Nanoscale properties of melting at the surface of semiconductors

In this study, we use density-functional simulations to investigate how nanoscale surface coatings can alter the melting dynamics of semiconductor surfaces. We demonstrate that a single-monolayer coating of GaAs can dramatically reduce the diffusive motion of the surface atoms of a Ge(110) crystal and cause superheating of the bulk at temperatures well above the Ge melting point on the 10 ps time scale. In direct contrast, a single-monolayer coating of Ge will induce surface melting of a GaAs(110) structure 300 K below the GaAs melting point. We also identify a metallization of the band structure and bond alterations in the charge density near the melting transition. In addition, we suggest that the Ge monolayer causes the GaAs(110) surface to melt through transient penetration of the Ge atoms into the bulk, which locally initiates the collective diffusive motion of large groups of Ga and As atoms. These studies on the effect of coatings in semiconductors clearly point to the surface material as the dominant determinant of the melting characteristics of a hybrid structure. These simulations have important implications for high-temperature materials design while simultaneously probing the fundamental features of the melting transition.

Figure 1

(Color) Computational supercells: (a) the (110) surface of Ge [Ge(110)]; (b) the Ge(110) surface with a single-monolayer coating of GaAs $[\mathrm{Ge}\left(110\right)+\mathrm{Ga}\mathrm{As}]$; (c) the (110) surface of GaAs [GaAs(110)]; and (d) the GaAs(110) surface with a single-monolayer coating of Ge $[\mathrm{Ga}\mathrm{As}\left(110\right)+\mathrm{Ge}]$. Ge atoms are shown in green, Ga in blue, As in red, and H in white.

Figure 2

(Color) Trajectories of the atoms on a Ge(110) surface at 1240 K for 10 ps, without (top) and with (bottom) a single-monolayer coating of GaAs, as they appear looking down the (110) direction. The ions are broken into groups based on their positions along the $z$ axis (perpendicular to the surface) at $t=0$. Trajectories of Ga atoms are shown in blue, As in red, and Ge in green. The black diamonds (Ga), ovals (As), and rectangles (Ge) mark the initial positions of the atoms at $t=0$. Note the decrease in diffusive motion of the Ge atoms in the presence of a GaAs monolayer coating, especially in the fourth layer where melting is practically quenched.

Figure 3

(Color) Mean-square displacement $⟨\Delta R^2\left(t\right)⟩$ averaged over the atoms within each of the top four layers of a Ge(110) surface at 1240 K (a) without and (b) with a monolayer coating of GaAs. The solid blue lines extending from $t=7\mathrm{ps}$ to $t=10\mathrm{ps}$ show $⟨\Delta R^2⟩$ for the fourth layer of atoms magnified by a factor of 5 to highlight the distinction between diffusive motion [linear $⟨\Delta R^2⟩$ in (a) and constant $⟨\Delta R^2⟩$ in (b)].

Figure 4

(Color) The kinetic energy of the $\mathrm{Ge}\left(110\right)+\mathrm{Ga}\mathrm{As}$ surface at 1240 K (orange line), averaged over the atoms in each layer and converted to an effective temperature using Eq. (4).

Figure 5

(Color) The band gap energy in eV for the Ge(110) and $\mathrm{Ge}\left(110\right)+\mathrm{Ga}\mathrm{As}$ surfaces at 1240 K. Notice the collapse of the $\mathrm{Ge}\left(110\right)+\mathrm{Ga}\mathrm{As}$ band gap at $t\approx 6\mathrm{ps}$ (orange line), signifying a change in character from semiconducting to metallic. The average Ge(110) band gap after $t=2\mathrm{ps}$, 0.06 eV, is marked by the horizontal, purple line.

Figure 6

(Color) Slices of the charge density of the $\mathrm{Ge}\left(110\right)+\mathrm{Ga}\mathrm{As}$ surface at (a) $t=0\mathrm{ps}$, (b) $t=4\mathrm{ps}$, and (c) $t=6\mathrm{ps}$. The top row of panels shows the view looking down the surface in the planes $z=1.8$, 5.1, 8.4, 11.6, 14.9 a.u. The bottom row of panels shows the side view looking down the $x$-axis in planes $x=0.5$, 4.2, 7.9, 11.6, 15.3, and 19 a.u. The planes are chosen by maximal average density. The color scheme is indicated on the right with maximum density in red and zero density in white.

Figure 7

(Color) Trajectories of the atoms in the top three layers of a GaAs(110) surface at 1240 K for 10 ps, without (top) and with (bottom) a single-monolayer coating of Ge, as they appear looking down the (110) direction. The color scheme is the same as in Fig. 2. Note how the Ge monolayer induces melting in the underlying layer of the GaAs crystal. The four atoms labeled $A,B,C$, and $D$ are highlighted because they display significant motion in the $z$ direction. The fourth layer of each system remains solid through $t=10\mathrm{ps}$.

Figure 8

(Color) Mean-square displacement $⟨\Delta R^2\left(t\right)⟩$ averaged over the atoms within each of the top four layers of a GaAs(110) surface at 1240 K (a) without and (b) with a monolayer coating of Ge. Note the large difference in scales between (a) and (b). The solid blue and green lines in (b) extending from $t=7\mathrm{ps}$ to $t=10\mathrm{ps}$ show $⟨\Delta R^2⟩$ for the third and fourth layers of atoms, respectively, magnified by a factor of 10 to highlight the absence of diffusive motion.

Figure 9

(Color) The band gap energy in eV for the GaAs(110) and $\mathrm{Ga}\mathrm{As}\left(110\right)+\mathrm{Ge}$ surfaces at 1240 K. Note that neither band gap is completely collapsed on the 10 ps time scale. The horizontal, purple line indicates the average value of the $\mathrm{Ga}\mathrm{As}\left(110\right)+\mathrm{Ge}$ band gap from $t=4\mathrm{ps}$ to $t=10\mathrm{ps}$ (0.13 eV).

Figure 10

(Color) Slices of the charge density of the $\mathrm{Ga}\mathrm{As}\left(110\right)+\mathrm{Ge}$ surface at (a) $t=0\mathrm{ps}$, (b) $t=4\mathrm{ps}$, and (c) $t=8\mathrm{ps}$. The top row of panels shows the view looking down the surface in the planes $z=1.5$, 4.4, 7.3, 10.2, and 13.1 a.u. The bottom row of panels shows the side view looking down the $x$ axis in planes $x=0.5$, 4.3, 8.1, 11.8, 15.6, and 19.4 a.u. The planes are chosen by maximal average density.

Figure 11

(Color) The $z$ component of the ionic coordinates of the four atoms in the surface monolayer coating of Ge on a GaAs(110) crystal that penetrate past the plane of the initial locations of the underlying layer of Ga and As atoms. The approximate extent of this layer of atoms is shown shaded in purple. The orange lines mark the times when atoms $A,B,C$, and $D$ cross the plane $z=11.2\mathrm{a.u.}$

Figure 12

(Color) The $(x,y)$ positions of the Ga (diamonds) and As (ovals) atoms in the layer below the Ge coating of the $\mathrm{Ga}\mathrm{As}\left(110\right)+\mathrm{Ge}$ surface, as well as the Ge (rectangles) atoms $A,B,C$, and $D$ marked in Figs. 7, 11. The size of each atom is proportional to its penetration distance into the crystal. The largest object is at $z\approx 10\mathrm{a.u.}$, the smallest is at $z\approx 16\mathrm{a.u.}$ (a) At $t=4\mathrm{ps}$, atom $A$ has transiently penetrated into the GaAs layer $(z\approx 11.2\mathrm{a.u.})$ and returned to the surface, while atom $B$ remains in the second layer, disrupting the nearby Ga-As bonds in one row. (b) By $t=8\mathrm{ps}$, all four atoms have penetrated into the second layer and the distortion is widespread.