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            Spectrometer is a critical component of MProbe measurement system. What is the connection between spectrometer specification     and thickness measurement ability? What  spectrometer parameters are important and  affect the measurement perfomance? How Dynamic Range(DNR) or Signal-To-Noise Ratio(SNR) are connected to  thickness and n&k measurement. How wavelength resolution or wavelength range are affecting measurable thickness range? 

Fig. 1 Low optical contast measurement – coating on substrate with R.I. difference < 0.1  Reflectance fringes p-p amplitude ~ 0.1%. Model is fitted to the data and thickness/n&k are determined accurately.

                    DYNAMIC RANGE

               Dynamic range is a ratio of the biggest and the smallest signals that can be measured. We are using 16 bit ADC, so maximum signal is 65535 ADC counts. The smallest signal is the RMS signal (noise) of the dark current. It is, primarily, determined by read-out noise of the detector. For CMOS S11639 detector, used in Ariel spectrometer, the RMS noise is ~ 13 to 14 ADC counts. This gives the dynamic range of ~ 5000. It follows, that we can measure reflectivity from 100% to 0.02%. Of cause, 0.02% will be the detection limit (signal =noise); so we can accurately measure ~ 0.1% reflectivity difference at low reflectivity level. One such measurement is shown on Fig.1 (left). The amplitude of the interference fringes in reflectance  spectrum is ~0.1% and they are very clear: the filmstack model is fit to the measured data and thickness/n&k can be accurately determined. 

                  For comparison, SonyILX and Toshiba 1304 detectors that are used in many popular visible spectrometers, have DNR ~ 1000. It would be more difficult to make the measurement  on Fig. 1 with one of those detectors. On another hand, high quality CCD detector like S10420 has DNR ~ 40K to 50K and one can, potentially, accurately measure 0.01% reflectivity. In practice, a very accurate calibration of fixed pattern noise would be  needed to measure a signal at that low signal level.  

Fig. 2 The effect of averaging on Dynamic Range and Signal-To-Noise.  


                 The SNR provides a measure of the signal quality – it compares the  power of the signal to the average power of noise. The largest SNR is achieved for the maximum signal. There are many sources of noise but the large signal is shot-noise limited i.e. the main contribution to the noise is coming from the photons shot-noise.Short noise is defined by the  fluctuation of the detected photons and  it is described by a square root of the number of photons. For CMOS S11639 detector, the full well electrons capacity is 80ke. Assuming ~ 0.6 Quantum efficiency, we have a maximum SNR ~ 350.  It is clear that SNR is significantly lower than Dynamic range.  For comparison, Sony ILX detector has ~ 250 SNR and Toshiba 1304 detector ~300 SNR. A high quality CCD S10420 has a maximum of ~ 550 SNR.   How can we improve it?


           Both Dynamic range and SNR can be improved by using signal averaging. Fig. 2 shows effects of 10 averages and additional boxcar averaging with different number of pixels. The default measurement recipe in MProbe system has 10 averages and 5 pixels boxcar average. This gives ~ 35K dynamic range and ~2500 SNR.

To increase DNR and SNR we trade-off measurement time and some wavelength resolution. Typical integration time is ~ 1ms (for 30% reflectivity). 10x averages increase integration time to ~ 10 ms. On the other hand, S10420 CCD detector has a minimum integration time of ~ 8ms. (In fact, S10420 has a low-noise/high DNR because it internally averages 64 rows of pixel – 8x improvement). This means that if there is enough light, one can achieve the better results with CMOS detector for the same integration/measurement time vs. CCD detector.


              CMOS S11639 is naturally linear for small signals (~ 30% of the range) and very non-linear for high signals. Non-linearity correction is critical for reflectance/ transmittance measurement because they rely on the reference to determine absolute values. In Ariel spectrometer – non-linearity is automatically corrected in the firmware. Non-linearity is always calibrated without offset. This means that offset and dark signal need to be accurately corrected for all measurements – otherwise non-linearity calibration will not be valid. In mass produced spectrometers, dark signal is not corrected and there is always offset. Users are expected to develop their own procedure to deal with that e.g. take and subtract dark signal measurement, etc.  In Ariel spectrometer dark signal and offset are calibrated and corrected for a range of operating temperature So, the measurements can be taken without any worry about dark signal, read more… The effect of the  offset is most prominent for low reflectance measurements ( Fig. 3) 

Fig. 3  Measurement of 35um polymer film.            Popular mass produced spectrometer is used as is, without offset/dark signal correction. Reflectance spectrum is limited and distorted , due to non-linearity and offset. Ariel spectrometer has automatic correction of dark signal/offset and gives correct spectrum measurement without additional steps.  

                      WAVELENGTH RESOLUTION

              Wavelength resolution is selected based on required thickness range. High resolution allows  measurement on thicker films but requires a more narrow wavelength range. But the narrow wavelength range limits the minimum thickness that can be measured. To maximize wavelength resolution for a given wavelength range one needs to minimize abberations and optimize the slit width.

For the Vis system wavelength range is ~ 400-1000nm (600 nm range) and for UVVis 200-1000nm (800nm range). For 2048 pixels detector we have a pixel resolution of ~ 0.3 -0.4nm. The RMS spot (abberations) is ~ 10um. This means that using 20um spit we can achieve <1nm resolution. Read more about thickness ranges

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