K. Ahlborn

Debye‐temperature–elastic‐constants relationship for materials with hexagonal and tetragonal symmetry

In the literature a relation is often used that correlates Debye temperature and bulk modulus by a square‐root law. It was recently shown that, for different cubic crystal structures, such a law is only fulfilled within relatively large error limits. If one takes, however, the average of the elastic constants of the transversal acoustic phonon modes as elastic modulus instead of the bulk modulus, the square‐root law is established with high precision. It is demonstrated that the same procedure may also be applied successfully to materials with hexagonal crystal symmetry such as hexagonal close‐packed metals and semiconducting compounds with the wurtzite structure, and to different structures of the tetragonal system. The adequate moduli are Gh={c44[c44(c11−c12)/2]1/2} 1/2 and Gt=[c44c66(c11−c12)/2]1/3 for materials with hexagonal and tetragonal symmetry, respectively. The difference between the various structures of a crystal system is quantitatively described by the different number of atoms in the cryst...

The plasticity of GaAs between 415 and 730°C

Abstract GaAs single crystals grown by the liquid-encapsulated Czochralski method are compressed along ‘123’ under a protective atmosphere of flowing Ar. The resulting stress-strain curves, which are rather similar to those observed in other III-V compounds, are analysed according to the beginning of plastic deformation and to dynamical recovery. The lower yield point is characterized by an activation energy of l·24eV and a stress exponent of 3·5. Both values compare favourably with those obtained from measurements of the dislocation velocity. From the strain-rate and temperature dependence of the stress τIII at the onset of the first recovery stage, an activation energy of approximately 2eV is derived, which may be regarded as a lower bound for the activation energy of self-diffusion of the slowest-moving species. Comparing these results with those obtained for other semiconductors corroborates a view increasingly supported in the literature, namely that moving dislocations emit or absorb point effects.

Steady-state deformation at intermediate and high temperatures

Abstract Experimental data of steady-state deformation obtained either in creep or in constant strain-rate experiments, which extend from high to intermediate temperatures, become increasingly available in the literature. While in many cases the high-temperature regime can be explained by the well-known power-law models, the incorporation of the results at intermediate temperatures is still under discussion. It is the aim of the present work to show by a careful analysis of the above mentioned data, that the jog-dragging model put forward by Barrett and Nix can account for the whole temperature range considered here and that the activation enthalpy of steady-state deformation is that of lattice self-diffusion.

Two independent mechanisms of dynamical recovery in the high-temperature deformation of silicon and germanium

Abstract As has been reported earlier, the stress-strain curves of monocrystalline silicon and germanium are characterized by two different stages of dynamical recovery at high temperatures, which have been associated with self-diffusion and cross-slip, respectively. In the present paper it is shown that both recovery processes can also be observed in steady-state creep and hot-working experiments on silicon. It is also considered why only one recovery process has been found in creep experiments on germanium. The implications of these findings on the basis of two independently operating recovery processes are discussed. Finally some consequences for f.c.c. metals are indicated.

Sensitivity limits of strain mapping procedures using high‐resolution electron microscopy

Strain detection limits achieved by several approaches of strain mapping differing in the procedure of determining positions of intensity maxima have been compared. Algorithms which simultaneously take into account the two‐dimensional intensity distribution around maximum positions yield similar detection limits and are superior to those performing successive one‐dimensional cuts. Investigations of the effect of image recording imply that the use of photographic plates is superior to direct image recording using a slow‐scan CCD camera because of larger sampling rates and a larger field of view. It is finally shown that the choice of specimen preparation technique substantially affects the strain detection limit with cleaved samples yielding results which are a factor of about three better than ion‐milled samples.

Dynamical recovery and self-diffusion in InP

Abstract Single crystals of InP with ⟨123⟩ orientation have been deformed at constant strain rates at temperatures between 540 and 780°C. The resulting stress–strain curves are rather similar to those obtained for other semiconductors such as Ge, Si and InSb, and two stages of dynamical recovery can be clearly identified. From the strain-rate and temperature dependences of the stress τiii at the beginning of the first recovery stage, an activation energy of 2.3 eV is deduced. This may be regarded as a lower bound for the activation energy of self-diffusion of the slowest-moving species; for the pre-exponential factor D0 of the diffusion coefficient a value between 10−3 and 10−2 cm2 s−1 is estimated.

The effect of solutes on the dynamical recovery of silicon and germanium

Abstract The present investigation reports on the influence of high doping on the stress-strain curves of Si and Ge with 〈123〉 orientation. As it is known for undoped semiconductors, two stages of dynamical recovery are observed. In contrast to these materials, however, the first recovery stage can no longer be interpreted by a diffusion-controlled mechanism. Rather a behavior similar to that found for the stationary deformation of metal alloys at high stresses may be realized. Although this effect is still under discussion in the literature, it is assumed that it has to do with the influence of the solute on the dislocation sub-structure evolving in the steady-state regime of the deforming crystals. The second stage of dynamical recovery shows the same behavior as observed in the undoped semiconductors; it is interpreted by a cross-slip mechanism.

A new regime of dynamic recovery in the high-temperature deformation of semiconductors

Abstract It is well established that cross-slip is a dominating process in the second stage of dynamical recovery in elemental and compound semiconductors. In the present work, new experimental results are presented which show that, besides cross-slip, a further hitherto unknown mechanism is involved in the deformation at high strains. This effect is only observed in measurements on crystals deformed along 〈123〉, but not for deformation along 〈111〉. It is suggested that this different behaviour may be traced back to the fact that the 〈111〉 orientation favours cross-slip while the 〈123〉 orientation does not. In Ge, where the stress—strain curves have been studied over a large temperature range, the new mechanism manifests itself in the occurrence of three recovery stages close to the melting point. Dynamic recrystallization is probably not the process underlying the new deformation stage.

Diffusion of gallium along small-angle grain boundaries in germanium

Abstract Diffusion profiles of gallium in germanium containing a small-angle symmetric tilt boundary have been determined as a function of temperature and misorientation angle. The observed diffusion tails cannot be described in terms of the phono-monological pipe diffusion or grain-boundary diffusion models. The results may be understood by diffusion along a second phase, containing Ge, which forms around the dislocations, and in which the solubility of gallium is about 102 103 times that in the unperturbed germanium matrix.

Dynamical recovery of InSb between 340 and 510°C

Abstract The stress-strain curves of InSb have been investigated in the temperature range extending from 340 to 510°C. The two stages of dynamical recovery typical for elemental and compound semiconductors are observed in this material. The underlying micromechanical processes are identified as diffusion-controlled climb and cross-slip respectively. There is no indication of a further regime of dynamical recovery, in contrast with the behaviour of Ge and Si with orientation.