Nonlinear Dependence of Photocarrier Radiometry Signals from p-Si Wafers on Optical Excitation Intensity

Abstract

The dependence of the photocarrier radiometric ͑PCR͒ signal on the intensity of exciting superbandgap laser radiation was investigated. It was shown that the amplitude of the PCR signal exhibits a supralinear dependence on laser intensity I 0 ␤ , with nonlinearity coefficient/exponent ␤ such that 1 Յ ␤ Յ 2. The power dependence of the amplitude is an important indicator of the photoexcited carrier recombination physics in semiconductors ranging between monopolar ͑␤ = 1͒ and bipolar ͑␤ = 2͒ limits. The study was made with laser beams of varying wavelength, power, and spotsize and with semiconductor silicon wafers with different transport parameters, especially recombination lifetime. One-dimensional and three-dimensional models of the nonlinear PCR signal dependence on ␤ vs modulation frequency were developed. It was found that the conventional linear approach using ␤ = 1 is not always consistent with experimental slopes of amplitude vs power and it may yield erroneous values of the electronic transport properties. Consideration of the fundamental and second harmonic amplitudes and phases of the PCR signal showed that the physical origin of the nonlinear dependence of the PCR amplitude on laser intensity is consistent with high-optical-injection of free-carriers in the semiconductor. The value of ␤ can also be determined by the second harmonic-to-fundamental-amplitude ratio and is controlled by the carrier relaxation time dependence on the optically injected excess diffusive photocarrier density wave.Among the physical parameters of semiconductors, the electronic transport properties, namely, carrier recombination lifetime , carrier diffusion coefficient D, and front-and rear-surface recombination velocity S 1 and S 2 , have attracted great attention in semiconductor device manufacturing. Evaluation of these parameters is essential for characterizing semiconductor wafers, for defect and contamination monitoring, and for device modeling. 1 The technique of laserinduced infrared photocarrier radiometry ͑PCR͒ is an optoelectronic carrier density-wave diagnostic method for noncontact characterization of the electronic transport properties of semiconductors. This technique is a form of quantitative dynamic photoluminescence; it relies on the detection of modulated diffuse radiative emissions from semiconductors obeying Kirchhoff's law under conditions of nearthermodynamic equilibrium of an electronic solid when the latter is optically excited by intensity-modulated laser radiation with photon energy greater than the fundamental energy gap of the material. To determine the transport properties, both amplitude and phase of the PCR signal are simultaneously recorded as functions of angular modulation frequency ͑ = 2f͒ over several orders of magnitude and then fitted to suitable theoretical models ͓either one dimensional ͑1D͒ or three dimensional ͑3D͔͒ via a multiparameter fitting procedure. 2,3 To date, PCR has been developed as a linear technique, in the sense that the amplitude of the signal depends linearly on laser po...

Statistical theory and applications of lock-in carrierographic image pixel brightness dependence on multi-crystalline Si solar cell efficiency and photovoltage

“…The radiatively recombining carriers are generated by the absorbed photon flux F A , and their density is limited by competing nonradiative and external electrical current generation processes. For photocarrier excitation modulated at angular frequency x M , leading, e.g., to PCR signals from a laser spot illumination and single photodetector element detection, or to ac carrierographic (LIC) imaging (broad surface excitation and camera detection), the emitted non-thermal optical current density identified as J PCR ðV hx Þ is proportional to the depth integral of the excess photogenerated carrier density DN(z,x) 18 over the wafer thickness L, generalized for the physics of non-linear radiative recombination processes 21 with non-linearity coefficient…”

Monitoring of amorfization of the oxygen implanted layers in silicon wafers using photothermal radiometry and modulated free carrier absorption methods

“…It gives an average value of the ratio q/Dose = 1/d = 2.66 9 10 4 cm -1 where, q is the concentration of ions. At the dose 5 9 10 14 ions/cm 2 , an average concentration of oxygen ions in the implanted layer q equals to 13.3 9 10 18 ions/ cm 3 , and it corresponds to the average value of the optical absorption coefficient equal to b = 13.2 9 10 4 cm…”

“…Measurement methods based on plasma waves are very attractive for monitoring electrical transport parameters (carrier diffusivity, lifetime of carriers and surface recombination velocities of carriers) in the ion implantated layer as well as in the substrate. Plasma waves can be detected by the measurement of the periodical component of the intensity of the IR radiation of the samples, in a PTR method, or by the measurement of the intensity of the periodical component of the transmitted probing IR beam of light in a MFCA method, or by the periodical photoluminescence in a photocarrier radiometry (PCR) method [1][2][3]. Analysis of the frequency characteristics enables determination of the recombination parameters of semiconductors with the PTR method [4,5] and the MFCA method [6][7][8][9][10][11][12].…”

Lock-in and Heterodyne Carrierographic Imaging Characterization of Industrial Multicrystalline Silicon Solar Cells

“…Because of the shorter ac diffusion length, the high-frequency carrier-wave density depth distribution samples regions closer to the surface, and the image is dominated by near-surface defects affecting the junction-area photovoltaic energy conversion. The HDCG amplitude depends on the same transport parameters as the LICG amplitude, but the existence of HDCG images hinges on the nonlinearity of the PCR (modulated PL) response [14]. The sources of PCR nonlinearity are the dependence of transport parameters on the level of injection, the band-to-band and/or band-to-defect recombination mechanisms, and the modulation of the p-n junction energy barrier [12].…”