at each extremum are stored for later use.

Once the extrema in the row have been located, all extrema having reflectance greater than Rhi are classified as fringe maxima; extrema having reflectance less than Rlo are classified as fringe minima. All others are classified as local extrema.
The extrema classifications are stored along with the grid coor-dinates for future processing.

2 Q ~ 8 For an example of the process, refer to Figure 15A, which shows a plot of reflectance data along a typical row. The extrema which must be found by the algorithm are visible to the reader in Figure 15A, and the following paragraphs summarize what would occur during the processing of such data.
The fitting of a straight line to the reflectance values at the left end of the plot of Figure 15A yields a positive slope;
thus, the trend is increasing, and a maximum is sought.
Figure 15B is a plot of the reflectance values for the columns in the vicinity of maximum 1501. Maximum 1501 is located along the row by sequentially examining each of the reflectance values in columns C = 1, 2, 3,..., J-2, J-1, and so on, while always storing the position of the largest value found in varia-ble EXTREME. The reflectance values are generally increasing until column J. Since it is the largest value found so far, J
is stored in variable EXTREME. The value in column J+1 is less than that in column J, as are the values in column J+2, and so on. Eventually, in column J+6, the reflectance has decreased from the value in column J by ~R. Thus, maximum 1501 is assigned to the location of column J, and column index J is stored for future use. The difference in position between the actual re-flectance extremum and the nearest grid site corresponding to column J is insignificant. After finding a maximum, a minimum is sought.
Refer to Figures 15A and 15C. Minimum 1503 is located along the row by sequentially examining the reflectance value from column J+7, J+g, and so on, always storing the column position of 2~68~8 the smallest value found in variable EXTREME. In Figure 15C, the reflectance values in the vicinity of 1517 of Figure 15A are plotted, and they are generally decreasing until column K. Since it is the smallest value found so far, K is stored in EXTREME.
The value in column K+1 is greater than that in column K, as are the ~alues in columns K+2, through K+10, but thereafter they tend to become less again. Since none of the reflectance values in columns K+1 through K+12 exceed the value in column K by more than ~R, column K is not considered to be the minimum. Thus, insignificant extrema are ignored at this stage. Refer to Fig-ures 15A and 15D. The reflectance values in the vicinity of 1503 are plotted. The process continues looking for a minimum, stor-ing the position of the smallest reflectance as the values in columns K+12 through L are examined. Eventually, in column L+9, the reflectance has increased by ~R from its value in column L.
Therefore, minimum 1503 is located in column L. Once a minimum is found, a maximum is sought in a similar manner to before.
Referring to Figure 15A, fringe maxima 1501, 1505, 1507, 1511, and 1513 are the extrema with maximum reflectance greater ~han Rhi, and fringe minima 1503 and 1509 are the extrema with minimum reflectance less than Rlo. Refer again to Figures 15B
and 15D. The threshold values are shown to identify fringe extrema.
Extrema are located and classified for any row of the fringe map in a similar manner. Likewise, the procedure i5 used on any portion of a row, by taking the starting and ending positions as required.

2~8~4~

BRACKET SITES

To reduce the number of independent thickness measurements that must be made while carrying out the method of the invention, a subset of the total set of grid sites comprising the fringe map is chosen for thickness determination. The members of the chosen subset are called bracket sites. The rules for selecting the locations of bracket sites will be presented for each embodiment of the invention.

THICKNESS DETERMINATION AT A SINGLE GRID SITE

Refer to Figures 4 and 22. The method for determining the ; thickness of the thin layer 404 at a specific site on specimen 490 will now be described. Positioning stage 2256 is moved to so that spot of illumination 2236 falls on the grid site at which the thickness is to be determined. Under the control of computer 2252, the reflectance is measured at each of the calibration wavelengths to yield the discrete reflectance spectrum at the site. The discrete reflectance spectrum is stored in a discrete reflectance table in computer 2252. The thickness of layer 404 at the specific grid site on specimen 490 is determined using computer 2252 to mathematically fit the discrete reflectance spectrum to its known functlonal form in the prior art manner referred to in BACKGROVND. The thickness at the grid site is 20~48 ored in the computer along with the coordinates of the grid site.

HALF-ORDER NUMBER DETERMINATION AT A SITE OF KNOWN THICKNESS

The half-order number at a site in the fringe map having known thickness is determined in the following manner. The fundamental thickness increment, d, is calculated by using equa-tion (4). The known thickness is divided by d; the decimal fractional part of the quotient is discarded; the resulting integer is the half-order number at the site.

THICKNESS MAPPING

The methods of the invention for converting the reflectance data stored in the fringe map to the thicknesses at the corre-sponding grid sites will now be described. Three methods will be described: (1) the TWO-DIMENSIONAL REGION PROCESSING METHOD; (2) the ROW-BY-ROW PROCESSIN~ METHOD; and (3) the NON-IDEAL DATA
PROCESSING METHOD. Methods (l) and (2) are used when the re-flectance data are ideal, that is, with uniform fringe contrast and without discontinuities or noise. Methods (1) and (2) are used to process a rectan~ular hlock of data that falls within the specimen boundaries. Methods (1) and (2) can readily be extended to process any area contained within the boundaries of a specimen that is made up of rectangles. Method (3) processes data that 2~68~

cannot be processed by Methods (1) and (2).

TWO-DIMENSIONAL REGION PROCESSING METHOD

The method of the invention for processing two-dimensional regions will be explained with reference to Figures 4A, 8B, lO, and 11. The steps in the method are also presented in the flow-chart of Figure 12. Specimen 490 of Figure 4A is representative of the rectangular area of a specimen wafer for which the thick-nesses at the grid sites are to be determined by the method of the invention.
The apparatus operator initiates the thickness mapping process by initializing parameters and issuing the commands necessary for computer 2252 to collect and process the data.

Step 1. Mapping the Monochromatic Interference Fringes.
The fringe map for the rectangular area of representative specimen 490 is obtained in the manner described above in the section Reflectance at Grid Sites - Fringe Mapping.

Step 2. Determining Threshold Values.
Rmax and Rmin for specimen 490 are calculated and threshold values Rhi and Rlo are determined, as previously described above in the section LOCATION OF FRINGE EXTREMA IN THE FRINGE MAP.
Rmid = (Rlo+Rhi)/2 is also calculated.

Step 3. Locating the Fringe Extrema~
The grid coordinates of the fringe extrema are determined 2~S~8~8 ar each row of the fringe map, in the manner described in the section LOCATION OF FRINGE EXTREMA IN THE FRINGE MAP.

Step 4. Partitioning into Regions With Fringe Extrema The next step is to partition the fringe map into regions, each region being the set of grid coordinates of contiguous sites that have the same half-order number. Areas between adjacent fringe extrema are suitable regions. Well known image segmenta-tion techniques are used to partition the data into the regions delineated by the fringe extrema, and each region is given a unique identification number. Image segmentation is described in Chapter 15 of DIGITAL IMAGE PROCESSING by Castleman and Chapters 7&8 of DIGITAL IMAGE PROCESSING by R.C. Gonzalez & P. Wintz published by Addison-Wesley (Mass. 1987) and other publications.
Amongst the known image segmentation techniques are region grow-ing and line segment extraction. The grid coordinates of the~ites within each region and the corresponding region identifica-tion number are stored together in computer 2252 for processing in the next step.

Figures 10 and 11 will be used to illustrate the result of the image segmentation process. Figure 10 is a representation of the regions of constant half-order number obtained by applying image segmentation techniques to the fringe map of Figure 8B.
Each grid coordinate is uniquely assigned to a region. 1001 and 1002 of Figure 10 are typical regions. Figure 11 is an enlarge-~5 ment o~ region 1001 of Figure 10, in which the dots are the posi-2~85~`~8 ions of grid sites belonging to region 1001. In practicing theinvention, the sites would be more densely packed. The density of sites shown within region lOO1 has been reduced for the sake of clarity; this reduction does not affect the method of the invention.

Step 5. Selecting a Region.
A region corresponding to one of the identification numbers is selected for thickness determination at the sites within the region.
For illustrative purposes, consider region lOO1 of Figure 11 to be the selected region.

Step 6. Selecting a Bracket Site Within the Selected Region.
A bracket site for the selected region is located in the following manner. The reflectance at each of the grid sites belonging to the selected region is compared with Rmid, and the grid coordinates of the site having reflectance closest in value to Rmid are stored. The storPd coordinates define the position of the bracket site in the selected region.
For illustrative purposes, consider "S" of Figure 11 to be the bracket site in region lOQ1.

Step 7. Determining the Half-Order Number for Selected Region.
The thickness of the thin layer at the brac~et site in the selected region is determined by the method described above, in the section THICKNESS DETERMINATION AT A SINGLE GRID SITE. The thickness is stored in an array called the "thickness map." The 2~5848 thickness map has the same grid coordinate system as the fringe map. The half-order number for the selected region is determined by determining the half-order number at the bracket site in the selected region as previously described in the section HALF-S ORDER NUM~ER DETERMINATION AT A SITE OF KNOWN THICKNESS.

Step 8. Calculating Thickness Values for Selected Region.
The thickness values at the remaining sites in the selected region are calculated as follows. A site in the selected region at which the thickness has not been determined is selected. The thickness at this site is calculated by substituting the reflect-ance value for the site retrieved from the fringe map and the half-order number for the selected region into equation (6a) when the half-order number is even, and into equation (6b) when it is odd; the calculated site thickness is stored at the appropriate location for the site in the thickness map. Equations (6a) and (6b~ are given in the section MONOCHROMATIC INTERFERENCE FRINGES.
The thicknesses at all sites in the selected region are deter-mined in a similar manner.

Step 9. Repeating For Remaining Regions.
The steps 5-8 are repeated until the thickness values have been determined for all regions of the fringe map.

The thickness map is obtained when all regions of the fringe map have been processed.

2~o~

ROW-BY-ROW PROCESSING METHOD

The row-by-row processing method will now be described. The row-by-row method is simpler to program for computer implementa-tion because advanced computer memory structures and algorithms to segment the fringe map are not required. Figure 13 is the flowchart for the row-by-row thickness mapping process.
The apparatus operator initiates the thickness mapping process by initializing parameters and issuing the commands necessary for computer 2252 to collect and process the data.

Step 1. Mapping the Monochromatic Interference Fringes.
The fringe map for the rectangular area of representative specimen 490 is obtained in the manner described above in the section Reflectance at Grid Sites - Fringe Mapping.

Step 2. Determining Threshold Values.
Rmax and Rmin for specimen 490 are calculated and threshold values Rhi and Rlo are determined, as previously described above in the section LOCATION OF FRINGE EXTREMA IN THE FRINGE MAP.
Rmid = (Rlo+Rhi)/2 is also calculated.

Step 3. Selectinq a Row of the Fringe Map.
A row of the frin~e map is selected for processing. Typi-cally, the first row selected is the row closest to the middle (centre) of the frin~e map. Let the row number of the first 20~ 4~
,lected row be m.

Step 4. Locating Fringe Extrema Along Selected Row.
The fringe extrema in the selected row are located, as previously described in the section LOCATION OF FRINGE EXTREMA IN
THE FRINGE MAP.

Step 5. Selecting Bracket Sites Along Selected Row.
A set of bracket sites for the selected row is chosen in the following manner.
The located fringe extrema for the selected row partition the row into intervals. The first interval is between the first column of the selected row and the first located fringe extremum.
Each pair of adjacent fringe extrema define an interval in the row. The last interval is between the last located fringe extre-mum and the last column of the selected row.
In each interval, the site having reflectance closest to ~mid in value is chosen as a bracket site for the selected row.
The grid coordinates of the bracket sites are stored in computer 2252 for future use.
For purposes of illustration, refer to Figure 15A~ The application of the above bracket site selection procedure locates the bracket sites 1500, 1502, 1504, 1508, 1510, lS12, 1514 and 1516.

Step 6. Determining Half-Order Number at Bracket Sites.

The half-order number is determined at each bracket site in 20868~
he selected row in following manner.
There are two cases to be considered: case 1) when the selected row is the first row to be processed; case 2~ when the first row is other than the first selected row.

Case 1). Half-order numbers are independently determined at each bracket site. To determine the half-order number independently at a particular bracket site:
the reflectance value, R, at the bracket site is retrieved from the fringe map and the quantity TEST = ¦R-Rmid¦ is calculat-ed;
if TEST < TOL, where TOL is defined in the section LOCATING
FRINGE EXTREMA IN THE FRINGE MAP, then the thickness, T, is determined at the bracket site as described in the section THICK~
NESS DETERMINATION AT A SINGLE GRID SITE, otherwise (TEST > TOL), a more suitable site for half-order number determination is sought along the column of the bracket site as follows:
fringe extrema are located along the column which contains the bracket site in the selected row; this is done in a similar manner to that described in LOCATION OF FRINGE E~TREMA IN THE
FRINGE MAP;
the interval between fringe extrema ~or between a fringe extremum and the edge of the fringe map) along the column which contains the bracket site in the selected row is identified;

2S the site in the identified interval which has reflectance most nearly equal to Rmid is located (this is the same procedure as choosing a bracket site along the column);

2~8~
the thickness T at the located site is determined in the manner described in the section THICKNESS DETERMINATION AT A
SINGLE GRID SITE;
The half-order number, H, is determined from the thickness T
in the manner described in the section HALF-ORDER NUMBER DETERMI-NATION AT A SITE OF KNOWN THICKNESS;
the half-order number at the bracket site is equal to H.

For purposes of illustration, refer to Figure 19. Site 1900 of Figure 19 is a bracket site at column C of the selected row N, where the half-order number is to be determined independently.
TEST is calculated and found to be ~reater than TOL; therefore another site in column C is sought. Typically, 1902 and 1904 are a fringe extrema, located in column C by the methods described previously in the section LOCATING FRINGE EXTREMA IN THE FRINGE
MAP. In the example of Figure 19, 1901 is the site between fringe extrema 1902 and 1904 which has reflectance closest to Rmid. The thickness and half-order number are determined at 1901 as previously described. The half-order number at 1900 is set equal to that at 1901.

Case 2). There is a previously processed adjacent row to the selected row. The half-order number at a particular bracket site in the selected row can often be quickly ascertained from values calculated for the previously processed adjacent row, as will now be described:
if any of the nearest R4 neighbours (in the adjacent row) to the bracket site are at fringe extrema, then an independent 2Q86~

determination of the half-order number for the bracket site is made, as described in case l); the value of K4 is specified by the operator of the apparatus (typically K4=3);
otherwise, the half-order number at the bracket site is equal to the half-order number at the site with the same column number in the previously processed adjacent row.

For illustrative purposes, refer to Figure 16A, which shows the arrangement of grid sites along a portion of several rows.
Row N is the currently selected row, and row N-1 is the previous-ly selected row. 1620 and 1630 are bracket sites in row N, wherethe half-order number is required. The thickness, and therefore half-order number, has already been determined at all of the sites in row N-l. For this example, K4 equals 3. If none of the sites 1622, 1624 or 1626 are located at fringe extrema, the half-order number at bracket site 1620 is equal to that at adja-cent site 1624; otherwise, an independent determination of half-order ~umber is required. Similarly, the half-order number at bracket site 1630 is set equal to the half-order number at site 1634, provided that none of the sites 1632, 1634 or 1636 are at a fringe extremum.

Step 7. Calculating Thickness Values for Selected Row.
Thickness values are calculated at sites across the selected row of the fringe map as follows.
The first bracket site in the selected row is chosen as starting point. ~ is set equal to the half-order number at the 2~ 48 tarting bracket site. Then H is used in the appropriate equa-tion (6a) or (6b) to calculate thickness for each site along the row to the right until a fringe extremum is reached. Each calcu-lated thickness value is stored in its place in the equivalent row of the thickness map. At the fringe extremum, H is set equal to the half-order number at the next bracket site along the row to the right of the fringe extremum. This value of H is then used in equation (6a) or (6b) until the next fringe extremum is reached. The calculations continue in this manner until the end of the row is reached. Then, the portion of the row to the left of the starting bracket site is processed in a similar fashion in a leftward direction, until the end of the row is reached. As a result of this, the thickness values (and half-order numbers) at all sites along the row are determined.
For purposes of illustration, refer to Figure 16B, which shows the arrangement of sites along a portion of a typical selected row of the fringe map. 1620 and 1630 bracket the site 1691, which has been previously identified as the site of a fringe extremum. In this example 1620 is selected as the start-ing point for the row.
The determined half-order number for bracket site 1620 i5 used in the appropriate equation (6a) or (6b) as previously described to calculate the thickness from reflectance values at each site sequentially to the right of 1620, and the thickness values are stored in the thickness map. At fringe extremum 1691 the half-order number from the next bracket site alon~ the row to the right, 163~, is used and the calculations using the appropri-2 Q 8 ~

te equation (6a) or (6b) continue for sites to the right.Processing continues in this manner, until the end of the row.
Upon reaching the right end of the row, the portion of the row to the left of starting bracket site 1620 (which has not been proc-essed) is processed to the left in the same manner as describedimmediately above.

Step 8. Repeating for Remaining Rows.
If there are more rows remaining to be processed in the fringe map, then an unprocessed row is selected adjacent to a previously processed row (step 3). After the first selected row, m, rows are selected in sequence m+1, m+2, ..., until the highest row; and then, the rows are selected in the sequence m-1, m-2,...
1, to complete the processing of the fringe map. Steps 4 through 7 are repeated for each selected row.

It will be apparent that the procedure just described is also applicable to processing fringe map data on a column-by-column basis. The thickness map can be verified after row-by-row processing by column-by-column processing.

NON-IDEAL DATA PROCESSING METHOD

The method of the invention for treating non-ideal data will now be described. Typically non-ideal data contains noise, spikes and contrast variations. See the section ~on-Ideal Data of CHARACTERISTICS OF THE FRINGE MAP for details. The method 2Q~'a~

removes noise and spikes from the data, and compensates for contrast variations. The steps of the method, which uses the techniques of row-by-row processing, will now be described. The sequence of steps for producing a thickness map from non-ideal data is shown as a flowchart in Figure 14.
The apparatus operator initiates the thickness mapping process by initializing parameters and issuing the commands necessary for computer 2252 to collect and process the data.

Step 1. Mapping the Monochromatic Interference Fringes.
The fringe map for a rectangular area is obtained in the manner described above in the section Reflectance at Grid Sites -Fringe Mapping. The area of the fringe map may extend beyond the boundaries of the specimen to be processed.

Refer to Figure 17. Figure 17A shows a typical row of non-ideal reflectance data. Figures 17B-E illustrate how the row of Figure 17A i~ affected by applying the steps of the non-ideal processing method.

Step 2. Identifying Invalid Areas.
The normal range of reflectance values for a particular type of ~pe~imen i5 known. The reflectances at sites in the fringe map are compared to the normal range. Sites at which the re-flectance is outside the normal range are assigned a flag value, typically -1. Areas of the fringe map having the flag value are considered to be invalid, and are ignored during processing.

2Q~848 Aese invalid areas are generally located outside the boundaries of the specimen.
Based upon experience, the apparatus operator identifies any additional invalid areas, such as the edge regions of the speci-men, which are to be excluded from processing.

Refer to Figure 17A, which is the typical row of reflectance data extending across the specimen. The ends of the row corre-spond to the edge regions of the specimen, and have been marked "INVALID". The invalid areas are not displayed in Figures 17B
through 17E.

Step 3. Partitioning Fringe Map into Discontinuity-Free Sub-Areas Gradient (edge finding) methods are used to search for and locate discontinuities. If discontinuities are present, they partition the fringe map into sub-areas. Each sub-area is free of discontinuities. Each of these sub-areas is processed indi-vidually. If the fringe map is entirely free of discontinui-ties, which is frequently the case, then the "sub-area" consists of the entire fringe map, less invalid areas. Figure 21 is a representation of a fringe discontinuity which divides the fringe map into two sub-areas. There may be many sub-areas in a specif-ic specimen, and they are identified and stored in a similar manner to that used to identify and store regions in the section TWO-DIMENSIONAL REGION PROCESSING METHOD.

Step 4. Selecting a Discontinuity-Free Sub-Area.

2n~ g one of the discontinuity-free sub-areas is selected for processing.

Refer again to Figure 17A, in which a discontinuity is evident in the reflectance data. The data to the left of the discontinuity belongs to one discontinuity-free sub-area, and the data to the right belongs to another sub-area. For illustrative purposes, the section to the left of the discontinuity is in the selected sub-area for further processing, and only this section is shown in Figures 17B-E.

Step 5. Smoothing Reflectance Data.
The data in the selected sub-area of the fringe map is smoothed in the manner previously described in the section DATA
CONDITIONING.

Figure 17B shows how the reflectance data along the typical row in the selected sub-area appears after smoothing.

Step 6. Determining Threshold Values.
Rmax and Rmin for the specimen being processed are calculat-ed and threshold values Rhi and Rlo are determined, as previously described above in the section LOCATION OF FRINGE EXTREMA IN THE

FRINGE MAP. Rmid = (Rlo+Rhi)/2 is also calculated.

The horizontal dashed Iines in Figure 17 are the theoretical minimum and maximum reflectance, Rmin and Rmax, of the specimen.

~g>~)~48 Step 7. Selecting a Row.
A row in the selected sub-area is selected for processing.
Typically, the first row selected is the row closest to the middle (centre) of the fringe map. Let the row number of the first selected row be m.

Step 8. Locating Extrema Along Selected Row.
Extrema are located along the selected row and classified as previously described, in the section LOCATION OF FRINGE EXTREMA
IN THE FRINGE MAP; grid coordinates of ALL located extrema are stored for future reference. In Figure 17B, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718 and 1719 are extrema in the typical selected row. The located extrema are initially classi-fied as "fringe" or "local'l type, according to the criteria of the section LOCATION OF FRINGE EXTREMA IN THE FRINGE MAP. In Figure 17C, extrema marked F are classified as fringe extrema, and extrema marked L are classified as local extrema.

Step 9. Selecting Bracket Sites Along Selected Row.
From the selected row, a set of sites which bracket the located fringe extrema in the row is determined as described in the section ROW-BY-ROW PROCESSING METHOD. In Figure 17C, bracket sites 1720, 1711, 1722, 1723, 1724, 1725, 1726, 1727, 1728, and 1729 are located. Note that the local extremum 1711 is also selected as a bracket site by this method.
The data values in the row are scanned to determine all of 2 ~ 4 ~

the locations where the Rmid threshold is crossed. The grid coordinates of the site having reflectance closest to Rmid at each crossing are temporarily stored. The locations of the crossing sites are compared to the locations of the previously determined bracket sites, and those crossing sites which are not already bracket sites are selected as additional bracket sites.
The correspondin~ crossing site grid coordinates are stored with the previously determined bracket site coordinates in the select-ed row for future use. As a result, all peaks and valleys of the reflectance along the row which extend across the Rmid threshold are bracketed, reqardless of "fringe" or "local" classification.

In Figure 17C, 1723 and 1728 are the additional bracket sites located by the Rmid threshold crossing technique. Extrema 1713 and 1717, which initially are classified as local extrema are now bracketed. The additional bracket sites allow the clas-sifications of the extrema to be verified, as discussed below.

Step 10. Determining Half-Order Number at Bracket Sites.
The half-order numbers for each of the bracket sites in the selected row are determined in the same manner as described in the ROW-BY-ROW PROCESSING METHOD.

Step 11. Rationalizing Extrema Classifications.
The half-order numbers of the bracket sites in the selected row are used to check the correctness of the initial extrema classifications. If the initial classification is correct, the 20g~ 4~
xtremum is considered verified. If the initial classification of the extremum is incorrect, the classification of the extremum is corrected. This procedure, which is called rationalization, will now be described.
The change in half-order number, Delta H, between each pair of adjacent bracket sites in the selected row is evaluated. The values for Delta H are integers, most often o or 1, but sometimes 2, 3 or higher. Each pair of adjacent bracket sites is selected in turn, and the number and type of the extrema between them are determined. The following cases must be considered for each pair of bracket sites.
Delta H = 0:
if the number of fringe extrema is equal to 0 or 1, the extrema within the pair of selected bracket sites are correctly classified;
if the number of fringe extrema is not equal to 0 or 1, all fringe extrema within the pair of selected bracket sites are reclassified as local extrema.

Delta H = 1:
if the number of fringe extrema is equal to 1, the extremum within the pair of selected bracket sites is correctly classified;
if the number of fringe extrema does not equal 1, then if there is no relativ~ phase chanqe between reflections at the two interfaces for the layer, which occurs when nC<nL<nS, then if the larger half-order number for the 208~4~

pair of bracket sites is even the local maximum within the bracket sites which has reflectance closest to Rmax is reclassified to be a fringe maximum;
if the larger half-order number for the pair of bracket sites is odd the local minimum within the bracket sites which has reflectance closest to Rmin is reclassified to be a fringe minimum;
or if there is a relative phase change of ~ radians between reflections at the two interfaces for the layer, then if the larger half-order number for the pair of bracket sites is odd the local maximum within the bracket sites which has reflectance closest to Rmax is reclassified to 2~ be a fringe maximum;
if the larger half-order number for the pair of bracket sites is e~en the local minimum within the bracket sites which has reflectance closest to Rmin is reclassified to be a fringe minimum;

2 ~ 8 elta H = 2:
if the number of fringe extrema is equal to 2, then the extremum within the pair of selected bracket sites is correctly classified;
if the number of fringe extrema equals o, then the local maximum closest to Rmax and local minimum closest to Rmin are reclassified to be fringe extrema;
if there is one fringe maximum, then the local minimum closest to Rmin is reclassified to be a fringe minimum;
if there is one fringe minimum, then the local maximum closest to Rmax is reclassified to be a fringe maximum.

The process for reclassifying extrema can be extended for cases when the value of Delta H is greater than 2 by applying the following rules.
1) Delta H has magnitude unity or zero for bracket sites around an interval containing a single fringe extremum;
2) Delta H has magnitude zero for bracket sites around an interval containing only local extrema.

3) Delta H equals the total number of fringe extrema in the interval between two bracket sites;

4) for even values of Delta H, the number of fringe maxima must equal the number of fringe minima between two bracket sites;

5) for odd values of Delta H, fringe maxima are one less or one greater in number than fringe minima in the interval between the bracket sites; when there is no relative phase change be-20~5348 tween reflections from the cover/layer interface and from the layer/substrate interface (nC<nL<nS), then there are more fringe maxima between two bracket sites when the larger H is even.
Conversely, there are more fringe minima between two bracket sites when the larger H is odd. For cases when there is a rela-tive phase shift of ~ radians between the reflections at the two different interfaces, then these stated rules for odd Delta H are reversed.

An example to illustrate the rationalization process in part follows. Consider the case where the interval between two brack-eting sites has a single fringe maximum and Delta H equals 2;
there is a misclassified local minimum in the region. The local minimum is reclassified to fringe minimum, even if it does not satisfy the Rlo threshold. As another example, if the refractive indices for the specimen are such that nC<nL<nS and an interval i8 bounded by two sites with half-order numbers of 137 and 142, then there must be 3 fringe maxima and 2 fringe minima between the sites. If the extrema classifications do not support this, then extrema are reclassified accordingly.

The correction of misclassifications may lead to more fringe extrema for the row. Each fringe extremum along the row is checked to determine whether or not it is bracketed. All addi-tional bracket sites that are needed to bracket the fringe extre-ma are selected and their half-order numbers are determined as before. The rationalization process continues until the row is fully rationalized, that is, the extrema classifications obey the ~Q~53~8 above stated rules.

For a specific example, refer to Figure 18, which is a composite of Eigures 17B and 17C on a larger scale. Typical changes in half-order number, Delta H, between each pair of adjacent bracketing sites, are listed below the data in Figure 18. Delta H has unit or zero magnitude around fringe extrema such as 1715, 1716, and 1718, in accordance with rule 1). Delta H around local extrema such as 1717 is zero, in accordance with rule 2).
Around local extremum 1713, the change in half-order number between the bracket sites 1722 and 1723 is found to be non-zero.
Therefore, 1713 is misclassified. The other extrema in the row depicted in Figure 18 are correctly classified.
Refer to Figure 17D, where 1713 is reclassified to be a fringe extremum (marked F).

Step 12. Stretching Reflectance Data.
The data values in the selected row are stretched so that the fringe minima have reflectance Rmin and the fringe maxima have reflectance Rmax. Intermediate data values are stretched proportionally between Rmin and Rmax.
Refer to Figure 17E, which illustrates the effect of stretching the reflectance data of Figure 17D. The method for stretching data will now be described.
Stretching transformations are the relations which transform observed data into a form from which thickness values can be 2Q~6~48 alculated using equation (6) of MONOCHROMATIC INTERFERENCE
FRINGES. The stretching transformations depend upon the local characteristics of the reflectance profile for the selected row.
There are three types of row "pieces", each of which requires a specific stretching procedure. The row is stretched piecewise until the whole row is stretched~ The different types of pieces and the corresponding stretching procedures will now be de-scribed.
1) The first type of piece to be considered is that which is between a fringe minimum and an adjacent fringe maximum (or between a fringe maximum and an adjacent fringe minimum). Refer to Figure 20A, which shows the reflectance profile along a row between a fringe minimum, W, and a fringe maximum, Z. The trans-formation for stretching the piece from W to Z will now be de-scribed. The quantities used to calculate the stretching trans-formation are shown in Figure 20A. ~1 and ~2 are the increments between the reflectance at W and Rmin and reflectance at Z and Rmax respectively:

RW + ~1 = Rmin, and Rz + ~2 = Rmax. (7) Let P be a site along the selected row in the W-Z interval having stored reflectance R (in the fringe map). P is located a distance u from the observed minimum, W, and a distance v from the observed maximum, Z. A preferred transformation for the 2~ reflectance R in the W-~ interval, is:

R' = R + ~

2~ ~ ~ 3 ~

( v ~l + u ~2 ) / ( u + v ) (8).

~1 and ~2 may differ significantly, and they can be positive or negative quantities. Within the row being processed, all such pieces between a fringe minimum and an adjacent fringe maximum are found. For each piece, ~l and ~2 are evaluated according to equation (7); the data within the piece are then stretched ac-cording to transformation (8). u and v are calculated for each site in the piece, and ~ is added to the reflectance value R in the fringe map to yield R'. The new value of reflectance R', is stored in the fringe map in place of the value R. The procedure is obviously extendable to the case where the fringe maximum is to the left of the fringe minimum.

2) The second type of piece to be considered is that which is between two fringe extrema of the same type, and with type 1 pieces on either side. The results of stretching the pieces of type 1 in the row are used in stretching pieces of type 2. Refer to Figure 20B, which presents a representative case of a type 2 piece, where there are two fringe maxima, E and F, with no inter-vening fringe minimum. The point Q is the most significant local minimum between the fringe maxima. Q is called the principle local extremum and has reflectance RLE. Q divides the piece be-tween the fringe maxima into the intervals of width A and B.
Reflectance values in the outside regions, C and D, have been transformed when type l pieces were stretched. ~Cl and ~C2 for region C and ~D1 and ~D2 for region D, have been determined. The amount by which Q is stretched will now be determined using the '~Q~34~
results from previously stretched type 1 pieces C and D. Two quantities R'C and R'D are first calculated. R'C is equal to the transformed reflectance of site, QC~ nearest Q in pi.ece C
which has reflectance equal to RLE. Similarly, R'D is equal to the transformed reflectance of site, QD~ nearest Q in piece D
which has reflectance equal to RLE. The relations used are:

R'C = RLE + SC
R'D = RLE + SD

where the Sc and SD are defined for the pieces C and D according to the equation (8). The transformed reflectance value for the principle local extremum, Q, will be:
R Q = (B R'-c + A R'D) / (A + B) and the increment for Q is:
SQ ( B ~C + A ~D ) / ( A + B ).

The reflectances at all sites in the intervals A and B are then stretched individually, using the same functional form as given by equation (8). For a site PA in interval A with reflectance R, R' = R + ( vA SC2 + uA SQ )/( uA + vA ).

As before, uA and vA are distances from a site in interval A to each bou~dary for the interval. Reflectance values in interval B
are transformed similarly.
It is readily apparent that the case where the piece to be stretche~ falls between two fri.nge minima can be treated in a 2Q~48 anner analogous to that described for a piece falling between two fringe maxima.

3) The third type of piece to be considered is that which falls between the end of a row and a type 1) piece. Refer to Figure 20C, which depicts the reflectance profile along one end of a typical row of the fringe map. J is at the end of the selected row. In this situation, the interval N to G is stretched with equation (8) as previously described for the type 1) pieces. O represents any point in the G to J interval with reflectance R. The point P in the interval N to G has reflect-ance R. The transformed reflectance at O is set equal to the transformed reflectance at P. This gives the same amount of stretching in the interval G-J as an adjacent interval N-G.

After the piecewise stretching of the portion of the row within the selected sub-area, the data are suitable for thickness calculations.

Step 13. Calculating Thic~ness Values for Selected Row.
Thickness values are calculated at sites across the selected row within the selected sub-area of the fringe map, as previously described under ROW-BY-ROW PROCESSING METHOD.

Step 14. Repeating for Remaining Rows.

Steps 7-13 are repeated for all remaining rows within the selected sub-area, in a similar manner to that descri~ed under ROW-BY-ROW PROCESSING METHOD.

208~48 Step 15. Repeating for Remaining Sub-Areas Steps 4-14 are repeated for all remaining sub-areas, thus completing the thickness map for the specimen.

USES FOR THE THICKNESS MAP

A typical use for the thickness map is to display the map as a colour coded video image on the computer 2252, for human in-spection. Statistics for the layer thickness, such as mean value and standard deviation, are also calculated from the values in the thickness map. These statistics can be displayed by computer 2252.
In practicing the invention, thickness maps are obtained for thin layers of material grown by molecular beam epitaxy (MBE) on semiconductor wafers, prior to the production of devices on the wafers. Thickness maps allow the useful area to ~e determined on each wafer, and various processing parameters are set according to the thickness values in the thickness maps. Also, detailed analysis of the thickness variations on the wafers has been made possi~le because of the introduction of the m~thods of the inven-tion. This has lead to improvements in the MBE growth techniques used.

CONCLUSION, RI~MIFICATIONS AND SCOPE

The methods and apparatus of the invention significantly reduce the number of spectral measurement operations which must be performed to map layer thickness, compared to the number required with prior art methods. Large speed improvements over prior art methods which make independent absolute thickness determinations at each site are achieved by using the information inherent in monochromatic interference fringes.
Because the methods of the present invention use high speed computer processing of data, which is available at relatively low cost, and a~e not dependent on fast measurement hardware, which is expensive, the methods of the present invention are more economical for thickness mapping than the prior art methods.
Improvements in computer processing speed will further enhance the advantages of the method of the invention over the prior art methods.
Three methods of the invention have been described under the separate headings l) TWO-DIMENSIONAL REGION PROCESSING METHOD, 2) ROW-BY-ROW PROCESSING METHOD and 3) NON-IDEAL DATA PROCESSING
METHOD; other methods which combine steps from these three methods are possible. For example, the following sequence of steps could be used to obtain a thickness map:
the monochromatic fringes are mapped (common to 1,2,3);
fringe map data are smoothed (from 3);
the extrema are located, stored, and classified in each row of the fringe map (from 1);
row-by-row rationalization and stretching procedures are applied to each row of the fringe map (from 3);
the fringe extrema are used to partition the fringe map into two dimensional regions of constant half-order number (from 1);

2~8~'~4~

region-by-region processing is used to calculate the thick-ness values (from 1).
As well, one of the three main methods of the invention can be used to verify the thickness map generated by one of the other methods. This can be done at the discretion of the apparatus operator. Thickness maps generated by row-by-row processing can also be verified by column-by-column processing.
Other variations in the mode of operation of the apparatus used to map thickness will now be described. If the reflectance data are sufficiently well behaved, thicknesses may be calculated along a row while the next data row is being collected by the apparatus. This would yield an improvement in speed.
The data collection and processing phases can be separated, and carried out with different computers. Processing the data on a computer other than apparatus-controlling computer 2252 in-creases the rate at which specimens are processed, because the apparatus of Figure 22 is free to collect data without having to pause to analyze the data. In this mode of operation, the appa-ratus obtains a fringe map, and determines the thickness of the layer at all required sites in advance of fringe map analysis.
This is possible when the specimens are known to have highly consistent thickness profiles. Epitaxial layers on semiconductor wafers, whi~h usually have monotonic thickness profiles from wafer centre to edge, tend to produce "bullseye" (concentric rings) fringe patterns. For this type of frin~e pattern, it is known that the only thickness measurements from spectral reflect-ance that are required are across the middle row of the fringe 6g 2Q~6~48 map. Therefore, the fringe map can be obtained, and the thick-ness determined at selected sites spaced across the middle row of the fringe map. The data can then be processed on another com-puter. When the fringe pattern is not of consistent form from specimen to specimen, the apparatus operator must select the sites where thickness measurement are made using spectral re-flectance.
The specimen studied by the thickness mapping instrument need not be a semiconductor wafer bearing a thin layer. The methods of the present invention are equally applicable to other materials, and even to thin films which are not supported by a substrate material, such as a thin polymer film web. It will be clear to those skilled in the art that the positioning stage could be adapted to bear such self-supporting thin dielectric layers for use with the present invention.
It will also be evident to those skilled in the art that thickness maps can be made when the material comprising the layer is partially absorbing to the light provided by the broadband source. This involves modifying equation (3) for absorbing (complex refractive index) materials; an analysis of this prob-lem is found in the previously mentioned textbook by Born & Wolf.
This modified form of the equation is implicitly dependent upon layer thickness, but is solvable by known numerical means (see for example U.S. Patent 4787749 by Ban et al.).
Other apparatus can be used to map thickness in accordance - with the methods of the present invention. For example, the described apparatus can be made confocal, giving slightly better 2 0 ~ 8 spatial resolution in the plane of the layer and much better resolution in depth. An autofocussing mechanism could also be installed, to help assure high quality of data.
In the description of the apparatus of the invention, a S broadband source which supplies visible and infrared wavelengths is described. However, it will be seen by those skilled in the art that there is no reason why the method cannot be employed with an apparatus containing broadband W light sources, if the specimen requires such wavelengths.
Another possible embodiment of the present invention com-prises a computerized ellipsometer which is adapted to map thick-nesses using the method of the invention. Those skilled in the art will be familiar with the techniques of ellipsometry, and it will be evident that an ellipsometer is capable of generating the required monochromatic reflectance data. In this case, the device would not employ the polarizer and the analyzer during the mapping of the monochromatic fringes. The monochromatic fringes would be observed at an oblique angle to the specimen. During the analysis of the fringe map, the absolute layer thickness at selected bracket sites would then be found from an ellipsometric ~easurement, which would also provide the refractive index and absorption of the layer. An ellipsometer can be used with all of the methods of the invention; the only change required is that the s~ep of determining the thickness from spectral reflectance measurement be replaced by the equivalent step of measuring the thickness using ellipsometry.

208~8 The scope of the invention should be determined by the ap-pended claims and their legal equivalents, and not snlely by the examples given.

Claims (6)

1. A method of determining a thickness of a thin layer of a specimen at sites on the specimen defined by a grid, said method using at least one of a monochromatic and spectral reflectance measuring apparatus that has been calibrated, said method comprising the steps of:
(a) measuring reflectance at various sites on said grid on the specimen;
(b) storing the reflectances measured;
(c) partitioning the sites in said grid into groups of contiguous sites where sites of the same group have the same half-order numbers;
(d) selecting a site within each group of contiguous sites and determining the half-order number of the sites selected;
(e) calculating the thickness of the layer for each of the sites selected; and (f) storing the thickness measurements for the sites.

2. A method of determining a thickness of a thin layer of a specimen as claimed in Claim 1 where the measured reflectances are stored in a first array, said first array having co-ordinates that correspond one-two-one to co-ordinates of said grid and storing the thickness measurement for various sites in a second array, the second array having co-ordinates corresponding to co-ordinates of said grid on a one-to-one basis.

3. A method of determining the thickness of a thin layer of a specimen at sites on the specimen defined by a grid, said method using a monochromatic reflectance measuring apparatus that has been calibrated, said method comprising the steps of:
(a) measuring the monochromatic reflectance at a particular site in said grid on the specimen;
(b) storing the measured monochromatic reflectance at the chosen site in a first array, said first array having co-ordinates that correspond one-to-one to co-ordinates of said grid;
(c) repeating steps (a) and (b) for additional sites where the monochromatic reflectance is to be measured;
(d) partitioning the sites in said grid into groups of contiguous sites for sites of the same group that have a same half-order number;
(e) selecting a site within each group of contiguous sites at which the half-order number is to be determined;
(f) determining the half-order number at each of said sites;
(g) selecting a group of contiguous sites;
(h) selecting a site within the selected group of contiguous sites at which the thickness of the layer is to be determined;
(i) calculating the layer thickness at the selected site utilizing the monochromatic reflectance data for that site from the first array and the half-order number of the selected group of contiguous sites;
(j) storing the thickness measurement for that site in the second array, the second array co-ordinates corresponding to grid co-ordinates on a one-to-one basis;
(k) repeating steps (h), (i) and (j) until the thicknesses of all of the sites within the selected group of contiguous sites have been calculated, repeating the steps (g), (h), (i) and (j) until the thicknesses at all of the sites within all of the groups of contiguous sites have been calculated, producing the measurements from the second array.

4. A method for mapping the thickness of a thin layer of a planar specimen comprising the steps of:
(a) determining the monochromatic reflectance at each site of a rectangular grid covering an area of the specimen;
(b) storing the reflectances in an array which has one-to-one correspondence with the sites of the grid;
(c) partitioning the grid sites, each partition consisting of the subset of grid co-ordinates for a contiguous group of grid sites having the same half-order number;
(d) selecting a site within each partition at which the half-order number is to be determined;
(e) determining the half-order number at the selected site in each partition;
(f) selecting a partition for processing;
(g) calculating the thickness at each grid co-ordinate within the selected partition using the reflectance value at the grid co-ordinate and the determined half-order number;

(h) storing the calculated thickness values in an array which has one-to-one correspondence with the sites of the grid; and (i) repeating steps (f) to (h) until all of the partitions have been processed.

5. The method of Claim 1 wherein step (d) is carried out manually by the operator of a reflectance measuring apparatus.

6. An instrument for determining a thickness of a thin layer of a specimen at sites of a specimen defined by a grid, said instrument comprising an optical scanner having at least one broad band light source, means to focus the light source on a small spot on said specimen, means to collect the light in reflection, a monochrometer with a diffraction grating to spectrally resolve the light, a photodetector to determine one of spectral and monochromatic reflection at said small spot, a computer connected to control the instrument to take measurements at various sites on said specimen, to calculate the reflectance and half-order number as well as the thickness of the thin layer at each site, to store the results obtained and to produce the results when desired.