As mentioned before, the light incident on the sample is measured by the reference cell with the EQE shown in figure 6-1 during the QSSPC measurements. The measured flux is then used to determine the cumulative photogeneration in the sample to calculate the minority carrier lifetimes from equation 3-1. Because of the reference cell EQE, as well as light reflection from the sample as-cut surface, there is a discrepancy between the incident light measured by the reference cell and the photogeneration in the sample [104].
Therefore, a coefficient is required to be defined in the QSSPC measurements to account for the such a discrepancy. The coefficient is called the optical constant and is to be set during the measurements, and is defined as:
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𝑂𝑝𝑡𝑖𝑐𝑎𝑙 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 =𝑇𝑜𝑡𝑎𝑙 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒
𝑇𝑜𝑡𝑎𝑙 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 𝑖𝑛 𝑡ℎ𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑐𝑒𝑙𝑙 6-1 The total photon absorption by the reference cell can be determined from the flash spectrum, filters transmissions and the reference cell EQE all illustrated in figure 6-1. However, the total effective photon absorption by the sample needs to be determined considering the sample surface reflection as well as the sample depth at which the photon absorption impact the lifetime measurements.
Figure 6-4: Absorption coefficient of the Cz p-type silicon block as-cut surface measured by a Lambda 1050 UV/VIS/NIR spectrophotometer from PerkinElmer Inc.
Figure 6-4 shows the surface absorption of the Cz p-type silicon block used in this section measured by a Lambda 1050 UV/VIS/NIR spectrophotometer from PerkinElmer Inc as a function of wavelengths. The total photons absorbed by the sample can be calculated from the flash spectrum and the filter transmissions in figure 6-1 and the absorption measured in figure 6-4. As
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mentioned, total effective photons are the photons absorbed by the sample mostly in the sensed region which affects QSSPC lifetime measurements but not far below the sample. Therefore, the depth assumption is important in determining the optical constant, particularly for the filters with longer cut-off wavelengths due to their larger proportion of photons with low absorption coefficients.
The calculated optical constants for each filter are shown in figure 6-5 as a function of depth for a standard '6 inch' rectangular silicon block with 156 mm thickness. The figure shows an almost flat optical constant as a function of depth for RG850 as most of the spectrum is short wavelengths photons absorbed just below the surface. Due to its deeper generation profile, RG1000 displays an increase as a function of depth below 5 mm and then a gradual increase afterward as there is little photogeneration beyond that depth. A similar increase is observed for EO1050 for depths greater than 40 mm. However, because of the relatively deep generation profile of EO1100 as well as the sharply decreasing tail in the EQE of the reference cell in that spectral range, the EO1100 optical constant varies strongly as a function of depth in the range up to 150 mm [104].
In principle, such a remarkable dependency on the sample depth could result in measured effective lifetimes that are less accurate, due to a higher sensitivity to the choice of the optical factor. Hence, there exists a trade-off between reducing the impact of the high SRV with deeper generation and the consequent uncertainty on the optical constant value.
Due to uncertainty in the reference cell EQE in the EO1100 filtered spectrum, the determined cumulative photogeneration is quite unreliable. Thus, the EO1100 filter is not a suitable choice for improved QSS lifetime measurements.
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Figure 6-5: Calculated optical constants for the four filters as a function of depth for a sample with an unpassivated as-cut surface measured by the BCT-400 system from Sinton Instruments.
There are several parameters to consider obtaining a proper depth for the suitable optical constant value to select during lifetime measurements, to ensure that the results are not overly affected by generation and recombination beyond that depth. The first is the tool sensitivity depth and its decay constant, which for the Sinton BCT-400 that is used in this work is about 2.5 mm, as discussed in detail in [80]. The carrier diffusion length is also an important factor as the lifetime measurement is affected by carriers diffusing into and out of the tool sensitivity range, which can cause miscounting of carrier generation and recombination. As the QSS conditions are generally only valid for lifetimes below 200 μs, the maximum expected carrier diffusion length is less than 1 mm to consider for the sample depth assumption. Moreover, as discussed above, the rate at which the optical constant value changes as a function of depth can also influence the results.
Considering the above factors, a depth of 10 mm was chosen in this work to calculate the optical constant values for the filters, as any generation and recombination beyond that depth will certainly not have any effect on the measurement results in this work.
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