edfas.org 9 ELECTRONIC DEV ICE FA I LURE ANALYSIS | VOLUME 24 NO . 4 This simplified example illustrates the need for appropriate noise floor determination as well as cutting off the noise data before applying the system transformation factor. The measured noise is caused either by parasitic light reaching the detector or by the thermal activities of the detector itself. However, both mechanisms result in the generation of countable events on the detector. These events generate the noise floor even during spectral photon emission measurements. As shown in Fig. 6 the application of the spatially related system transformation factor Csys(λ) to a noise signal itself produces an unevenly distributed spectrum. Therefore, it is essential to cut off the noise floor from themeasured raw data before applying Csys(λ). To do so, we have chosen to truncate the raw data at a threshold (TH) that is calculated by the median of the noise floor (NFmedian) plus a variable percentage of NFmedian: TH = NFmedian + NFmedian · ζ | ζε[0;1] Eq 3 Figure 7 shows a spectrum measured from a FET in saturation with a varying noise cut off threshold value ζ of 0 to 4%. Correction of bulk silicon absorption. The system transformation factor Csys(λ) compensates for the properties of the SPEMsystemitself. However, if the photon emission has to pass bulk silicon before reaching the optical parts of the SPEM system, the absorption that occurs within the bulk silicon is not addressed by the system transformation factor Csys(λ). The absorption characteristics of siliconhighly dependon thewavelength considered as well as the doping concentration of the silicon.[13] For substrate doping concentrations well below 1016 cm-3, an absorption coefficient α(λ) as given in References 14 and 15 can be assumed. It must be kept in mind that these values do not reflect the doping concentration. However, photon emission detectors like an InGaAs or a MCT detector are sensitive in the spectral range where the absorption characteristics of silicon are strongly affected by the doping concentration. Therefore, the choice of the correct absorption coefficient data set is important to compensate for absorption within the bulk silicon. More accurate data sets can be extracted from commercial software such as TCAD. Once a suitable dataset is selected, thewavelengthdependent intensity loss due to bulk absorption can be compensated using the Beer-Lambert law:[16,17] I(z,λ) = I0(λ) · e-a(λ)z Eq 4 Whereas I(z,λ) are from the PE detector measured raw data Iraw(z,λ), α(λ) is wavelength dependent absorption coefficient, and z is the thickness of the bulk silicon. A fewsimple transformation steps give thewavelength dependent intensity of the photon emission I0(λ): I0(λ) = Iraw(z,λ) · ea(l)z Eq 5 In Reference 12 the tab “Correction of absorption” shows an exemplary implementation for the correction of the bulk silicon absorption. Applying lens-specific system transformation factor. The correct raw data was extracted, taking into account the noise levels as well as the absorption within the bulk silicon. Now the nonlinear signal transformation due to the optical system can be addressed by applying the system transformation factor Csys(λ). Equation 2 can be used directly to give the correct spectral data Ispec(λ): Ispec(λ) = I0(λ) · Csys(λ) Eq 6 Normalizing (optional). The absolute intensity of the measured spectra cannot be easily compared to each other. If several measurements are to be compared to each other, it is recommended to normalize the extracted spectra to a predefined wavelength. This should be done automatically with a predefined wavelength as implemented in Reference 12 in the tab “DataProcessing.” Smoothing (optional). Even though the noise floor has been removed as described previously, noise is an additive phenomenon. This means that when measuring low intensity spectra, the noise may still be at least partially in the order of magnitude of the signal itself. An additional smoothing algorithm, for example moving average, can be implemented. Fig. 7 Spectral photon emission data from a FET in saturation with different threshold values chosen to determine the noise floor.
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