Perfect Silicon Single Crystals Research Articles

Research on Classification Algorithm of Silicon Single-Crystal Growth Temperature Gradient Trend Based on Multi-Level Feature Fusion.

In the process of silicon single-crystal preparation, the timely identification and adjustment of abnormal conditions are crucial. Failure to promptly detect and resolve issues may result in a substandard silicon crystal product quality or even crystal pulling failure. Therefore, the early identification of abnormal furnace conditions is essential for ensuring the preparation of perfect silicon single crystals. Additionally, since the thermal field is the fundamental driving force for stable crystal growth and the primary assurance of crystal quality, this paper proposes a silicon single-crystal growth temperature gradient trend classification algorithm based on multi-level feature fusion. The aim is to accurately identify temperature gradient changes during silicon crystal growth, in order to promptly react to early growth failures and ensure the stable growth of high-quality silicon single crystals to meet industrial production requirements. The algorithm first divides the temperature gradient trend into reasonable categories based on expert knowledge and qualitative analysis methods. Then, it fuses the original features of actual production data, shallow features extracted based on statistical information, and deep features extracted through deep learning. During the fusion process, the algorithm considers the impact of different features on the target variable and calculates mutual information based on the difference between information entropy and conditional entropy, ultimately using mutual information for feature weighting. Subsequently, the fused multi-level feature vectors and their corresponding trend labels are input into a Deep Belief Network (DBN) model to capture process dynamics and classify trend changes. Finally, the experimental results demonstrate that the proposed algorithm can effectively predict the changing trend of thermal field temperature gradients. The introduction of this algorithm will help improve the accuracy of fault trend prediction in silicon single-crystal preparation, thereby minimizing product quality issues and production interruptions caused by abnormal conditions.

STRUCTURAL FEATURES OF DOPED SILICON SINGLE CRYSTALS

The nature of the change in the Fermi level of silicon under the influence of dopants, point defects, and dislocations has been determined. The parameters of the diffusion of impurities, the conditions for their appearance and removal in the process of directional crystallization and the post-crystallization period have been established. The expediency of doping silicon with boron and phosphorus was shown, and large single crystals were obtained. The mechanisms of elimination of structural defects have been clarified. The mobility and lifetime of charge carriers in perfect silicon single crystals under radiation exposure have been determined. The expediency of using p-type silicon as a base material for solar modules for space purposes is shown.

Method for the X-ray Diffraction Diagnostics of Crystal Imperfections

Images of crystal imperfections are experimentally studied depending on their location with the use of special perfect silicon single crystals, whose surface layers are deformed by rough mechanical treatment (grinding). A new X-ray diffraction method based on the interpretation of a section topogram is proposed for studying crystal imperfections. It is shown that thin lines in the topogram are produced by kinematic scattering, and its central band is a result of dynamic scattering, i.e., this method provides the simultaneous observation of both kinematic and dynamic X-ray scattering from the same crystal.

A double-crystal monochromator for neutron stress diffractometry

The problem of developing a dedicated neutron diffractometer for placement on a horizontal reactor channel to measure internal stresses in bulk materials and components under conditions of a limited space is considered. It is shown that the use of a double-crystal monochromator composed of pyrolytic graphite and a focusing bent perfect silicon single crystal is the optimal solution to this problem. The diffractometer with such a monochromator that is installed at the IR-8 reactor of the National Research Center Kurchatov Institute is comparable in luminosity and resolution at a reactor power of 6 MW to modern stress diffractometers at more powerful reactors.

Effect of anomalous absorption of neutrons undergoing Laue diffraction at Bragg angles close to π/2

A direct experimental observation of the anomalous absorption of neutrons undergoing Laue diffraction in a highly perfect silicon single crystal of size about 200 mm at Bragg angles close to π/2 is reported. It is shown that, in the case of diffraction at the (220) plane, the neutron absorption length may be several meters, which is nearly one order of magnitude longer than the mean absorption length for neutrons of the same wavelength. This circumstance makes it possible to study effects accompanying Laue diffraction at Bragg angles of up to 88° and a crystal size of about 200 mm.

Ultrasound effect on neutron Bragg diffraction in a perfect and deformed silicon single crystal

The features of neutron Bragg diffraction in a perfect and bent (deformed) silicon single crystal have been studied under ultrasound excitation. In contrast to a perfect crystal where an increase in the diffraction intensity has been observed with an increase in the ultrasound wave’s amplitude, in a deformed silicon crystal the intensity sharply decreases (two times) already at small voltages on a piezoelectric transducer. The depth and position of minima of the total intensity depend on the ultrasound wave’s amplitude and the bending radius of a crystal. To explain the observed effects the modified Penning-Polder-Kato model has been successfully used, in which the role of ultrasound is reduced to the formation of resonance transitions of imaging points between different sheets of dispersion surface. Experimental proofs of validity of the used model are presented. Estimations of the probabilities of one- and multiphonon scattering processes obtained from experimental data have a good agreement with theoretical ones.

The FOCAL spectrometer for accurate X-ray spectroscopy of fast heavy ions

A system of two crystal spectrometers for accurate wavelength measurements of hard X-rays emitted by heavy ions in flight is presently being completed. The configuration is working in the focusing compensated asymmetric laue (FOCAL) mode along with high performance two-dimensional position sensitive micro-strip Ge detectors. Recent tests of the spectrometer have been performed securing quantitatively spectral resolving power and efficiency predicted by numerical simulations. For the proposed application, nearly perfect Silicon single crystals need to be bent cylindrically using a precision crystal-bending device, close to the limit where they start to break.

Calculation of x-ray wave fields in perfect crystals by applying Riemann’s method to solve the Takagi-Taupin equations

The Takagi-Taupin equations are a set of partial differential equations that are fundamental in the dynamical theory of x-ray diffraction. We show how they can be manipulated to make them suitable for the application of Riemann’s method and present in detail the steps leading to their solution. To help readers gain insight into coherent x-ray wave fields, we calculate the intensity distribution of x-ray beams from mono- and polylithic perfect silicon single crystals. As an example of the interplay between wave fields, we illustrate the Pendellösung effect. We did some of the algebraic manipulations and most of the numerical calculations by using Mathematica.

On a possible use of multiple Bragg reflections for high-resolution monochromatization of neutrons

Multiple diffraction effects resulting in Umweganregung have been studied in cylindrically bent perfect silicon single crystals. The aim of this experiment was to find strong umweg-effects providing a highly monochromatic and collimated beam for a possible practical use. Using three different cuts of the Si crystal slabs, several very intensive umweg-effects in the thermal region from 0.1 to 0.25 nm which could be used for high-resolution monochromatization namely at high-flux neutron sources have been found. The advantage of such umweg-monochromators would be their tunability through the variation of the curvature and thus the variability of the bandwidth Δ λ/ λ in the range from 10 −4 to 10 −3 and collimation of the orders of minutes of arc without any employment of Soller collimators.

Dynamical diffraction imaging of voids in nearly perfect silicon

X-ray diffraction topographs of extremely pure and perfect silicon singlecrystals are made using low-energy undulator radiation from a positron storagering. Typical defect images observed are rather large round images having ablack-white contrast and a diameter of about 40 µm. Applying the dynamicaltheory of x-ray diffraction, the defect contrast is explained by tensile strainin the lattice around voids close to the exit surface. This discovery ofvoid-like microdefects explains, at least in part, the reduced density of thecrystal intended to be used for a redefinition of the unit of mass, thekilogram.

Comprehensive investigation of defects in highly perfect silicon single crystals

Comprehensive investigation of defects in highly perfect silicon single crystals

X-ray angle interferometry: a practical set-up for calibration in the microrad range with nanorad resolution

X-ray interferometry is a crystallographic diffraction technique utilizing a moiré effect generated by the lattice. If almost perfect silicon single crystals are employed, scanning of the periodic moiré can be used for the calibration of translation or rotation on a nanometric scale since the lattice parameter is well known in terms of the SI unit of length. A monolithic x-ray angle interferometer consisting of two crystal blocks and a connecting flexure spring allowing relative rotation was manufactured. Each block supports two x-ray optical lamellae. Their optimum thickness for good visibility of the angular moiré fringes during rotation was calculated using the dynamical theory of x-ray diffraction. The main block serves as the base of the interferometer and also incorporates the piezoelectric drive. This arrangement of three bimorph actuator blades allows angular scanning through the zero degree position in order to use the full Bragg reflection width. Pre-tensioning of the flexure spring, balancing of the rotating part and angular scanning are possible simultaneously. Different operating modes, free-running and locked to the fringe slope, were tested. This very compact device can be used as a stand-alone instrument or as a fine scale in a large angle measuring calibrating facility.

Neutron reflectivity of perfect crystals excited by high‐frequency ultrasound

AbstractNeutron scattering double‐crystal experiments were realized using high‐frequency ultrasonic excitation in a perfect silicon single crystal. The dependence of rocking curves on the ultrasonic amplitude was measured and compared with the dynamical theory. It was found that the method of the transfer matrix is very useful for the analysis of the influence of the acoustic wave (AW) on the diffraction in very thick crystals. In particular, the pendellösung oscillations are simply and exactly removed from the whole picture of the diffraction pattern. Some exact theoretical conclusions concerning the maximum influence of ultrasound and the deformation at the peak intensity in a double‐crystal spectrometer were also reviewed.

The silicon-28 path to the Avogadro constant-first experiments and outlook

For the first time an attempt has been made to determine the lattice parameter, density, and molar mass of an isotopically highly enriched silicon-28 crystal. The goal was to achieve an independent value of Avogadro's constant of accuracy equal or superior to current best values obtained from similar measurements of very pure and highly perfect silicon single crystals of natural isotopic composition. That aim has been foiled by unexplained contaminations of the /sup 28/Si crystal and perhaps other unidentified causes. Under these circumstances this paper restricts itself to a brief record of the method used and the results obtained. The value of the Avogadro constant so derived is considered of no further significance and differs from the CODATA and other credible values by about 1/spl middot/10-/sup 5/N/sub A/.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The resolution function of a triple-crystal diffractometer for high-energy synchrotron radiation in nondispersive Laue geometry

The k-space resolution function of a triple-crystal diffractometer is calculated for an arrangement of three perfect silicon single crystals Bragg diffracting in nondispersive Laue geometry. A comparison is made with the results of measurements using synchrotron radiation in the energy range from 80 to 150 keV. In this case, absorption is very weak and according to dynamical theory the width of the diffraction pattern of thick perfect single crystals is proportional to the wavelength λ, whereas its Lorentzian tails are proportional to λ2. Together with the fact that the Bragg angles are only of the order of 2°, this leads to a concentration of the starlike k-space resolution function into a narrow band parallel to the reciprocal-lattice vector G. For diffraction of 80 keV synchrotron radiation at the silicon 111 reflection, the full width at half-maximum (FWHM) of the intensity distribution in the scattering plane is 1.1 × 10−5 Å−1 perpendicular to G and 2.2 × 10−4 Å−1 parallel to G. The observed differences in the contributions from monochromator and analyzer crystal to the resolution function are explained by the finite width of the electronic window of the detector counting chain and the non-Bragg scattering contribution from the crystals. If annealed Czochralski-grown silicon single crystals with a mosaicity of ~3′′ are used as monochromator and analyzer, the resolution is reduced by one order of magnitude, but for studies of imperfect samples or of diffuse scattering large gains in intensity can be accomplished this way.

Incremental sheet resistance and spreading resistance: A comparison

Spreading resistance measurements are widely used to obtain carrier depth profiles in shallow silicon diffused layers. The transformation of the raw spreading resistance data into concentration data relies on the calibration of the system against standards of known resistivity. This procedure implies that, for a given carrier concentration, the analyzed sample and the standards have the same carrier mobility. However, this hypothesis is not verified when other carrier scattering centers, in addition to those active in a perfect silicon single crystal (lattice and ionized impurities), are present in the sample. In this case spreading resistance cannot give the correct carrier concentration and an independent measurement of carrier mobility must be performed. In addition, uniform standards are not easily available at the very high doping levels used, for instance, for the source and drain diffusion of complementary metal–oxide semiconductor devices, or for the emitter diffusion in bipolar devices. In this paper we compare the results obtained with incremental sheet resistance and sheet Hall coefficient, secondary ion mass spectrometry, and spreading resistance measurements on samples implanted with BF2 at high fluence and annealed at low temperatures, and on high fluence arsenic implanted layers. Rapid thermal annealed samples, implanted with As, As and P, and BF2 have been also studied, due to the present interest in this low thermal budget method for dopant activation.

A quantitative study of diffracted X-ray intensities from type I natural diamond crystals by high resolution X-ray diffractometry and comparison with nearly perfect silicon single crystals

Results of accurate measurements of peak and integrated intensities of\(\bar 220,\bar 440,\bar 2\bar 24,\bar 1\bar 13\), 111 and 333 reflections of natural diamonds of type I and nearly perfect silicon single crystals are reported. Highly monochromated and collimated MoK α 1 exploring beam was used. A quadrupole crystal X-ray diffractometer was employed in (+, −, +) and (+, −, +, −) settings. (111) platelets of diamond and silicon crystals with thicknesses of about 1 mm were selected. High resolution diffraction curves, stationary and traverse topographs were recorded. Diffraction curve half widths of diamond and silicon crystals were in the range: 45–200 arc sec and a few arc sec respectively. The experimental values of integrated intensitiesρ for diamond crystals were found to lie between the theoretical values for ideally perfect and ideally imperfect crystals. Experimental values ofρ for silicon were closer to the “perfect crystal” values. This is consistent with the results of diffractometric and topographic evaluation. The peak intensities of all reflections were higher for diamond crystals in comparison to the silicon crystals. The ratioI C/I Si lies in the range 1.3 (111 reflection) to 10.5\((\bar 1\bar 13)\) and (333) reflections. This is anomalous and cannot be accounted for by considering the degree of perfection, structure factor and difference in absorption coefficient.

Sophisticated equipment developed for growth and evaluation of perfection of nearly perfect crystals

This paper reviews four major equipment developed at the National Physical Laboratory for growth and perfection evaluation of single crystals, namely (i) a crystal puller for growth of nearly perfect crystals by the Czochralski method; (ii) a microfocus x-ray generator; (iii) an x-ray diffraction topography camera; and (iv) a triple crystal x-ray diffractometer. The crystal puller can provide smooth, uniform and variable pulling rates. The maximum length of pull is nearly 60cm. Efforts have been made to isolate vibrations. Nearly perfect single crystals of KCl, KBr and NaCl with maximum diameter of ∼ 60 mm have been grown. The crystals give diffraction curves with half width in the range of 10–30 sec of arc. In the projection topographs, dislocations can be resolved and characterized. The microfocus x-ray generator is a demountable continuously evacuated system with specially designed electron gun and anode assembly. The vacuum is continuously monitored for ease of maintenance. In the point focus mode the spot size is 40 µm on the anode. X-ray topography system is a versatile equipment used for projection and section topography. It can provide 360° rotations to the specimen disc around an axis perpendicular to it. Rotations of a few sec of arc can be given to the specimen around a vertical axis. Typical diffraction curves of a dislocation-free crystal and a crystal with boundaries are shown. Well-resolved images of dislocations are shown in a topograph as an illustration. In the triple crystal x-ray diffractometer a highly collimated and monochromated Kα1 exploring x-ray beam is obtained by combining microfocus source, a special collimator and crystal monochromators of Bonse-Hart type. With this beam very narrow diffraction curves with half width of about 5 sec of arc can be recorded. Typical results of measurement of diffuse x-ray scattering (dxs) on nearly perfect silicon single crystals are discussed. It has been observed that the contribution of phonons to thedxs is negligible. Thedxs is mainly due to point defect aggregates.

Mode selection and intensity enhancement of x rays in crystals

Previously unreported intensity enhancement of x rays obtained by two-mode excitation is observed on the direct incident beam of synchrotron radiation. The excitation utilizes the coherent interaction of a six-beam Borrmann diffraction in a perfect silicon single crystal. The experiment provides a means of obtaining nearly divergenceless, monochromatic, spatially coherent, and intense x-ray sources for x-ray diffraction and imaging studies. Single mode excitation can be achieved by using a thick crystal.

Direct observation of TDS profiles from perfect silicon single crystals on a neutron diffractometer

TDS profiles convoluted with the instrument resolution were obtained by forming differences between diffraction profiles measured with neutrons of wavelength 0.60 Å on three perfect Si crystals of different thickness. The profiles were measured with two detector apertures for the reflections 022, 004, 044, 026, 008 and 066. From these measurements TDS correction factors α and hence a correction term ΔB for the temperature parameter of Si were derived. The temperature parameter of Si was determined for two temperatures, 92 and 292 K, as B92 = 0.212 (3) Å2 and B292 = 0.422 (3) Å2, respectively, from the refinement of 100 symmetry-inequivalent reflections measured with neutrons of wavelength 0.53 Å on an imperfect Si crystal.