Competition between Kardar–Parisi–Zhang and Berezinskii–Kosterlitz–Thouless kinetic roughening on (001) singular surface during steady crystal growth

<jats:title>Abstract</jats:title> <jats:p> Kinetic roughening of the (001) singular surface during steady crystal growth is studied on the basis of a lattice model using the Monte Carlo method. At a sufficiently low temperature, there are known to be two kinetic roughening points as the driving force for crystal growth <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$\Delta \mu $$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> increases. At a low driving force <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$\Delta \mu _\text{KPZ}^{(001)}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msubsup> <mml:mi>μ</mml:mi> <mml:mtext>KPZ</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>001</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> , there is the Karder–Parisi–Zhang (KPZ) roughening transition point. On the KPZ rough surface, elementary steps around islands are well defined though the surface is thermodynamically rough, with a roughness exponent <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$\alpha $$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> consistent with the KPZ universal value of 0.3869. Island-on-island structures were found to be crucial in forming the KPZ rough surface. To understand the effects of the atomical roughness of the (001) surface and the interplay of steps on long-period undulations on this surface, the dependence on the temperature <jats:italic>T</jats:italic> and driving force for crystal growth <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$\Delta \mu $$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> of surface quantities is investigated. At higher temperatures, additional Berezinskii–Kosterlitz–Thouless (BKT) rough and re-entrant KPZ regions are found for large <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$\Delta \mu $$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> , where the crystal surface grows adhesively. A <jats:italic>T</jats:italic> – <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$\Delta \mu $$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> kinetic roughening diagram is also presented. </jats:p>