(Color online) Excess carrier density Δn(x,τb ) in a silicon brick as a function of bulk lifetime τb and absorption depth corresponding to an illumination at 900 nm and infinite surface recombination velocity after Bowden et al. 11 Δn(x,τb ) globally increases with increasing bulk lifetime and the maximum of Δn(x,τb ) shifts to larger sample depths. The boxes represent the values for Δnavg and Weff assuming a bulk lifetime of 10 and 100 μs, respectively.
(Color online) Luminescence intensity spectrum emitted by a volume element at a depth of 500 μm with and without photon reabsorption calculated for 270 and 300 K sample temperature. A strongly reduced signal in the short wavelength range of the spectrum is visible. The temperature dependence of the spectrum is reduced in case of a long optical pathway as it is chosen here.
(Color online) Comparison of the calculated luminescence intensity as a function of wavelength λ and bulk lifetime τb for both short (950–1000 nm) and long pass (1050–1180 nm) configuration with a measurement setup using a silicon CCD camera (left). The integral luminescence intensity (right) measured with a long pass filter increases more strongly with increasing bulk lifetime than the signal measured with a short pass filter.
(Color online) Calculated photoluminescence intensity ratio (PLIR) transfer function as a function of bulk lifetime for the experimental setup used in this study. The PLIR transfer function is shown in both linear (left) and double logarithmic scale (right) revealing a significantly smaller absolute PLIR for n-type than for p-type silicon.
(Color online) High resolution absolute bulk lifetime image obtained by a single doping normalized photoluminescence image calibrated with QSSPC data. The color scale gives the absolute bulk lifetime in μs. This center brick shows highest lifetimes in the middle of the brick with strong gradients to the bottom and top.
(Color online) Absolute bulk lifetime image obtained by a photoluminescence intensity ratio from a side face of an edge brick. The color scale gives the absolute bulk lifetime in μs. The vertical stripes are due to surface artifacts caused by an inhomogeneous polish.
(Color online) Relative doping density image of the same brick side face as in Fig. 6. The positive gradient of active dopants is visible from bottom to the top of the brick. The illustrated lower doping in the bottom and top region of the brick and in the low lifetime region on the side is caused by an artifact in the PLIR method potentially caused by a defect luminescence signal.
(Color online) Bulk lifetime from a single PL image calibrated with QSSPC (left) in direct comparison with the PLIR image (middle) of the same brick side face. Both images are shown on the same relative color scale revealing good qualitative and quantitative agreement in the center part of the brick. The indicated line scan confirms good quantitative agreement in high lifetime regions in the central part of the brick (right). Artificially high lifetimes are reported by the PLIR method in areas of low lifetime especially at the top and bottom of the brick as indicated.
(Color online) Doping density profile obtained from photoluminescence intensity ratio throughout the brick in comparison with Eddy current data and the Scheil equation. The photoluminescence data matches well to both the Eddy current data and the calculations from the Scheil equation in the center of the brick (fraction 0.2–0.85), but it does not contain correct doping density information in the bottom and top region of the brick. A particular good match of the luminescence data is found in a narrow quasi-mono crystalline part of the brick (labeled PLIR narrow).
(Color online) The intensity ratio transfer function calculated for three different excitation wavelengths on double logarithmic scale for p-type silicon. The ratio increases with increasing laser excitation wavelength. The corresponding coefficient is calculated to be constant with bulk lifetime at 0.23% per nm.
(Color online) Intensity ratio transfer function calculated for three different sample temperatures on double logarithmic scale for p-type silicon. The ratio reduces with increasing temperature resulting in a negative temperature coefficient. The temperature induced change in the intensity ratio can be quantified to be in the range of −0.4 to −1% per Kelvin finding its minimum at around 20 μs.
Estimated parameter uncertainties and calculated resulting uncertainties on the intensity ratio transfer function PLIR and on the bulk lifetime τb itself.a
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