This study improves and expands the scope of application of the theoretical model previously proposed by the authors, which describes the relationship between the strength and electromigration ...(diffusion) properties of interfaces formed by connected materials. In the developed model, a linear relationship is established between the values of the work of reversible interface separation
and electromigration activation energy
in the interface. Estimates are made and the coefficients of the resulting relation are compared with experiments studying electromigration in a copper conductor coated with a protective dielectric. Using also the model previously developed by the authors, which describes the dependence of the quantity
on the concentrations of nonequilibrium lattice defects presenting in the volumes of connected materials, a number of effects due to the influence of such defects on processes caused by electromigration are predicted and studied. This study shows that by introducing nonequilibrium lattice defects in the form of atomic interstitial or substitutional impurities into the volumes of the joined materials, we can effectively influence on the characteristics of the electromigration instability of the shape of the interlayer boundary. For interstitial impurities, quantitative analytical estimates of the impurity concentration required to significantly change (both increase and decrease) the characteristic growth time of the instability of the shape of an initially flat interface are performed.
In order to study the strength reliability of interconnections, a generalized model for quantifying the effect of nonequilibrium point crystal defects on the value of the work of the reversible ...separation of joined materials along the boundary (interface) of their union, generalizing an approach proposed previously by the authors to the description of the mechanism of defect adsorption in the interface area. The developed model makes it possible not to be limited to the situation when the defects of each of the contacting materials are distributed independently in the boundary, over their sublattices, and the transitions of defects between these sublattices are also taken into account, that significantly expands the possibilities of applying the obtained theoretical results. The corresponding system of equations is formulated, that makes it possible to find and study the value of the work of reversible separation as a function of defect concentrations in the bulks of materials. In the case when the interstitial impurity atoms are the defects, the problem of the critical impurity concentrations at which the work of reversible separation vanishes and the bonding of the materials becomes thermodynamically unstable is studied in detail by analytical methods; the role of defect transitions between the sublattices, in which defects are localized at the interface, is explained. Impurity concentrations are estimated at which the effect of the interface instability can be realized, significantly affecting the reliability characteristics of the interconnections.
A novel type of sub-lattice of the Jahn-Teller (JT) centers was arranged in Ti-doped barium hexaferrite BaFe
O
. In the un-doped crystal all iron ions, sitting in five different crystallographic ...positions, are Fe
in the high-spin configuration (S = 5/2) and have a non-degenerate ground state. We show that the electron-donor Ti substitution converts the ions to Fe
predominantly in tetrahedral coordination, resulting in doubly-degenerate states subject to the Formula: see text problem of the JT effect. The arranged JT complexes, Fe
O
, their adiabatic potential energy, non-linear and quantum dynamics, have been studied by means of ultrasound and terahertz-infrared spectroscopies. The JT complexes are sensitive to external stress and applied magnetic field. For that reason, the properties of the doped crystal can be controlled by the amount and state of the JT complexes.
The influence of an external magnetic field on the complex elastic moduli of crystals with a sphalerite or zinc blende (ZnSe) and wurtzite (CdSe) structure lightly doped by Cr
2+
ions has been ...investigated. Measurements have been performed in the frequency interval 26–32 MHz at 1.4 K. In II–VI crystals, bivalent chromium cations are triply orbital-degenerate in the ground state and, being in a tetrahedral environment, produce Jahn–Teller complexes. These complexes are described in terms of the
T
(
e
+
t
2
)-problem and exhibit the adiabatic potential energy surface with the global minima of tetragonal symmetry. It has been found that in ZnSe:Cr
2+
crystals, a magnetic field directed along the 001 and 110 axes influences modulus (
c
11
–
c
12
)/2 and does not influence modulus
c
44
. In CdSe:Cr
2+
crystals, however, moduli
c
55
and
c
66
, which are the analogs of (
c
11
–
c
12
)/2 and
c
44
, depend on the magnetic field directed along the
and
axes, respectively. The discovered anomalous behavior of the elastic moduli with magnetic field has been treated in terms of a model that takes into account the crystal field, vibronic and spin-orbital interactions, and the contribution of the Jahn–Teller subsystem to isothermal moduli determined at a constant magnetic induction. Good agreement with experimental dependences of the elastic moduli in strong magnetic fields has been obtained, and it has been shown that the nonmonotonic variation in weak magnetic fields (below 2 T) should be associated with a magnetic field dependence of the relaxation time.
Expressions for the stabilization energies of tetrahedral complexes in doped II–VI:3
d
crystals with a wurtzite structure have been obtained by the example of a CdSe:Cr
2+
crystal within the linear
...problem of the Jahn–Teller effect. It has been shown that the crystallographic anisotropy of a hexagonal lattice leads to an increase in one of the global minima of the lower sheet of the adiabatic potential, which significantly differs from the adiabatic potential of the same complexes in cubic II–VI:3
d
crystals and affects isothermal elastic moduli and the manifestation of the Jahn–Teller effect in an ultrasonic experiment.
The paper proposes a theory describing the effect of ion migration induced by electric current at initially plane interfaces of integrated circuit (IC) conducting layers on the interface stability ...with account of mechanical (residual) stress from IC wafers. A system of equations is derived and solved to trace the relation between the interface profile and mechanical stress induced at the interface by ion electromigration due to spatially periodic interface perturbation. Criteria are formulated to judge the buildup of perturbation with time, i.e., the interface profile instability under external conditions. The theory is applied to two practically significant cases: to interfaces between identical materials and between dissimilar materials of which one can be taken free of ion diffusion. Analytical expressions are presented for the influence of external conditions (temperature, current density, residual mechanical stress from wafers) on the range of perturbation wavelengths at which interface instability occurs and for the characteristic time of exponential perturbation buildup. Our estimates show that the interface of IC layers can get unstable via electromigration under typical acceleration conditions. For example, at
T
~ 100–500°C, |
j
| ~ 10
10
–10
12
A/m
2
, the perturbation (e.g., vibration) wavelength responsible for instability measures λ ~ 10–1000 μm. The results of this study can be useful for increasing the reliability of micro- and nanoelectronic structures.
A model is developed for the description of the effect of nonequilibrium crystal defects on the kinetics of instability of the shape of the boundary (interface) between layers of joined conductive ...materials, which arises due to the electromigration of ions in these materials. The mechanism of the origination of instability takes into account the action of mechanical stresses in the system, including the stresses due to the differing materials of the substrate and the film deposited on it (residual stresses). General relationships describing the dependence of the conditions of the origination of the instability of a spatially periodic perturbation for an initially flat interface and the characteristic times of its development on concentrations of nonequilibrium lattice defects in volumes of the joined materials are obtained. For more accurate analysis and estimations, two specific cases are considered: first, the interface is formed by joining the same two materials and, second, the joined materials are substantially different in such a way that the diffusion mobility in one of them may be neglected.
A method is developed to determine the symmetry properties of strains and the type of Jahn–Teller effect in crystals with impurity ions in a triply degenerate electronic
T
state. This method is based ...on a calculation of the isothermal contribution of the impurity subsystem to the elastic moduli of a crystal and the absorption and velocity of normal modes for all three possible problems, namely,
T
⊗
e
,
T
⊗
t
2
, and
T
⊗ (
e
+
t
2
). The calculation results are compared with experimental data. The efficiency of the method is demonstrated for a CdSe:Cr
2+
crystal. The CrSe
4
center is found to be described in terms of the problem
T
⊗
e
. The parameters of the ground-state adiabatic potential are determined.
The results of the study of the temperature dependence of attenuation and velocity of ultrasonic waves are presented for CaF
2
:Cr and CaF
2
:Ni crystals in which Cr
2+
and Ni
2+
ions substitute ...calcium ions, forming Jahn–Teller (JT) complexes CrF
8
6–
and NiF
8
6–
. The Cr
2+
and Ni
2+
ions in the fluorite structure have threefold orbital degeneracy in the ground state, are described by the
T
(
e
+
t
2
) Jahn–Teller effect (JTE) problem, and have an adiabatic potential energy surface (APES) defined in the five-dimensional space of trigonal and tetragonal symmetrized coordinates whose lower sheet is a simply connected surface with orthorhombic minima separated by potential energy barriers. The temperature dependence of the ultrasonic attenuation and velocity exhibits anomalies typical of the relaxation contributions of systems of JT complexes in the low-temperature region. The effect of tunneling relaxation mechanisms (direct and two-phonon transitions) on the JT contribution to the complex elastic moduli and to the error in determining the relaxation time is analyzed. Based on the approach that takes into account both tunneling and activation mechanisms of relaxation, the activation energies and the constants characterizing these relaxation mechanisms are determined in CaF
2
:Cr
2+
and CaF
2
:Ni
2+
crystals.
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