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Surface Science

Volume 423, Issues 2-3
10 March 1999
Pages 189-207

PII: S0039-6028(98)00906-6
Copyright © 1999 Elsevier Science B.V. All rights reserved.

Temperature dependence of kinetic roughening during metal(100) homoepitaxy: transition between `mounding' and smooth growth

M. C. Bartelta, , and J. W. Evansb

a Computational Materials Science Department, Sandia National Laboratories, Livermore, CA 94550, USA
b Department of Mathematics, and Ames Laboratory, Iowa State University, Ames, IA 50011, USA

Received 18 November 1996; accepted 30 November 1998. Available online 15 March 1999.

Abstract

From simulations of a realistic lattice-gas model for metal(100) homoepitaxy, we analyze the temperature (T) dependence of the film roughness (or interface width), of the effective roughening exponent, of the local step-density, and of the persistence of the Bragg intensity oscillations. By also analyzing the dependence on T of the lateral mass currents of deposited atoms, we reveal a kinetic phase transition from a regime of `mounding' at higher T, to a regime of `reentrant' smooth growth at lower T. Application of these results for the cases of Ag, Fe, and Cu homoepitaxy is discussed. Finally, we also describe some features of the dynamics of deposited atoms that could lead to the recovery of rough growth at very low T.

Author Keywords: Kinetic roughening; Metal(100) homoepitaxy; Mound formation; Step-edge barriers

Article Outline

1. Introduction
2. Model details and parameters for metal(100) homoepitaxy
3. Simulation results: temperature dependence of film growth
3.1. Growth behavior for small step-edge barrier
3.2. Growth behavior for large step-edge barrier
3.3. Application to specific systems
3.3.1. Ag/Ag(100)
3.3.2. Fe/Fe(100)
3.3.3. Cu/Cu(100)
4. Lateral mass currents controlling film growth
4.1. Uphill (destabilizing) current
4.2. Downhill (stabilizing) current
5. Mounding, slope selection, and the kinetic phase transition
6. `Anomalous' behavior for low temperature
6.1. Long-range lateral correlations at low T
6.2. Breakdown of downward funneling
6.3. Multilayer growth at T0 K
7. Conclusions
Acknowledgements
Appendix A. Discrete treatment of deposition dynamics
Appendix B. Simulation of slope dependence of mass currents
Appendix C. Analysis of the downward funneling current
References


 (16K)
Fig. 1. Schematic of our model for metal(100) homoepitaxial growth without bond-scission.

(16K)
Fig. 2. Temperature dependence of film growth in metal(100) homoepitaxy for small Ehrlich¯Schwoebel barrier with =Ese/Ed0.1. Simulation parameters are chosen to roughly match Ag/Ag(100): Ed=325 meV, Ese=25 meV, =1012 s-1, and F=0.06 ML s-1 [33, 34 and 35]. Results for: (a) W at 30 ML; (b) the effective determined in the range 20¯30 ML (which matches the experimental values [33, 34 and 35] at both 200 K and 300 K); (c) the local slope determined from the local step-density at 30 ML; (d) anti-phase Bragg intensity oscillations; data were scaled so that the maximum at ~1 ML has the same value for all T: A(×1)-300 K; B(×4.4)-200 K; C(×9.2)-100 K. Curves B and C were shifted up for clarity.

(34K)
Fig. 3. Snapshots of a 170a/×170a/ region of 200 ML films obtained in simulations at T=100, 200, and 300 K, as indicated, using Ed=325  meV, Ese=25 meV (so 0.08), =1012 s-1, and F=0.06 ML s-1. Darker regions have a lower height.

(15K)
Fig. 4. Dependence on h/F of film growth in metal(100) homoepitaxy for infinite Ehrlich¯Schwoebel barrier, so =Ese/Ed=. Simulation results for: (a) W at 30 ML; (b) W2 versus , for h/F=106¯109 as indicated (the dashed line is W2=); (c) the local slope determined from the local step-density at 30 ML; (d) anti-phase Bragg intensity oscillations (A: h/F0, B: h/F102, C: h/F104). Curves B and C were shifted up for clarity.

(34K)
Fig. 5. Snapshots of a 170a/×170a/ region of 200 ML films obtained in simulations for h/F0, 105, and 108 (corresponding to T=100, 200, and 300 K, respectively, as indicated, if Ed=325 meV, =1012 s-1, and F=0.06 ML s-1), and Ese=. Darker regions have a lower height.

(5K)
Fig. 6. Schematic of the uphill `Schwoebel' current, Jup, and the downhill `downward funneling' current, JDF.

(10K)
Fig. 7. Simulation results for the temperature dependence of Jupx/F versus Mx. Parameters were chosen to roughly match Fe/Fe(100): Ed=450 meV, Ese=30 meV (so 0.07), =1011 s-1, and F=0.7  ML min-1 [14, 15, 36, 37 and 38].

(4K)
Fig. 8. Data in Fig.7 plotted as Jupx/[FS(Lav)2Mx] versus LavMx for T=250, 275, 300, and 350 K, for which one has Lav8, 11, 14, and 20 (in units of `a') and S0.75, 0.72, 0.69, and 0.63, respectively.

(46K)
Fig. 9. Snapshots of a 170a/×170a/ region of 0.5 and 50 ML films obtained in simulations at 200 K (h/F102) and 300 K (h/F106), as indicated, for a perfect vicinal surface, using parameters as in Fig.7. Darker regions have lower height.

(4K)
Fig. 10. Simulation results for the temperature dependence of |JDFx|/F versus Mx, using parameters as in Fig.7. The slopes give CDF0.491, 0.467, 0.440, 0.413, and 0.392, at T=225, 250, 275, 300, and 350 K, respectively.

(11K)
Fig. 11. Temperature dependence of the variation of the uphill and downhill currents with slope (data from Fig. 7 and Fig. 9). This sequence illustrates the kinetic phase transition as T decreases and the curves for the two currents `uncross'.

(12K)
Fig. 12. Schematic of key trap sites, S21, S12, S03, S13 and S23, that induce a breakdown of downward funneling deposition dynamics, and enhance overhang and defect formation.

(9K)
Fig. 13. Bird's-eye view of the geometry of a growing surface during metal(100) homoepitaxy. Subarrays of vertical columns are indicated by + and -.

(27K)
Fig. 14. Top and side views of a periodic vicinal staircase of single-steps (up from left to right). Here, k=1, L=4, and =9/2, and pA=1/2, dA=-1/2, pB=1, dB=-1/2.

(30K)
Fig. 15. Top and side views of a periodic vicinal staircase of pairs of double-step up and single-step down, from left to right. Here, k=1, L=9, and =19/2, and pA=1/2, dA=+1/2, pB=1, dB=+1/2, pC=1/2, dC=-1, pD=1, dD=-1, pE=1, dE=-1/2.

(20K)
Fig. 16. Snapshots of 170a/×170a/ regions of periodic vicinal staircases with (a) single-steps up, and (b) pairs of double-step up and single-step down. Darker regions have a lower height. (c) Corresponding simulation results for |JDFx|/F versus Mx. The slopes give CDF0.377 (Class 1) and CDF0.629 (Class 2).

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Corresponding author. Fax: +1 925-294-3231; email: mcb@io.ca.sandia.gov
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Surface Science
Volume 423, Issues 2-3
10 March 1999
Pages 189-207


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