AFM investigation of step kinetics and hillock morphology of the {1 0 0} face of KDP
Introduction
Potassium dihydrogen phosphate (KDP) is widely known for its non-linear optical properties and its applications in laser technology. In addition, due to its ease of crystallization and long history as the subject of crystal growth studies, KDP has become the canonical solution-grown crystal for investigating the fundamental physical controls on crystal growth. In particular, extensive studies on the growth of KDP in solution were performed using Michelson-type interferometry [1], [2], [3], [4], [5], [6], [7]. Many useful parameters, such as step edge energies and kinetic coefficients [1], were determined by measuring the dependencies of hillock slope and tangential growth rates on supersaturation. Subsequently, atomic force microscopy (AFM) studies on KDP and other systems provided detailed information on the structures of dislocation sources, the corresponding Burger's vectors, and the growth dynamics of those sources [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23]. AFM has a considerable technical advance over earlier methods of investigation in that step velocities, impurity effects, and step-edge fluctuations can all been observed in situ at molecular length scales [22], [23], [24], [25].
Using AFM, Land et al. [23] performed a qualitative comparison between step structure and kinetics on the {1 0 0} and {1 0 1} faces of KDP. They found that while growth on the {1 0 1} face proceeded entirely via elementary step motion, growth on the {1 0 0} face occurred almost exclusively on macrosteps consisting of bunched elementary steps. Those macrosteps increased in height and terrace width with distance from the top of a hillock. However, no quantitative AFM study has been reported on hillock structure, step kinetics, or the progression of step bunching on the {1 0 0} face.
In this paper, we report AFM measurements of the {1 0 0} face collected over the supersaturation range of 0<σ<0.15 with solution flow rates adequate to ensure that mass transport to the step was rapid relative to the step kinetics. We present the dependence of hillock slope and step speed on supersaturation as well as the variation in step height with distance from the top of the hillock. We show that the thickness of a single molecular layer is 3.7 Å, rather than the 7.4 Å spacing of the unit cell as assumed from earlier interferometry experiments. We find that the dead zone caused by impurities and always observed in previous studies can be eliminated via the use of the purest KDP available and proper solution storage. We also report values for the average step edge free energy, activation energy for step motion, and kinetic coefficients calculated from our experimental data. This report on the behavior of the pure system provides a foundation for future investigations in which we present the results of systematic investigations on the impact of impurity interactions on morphology and kinetics as well as deviations from the Cabrera–Vermilyea model of step pinning.
Section snippets
Experimental procedure
Solutions of KDP were prepared by dissolving high purity KDP salt in 18 MΩ water. Salt purity was determined using inductively coupled mass spectrometry (ICP-MS) following separation of K+ by ion exchange with a cation resin [11]. Total metal impurities in KDP ranged between <50–500 ppb by weight (see Table 1). Solutions were stored in polymethylpentene and Teflon containers to prevent contamination of the KDP solution by iron, boron, and aluminum, which leaches from glass containers [8]. The
Dislocation sources and structure of hillocks
KDP crystals grown at σ<0.25 exhibited growth spirals consisting of monomolecular steps generated by screw dislocations [8], [23]. We measured the height of single steps to be 3.7 Å in height, or one half the unit cell parameter of 7.4 Å in the 〈1 0 0〉 direction [9]. As previously reported by others [1] and as shown in Fig. 1, ex situ images of the {1 0 0} face typically reveal dislocation-growth hillocks in the shape of a “rounded parallelogram”, that exhibit the two-fold rotational symmetry of the
Derivation of step-edge free energy
The data presented above allows us to derive a number of important elementary parameters that control growth and to examine the applicability of well-known models. In the absence of hollow dislocation cores, the BCF model predicts that the step spacing scales linearly with critical radius, rc, (where rc is defined as rc=αω/ktσ) or in the case of polygonized hillocks, with the critical length, lc (where lc is defined as ) [10], [14]. Because rc and lc in turn depend on the value of
Conclusions
The AFM has allowed us to quantitatively investigate the growth of KDP {1 0 0} faces in much greater detail than in previous studies, allowing in situ observations of the growth at dislocation sources and of step bunching. We found that a flow of at least 6 ml/min was necessary in order to ensure that growth was not mass-transport limited at the highest supersaturation used in this study (20%). We measured the dependence of hillock slope, step speed, and macrostep height as well as its growth with
Acknowledgements
We thank Dave Wruck for the elemental analysis of our samples and US DOE grant DE-FG03-02ER15325 (to WHC) for support. This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. (UCRL-JC-152309)
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