Knowledge

The benefits of the BMT TRICI Transmission Infrared Correlation Interferometer operation principle

Theoretical considerations regarding the common interferometers

Usually the commercially available instruments to measure the wafer thickness which are based on short coherence interferometry evaluate the reflected light beams from the top interface and the bottom interface of the sample.

There is no problem with this kind of setup as long as the surface isn’t coated by one or several layers, e.g. SiO₂ or Si₃N₄.
As one can see from the sketch above the film on the Si surface forms a Fabry-Perrot interferometer with unfavourable consequences for the resulting interferogram. Depending on the layer thickness and layer material totally unpredictable results may arise. The reason for this is due to phase shifts of the light rays which are reflected from the interfaces. If one knows the physical parameters of the layer system a simulation of the resulting interferogram can be done from which one can judge the fidelity of the thickness measurement. A detailed discussion how to calculate the resulting interferogram for a given layer system is given in the references.

The dielectric layer acts as a coupled resonator and shifts the phase of the transmission depending on the thickness of the substrate and layer configuration in an unmonotone unlinear manner. This additional phase shift cannot be compensated for by calibration.

It turns out that interferometer configurations which measure the substrate thickness in reflection show large resonance phases and measurement errors which are impossible to compensate for.

The following graph shows the so-called complex contrast (which is a measure for the visiblity of the fringes and therefore the measurement result) for a silicon substrate which is coated with a SiO₂ film. The graph must be read as follows. The visibilty is represented by the curve for various thicknesses t of the layer. At the right hand side the curve starts at t=0. The visibility is given by the distance of the various points on the graph to the origin. The distance between the marked points on the graph is 4 nm thickness increase of the layer along the graph from the starting point t=0. As can be seen up to a layer thickness of approx. 150 nm the

visiblity changes more or less monotonically and therefore the measurement result is predictable if one calibrates the instru-ment properly. But if the layer thickness gets larger then the curve turns round which means that in spite of the fact that the true layer thickness increases the measurement result indicates a smaller thickness of the silicon substrate/layer system. As can be clearly seen the graph changes its direction in an unpredictable manner with increasing layer thickness which means that the measurement result is more or less wrong. For certain layer thicknesses the graph aprooaches the origin which means that there is no measurement possible since the visibility of the fringes is zero. For different substrate/layer systems the graph will look different and for more than one layer more complicated which makes it impossible to get out of this predicament.

In the following graph the dotted line represents the increasing sample thickness (substrate + layer) and the (periodic) curve below shows the measurement result of an interferometer measuring in reflection.

The above graph shows the shift of the interferogram due to an SiO₂ layer on a Si substrate for the reflective operation mode of common interferometer devices.

New transmissive interferometer

In order to minimise and even avoid the measurement errors of common systems an alternative method was devised. The setup is shown below.

The incident light beam is not reflected by the wafer but passes it and is reflected by a mirror. On it’s way to the detector it pas-ses a second time the sample which increases the signal/noise ratio. In this setup the wafer shifts the phase of the measurement branch beam with respect to the reference beam which is a measure of the thickness of the wafer.

Calculating the complex contrast for this setup in analogy to the reflective mode interferometer as discussed above results in this graph:

The simulation was done for a silicon substrate thickness of 379 µm and for a variable layer thickness d:  0 nm < d < 425 nm. The layer thickness t is shown on the red curve starting from t=0 in steps of 5 nm. The resulting contrast K as defined by Michelson is given by

that is the distance of the curve points (=layer thicknesses) to the origin. The contrast K is smaller than 1 since some light is lost due to reflections at the sample surfaces. As can be seen the contrast varies with increasing layer thickness. The induced additional phase is given by the angle between the point on the curve under consideration and the real axis. For interferometers working in the reflective mode these phase effects can assume large values corresponding to large errors. Comparing the graph above with that on page 2 the difference is obvious. For the transmissive interferometer the phase changes are not only very much smaller but also entirely predictable which enables a calibration of this kind of instrument.The following graph shows the shift of the interferogram due to the phase changes of an SiO₂ layer on a silicon wafer with a thickness of 379 µm.
The bottom line (which is the difference between the straight line and the phase shift) represents the additional phase shift induced by the layer. Again, there is a marked difference to the graph on page 3. Not only is the phase change much smaller but also slowly changing in a predictable manner.

The following graph shows exemplary interferograms.

For a silicon substrate with thickness 379 µm and a SiO₂ layer of thickness 100 nm a shift of the correlogramm as shown in the bottom picture is measured.

Surface roughness

All simulations were done for smooth surfaces. Increasing roughness results in an increasing deterioration of the correlogram.

[1] K. Leonhardt and H. J. Tiziani, Optical Topometry …, Journal of Modern Optics, (1999) page 101..114.

TRICI Short Coherence Transmitted Light Interferometer for the Thickness Measurement of Si Membranes

The thickness of thin membranes and MEMS can be measured in a simple and automated manner using a transmission short coherence interference technique by choosing a suitable wavelength range in the infrared. The method evaluates the phase difference between the object and reference beam and the actual instrument can accommodate a wide range of thickness measurements.

1. Introduction
There is a need for the thickness and surface profile measurements of coatings, overlays, foils and membranes of different materials. Whereas in some applications the speed of measurement is important in others a high accuracy is required and a suitable measurement method must take into account features such as optical transparency, surface roughness and changes of material. As has previously been shown a change of material gives rise to a phase jump thereby modifying the thickness measurement independent of the measurement method used. One can easily deduce from the Heisenberg uncertainty principle that there are only two possible kinds of optical displacement measurement methods. The first is the aperture dependent procedure of which a variety of different implementations exist, such as autofocusing, confocal microscopy, triangulation, fringe projection, conoscopy and the chromatic abberation method whereas the second type has only one representative which is commonly called white light interferometry. This latter method has the unique feature that the measurement uncertainty is independent on the aperture of the objective lens which enables in many cases, unless the light level is too low, to measure surface features with a high aspect ratio. The accuracy of this method is unlimited by the underlying physics but in the end is determined by the signal to noise ratio, the surface roughness and scattering behaviour of the object, and instrumental features such as dynamic range, transfer function and thermal and mechanical stability.
We have chosen  to use for the thickness measurement of Si membranes a short coherence interferometric method which allows a reasonable stand off independent of the measurement accuracy and has some distinct advantages as outlined below.
The principle of two-beam interferometry¹ is applied for this new transmission infrared short coherence interferometry method (TRICI).

The need to measure the thickness and surface profiles of Si membranes isn’t new. A first instrument for such an application was developed and built by one of the authors 15 years ago for IBM to measure the stress in silicon masks used for X ray lithography².
Due to the delicate nature of membranes only non contact measurement methods are applicable and a natural choice is then an optical method, namely an autofocusing sensor. These instruments feature high accuracy, are very fast³ and have a small footprint of the probing beam.

The thickness of thin membranes and MEMS can be measured in a simple and automated manner using a transmission short coherence interference technique by choosing a suitable wavelength range in the infrared. The method evaluates the phase difference between the object and reference beam and the actual instrument can accommodate a wide range of thickness measurements.

Fig. 1   Instrument with 2 sensors

A suitable setup is shown in Fig.1. Two opposing sensors are mounted to a stable U shaped bracket and measure both sides of the object.

The results which one gets from this instrument are satisfactory but an inherent weakness is the thermal stability of the dimensions of the sensor holder and the sensor itself which may heat up whereby the measured displacement value then shows some drift. A frequently used nulling procedure is therefore advisable utilising a suitable thickness standard.                                                                              

A number of instruments of this kind are presently used in industry for the non-contact thickness measurement of various objects, be they transparent or opaque.
In the visible wavelength range transparent for objects with reasonably smooth surfaces we employed a modification of the method described above. This means only one autofocus sensor is required. As illustrated in Fig. 2a the objective lens is scanned through it’s displacement range and this procedure delivers two intensity peaks with a displacement of n·t when the beam focus coincides with the object surfaces. This can even be extended to several interfaces. It has been shown that such a thickness measuring method works even for glass or plastic plates with a thickness of more than 1 mm but there must be sufficient light reflected from the second surface.

Fig. 2 a+b  Thickness measurement with one sensor

Another embodiment is depicted in Fig. 2b.

The sensor measures the distance to a reflecting surface and the object thickness modifies the length of the light path n·t. A shortcoming is the resulting abberation of the beam spot which is dependent on the refractive index n. Also good measurement accuracy depends on a high numerical aperture thereby restricting the working distance. Designed in this way the instrument is less sensitive to vibrations and thermal drift.

Fig. 3  TRIRCI for thickness measurement

The advantages of this white light interferometric displacement measuring method makes it a suitable procedure for the thickness measurement application which is described in the following paragraphs.


3. Theoretical considerations
The useful applications of the TRIRCI (Transmission-Infrared-Coherence-Interferometer) are:

1.  to find a suitable spectral range for the thickness measurement of Si membranes using WLI
2.  to recognise and find possible error signals and echos within the interferograms
3.  to calculate the interference characteristic curves which vary with the membrane thickness and the
necessary displacement of the piezo actuator.


3.1 Simulation of the interferogram
A monochromatic plane wave-component, originating from the centre C of the entrance pupil EP in Fig. 3, reflected by the mirror MO, and passing through the silicon membrane twice can be written as:

Fig. 4 Spectral distribution of the tungsten light, the spectral response of the camera and the resulting total spectral weight |a0|2.

Fig. 5 Spectral tansmissivity of a silicon membrane of thickness d = 5000 nm.

With increasing thickness d of the plate the transmissivity shifts to longer wavelengths and the variations with wavelength get more and more irregular. In Fig. 6 a thickness of t = 50000 nm is depicted. Note that the membranes are transmitted twice in each arm and the quadrate of the transmissivity gets effective in the interferograms. The beam splitters BS1 and BS2 have been modelled for simulation as a metal - dielectric layer system reproducing the spectral curves, given by the supplier of the components, as close as possible.

Fig. 6 Spectral tansmissivity of a silicon plate of thickness d=50µm

3.3 Interferograms

The integration over the wavelength range according to equation (5) was realised by a superposition of 320 spectral contributions with wavelength increments of Dl = 3.125 nm. Fig. 7 shows the result of these simulations. In Fig. 7a, the empty interferometer (without any plate in the object- and reference plate, d_Obj = d_Rf = 0) is depicted. The group of fringes is very narrow and the evaluation of the fringe maximum or the fringe centroid according to well established criterions should pose no problems. In Fig. 7b an object plate with d = 5000 nm is inserted into the object arm and a path difference is introduced to shift the centre of the resulting interferogram into a zero position. The central group is now broadened and accompanied by echoes of different orders, but the central group is still dominant and is separated from these echoes by displacements of very low modulation.

Fig. 7    Simulated interferogram. a) = top: Balanced interferometer with no plates in the object b) = bottom: An object membrane with d = 5000 nm is inserted into the object arm and a path difference is introduced to shift the centre of the resulting interferogram into zero position.	Fig. 8 a) = top: Balanced interferometer, b) = bottom: an object plate with  and in the reference beam, dObj = dRf = 0 d=  7500 nm is inserted into the object arm. The displacement of the interferogram is a function of the plate thickness.

In Fig. 8b the displacement of the central group is shown for a membrane thickness d = 7500 nm relative to the balanced interferogram in Fig. 7a. This displacement can be measured and can be related to the thickness of the plate. In Fig. 9 this relative displacement D is shown as a function of the thickness. Using a reference plate of thickness d_Rf = 45 µm, fringes within a thickness range of 42.5µm < d_Obj < 50µm can be captured using a stroke of 60 µm of the piezo translator. The simulation of this measurement shows an excellently linear dependence of the displacement on thickness d. The slope of this displacement curve is practically constant. Based on this dependence and using a set of well matched reference plates a large range of plate thicknesses up to approx. 80 µm can be covered. Assuming an uncertainty dD = l/10 of the interferometric measurement, for an average wavelength of the light of l_m = 1000 nm, the uncertainty of the thickness measurement would be better than dd = 30 nm.

4. Description of the instrument

The instrument is based on a Michelson interferometer whereby the reference mirror is periodically shifted using a piezo translator. The object beam is also reflected by a stationary mirror and the membrane under measurement is positioned in front of this mirror. Since the working distance is reasonably large there are no space problems. The reference path features a disk with several holes each of these being covered with a reference silicon specimen of known thickness.

Fig. 9 Displacement D = f(membrane thickness)

Both the reference and the object membrane introduce a phase shift in their light paths and as explained above the mutual shift of the corresponding correlograms represent the thickness difference between the reference and membrane specimens. By manually rotating the disk with the reference pieces one therefore determines the center of the thickness measuring range. If the displacement range of the actuator is large enough the reference membranes aren’t required.

The probing beam comes from a tungsten incandescent lamp and only the infrared part is used where the silicon is sufficiently transparent. Basically one can use this design for both spot and area thickness measurements whereby the area measurement requires a more expensive infrared sensitive camera. In order to be able to position the specimen adequately a separate illumination in the visible spectrum is provided and then on the monitor one sees the surface of the sample.

The measurement system comprises of the optical measurement head, a stable granite stand with X and Y motorised stages, the wafer holder and the customised software. It runs under Windows XP. The user puts the wafer with the etched membrane fingers/structures into the holder while the stages are in their loading position. Clicking on the Start key results in a completely automated measurement run.

In a table the user defines beforehand the measurement positions on the wafer and these are then measured one after the other.
The thickness data can be exported to Excel or processed otherwise. The system features a camera which serves to accurately find the measurement positions and to observe the individual features to be measured.

5. Summary
The instrument as described represents a new application of a transmission short coherence interferometer working in the infrared which lends itself well to measure the thickness and even area thickness variations of silicon membranes and MEMS upto 200 µm. In contrast to a tomographic interferometric set up, where the reflected wavefronts from the front and backside of the plate are detected in reflection, this instrument features a real “end mirror” in both arms of an interferometer providing superior performance. The object and reference plates are passed twice by the beam in each arm.
The reproducibility of the thickness measurements as found by extensive tests is in the nanometer range.

References

[1]     Born, M., and Wolf, E., Principles of Optics, Pergamon Press, 1970.
[2]     Breitmeier, U., Das Profil von Silizium, Elektronik 26/1991
[3]     Leonhardt, K. et al., Topometry for locally changing materials, Optics Letters 29 (1998), 1772-1774