Doped Silicon Crystals Research Articles

Defect behavior during growth of heavily phosphorus doped Czochralski silicon crystals (II): Theoretical study

Defect behavior during growth of heavily phosphorus doped Czochralski silicon crystals (II): Theoretical study

Impurity-induced enhancement of parity-forbidden optical intracenter transitions of shallow donors in silicon

Different defects in silicon crystals cause lattice distortion that may violate selection rules for certain intracenter optical transitions of hydrogen-like donor centers. Perturbations due to large concentration of substitutional donors enhance all parity-forbidden atomic transitions, but cause large concentration broadening of the transition lines, prohibiting observation of transitions at close energies. Substitutional residual carbon atoms in silicon induce, in contrast, a weak-to-moderate broadening of donor absorption lines enabling the resolution of some parity-forbidden intracenter transitions in impurity absorption spectra at moderate donor densities. Binding energies of several series of s- and d-type states were obtained by resolving of intracenter transitions terminating in these states, by low-temperature infrared absorption spectroscopy in carbon-rich and/or heavily doped silicon crystals.

Investigation of Facetted Growth in Heavily Doped Silicon Crystals Grown in Mirror Furnaces

Herein, facets and related phenomena are studied for silicon crystals grown in the <100> and <111> directions, using the Zone Melting and Floating Zone techniques. Investigating the central facets of dislocation-free <111> crystals as a baseline allowed for the determination of the local temperature gradients. When comparing these results to dislocated <111> crystals, the presence of dislocations caused a clear reduction in the facet size, correlated with a reduction in the required local supercooling to estimated maximum values of around 0.6 K. Furthermore, for crystals grown on the rough {100} interface, attempts to provoke a morphological instability of the local phase boundary succeeded for crystallization velocities in the range of 10–16 mm/min, in good agreement with theory. Contrary to this observation, crystals grown in the <111> direction remained morphologically stable even at higher crystallization velocities due to the stabilizing effect of the atomically smooth interface. Additionally, crystals grown in the <111> direction with an oxygen skin by the Zone Melting technique reproducibly showed a non-periodic fluctuation of the central facet diameter at a certain translation velocity.

Numerical analysis of constitutional supercooling in heavily doped silicon crystals grown using the Czochralski method

In the growth of silicon single crystal using the Czochralski method, heavy doping using species such as B, P, and As increases the probability of the deterioration of the crystal quality. This is attributed to morphological instability at the growth interface in the crystal because of constitutional supercooling occurring near the growth interface. Therefore, it is necessary to control constitutional supercooling during growth to stabilize the growth of heavily doped Si single crystals. In this paper, we proposed a new approach to predict the formation and distribution of constitutional supercooling based on a three-dimensional numerical model accounting for heat and mass transport, including the segregation effects of the dopants. The dependency of the growth rate, dopant type, and dopant concentration on the formation of constitutional supercooling was evaluated using this approach. Furthermore, the way to suppress constitutional supercooling was discussed through the example of the effect of crystal rotation rate.

Terahertz transient stimulated emission from doped silicon

Transient-type stimulated emission in the terahertz (THz) frequency range has been achieved from phosphorus doped silicon crystals under optical excitation by a few-picosecond-long pulses generated by the infrared free electron lasers FELIX and CLIO. The analysis of the lasing threshold and emission spectra indicates that the stimulated emission occurs due to combined population inversion based lasing and stimulated Raman scattering. Giant gain has been obtained in the optically pumped silicon due to large THz cross sections of intracenter impurity transitions and resonant intracenter electronic scattering. The transient-type emission is formed under conditions when the pump pulse intervals exceed significantly the photon lifetime in the laser resonator.

Impact of arsenic and phosphorus concentration on oxygen content in heavily doped silicon single crystal

This study investigates the impact of the arsenic and phosphorus concentration on the oxygen content in heavily doped silicon crystals. The resistivity and the oxygen measurements were made on 200 mm crystals grown with the Czochralski method. The oxygen concentration, measured by Gas Fusion Analysis, decreases with the increase of dopant concentration. Two mechanisms related to the effect of the arsenic and phosphorus concentration on the oxygen contents are discussed: one is the possible inhibition of the oxygen segregation inside the silicon crystal due to the lattice deformation and the other is the oxygen evaporation enhancement from the melt through dopant-oxides formation.

Edge facet dynamics during the growth of heavily doped n-type silicon by the Czochralski-method

During the growth of [0 0 1]-oriented, heavily n-type doped silicon crystals by the Czochralski (CZ) method dislocation formation occurs frequently which leads to a reduction of the crystal yield. In this publication the evolution of the solid-liquid interface and the formation of the {1 1 1} edge facets are analyzed on a microscopic scale as possible reason for dislocation formation in heavily n-type doped [0 0 1]-oriented CZ crystals. A correlation between the length of the {1 1 1} edge facets and the curvature of the interface is found. They ultimately promote supercooled areas and interrupted growth kinetics, which increase the probability for dislocation formation at the boundary between the {1 1 1} edge facets and the atomically rough interface.

Influence of different thermal treatment regimes on the hall parameters and the lifetime of charge carriers of transmutation doped silicon crystals

Influence of different thermal treatment regimes on the hall parameters and the lifetime of charge carriers of transmutation doped silicon crystals

Thermal conductivity of silicon doped by phosphorus: ab initio study

AbstractAn original approach to the theoretical calculations of the heat conductivity of crystals based on the first principles molecular dynamics has been proposed. The proposed approach exploits the kinetic theory of phonon heat conductivity and permits calculating several material properties at certain temperature: specific heat, elastic constant, acoustic velocity, mean phonon scattering time and coefficient of thermal conductivity. The method has been applied to silicon and phosphorus doped silicon crystals and the obtained results have been found to be in satisfactory agreement with corresponding experimental data. The proposed computation technique may be applied to the calculations of heat conductivity of pure and doped semiconductors and isolators.

Dislocation formation in heavily As‐doped Czochralski grown silicon

During the growth of <100>‐oriented, heavily n‐type doped silicon crystals by the Czochralski method dislocation formation occurs frequently, leading to a reduction of the crystal yield. Up to now, it is not clear where and why the dislocations form. Therefore, heavily As‐doped crystals were studied in this work in more detail by means of X‐ray topography (XRT) and synchrotron X‐ray topography (SXRT). From the data obtained it is concluded that dislocations form during growth of the top cone of the crystals in the vicinity of one of the four so‐called growth ridges.

Sample thickness effect of thermal vibration correction within X-ray dynamical theory for germanium-doped silicon

As of today, highly germanium doped Czochralski silicon crystals are used in applications. However, it is not clear how a germanium content in the range of 1018 atoms/cm3 influences the oxygen precipitation behavior, which is highly relevant for the gettering potential of the wafer. In this context, high energy X-ray diffraction is a promising tool to monitor real-time the strain introduced by the oxygen agglomeration and growth. Nevertheless, in particular, in the dynamical limit of X-ray diffraction and at elevated temperatures, the strain originating from the precipitation process has to be clearly distinguished from the intensity contribution of thermal vibrations. In Laue geometry, dynamical effects can even lead to an increment of the integrated intensity with temperature completely unexpected in the kinematical limit, where temperature is tackled solely by a Debye-Waller factor. In the following, an approach is presented allowing us to completely correct the influence of thermal vibrations in the dynamical limit. This approach is applied to undoped and highly germanium doped silicon crystals, clearly revealing an enhanced inventory of grown-in precipitates with germanium doping and suggesting a morphological transformation towards a phase of higher strain of the grown-in precipitates in the range between room temperature and 800 °C.

Thermal equilibrium concentration of intrinsic point defects in heavily doped silicon crystals - Theoretical study of formation energy and formation entropy in area of influence of dopant atoms-

It is well known that p-type, neutral and n-type dopants affect the intrinsic point defect (vacancy V and self-interstitial I) behavior in single crystal Si. By the interaction with V and/or I, (1) growing Si crystals become more V- or I-rich, (2) oxygen precipitation is enhanced or retarded, and (3) dopant diffusion is enhanced or retarded, depending on the type and concentration of dopant atoms. Since these interactions affect a wide range of Si properties ranging from as-grown crystal quality to LSI performance, numerical simulations are used to predict and to control the behavior of both dopant atoms and intrinsic point defects. In most cases, the thermal equilibrium concentrations of dopant-point defect pairs are evaluated using the mass action law by taking only the binding energy of closest pair to each other into account. The impacts of dopant atoms on the formation of V and I more distant than 1st neighbor and on the change of formation entropy are usually neglected. In this study, we have evaluated the thermal equilibrium concentrations of intrinsic point defects in heavily doped Si crystals. Density functional theory (DFT) calculations were performed to obtain the formation energy (Ef) of the uncharged V and I at all sites in a 64-atom supercell around a substitutional p-type (B, Ga, In, and Tl), neutral (C, Ge, and Sn) and n-type (P, As, and Sb) dopant atom. The formation (vibration) entropies (Sf) of free I, V and I, V at 1st neighboring site from B, C, Sn, P and As atoms were also calculated with the linear response method. The dependences of the thermal equilibrium concentrations of trapped and total intrinsic point defects (sum of free I or V and I or V trapped with dopant atoms) on the concentrations of B, C, Sn, P and As in Si were obtained. Furthermore, the present evaluations well explain the experimental results of the so-called “Voronkov criterion” in B and C doped Si, and also the observed dopant dependent void sizes in P and As doped Si crystals. The expressions obtained in the present work are very useful for the numerical simulation of grown-in defect behavior, oxygen precipitation and dopant diffusion in heavily doped Si. DFT calculations also showed that Coulomb interaction reaches approximately 30Å from p (n)-type dopant atoms to I (V) in Si.

The role of materials science in the evolution of microelectronics

Abstract

Terahertz emission from lithium doped silicon under continuous wave interband optical excitation

We report on experimental observation and study of terahertz emission from lithium doped silicon crystals under continuous wave band-to-band optical excitation. It is shown that radiative transitions of electrons from 2P excited states of lithium donor to the 1S(A1) donor ground state prevail in the emission spectrum. The terahertz emission occurs due to capture of nonequilibrium electrons to charged donors, which in turn are generated in the crystal as a result of impurity assisted electron-hole recombination. Besides the intracentre radiative transitions the terahertz emission spectrum exhibits also features at about 12.7 and 15.27 meV, which could be related to intraexciton transitions and transitions from the continuum to the free exciton ground state.

Constitutional Supercooling in Czochralski Growth οf Heavily Doped Silicon Crystals

This study analyses the phenomenon of constitutional supercooling, which is one of the major problems in industrial growth of heavily doped (> 10 atoms/cm) silicon crystals by the Czochralski technique. The systematic study is based on theoretical models and experimental data considering the e ect of three important dopants (B, P, and As) in dependence of the relevant growth parameters for the Czochralski process. Based on these results, conclusions will be drawn for the stability limits of the Czochralski growth of dislocation-free heavily doped silicon crystals in dependence of the doping species and their concentration.

Growth and characterization of heavily doped silicon crystals

AbstractSilicon crystals grown with the Czochralski method are still the most common material used for the production of electronic devices. In recent years, a growing need of large diameter crystals with increasingly higher doping levels is observed, especially to support the expanding market of discrete devices and its trend towards lower and lower resistivity levels for the silicon substrate. The growth of such heavily doped, large‐diameter crystals poses several new challenges to the crystal grower, and the presence of a high dopant concentration in the crystal affects significantly its main properties, requiring also the development of dedicated characterization techniques. This paper illustrates the recent advances in the growth and characterization of silicon crystals heavily doped with antimony, arsenic, phosphorus and boron. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A density functional theory study of the atomic structure, formation energy, and vibrational properties of nitrogen-vacancy-oxygen defects in silicon

The atomic structure, energy, stability, vibrational spectra, and infrared absorption intensities of major intrinsic nitrogen-related defects in nitrogen doped silicon crystals have been investigated using ab initio density functional theory and semi-empirical quantum mechanics methods. The defects that are of interest are nitrogen-vacancy-oxygen complexes which are believed to affect oxygen precipitation and void formation as well as nitrogen concentration measurement in nitrogen-doped silicon. Several chemical reactions involving nitrogen, Si vacancies and oxygen interstitial have been studied. After relaxation, the local vibrational modes of each complex are calculated within the harmonic oscillator approximation and the infrared absorption intensities are evaluated from the dipole moment derivatives. By cross correlating the stability and the infrared active lines of the defect, and taking into consideration the symmetry group of each complex, we were able to emphasize which nitrogen related complexes are likely to control the oxygen precipitation and voids formation and to assert a new calibration relationship for nitrogen concentration measurement in nitrogen doped Czochralski and float zone silicon wafers.

The effect of dopants on the brittle-to-ductile transition in silicon single crystals

The brittle-to-ductile transition (BDT) in boron, antimony and arsenic doped Cz silicon crystals has been experimentally studied, respectively. The BDT temperatures in antimony and arsenic doped silicon wafers are lower than that in a non-doped wafer while the BDT temperature in a boron doped wafer is almost the same as that in the non-doped wafer. The activation energy was obtained from the strain rate dependence of the BDT temperature. It was found that the values of the activation energy in the antimony and arsenic doped wafers are lower than that in the non-doped and boron doped wafers, indicating that the dislocation velocity in the antimony and arsenic doped silicon is faster than that in the non-doped while the dislocation velocity in the boron doped is the same as that in the non-doped. The effect of increasing in dislocation velocity on the BDT temperature was calculated by two-dimensional discrete dislocation dynamics simulations, indicating that the increasing in dislocation velocity decreases the BDT temperature in silicon single crystals.

Detection of arsenic dopant atoms in a silicon crystal using a spherical aberration corrected scanning transmission electron microscope

In recent silicon transistors, fluctuation of the gate threshold voltage due to statistical variation in the number of dopant atoms has been pointed out to be a serious problem. For this reason, characterization methods are required which can detect individual dopant atoms within the transistor. In this paper, we present a technique for visualizing individual arsenic (As) atoms in a doped silicon crystal using our developed spherical aberration corrected scanning transmission electron microscope (STEM) with a convergent electron probe with a half angle of 30 mrad to view very thin doped silicon crystals from the [001] direction. The STEM images show the distribution of As dopant atoms within a 2.7 nm defocusing range around the focal position. It was found that in a highly doped silicon wafer following rapid thermal annealing, clustering of As atoms was extremely rare.

Detection of Individual Dopant Atoms and Clusters in the Doped Silicon Crystal

Detection of Individual Dopant Atoms and Clusters in the Doped Silicon Crystal