Steady-state Photocarrier Grating Research Articles

Simulation and Analysis of Field-dependent Measurements for Different a-Si:H and nc-Si:H Samples

Abstract: A simulation based on the method of weighted residuals is conducted to reproduce the available experimental data of field-dependent steady-state photocarrier grating (SSPG). Different samples of amorphous hydrogenated silicon (a- Si: H) and nanocrystalline hydrogenated silicon (nc- Si: H) thin films prepared by plasma-enhanced chemical vapor deposition (PECVD) technique are employed in the simulation. The reproduced field-dependent data are optimized using 2 indicator. Approximate and correct values of important photoelectronic parameters are extracted from the analysis of results. The analysis reveals values of small-signal response lifetime and electron and hole mobilities comparable to the values obtained from other methods’ applications. The difference between approximate and correct values lies within the experimental error of 5% with one exception regarding a poorly conductive sample. Moreover, the extracted values of both ambipolar diffusion length and charge carrier density are found reasonable and justify the success of the application of the adopted method on the chosen samples. Keywords: Electronic transport phenomena in thin films; Charge carriers: generation, recombination, lifetime, trapping, mean free paths; Photoconduction and photovoltaic effects.

Numerical modeling based on the analytical solution of the steady-state small signal photocarrier grating equations and analysis of field-dependent measurements for noncrystalline Si: H samples

The available experimental data of field-dependent steady-state photocarrier grating (SSPG) are numerically modeled employing the derived formula of [Formula: see text] (where [Formula: see text] represents the ratio of coherent to incoherent currents in SSPG technique) obtained from the analytical solution of the small signal steady-state grating problem by applying Galerkin’s method. This numerical analysis shows the extent of validity and success of using the derived formula of [Formula: see text] [R. I. Badran, Results Phys. 17, 103079 (2020)] in reproducing the field-dependent data for noncrystalline Si: H samples. The best quality of fittings is reproduced when [Formula: see text] value is minimum. This analysis provides us with approximate and corrected values for each of transport quantities, namely, the small-signal response lifetime, electron and hole mobilities that are found in agreement with the values obtained from the applications of other methods. For two polymorphous (pm) Si: H samples, the average estimated, corrected values for the carrier density and mobility-lifetime product, namely, [Formula: see text][Formula: see text]cm[Formula: see text] and [Formula: see text][Formula: see text]cm[Formula: see text] and ([Formula: see text][Formula: see text]cm2V[Formula: see text] and [Formula: see text][Formula: see text]cm2V[Formula: see text], respectively, are obtained. The analysis is also extended to analyze the field-dependent data for nanocrystalline (nc) Si: H samples at low temperatures. The extracted values of [Formula: see text] and ([Formula: see text] are [Formula: see text][Formula: see text]cm[Formula: see text] and [Formula: see text][Formula: see text]cm2V[Formula: see text].

Subgap density of states spectroscopy using steady-state photoconductivity-based experiments

We solve the general equations for a semiconductor of photoconductivity dominated by one type of carrier and obtain two pairs of analytical formulas for a density of state (DOS) spectroscopy inside the band gap from the measurement of the diffusion lengths at different temperatures and generation rates. The equations are tested initially with a numerical simulation and then experimentally for unintentionally-doped hydrogenated amorphous silicon due to the extended consensus about its DOS shape. We estimate the diffusion lengths of the photocarriers using the steady-state photocurrent and the steady-state photocarrier grating. The energy dependence of the DOS below the Fermi energy is estimated. We extract the characteristic temperatures of the valence band tails and their hole capture coefficients, which are in perfect agreement with the bibliographical consensus. For the first time, we provide a consistent explanation of the free-hole concentration decrease with temperature, observed at low temperatures in this amorphous material.

Increasing the scope and precision of the steady-state photocarrier grating technique by measuring the photocurrents at several voltages

The steady-state photocarrier grating (SSPG) experiment is a popular technique for extracting the minority carrier diffusion length of photoconductive thin films in coplanar configuration. The diffusion length is basically obtained from the measurement of the steady-state photocurrent produced by a low applied voltage while the material is illuminated by two monochromatic laser beams of different intensities that interfere between the electrical contacts of the sample. Despite its simplicity and popularity, it is well known that the technique can overestimate the minority carrier diffusion length in some samples. In this paper, we show that the precision of the technique can be substantially increased by performing the same experiment at different voltages. Additionally, we show how to estimate fundamental material parameters from the experiment, such as the density of states at the majority carrier quasi-Fermi energy and the ratio between the recombination states’ capture coefficient and mobility of majority carriers. First, we show that the procedures found in the literature for correcting the overestimation produced by the standard technique do not work properly due to an oversimplification in the modeling. Then, we use a numerical simulation of an unintentionally-doped hydrogenated-amorphous-silicon-like material to evaluate the precision of the new formulas and procedures presented. We clarify the conditions under which the standard SSPG technique produces large overestimations. In these cases, we show that the precision of the new procedure can be more than ten times higher. Finally, we use the standard and the new method to characterize a hydrogenated amorphous (a-Si:H) and a hydrogenated polymorphous (pm-Si:H) silicon sample at different temperatures. We observe that the overestimations produced by the standard technique increase with the ratio between the majority and minority carrier diffusion lengths and the ratio between the recombination states’ capture coefficient and mobility of majority carriers.

Analytical solution of phototransport problem under the presence of a small-signal photocurrent based on method of weighted residuals

The nonlinear phototransport differential equations are analytically solved for a small-signal steady-state photocarrier grating in the presence of external electric field using the method of weighted residuals. Two-term ansatz sinusoidal solution is initially considered as approximate and is then corrected to get the optimum derived expressions for density grating of photoelectrons and photoholes. Both the approximate and corrected expressions of the derived grating amplitudes of the two photocarriers are employed to find corresponding expressions of the coefficient β. The expressions of β are examined by re-producing the field-dependent experimental data of β obtained at room temperature from steady-state photocarrier grating (SSPG) technique for a hydrogenated nanocrystalline silicon sample. The fittings to experimental data are obtained using physical transport quantities as adjustable parameters. We believe that the average value of ambipolar diffusion length of 212 nm with an uncertainty of ~ 6%, obtained from this analysis, which is close to the experimental error of the SSPG measurements, is acceptable. The excess photoelectron and photohole densities in addition to electric field grating are demonstrated. The current analysis reveals that the spatial electric field grating exhibits an increase with increasing applied field and until a certain point where it starts slowly falling off at high values of applied field. This fall off becomes shallower with increasing grating periods.

The effects of air, oxygen and water exposure on the sub-bandgap absorption, the electronic conductivity and the ambipolar diffusion length in highly crystalline microcrystalline silicon films for photovoltaic applications

Reversible and irreversible changes due to long term air and short term de-ionized water (DIW) or pure oxygen exposure were investigated in about 1 µm thick hydrogenated microcrystalline silicon (µc-Si:H) films deposited on rough glass substrates, thereby comparing highly crystalline with compact material. Time and temperature dependent dark conductivity, steady-state photoconductivity, the steady-state photocarrier grating and dual-beam photoconductivity methods have been used to study the effects. Standard measurement procedures defined previously have been carefully applied to record the changes after different treatments using the steady-state methods under light. After long term air exposure of highly crystalline µc-Si:H films, a thermal annealing step leads to an increase in dark conductivity (σD) and steady-state photoconductivity (σph) as well as to a significant increase in the sub-bandgap absorption. These effects are likely due to a reversible recovery from surface adsorbents in a porous microstructure after air exposure resulting in surface charge and Fermi level shifts in agreement with earlier results. Compact µc-Si:H films showed only marginal effects upon an annealing after long term air exposure suggesting much reduced susceptibility to surface adsorbent induced by Fermi level shifts. Five hours exposure to de-ionized water at 80 °C caused more than an order of magnitude increase in σD and σph and a substantial decrease in the sub-bandgap absorption spectrum in highly crystalline as well as in compact µc-Si:H films. In addition, minority carrier diffusion lengths measured by the steady-state photocarrier grating method improved significantly. The changes after exposure to water were not reversible upon our standard annealing procedure. Exposure to high purity oxygen gas at 150 °C resulted in similar effects like the exposure to DIW. Also here the changes in material properties were not reversible upon annealing. Results are discussed in terms of adsorption and chemical reactions on surfaces in the porous highly crystalline material versus the materials with more compact structures. Results are compared to earlier observations and consequences for device application will be indicated.

Study of transport parameters and defect states in thin film perovskites under different environments − air or vacuum − and after light-soaking

We present some advanced characterization techniques developed to investigate on the opto-electronic properties of thin film semiconductors and apply them to perovskite layers. These techniques are the steady state photocarrier grating (SSPG) and the Fourier transform photocurrent spectroscopy (FTPS). The SSPG was developed to study the ambipolar diffusion length of carriers and the FTPS was imagined to measure the variations of the below gap absorption coefficient with the light energy, giving information on the defect densities of the gap responsible for this absorption. The potentialities of these techniques are first detailed and then exemplified by their application to thin film perovskites. To study their stability, these films were exposed to different environments, air or vacuum, and in their as-deposited state or after light-soaking with heavy light. We find that the diffusion length and density of states are quite stable, even after light-soaking, and suggest that the degradation of devices exposed to 1 sun mainly comes from the evolution of the contacts instead of the perovkite itself.

Binary metal zinc-lead perovskite built-in air ambient: Towards lead-less and stable perovskite materials

Organo-metal halide perovskites are promising new-generation photovoltaic materials owing to their efficient electrical/optical characteristics. Despite having high efficiency, perovskites are toxic due to the presence of lead and instable in air ambient. Therefore, the toxicity and instability call for more efforts in this area. Here, methylammonium-zinc-lead iodide (MAZn0.2Pb0.8I3) is synthesized in air ambient as lead-less and more stable perovskite material for applying as the active layer of solar cells. 1.65 eV optical band gap and 51 nm minority carrier diffusion length (Ldiff) have been obtained with the help of UV–Visible spectroscopy (UV–Vis) and steady-state photocarrier grating (SSPG) technique respectively. Structural, chemical bonding and surface studies are done by X-ray powder diffraction (XRPD), Fourier-transform infrared spectroscopy (FTIR) and Field Emission Scanning Electron Microscope (FESEM) respectively. The sample has been stored in dark air ambient with average relative humidity of 45% at room temperature (27 °C) for 60 days and the properties of 60 days aged sample is investigated and compared with characteristics of 60 days aged MAPbI3. The results confirm MAZn0.2Pb0.8I3 is more stable than MAPbI3.

Impact of Environmental Stresses Onto Transport Properties of Hybrid Perovskite Investigated by Steady State Photocarrier Grating and Steady State Photocurrent Techniques

In this study, the transport properties of high quality double and triple cation perovskite are explored under different environmental stresses by Steady State Photocurrent (SSPC) and Steady State Photocarrier Grating (SSPG) measurements. SSPG allows a direct measurement of the ambipolar diffusion length that is significantly higher for the cesium containing perovskite (1.4 micron compared to 0.57 micron for a double cation compound). This positive effect is shown to be reversibly annihilated as the samples are put under vacuum, and to be accelerated with the increase of the temperature. The degradation of the material properties appears together with the activation of a defect trap level and a rise of the doping level in the material. This behavior is discussed considering the interaction between the iodine vacancies contained in the perovskite and oxygen which is known to lead to trap passivation.

Diffusion Length Measurement in CdS Thin Film by Steady State Photocarrier Grating Technique

Diffusion Length Measurement in CdS Thin Film by Steady State Photocarrier Grating Technique

Determination of diffusion lengths in organic semiconductors: Correlation with solar cell performances

Organic semiconductors are promising candidates for future applications in solar energy conversion. Recent investigations of bulk heterojunction (BHJ) semiconductors have suggested a density of states and transport mechanisms by multiple trapping close to those observed in disordered inorganic thin films. That is why we have applied to BHJ thin films experiments that are currently used for disordered semiconductors. In addition to the steady state photoconductivity we have tested the ability of the steady state photocarrier grating (SSPG) technique to provide information on the minority carrier diffusion length. We found that SSPG can be applied to P3HT:PCBM thin films leading, for the best sample, to a diffusion length of the order of 125 nm. From the comparison of the transport parameters obtained on thin films with the performances of the devices integrating the latter, we conclude that SSPG is a very powerful tool for optimizing the BHJ thin film properties before their incorporation in solar devices.

Effect of Pressure on Bonding Environment and Carrier Transport of a-Si:H Thin Films Deposited Using 27.12 MHz Assisted PECVD Process

Investigation of carrier transport in hydrogenated amorphous silicon (a-Si:H) thin films deposited at various pressures (0.03 - 0.53 Torr) using 27.12 MHz assisted high frequency Plasma Enhanced Chemical vapor Deposition (PECVD) process is presented. From results of Steady State Photocarrier Grating (SSPG) the carrier diffusion length was found to vary from 0.098 - 0.189 μm. Moreover a direct influence of ambipolar diffusion length was observed with the transport mechanism for deposition pressure in the range (0.13 - 0.53 Torr). There was a correlation observed for photosensitivity and microstructure parameter with mobility lifetime (μτ) product and diffusion length of carriers. Diffusion length and μτ product were observed to be maximum (0.189 μm and 0.471 x 10 −8 cm 2V−1) for the film having high photosensitivity (7.2x10 3) deposited at a rate ∼1.39 A/s at 0.53 Torr deposition pressure. In addition to electrical transport properties, the effect of deposition pressure on structural and optical properties was also studied using various characterization tools such as Raman, UV-Vis and infrared spectroscopy.

Theoretical Analysis of Nonlinear Recombination Process and Its Influence on Diffraction Efficiency of Steady-State Photocarrier Grating

A theoretical analysis of the steady-state photocarrier grating (SSPCG), which takes the nonlinear carrier recombination processes into account, has been presented. First, the nonlinear diffusion equation, containing the bimolecular radiative recombination and Auger recombination terms, has been numerically solved, and the spatial distribution of the carrier concentration of the SSPCG has been obtained. Second, using Fourier analysis, the amplitude of the carrier concentration is determined based on the numerical results. Finally, using the band-filling theory and rigorous coupled-wave analysis, all the optical parameters of the SSPCG are determined and the diffraction efficiency is estimated. The results show that, for an InP-based SSPCG, the bimolecular radiative recombination plays a dominant role in the diffusion equation at a given excitation level. The +1st-order diffraction efficiency of the SSPCG increased less by the increase of the grating period, and the rising rate was reduced by it. In spite of the diffraction efficiency (about 0.7 %), it has the potential to be an optical signal processing component.

Influence of Carrier Transport on Diffraction Efficiency of Steady-State Photocarrier Grating

A two-dimensional theoretical model of a diffractive steady-state photocarrier grating (SSPCG) has been developed. The carrier diffusion equation with a spatially periodic excitation source was solved, and an analytical expression of the carrier density distribution was obtained. Based on the band-filling theory and the Kramers–Kronig relation, the carrier-induced refractive index change of SSPCG was estimated, and the refractive index profile was determined. The diffraction efficiency of the SSPCG was calculated by multilevel rigorous coupled-wave analysis. Simulations were carried out to investigate the influence of the carrier transport properties on the diffraction efficiency of the SSPCG. The results show that a semiconductor material with a longer lifetime and a smaller diffusivity will have a higher diffraction efficiency. The spatial amplitude of the carrier density and the grating strength of the SSPCG are closely related to the grating period. For an InP-based SSPCG, the diffraction efficiency of the $$+1\mathrm{st}$$ transmitted wave reaches its maximum value (25 %) when the grating provides a $$\pi $$ phase shift. The theoretical analysis and conclusions are helpful for material selection and experimental parameter determination of a diffractive SSPCG.

Investigation of meta- and in-stability effects in hydrogenated microcrystalline silicon thin films by the steady-state measurement methods

Metastability effects because of atmospheric exposure, high purity gasses, and deionized water in hydrogenated microcrystalline silicon thin films with different crystalline volume fractions were studied using well accepted steady-state characterization methods of dark conductivity, steady-state photoconductivity, steady-state photocarrier grating (SSPG) and dual beam photoconductivity (DBP) methods. A standard measurement procedure has been established before using the steady state methods, in which a steady state condition of dark conductivity was established by monitoring the time dependence of dark conductivity. Samples deposited on smooth glass and rough glass substrates exhibit similar reversible and irreversible changes in the properties of microcrystalline silicon film. A reliable correlation of reversible and irreversible changes indicate that dark conductivity and photoconductivity values increase, sub-bandgap absorption spectrum obtained from DBP method decrease and correspondingly minority carrier diffusion lengths obtained from the SSPG method increase in the metastable state in various amount for microcrystalline films with crystalline volume fraction, [Formula: see text] > 0.30. Amorphous silicon and microcrystalline silicon films with [Formula: see text] < 0.30 do not show detectable metastable changes as samples exposed to atmospheric condition as well as high purity oxygen gas and deionized water.

An automated steady state photocarrier grating experiment

The design of an automated steady state photocarrier grating (SSPG) experiment is presented that matches most of the requirements of an industrial environment. We first briefly recall the bases of the SSPG technique and that the minority carrier diffusion length deduced from this experiment is a key parameter in the fabrication of thin film solar devices. We then underline the main drawbacks of the use of the classical SSPG technique as an industrial and systematic characterization technique mostly that all the adjustments have to be done manually. We show that this issue can be overcome to end with a compact (90 × 60 cm(2)), fast, reliable, and easy-to-use system that could become a routine characterization technique for research laboratories and thin film solar industry. We illustrate the possibilities of this new system by showing some of the results obtained with it on very different thin films.

Determination of the transport parameters of nanocrystalline CdSe:Cu thin films

Thin films of copper (Cu)-doped CdSe are prepared by the physical vapor deposition technique. X-ray diffraction analysis shows that the films crystallize in hexagonal structure with (100) as the preferred orientation. Scanning electron microscope studies reveal that the grains are spherical in shape and uniformly distributed all over the surface of the substrates. The transport properties of Cu-doped CdSe thin films have been investigated by the time-of-flight measurement, steady-state photocarrier grating and steady-state photoconductivity techniques. The temperature dependence of dark conductivity and photoconductivity data reflects the existence of two independent donor energy levels. The bimolecular recombination nature of the thin films has been found from the photocurrent-illumination dependence at different applied voltages. The minority carrier diffusion length (Ldiff) is obtained both from the best fit of the experimental photocurrent ratio β versus grating period (Λ) and from the ‘Balberg plot’. A straight line has been obtained from the best fit, which confirms that the measured length is the ambipolar diffusion length.

Measurement of the diffusion length of minority carriers using a steady-state photocarrier grating

An improper orientation of the sample electrodes with respect to the interference fringes in the steady-state photocarrier grating (SSPG) setup can lead to large errors in the measured diffusion length ( L ). A simple analysis shows that the measured L is always larger than the actual L if the sample is misaligned. The analysis compares well with the experimental data taken on a hydrogenated amorphous silicon sample.

Photocarrier diffusion lengths of high-growth-rate microcrystalline silicon

We report on photocarrier transport of high-growth-rate microcrystalline Si (μc-Si) in conjunction with the lateral size, σL, of crystallites’ conglomerate (grain) determined from the atomic force microscope (AFM) topographic images on the basis of fractal concepts. μc-Si films were prepared using very-high-frequency plasma-enhanced chemical vapor deposition at a high deposition rate of 6.8±0.5nm/s. μc-Si thicknesses, d, were varied from 0.53μm to 5.6μm. With an increase in d, σL increased from 70nm to 590nm. At the same time, the ambipolar diffusion lengths, Lamb, of photocarriers, observed using the steady-state photocarrier grating (SSPG) technique, increased from 50nm to 420nm. Log–log plots of Lamb versus d and σL versus d were both expressed as a power law with an exponent of 0.9, yielding a simple linear relation between Lamb and σL. Moreover, their ratio, Lamb/σL, was below unity, implying the intra-grain carrier diffusion. From these results, the role of the grain (column) boundaries for photocarrier diffusion in μc-Si is discussed.

Analysis of field dependent steady-state photocarrier grating measurements on polymorphous and microcrystalline silicon films

The steady-state photocarrier grating (SSPG) technique has been employed to investigate the field dependence of different polymorphous and microcrystalline silicon samples prepared by plasma enhanced chemical vapor deposition technique. The field-dependent experimental data at different temperatures are analyzed using two different approaches based on the small-signal photocurrent to extract more information on the electronic properties (like small signal mobility life time product, average drift length for holes and electrons,... etc.). The quality of the fits is tested by the χ2 indicator and the best choice of the transport parameters is obtained in each approach. The values of electron and hole drift mobilities obtained from one approach are compared to those found by others. The trapped charge density can be determined, for all samples, and correlated to minority-carrier diffusion length. It is also found that the decrease in temperature in a microcrystalline sample may result in an increase of the trapped charge density. This increase in trapped carrier density may be consistent with the increase in sub-gap absorption. Such behavior is found in agreement with that reported in the literature. In addition, the polymorphous samples that have values of diffusion lengths comparable to those of microcrystalline samples exhibit higher values of trapped carrier density.