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Persistence in nonequilibrium surface growth.

M Constantin1, C Dasgupta, P Punyindu Chatraphorn

  • 1Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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This study investigates surface growth models using kinetic Monte Carlo simulations. Nonlinearity in molecular beam epitaxy (MBE) models affects persistence exponents, with distinct positive and negative values found in steady states.

Area of Science:

  • Condensed Matter Physics
  • Surface Science
  • Statistical Mechanics

Background:

  • Surface growth phenomena are crucial in materials science and nanotechnology.
  • Understanding the dynamics of interfaces in stochastic growth models is key.
  • The molecular beam epitaxy (MBE) universality class describes specific surface growth behaviors.

Purpose of the Study:

  • To investigate persistence probabilities of interface height in (1+1) and (2+1)-dimensional atomistic surface growth models.
  • To analyze models belonging to the molecular beam epitaxy (MBE) universality class.
  • To explore both initial transient and long-time steady-state regimes of surface growth.

Main Methods:

  • Kinetic Monte Carlo (KMC) simulations were employed to study surface growth models.

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  • Noise reduction techniques were applied to (1+1)-dimensional models for accurate exponent determination.
  • Analytical methods were used to establish relationships between persistence and dynamic growth exponents.

    • Main Results:

    • Nonlinearity in MBE universality class models is reflected in differing positive and negative persistence exponents.
    • Steady-state persistence exponents for MBE class models were determined: θ(S)+ = 0.66±0.02 and θ(S)- = 0.78±0.02 in (1+1)D; θ(S)+ = 0.76±0.02 and θ(S)- = 0.85±0.02 in (2+1)D.
    • A predicted relation between steady-state persistence and dynamic growth exponents holds for the smaller persistence exponent in nonlinear models.

    Conclusions:

    • The study confirms that nonlinearity significantly impacts persistence behavior in MBE surface growth models.
    • Steady-state persistence exponents can be accurately determined from shorter simulation times than previously thought.
    • Persistence probability exhibits scaling behavior with system size and sampling time.