Dislocation substructures belongs to small angle grain patterns which are already well studied in bended and rolled metals and alloys due to their essential effect on material strength. But there is also an increasing need for clarification of such features in semiconductors and dielectric crystals because they markedly influence the device quality. For instance, in as-grown semi-insulating GaAs, important for production of low-noise high-frequency devices, a mesoscopic resistivity variation does occur due to the accumulation of As_Ga antisite defects (EL2) along the low-angle grain walls that requires a well sophisticated after-annealing step. Further, the wide application of Cd_1-xZn_xTe crystals as most promising candidates for radiation-detection systems is still hindered by the charge-transport non-uniformities along such cellular substructures which, additionally, are decorated by impurities and secondary phase particles affecting the energy and spatial resolution too. Or, in multicrystalline silicon (mc-Si) for photovoltaic an enhanced recombination is occurred due to metal decoration in combination with oxygen at the subgrain boundaries leading to degradation of carrier life time and, thus, solar cell efficiency. Finally, as it is well known in crystals for optical applications, such as CaF₂ for UV photolithography, subgrain networks impair the transparency and resolution quality.

Undoubted, there is a correlation between substructures and stored dislocations. It is also well known that dislocation networks are observed in crystals independently by which method of phase transition they have been grown¹. However, the origins and genesis of their appearance can be somewhat varied. Let’s differ in three processes – i) dynamic polygonization (DP) in the course of plastic relaxation due to thermomechanical stress, ii) high-temperature dislocation dynamics (DD) combining glide with point-defect assisted claim, and iii) morphological instability of the propagating crystallization front in the form of cellular interface shape. Of course, i) and ii) are close correlating. However, whereas DP requires in any case stress-related driving force DD implies along with screening effects also evidences of self-organized (dissipative) structuring in the course of irreversible thermodynamics (de facto, each directional crystallization system is an “open” one steadily importing and exporting energy). DD takes place at high temperatures where the point defect diffusivity is still high enough. It is noteworthy that the formation of spatial cellular patterns is only possible when three-dimensional dislocation movements like climb and cross glide can take place. Glide alone could be not responsible for. Actually, as it was observed by real-time synchrotron x-ray topography on Al the cell formation takes place near (some millimetre) behind the propagating interface².

In general, dislocation cell structures consist of walls with high dislocation density separated by interiors of markedly dislocation-reduced or even dislocation-free material. The ripening level depends on various material and process parameters like dislocation density and mobility as well as stress-time devolution, respectively. The genesis is also markedly influenced by obstacles such as second phase particles, large angle grain boundaries or sessile dislocations.

The detailed analysis by x-ray synchrotron topography of dislocation cells in as-grown 6” vapor-pressure-controlled GaAs crystal showed that the dislocations are accumulated in fuzzy walls³. Typically, numerous junctions and pins form a sessile dislocation jungle which is rather stable against post-growth annealing. Only very small mean tilt angles around 10 arcsec do exist between the cells. In comparison, in CdTe, PbTe, mc-Si and CaF₂ the matrix contains still numerous isolated dislocations and the cell walls are formed much sharper consisting of only one row of dislocation pits as it can be ascertained by transmission electron microscopy⁴. Such behaviour is well-known from the standard type of polygonized low-angle grain boundaries (primary subgrain formation) containing only the excess dislocations of similar Burgers vector after the annihilation is completed. Tilt angles of 60 - 120 arcsec were reported for such crystals⁵. Obviously, compared with GaAs in these materials the substructure reacts much more sensitively to variations of the stress field acting during crystal growth. Additionally, in II-VI and IV-VI substances the dislocation mobility is markedly enhanced compared with III-Vs. Finally, the point defect situation is of crucial influence on the DD. For instance, it was shown that the minimization of the native point defect content by nearly stoichiometric growth of compounds restrains cellular structures⁶ as it was prognosticated numerically⁷. In mc-Si ingots grown under typical v/G-conditions (v - growth velocity, G - temperature gradient) > 1.34 x 10^-3 cm²/K min⁸ the generation of vacancies  dominates which are immediately absorbed by the presented dislocations. As a result, the dislocations are able to claim enhancing globular cell formation.

Ascertaining the mean cell diameter thanks to the rules of correspondence being valid for most materials⁹ we are able to estimate the value of once acting thermo-mechanical stress. At first, after Holt’s relation d r^1/2 ≅ 10 (d - cell diameter, r - dislocation density) there is a correlation between cell size and dislocation content. According to the rule of Kuhlmann-Wilsdorf d = K G b t ^-1 (G - shear modulus, b - Burgers vector, t - shear stress, K - constant » 20) a mean cell diameter of 100 µm within in as-grown crystal correlates with a formerly t of about 3-5 MPa. Finally, Taylor’s rule t = K G b r ^½shows the relation between stress and expected dislocation density. Of course, from these relations follows that substructures should be damped by adherence of lowest as possible thermomechanical stress during growth, i.e. assurance either of even or as it was postulated by Indenbom¹⁰ polynomial shaped isotherms. Additionally, solution hardening by doping in order to increase the critical resolved shear stress proves to be helpful¹.

As it was demonstrated by real-time synchrotron x-ray topography on Al-Cu alloys¹¹ also a cellular interface shape, generated by constitutional supercooling (origin iii), is able to redirect and collect growing-in dislocations along the elongated grain boundaries. It seems that charac-teristic substructures in low-temperature solution-grown THM Cd_1-xZn_xTe and Hg_1-xCd_xTe crystals are correlating with such mode, especially, due to the high Te enrichment as solvent ahead the crystallization front. An effective mixing measure is required to prevent morphological instability and tellurium inclusions.

Finally, as was mentioned above, locally and temporally varying growth parameters should be considered. This leads to gradients and flows - the basic preconditions of irreversible thermodynamics. According Kubin¹² in either case, the plastic flow is not uniform at a fine scale. The inhomogeneous release of elastic energy gives rise to the emission of acoustic waves (avalanches) interplaying with stored sessile dislocations and micro obstacles (precipitates, vacancy condensations). In the course of cooling down sporadic clouded dislocation patterns are frozen up remembering our well-known cluster structures in mc-silicon. Thus, it will be hard for crystal growers to maintain perfect homogeneously distributed stored dislocations.

  1.   P. Rudolph, Crystal Res. Technology 40 (2005) 7.

  2.   G. Grange, C. Jourdan, A.L. Coulet, J. Gastaldi, J. Crystal Growth 72 (1985) 748.

  3.   T. Tuomi et al., J. Crystal Growth 237 (2002) 350.

  4.   K. Durose, G.J. Russel, J. Crystal Growth 86 (1988) 471.

  5.   P. Rudolph, Progr. Crystal Growth and Characterization 29 (1994) 275.

  6.   P. Rudolph, C. Frank-Rotsch, U. Juda, F. Kiessling, Mat.Sci.Engin. A400 (2005) 170.

  7.   B. Bako et al, Computational Materials Science 38 (2006) 22.

  8.   V.V. Voronkov, J. Crystal Growth 59 (1982) 625.

  9.   M. Zaiser in: G. Müller et al. (eds.), Crystal Growth (Elsevier 2004) p. 215.

 10.  V.L. Indenbom, Kristall und Technik 14 (1979) 493.

 11.  G. Grange, B. Billia, J. Phys. France 4 (1994) 293.

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