Annealing behavior ot trap-centers in silicon containing A-swirl defects

The annealing behavior of trap-centers was studied in float-zone silicon wafers containing A-swirl defects. Samples from areas of high and low A-swirl density were annealed in nitrogen ambient between 100° and 900 °C, and analysed using the Deep Level Transient Spectroscopy. The results indicate, that two levels atE _c }-0.07 eV, _n=4.6×10^–16 cm², andE _c–0.49eV, _n=6.6×10^–16cm² are caused by one defect, for which the silicon di-selfinterstitial is a likely interpretation. A level atE _c }-0.11 eV was assigned to interstitial carbon. Both defects annealed out at about 170 °C. After 600 °C annealing an additional level atE _c–0.2 eV was detected, which was attributed to an interstitial silicon carbon complex. Heat treatment at 800 °C generated a new level atE _c–0.49 eV, _n=2.9×10^–16cm² only in the area of high A-swirl defect density. This level was also observed after oxidation and subsequent annealing of silicon.     

Kronecker products of matrices and an application to Fermi systems

An identity for the trace of an exponential function of Kronecker products of matrices is proved. This identity plays an important role for the calculation of the grand potential of interacting Fermi systems. For the HamiltonianH= _i n _i n _i wheren _i =c _i ⁺ n _i (c _i ⁺ : Fermi creation operator at the ith site with spin) we calculate the specific heat for different numbers of electrons per lattice site. Finally, we extend our calculations to find approximative solutions of the Hubbard model.     

Existence of the critical point in φ4 field theory

We consider the ⁴ quantum field theory in two and three spacetime dimensions. In the single phase region the physical mass (inverse correlation length)m() decreases continuously to zero as the bare mass parameter approaches a critical value _c from above. In three dimensions the critical point _c is in the single phase region and the physical mass vanishes there,m( _c )=0.A consequence of our results is that the critical exponentv governing the approach to infinite correlations is bounded below (rigorously) by its classical value, 1/2.Supported in part by the National Science Foundation under Grant MPS74-13252     

Random walks on cubic lattices with bond disorder

We consider diffusive systems with static disorder, such as Lorentz gases, lattice percolation, ants in a labyrinth, termite problems, random resistor networks, etc. In the case of diluted randomness we can apply the methods of kinetic theory to obtain systematic expansions of dc and ac transport properties in powers of the impurity concentrationc. The method is applied to a hopping model on ad-dimensional cubic lattice having two types of bonds with conductivity and ₀=1, with concentrationsc and 1–c, respectively. For the square lattice we explicitly calculate the diffusion coefficientD(c,) as a function ofc, to O(c²) terms included for different ratios of the bond conductivity. The probability of return at long times is given byP ₀(t) [4D(c,)t]^–d/2, which is determined by the diffusion coefficient of the disordered system.     

Self-diffusion of V-48 in the FeV σ-phase and in an Fe-47 wt.% V solid solution

Self-diffusion coefficients of vanadium in the FeV -phase and in the corresponding -solid solution (Fe-47 wt.% V) measured in the temperature ranges 1002–1115 °C (-phase) and 1230–1320 °C are reported. The found results differ fundamentally and significantly from the relations in ordered and disordered solid solutions [9]. The diffusivity in -phase at the transition temperature (T _/=1200 °C) is cca 14 times lower than the diffusivity in the b.c.c. solid solution, the chemical composition of which is the same. The lowering is caused by the different values of frequency factors,D _O=0.11 cm²/s andD _O=45 cm²/s. The effect of the corresponding activation enthalpiesH =252 kJ/mole andH =293 kJ/mole is small and quite opposite. The occurence of higher activation enthalpyH in the -solid solution at temperaturesT>T _/ may be attributed to a certain amount of the f.c.c. phase coexisting in the b.c.c. matrix at concentrationsc _v>27 wt.% at sufficiently high temperatures [7]. A comparison of vanadium self-diffusion characteristics measured in the -phase to the extrapolated values obtained on the basis of the previous measurements [1] in the Fe-V primary solid solutions ₁ shows that the diffusivity ratioD ₁/D (1473 K)=33 and that the activation enthalpyH is by about 3% higher than the valuesH ₁ (eq. (5)) measured in the uniphase b.c.c. solid solutions.     

Interchangeability and bounds on the effective conductivity of the square lattice

The effective conductivity ^* of an infinitely interchangeable two-component random medium is considered. This class of media includes cell materials in the continuum and the bond lattice on ^d , where the cells or bonds are randomly assigned the conductivities ₁ and ₂ ( ₁, ₂ne0) with probabilitiesp ₁ andp ₂=1–p ₁. A rigorous basis for the very old and widely used low volume fraction expansion of ^* is established, by proving that ^* is an analytic function ofp ₂ in a suitable domain containing [0, 1]. In the case of the bond lattice ind=2, rigorous fourth-order upper and lower bounds on ^* valid for allp ₂, ₁, and ₂ are derived. The four perturbation coefficients entering into the bounds are obtained from the first-order volume fraction coefficient using the method of infinite interchangeability.     

Nature of contact resistance in high-T c YBa2Cu3O7−δ Superconductors

The contacts between various metals and the high-T_c superconductor YBa₂Cu₃O_7– are characterized by contact resistance,R _c, andI–V measurements from 300 K to 90 K. The contacts with bulk superconductor were made by vacuum deposition. Four metals, Au, Ag, Al, and Bi were investigated. The current transport across the contact is by carrier tunneling. All contacts were ohmic as theirI–V characteristics were symmetrical with respect to current direction.R _c values range between 10^–2 to 10¹ cm² and increase linearly as the temperature is lowered. The contact resistance originates from two distinct physical processes. One is the modification of the carrier concentration at the interface by the contact metal. The second is the nature of carrier injection at the free surface of the superconductor. TheR _c values depend on the contact metal-oxygen interaction parameter signifying the need for oxygen passivation for obtaining low contact resistances.     

Solution of Ornstein-Zernike equation for wall-particle distribution function

The Ornstein-Zernike (OZ) equation is considered for the wall-particle distribution functiong ₀(x) in the case of a flat, impenetrable wall atx = 0 and a fluid of hard-core particles whose centers are constrained by the wall to occupy the semiinfinite spacex >/2, where is the particle diameter. A solution is given in terms of the wall-particle direct correlation function c₀(x) forx >/2, the bulk-fluid direct correlation function c_B (t), and p_B, the average bulk density. Explicit formulas for the contact surface density, total excess surface density, and the Laplace transform of the fluid density near the wall are given. For mean spherical type approximations, c₀ (x) forx >/2 and c_B (t) are both prescribed functions; for this case, a closed-form solution is obtained. An example is discussed and additional equations that enable one to go beyond the approximations considered above are introduced.Report #270, February 1976.The observation of this paper that the wall-particle problem can be treated using standard Wiener-Hopf techniques was independently made by Percus in his work, which came to our attention too late to be compared to, or incorporated into, our own results here.     

Magnetic penetration depth of 585-01585-01585-01: Tc ∼ σ0 in the overdoped region

We report transverse field muon spin rotation experiments carried out on Tl₂Ba₂CuO₆₊. This system spans the whole overdoped regime, in which T_c is reduced by excess oxygen doping despite an increasing normal state carrier concentration. In the heavily overdoped regime the extrapolated low temperature depolarization rate(0) is found to scale linearly with the superconducting critical temperature T_c similar to the behavior previously observed for other cuprates in the underdoped regime. In the framework of the clean limit London model,(0) ^–2 n _s (0)/m _s ^* , suggesting that the depression of T_c by overdoping is associated with a decrease of the superconducting condensate density. This needs to be understood in view of the observed increase in the normal state carrier density. We discuss some possible explanations for this behavior.     

Electrical properties of doped single crystals of Zn4Sb3

Conductivity , thermo-emf , and Hall constant R are presented as functions of temperature for pure Zn₄Sb₃ single crystals and for ones doped with Ag, Au, Ga, In, Sn, Pb, and Te. Here Ag, Au, Sn, and Pb act as acceptors. Increased hole concentration and , together with the reduced , are produced by In, Te, and Ga, on account of formation of solid solutions of InSb, GaSb, and ZnTe in Zn₄Sb₃.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Formation of the intermediate semiconductor larger for the Ohmic contact to silicon carbide using Germanium implantation

By formation of an intermediate semiconductor layer (ISL) with a narrow band gap at the metallic contact/SiC interface, this paper realises a new method to fabricate the low-resistance Ohmic contacts for SiC. An array of transfer length method (TLM) test patterns is formed on N-wells created by P⁺ ion implantation into Si-faced p-type 4H-SiC epilayer. The ISL of nickel-metal Ohmic contacts to n-type 4H-SiC could be formed by using Germanium ion implantation into SiC. The specific contact resistance ρ_c as low as 4.23× 10^-5~Ωega \cdotcm² is achieved after annealing in N₂ at 800~°C for 3~min, which is much lower than that (>900~°C) in the typical SiC metallisation process. The sheet resistance R_sh of the implanted layers is 1.5~kΩega /\Box. The technique for converting photoresist into nanocrystalline graphite is used to protect the SiC surface in the annealing after Ge⁺ ion implantations.     

Photon-deuteron diffractive scattering

One expects a similarity of the energy dependence of the difference _tot(*p)– _tot(*n) for virtual (deep inelastic scatteringQ ²m ²) and real (Q ²=0) photons. Previous analysis of D structure functions with allowence for nuclear shadowing (NS) in the deuteron has led to conclusion that _tot(*p)– _tot(*n)<0>x<0.015. the=" early=" evidence=" from=" the=" real=" photoproduction=" data="> _tot(p)– _tot(n)<0. we=" critically=" reexamine=" determinations=" of=" the="> _tot(p)– _tot(n), using more accurate calculations of NS correction to _tot(D), and discuss a possibility of _tot(n) _tot(p) at moderately high energies.     

Resistance to dislocation motion in copper-based solid solutions with a statistically disordered atomic distribution

The stress _F due to friction forces in copper-based solid solutions was determined. Under the conditions of the procedure used to measure _F, on the basis of the half-wave hysteresis with polycrystalline samples, the value of d: _F = _F0 + K_Fd^–(1/2) where _F0 is the resistance to dislocation motion in an alloy having an infinite grain size, and K_F is a constant. It is shown that _F0 is governed by the interaction of moving dislocations with impurity atoms in the case of a statistically disordered atomic distribution. A study was made of the effects of various factors on _F and of the nature of the changes in _F0 caused by alloying.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No.3, pp. 18–23, March, 1971.     

Interfaces in the Potts model II: Antonov's rule and rigidity of the order disorder interface

Within the ferromagneticq-state Potts model we discuss the wetting of the interface between two ordered phasesa andb by the disordered phasef at the transition temperature. In two or more dimensions and forq large we establish the validity of the Antonov's rule, _ab = _af + _fb , where denotes the surface tension between the considered phases. We also prove that at this temperature, in three or more dimensions the interface between any ordered phase and the disordered one is rigid.Laboratoire Propre du CNRS: LP 7061     

Ion mixing in Al,Si, and their oxides

The redistribution of thin metallic markers due to ion irradiation was studied by backscattering spectrometry in Al, Al₂O₃, Si, and SiO₂. Marker species were selected for their similar masses and different chemical reactivities with the host media and included Ti, Fe, W, Pt, and Au. It was found that the marker signals are Gaussian and that the variance ² of the marker atom distributions increases linearly with the dose of the irradiation, is insensitive to the temperature of irradiation in the range of 80–300 K, and depends linearly on the nuclear stopping power of the incident ions. The absolute values of ² for Ti, Fe, W, Pt, and Au markers in Al and Al₂O₃, W, and Pt in SiO₂ and W in Si is, within±50 %, of 6.5×10³Å² for 300 keV, 8×10¹⁵ Xe ions/cm². These observations suggest that collisional cascade mixing is a dominant mechanism in this type of impurity-matrix combinations. Only Au and Pt in Si mix at a larger rate: ² for Pt is about 3 and for Au about 5 times larger than ² for all other markers. Lower threshold displacement energies and/or the contribution of processes other than cascade mixing are possible considered reasons. In polycrystalline Al, a rapid migration of Au and Pt atoms throughout the Al layer, similar to grain boundary diffusion, is observed.     

Numerical studies on the anderson localization problem

Our study of Anderson's tight binding model for strongly disordered electronic systems is extended to a numerical treatment of thed c-conductivity atT=0. For 100 × 100 square lattices, 129 × 129 triangular lattices, and for diamond lattices with 27,000 sites, the behaviour of is studied as a function of the Fermi energy and the disorder. The calculations are based on the exact eigenfunction representation of the Kubo formula, which is evaluated by the systematic application of recursion algorithms. Our results are in favour of Mott's original suggestion of a minimum metallic conductivity _min, both in two and three dimensions. In two dimensions we find the universal value of _min=(0.11 ±0.02)e ²/. Based on the thesis of J. Stein, Regensburg 1979     

Electrical and thermal properties of chalcogenide glass system Se75Ge25−x Sb x

The dc and thermal conductivities of five different compositions of the chalcogenide glass system Se₇₅Ge_25–x Sb _x have been studied in a temperature range below T _g. The dc conductivity results indicate that each composition has a single activation energy in the considered temperature range. The coefficient of thermal conductivity increased linearly with temperature below T _g for the compositions investigated. The increase of Sb content in the chalcogenide glass system leads to an increased coefficient of electrical conductivity , an increased coefficient of thermal conductivity , and to a decreased activation energy E and pre-exponential factor ₀. The observed compositional dependencies of and E have been correlated with the increase of weak bond density and the decrease of covalent bond density in the structure of the compositions investigated with increasing Sb content at the expense of Ge content. The decrease in ₀ and the increase in has been, respectively, correlated with the decrease in mobility and the increase in phonon velocity.     

The creep of alpha iron in the temperature range 220–900°C

The creep of alpha iron of about 99·9% purity has been studied by means of the isothermal test technique in the temperature interval of 500–1170°K. At temperatures lower than 800°K the apparent activation energy of creep depends primarily on the stress, at temperatures higher than 800°K but lower than the Curie temperatureT _c=1042°K it depends mainly on the temperature. At the Curie temperature the apparent activation energy reaches a value of about 175 kcal mol^–1. The stress dependence of the minimum creep rate cannot be generally described either by a simple power function of the ⁿ type, or by a simple function of the exp () type.An analysis of the results obtained leads to the conclusion that the minimum creep rate is controlled by the gliding movement of dislocations dependent on lattice self-diffusion. The mechanism controlling the creep rate at temperatures above the Curie point needs further study.     

Measurement of the2H(d, γ)4He reaction at intermediate excitation energies

The²H(d, )⁴He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between _cm=45° and _cm=135°. AtE _d =28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratioR=d/d (_cm=90°)/d/d (_cm=135°) was measured for each deuteron energy.