Modulated Free Carrier Absorption Research Articles

Investigations and modeling aspects of the influence of the high energy and high dose implantation on the optical and transport parameters of implanted layers in silicon

This paper presents results of investigations and modeling aspects of the influence of Ge+ high energy (100 keV) and high dose (1014 cm−2) implantation on the optical and recombination parameters of implanted layers in silicon. The nondestructive and contactless MFCA (Modulated Free Carrier Absorption) method was used as it is sensitive to changes of these parameters expected for implanted layers. Several model cases describing the MFCA spectrum as a function of the energy of photons of the excitation laser light are presented, compared and discussed. The simplified one-layer model and the full two-layer model of the MFCA signal have been analyzed and compared. The possibility and correctness of determination of the optical absorption coefficient spectra of the implanted layers with the use of the one-layer simplified model has been discussed.

Correction to: Au2+-Implanted Regions in Silicon Visualized Using a Modulated Free-Carrier Absorption Method

Correction to: Au2+-Implanted Regions in Silicon Visualized Using a Modulated Free-Carrier Absorption Method

Properties of silicon implanted with Fe+, Ge+, Mn+ ions investigated using a frequency contactless modulated free-carrier absorption technique

This paper presents results of investigations of Fe+, Ge+, Mn+ ions implanted silicon samples with the use of the modulated free carrier absorption (MFCA) technique. These ions are significant in a modern electronics. The nondestructive character of the MFCA method makes it very useful for characterization of implanted materials. Spatial distributions and profiles of the amplitudes of the modulated free carrier absorption signal of the implanted silicon samples were measured and analyzed. The amplitude and phase frequency characteristics of the MFCA signal for the ion implanted regions have been measured and interpreted for different wavelengths of the illuminating light. The dependence of the amplitude of the MFCA signal on the lifetime of carriers and the optical absorption coefficient of the implanted layer has been analyzed theoretically and discussed. The influence of the ion implantation process on the values of the optical absorption coefficient and the lifetime of carriers of the implanted layers has been determined.

Hbox {Au}^{2+}-Implanted Regions in Silicon Visualized Using a Modulated Free-Carrier Absorption Method

Silicon samples were implanted with hbox {Au}^{2+} ions of energy 100 keV and doses of 10^{14},hbox { cm}^{-2}. The area of the implanted region was 2,hbox {mm}times 2,hbox {mm}. The size of the Si substrate samples was 5,hbox {mm}times 5,hbox {mm}times 0.4,hbox {mm}. Spatial distributions of the amplitude and profiles of the modulated free-carrier absorption (MFCA) signal of the implanted silicon samples were recorded and analyzed. The data were obtained using an experimental setup built specifically for MFCA amplitude mapping and measurements of frequency characteristics. For example, the maps and profiles showed that for 520 nm laser illumination, the MFCA amplitude in the implanted region was considerably smaller than that for the substrate. The values of the amplitude of the MFCA signal from the implanted region depended on the wavelength of illuminating light. They convey information related to the optical absorption coefficient of the implanted layers.

Modulated free‐carrier absorption in silicon – a spectroscopy approach

In the paper, an analysis of the spectral characteristics of the MFCA (modulated free‐carrier absorption) signal for silicon 3–5 Ω cm, n‐type is presented. During the change of the wavelength of a probe light, three distinctive regions are observed in the amplitude and the phase characteristics. In the first region (λprobe << hc/Eg), only the PCR (photocarrier radiometry) signal exists. The second region (λprobe > hc/Eg) is typical for the MFCA signal. The nature of the third region (λprobe near hc/Eg), characterized by a long relaxation time is being studied here. The spectroscopy approach to the MFCA technique provided an opportunity to explain the type of free‐carrier scattering mechanism that dominates in the NIR region. In the paper, an attempt was also undertaken to estimate the recombination parameters of the sample.

Influence of Reflectance on Determination of Free Carrier Absorption of Silicon Wafer

A revised modulated free carrier absorption (MFCA) theory is proposed, in which photomodulated thermal reflectance (PMTR) is subtracted from the transmitted signals of semiconductors. With this theory, one simultaneously extracts the carrier transport properties, such as the carrier lifetime, carrier diffusion coefficient, and the front surface recombination velocity, of silicon wafers. Proof-of-concept experiments were performed on a single crystal p-type, 100 cut silicon having $$8\,\Omega {\cdot }\hbox {cm}$$ to $$12\,\Omega {\cdot }\hbox {cm}$$ resistivity. MFCA and transmitted data (composed of MFCA and PMTR) are fitted to an MFCA theoretical model. Fitted results showed that the accuracies of fitted transport properties can be greatly improved by the MFCA technique if the PMTR component is subtracted from the transmitted signal.

Measurements of the optical absorption coefficient of Ar8+ ion implanted silicon layers using the photothermal radiometry and the modulated free carrier absorption methods

This paper presents a method of the measurement of the optical absorption coefficient of the Ar8+ ions implanted layers in the p-type silicon substrate. The absorption coefficient is calculated using a value of the attenuation of amplitudes of a photothermal radiometry (PTR) and/or a modulation free carrier absorption (MFCA) signals and the implanted layer thickness calculated by means of the TRIM program. The proposed method can be used to indicate the amorphization of the ions implanted layers.

Self-eliminating instrumental frequency response from free carrier absorption signals for silicon wafer characterization

Accurate determination of electronic transport properties of semiconductor wafers with modulated free carrier absorption (MFCA) and multiparameter fitting requires the total elimination of instrumental response from the MFCA signals. In this paper, an approach to eliminate the effect of instrumental response on the frequency dependence of MFCA amplitude and phase is developed both theoretically and experimentally to simultaneously determine the transport properties (minority-carrier lifetime, carrier diffusion coefficient, and front surface recombination velocity) of silicon wafers. Experimental results showed that with the proposed method the instrumental frequency response was fully eliminated from the experimental MFCA data and had no impact on the multiparameter fitting, while with conventional methods the accuracy of the fitted transport parameters was influenced detrimentally by the errors of the measured instrumental frequency responses, in particular for the minority-carrier lifetime and the front surface recombination velocity.

Electronic transport characterization of silicon wafers by combination of modulated free carrier absorption and photocarrier radiometry

A combined modulated free carrier absorption (MFCA) and photocarrier radiometry (PCR) technique is developed to determine simultaneously the electronic transport properties (carrier diffusion coefficient, carrier lifetime, and front surface recombination velocity) of silicon wafers. Comparative computer simulations are carried out to investigate how the experimental measurement errors affect the simultaneous determination of the electronic transport parameters by introducing random or systematic errors into the simulated MFCA and PCR data and statistically analyzing the fitted results, by means of separate MFCA and PCR, as well as the combined MFCA and PCR through fitting the experimental dependences of signal amplitudes and phases to the corresponding theoretical models via a multiparameter fitting procedure, respectively. The simulation results show that with the combined MFCA and PCR the effect of experimental errors on the simultaneous determination of the transport parameters is significantly reduced and therefore the accuracy of the fitted results is greatly improved. Experiments with two c-Si wafers with the three methods were performed and the results were compared. The experimental results showed that the combined MFCA and PCR provided the most accurate fitted transport parameters, in agreement with the simulation results.

Influence of probe beam size on signal analysis of modulated free carrier absorption technique

A three-dimensional modulated free carrier absorption (MFCA) model taking into account the size of a Gaussian-profile probe beam, referred as the accurate model, is developed to describe the influence of the probe beam size on signal analysis of the MFCA technique. Numerical simulations are presented to investigate the influences of different probe beam radii on the amplitude and phase of the laterally resolved MFCA (LR-MFCA) signal at 2kHz and 200kHz, respectively. The MFCA signals obtained by this accurate model are compared to those obtained by a model assuming a point detection (referred as the point model). The conditions that the probe beam size can be neglected are given.

Analysis of modulated free-carrier absorption measurement of electronic transport properties of silicon wafers

Based on a three-dimensional modulated free carrier absorption (MFCA) model, theoretical analysis is performed to investigate the dependences of MFCA amplitude and phase on the electronic transport properties (the carrier lifetime, the carrier diffusivity, and the front surface recombination velocity) at different pump-to-probe separations and different modulation frequencies. The sensitivity of the multi-parameter estimate employing the dependences of the MFCA amplitude and phase on the modulation frequency at several pump-to-probe separations is theoretically compared with that employing the dependences on the pump-to-probe separation measured at several modulation frequencies. Simulation results show that the two approaches have comparable sensitivities to the electronic transport properties of silicon wafers. As for the MFCA experiments, the frequency scan data measured at different pump-to-probe separations have higher signal-to-noise ratios and therefore should be preferable to the simultaneous determination of the multiple transport properties.

Modulated free carrier absorption characterization of semiconductor wafers by frequency scans at different pump-to-probe separations

Based on a three-dimensional modulated free carrier absorption （MFCA） model，simulation was performed to investigate the dependences of MFCA amplitude and phase on the electronic transport properties （the carrier lifetime，the carrier diffusivity，and the front surface recombination velocity） of semiconductor wafers at different pump-to-probe separations and different modulation frequencies. Experiments were performed with a silicon wafer，in which amplitude and phase were recorded as functions of modulation frequencies at several different two-beam separations. The electronic transport properties of semiconductor wafers were determined simultaneously via multi-parameter fitting procedure. These results showed that the method is capable of improving the measurement precision of the simultaneous multi-parameter determination of transport properties.

Accuracy analysis for the determination of electronic transport properties of Si wafers using modulated free carrier absorption

Computer simulations are carried out to investigate the sensitivity of simultaneous determination of three electronic transport properties (carrier lifetime, carrier diffusivity, and front surface recombination velocity) of silicon wafers by modulated free carrier absorption (MFCA) via a multiparameter fitting procedure. The relative accuracy of the transport parameter determination by laterally resolved MFCA (LR-MFCA), in which the amplitude and phase are measured as functions of the pump-probe-beam separation at several modulation frequencies covering an appropriate range, and by conventional frequency-scan MFCA (FS-MFCA), in which only the modulation frequency dependences of the amplitude and phase are recorded, is theoretically analyzed and experimentally estimated by calculating the dependence of the mean square variance on individual transport parameter via a multiparameter estimation process. Simulated and experimental results show that the determination of the transport properties of silicon wafers by LR-MFCA are more accurate, compared with that by FS-MFCA. Comparative experiments are performed with a silicon wafer and the estimated uncertainties of the carrier diffusivity; lifetime and front surface recombination velocity are approximately ±3.7%, ±25%, and ±35% for LR-MFCA and ±7.5%, ±31%, and ±24% for FS-MFCA, respectively.

Sensitivity analysis of laterally resolved free carrier absorption determination of electronic transport properties of silicon wafers

Simulations are performed to investigate the uniqueness of simultaneous determination of electronic transport properties (the carrier lifetime, the carrier diffusivity, and the front surface recombination velocity) of silicon wafers by laterally resolved modulated free carrier absorption (MFCA) and multiparameter fitting. The dependences of MFCA amplitude and phase on these transport properties at different pump-probe-beam separations and modulation frequencies are analyzed. The uncertainties of the fitted parameter values are analyzed by investigating the dependences of a mean square variance including both the amplitude error and phase error on corresponding electronic transport parameters. Simulation results show that the electronic transport parameters can be determined accurately through fitting experimental MFCA data carrying both frequency- and space-domain information of carrier diffusion to a rigorous MFCA model. Among the three transport parameters, the carrier diffusivity can be determined most precisely, with an uncertainty of less than ±5%, due to the highest sensitivity of the laterally resolved MFCA signal to the diffusivity. The highly accurate determination of the diffusivity further improves the precision of the carrier lifetime and the front surface recombination velocity values simultaneously determined via multiparameter fitting. Experiments were performed with a silicon wafer and the results were in good agreement with the theoretical simulations.

Analysis of free carrier absorption measurement of electronic transport properties of silicon wafers

Sensitivity analysis of electronic transport property measurement of silicon wafers with modulated free carrier absorption (MFCA) technique and multi-parameter fitting procedure is performed. The sensitivity of the multi-parameter estimate employing the dependences of the MFCA amplitude and phase on the pump-probe-beam separation measured at several modulation frequencies covering an appropriate range is theoretically compared with that employing only the dependences of the MFCA amplitude and phase on the modulation frequency. Simulation results show that the dependences of the MFCA amplitude and phase on the pump-probe beam separation are more sensitive to the electronic transport properties of silicon wafers than the frequency dependences. The electronic transport properties of the silicon wafers determined with the two-beam separation dependence are therefore more accurate than that determined with the frequency dependence. Comparative experiments with a silicon wafer are performed and the carrier lifetime, the carrier diffusivity, and the front surface recombination velocity are determined simultaneously and unambiguously with both techniques.

Time-domain modulated free-carrier absorption measurements of recombination process in silicon wafers

A time-domain modulated free-carrier absorption (MFCA) is developed both experimentally and theoretically to investigate the photo-carrier dynamics of silicon wafers illuminated by a square-wave-modulated super-band-gap laser beam. An explicit three-dimensional (3-D) theoretical expression for the temporal behavior of the MFCA signal is obtained by solving a 3-D carrier-diffusion equation The time-domain MFCA model is used to fit the experimental MFCA signals of p- and n-type Si wafers via a multi-parameter fitting procedure to determine simultaneously the electronic transport properties, that is, the bulk lifetime, the ambipolor diffusivity, and the front surface recombination velocity. The uncertainties of the fitted parameter values are estimated.

Measurement of electronic transport property of semiconductors by three-dimensional modulated free carrier absorption technique

A three-dimensional model for the modulated free carrier absorption (MFCA) is developed to measure the electronic transport properties (the carrier lifetime, the carrier diffusivity, and the front surface recombination velocity) of semiconductor wafers. The dependence of MFCA amplitude and phase on the electronic transport properties at different pump-probe-beam separation and different modulation frequencies is investigated. It is found that the sensitivities of MFCA signal to individual transport parameters increase with increasing two-beam separation. An experiment with a silicon wafer is performed and the carrier lifetime, carrier diffusivity, and front surface recombination velocity are determined simultaneously and unambiguously by fitting the observed values of the MFCA amplitude and phase as functions of the separation between the pump and probe laser spots, measured at several modulation frequencies covering an appropriate range.

Electronic transport characterization of silicon wafers by laterally resolved free-carrier absorption and multiparameter fitting

Laterally resolved modulated free-carrier absorption (MFCA) is applied to the simultaneous determination of the electronic transport properties of semiconductor wafers. A rigorous three-dimensional carrier diffusion model is used to fit the observed dependences of the MFCA signal amplitude and phase on the separation between the pump and probe laser spots, measured at several modulation frequencies covering an appropriate range. This leads to a simultaneous and unambiguous determination of the values of three transport parameters, namely, the minority-carrier lifetime τ, the carrier diffusivity D, and the front surface recombination velocity s1. The extracted values for a n-type Si wafer with a resistivity of 7–10Ωcm are 53μs (τ), 16.6cm2∕s (D), and <200cm∕s (s1), respectively.

Silicon Surface Passivation by Organic Monolayers: Minority Charge Carrier Lifetime Measurements and Kelvin Probe Investigations

The silicon surface passivation of monolayers of organic compounds that are bound to Si surfaces by a covalent Si−C bond has been investigated. The effective lifetime τeff of minority charge carriers in the surface-modified semiconductor has been determined by modulated free carrier absorption (MFCA) measurements. The results show that on 1−2 Ω·cm p-type Si(100) surfaces modified with a monolayer obtained from CH2CH(CH2)8C(O)OCH3 maximum effective lifetimes τeff ≥ 130 μs can be obtained. This value corresponds to a maximum surface recombination velocity Seff of 120 cm/s, a value that is similar to those obtained using other passivation techniques, which demonstrates that these monolayers provide an interesting alternative for silicon surface passivation. During these MFCA measurements an unusual time dependence of the effective lifetime is observed: τeff rises continuously during illumination of the substrate. Kelvin probe measurements show that there is a slow shift of the Fermi level of the semiconduct...

Measurement of differential and actual recombination parameters on crystalline silicon wafers [solar cells

In this paper, for the first time, measurements of differential and actual recombination parameters on crystalline silicon wafers are directly compared. In order to determine the differential bulk lifetime and the differential surface recombination velocity (SRV), small-signal light-biased microwave-detected photoconductance decay (MW-PCD) and modulated free-carrier absorption (MFCA) measurements are performed. The results obtained by these widespread techniques are compared with quasi-steady-state photoconductance (QSSPC) measurements, which directly determine the actual recombination parameters. On high-resistivity (1000 /spl Omega/cm) float-zone (FZ) n-type silicon at high injection levels, it is shown that the differentially measured Auger lifetime is a factor of three smaller than the actual Auger lifetime. This finding is in excellent agreement with the theory derived in this work. Thermally oxidized low-resistivity (/spl sim/1 /spl Omega/cm) p-Si wafers serve as an experimental vehicle to compare the differential and the actual injection-level dependent SRV of the Si-SiO/sub 2/ interface under low-injection conditions. Using two different integration procedures, the actual SRV is calculated from the differentially measured quantity. The actual SRV measured by the QSSPC technique is found to match perfectly the actual SRV obtained by integration.