Heterovalent interlayers and interface states: An ab initio study of $\mathrm{Ga}\mathrm{As}∕\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (110) and (100) heterostructures

We have investigated ab initio the existence of localized states and resonances in abrupt $\mathrm{Ga}\mathrm{As}∕\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (110)- and (100)-oriented heterostructures incorporating one or two monolayers (MLs) of Si, as well as in the fully developed $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (110) heterojunction. In (100)-oriented structures, we find both valence- and conduction-band related near-band edge states localized at the $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ interface. In the (110) systems, instead, interface states occur deeper in the valence band, the highest valence-related resonances being about $1\mathrm{eV}$ below the GaAs valence-band maximum. Using their characteristic bonding properties and atomic characters, we are able to follow the evolution of the localized states and resonances from the fully developed $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ binary junction to the ternary $\mathrm{Ga}\mathrm{As}∕\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (110) systems incorporating two or one ML(s) of Si. This approach also allows us to show the link between the interface states of the (110) and (100) systems. Finally, the conditions for the existence of localized states at the $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (110) interface are discussed based on a Koster-Slater model developed for the interface-state problem.

Figure 1

Dispersion of the interface states (thick lines) of the $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (110) heterojunction relative to the PBS of the Si and GaAs bulk materials (gray). The dashed line is a resonant state localized on the first Si bilayer from the interface (see text).

Figure 2

Contour plot of the probability density $\rho$ (in $e∕\text{supercell}$) in the $\left(\overline{1}10\right)$ plane and the planar average of the probability density $\left(\overline{\rho }\right)$ along the [110] direction of selected interface states of the $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (110) heterojunction. (a) As-derived $s$ state at ${\overline{X}}^{\prime }$. (b) Si-derived $s$ state at ${\overline{X}}^{\prime }$. (c) Si- and As-derived $p$ state at ${\overline{X}}^{\prime }$. (d) Si- and Ga-derived $p$ state at ${\overline{X}}^{\prime }$. (e) Si- and Ga-derived $s\text{−}p$ states at $\overline{M}$. $\left({\mathrm{e}}^{\prime }\right)$ The contour plot of the (e) state in the Si (110) plane adjacent to the interface [dashed line in the (e) plot]. The probability density of the above states in atomic planes other than the ones considered is a small fraction of the one shown.

Figure 3

Contour plot of the probability density of two $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (110) interface states in two different (110) planes containing Ga and As atoms (a) and Si atoms (b) at the interface and the corresponding planar average $\left(\overline{\rho }\right)$ along the [110] direction. Both states are at the ${\overline{X}}^{\prime }$ point of the zone. The dashed lines indicate the position of the planes where the contour plots were drawn.

Figure 4

Dispersion of the localized states and resonances (thick lines) induced by one ML of Si (110) in GaAs relative to the GaAs bulk PBS.

Figure 5

Contour plot of the probability density $\rho$ in the $\left(\overline{1}10\right)$ plane and the planar average of the probability density $\left(\overline{\rho }\right)$ along the [110] direction of selected states of the $\mathrm{Ga}\mathrm{As}∕1\mathrm{Si}\mathrm{ML}∕\mathrm{Ga}\mathrm{As}$ (110) heterostructure. (a) As-derived $s$ state at ${\overline{X}}^{\prime }$. (b) Si-derived $s$ state at ${\overline{X}}^{\prime }$. (c) Ga-derived $s$ state at $\overline{\Gamma }$. (d) Si- and As-derived $p$ state at ${\overline{X}}^{\prime }$. (e) Si- and Ga-derived $p$ state at ${\overline{X}}^{\prime }$. The probability density of the above states in atomic planes other than the ones considered is a small fraction of the one shown.

Figure 6

Left: Contour plot of the probability density $\rho$ in the $\left(\overline{1}10\right)$ plane and the planar average of the probability density $\left(\overline{\rho }\right)$ along the [110] direction of three states of the $\mathrm{Ga}\mathrm{As}∕1\mathrm{Si}\mathrm{ML}∕\mathrm{Ga}\mathrm{As}$ (110) heterostructure. Right: Contour plot of the same states in the (110) plane indicated by the dashed line. (a) $sp\text{−}\mathrm{Si}$ and $p\text{−}\mathrm{As}$ derived state at ${\overline{X}}^{\prime }$. (b) Si- and Ga-derived $s$ state at $\overline{M}$. (c) Ga-derived $s$ state at $\overline{M}$. The probability density of the above states in atomic planes other than the ones considered is a small fraction of the one shown.

Figure 7

Contour plot of the probability density $\rho$ in the (110) plane, indicated by the dashed line, and the planar average $\left(\overline{\rho }\right)$ along the [110] direction of three states of the $\mathrm{Ga}\mathrm{As}∕1\mathrm{Si}\mathrm{ML}∕\mathrm{Ga}\mathrm{As}$ (110) heterostructure. All states are at the ${\overline{X}}^{\prime }$ point of the zone. The dashed lines indicate the position of the planes where the contour plots have been drawn.

Figure 8

Dispersion of the localized and resonant states induced by two MLs of Si (110) in GaAs relative to the GaAs bulk PBS. Solid lines are the symmetric (by ${\sigma }_{xy}$ reflection) states. The dashed-dotted lines represent the corresponding antisymmetric states.

Figure 9

Dispersion of the localized and resonant states (thick lines) induced by two MLs of Si in the (100) GaAs homojunction relative to the PBS of the GaAs bulks, $\mathrm{Ga}{\mathrm{As}}^u$ and $\mathrm{Ga}{\mathrm{As}}^d$, which are shifted one with respect to the other by the dipole potential induced by the Si interlayer. The dashed line indicates the state corresponding to the $S_{\mathrm{Ga}}$ state of the $\mathrm{Ga}\mathrm{As}∕1\mathrm{Si}\mathrm{ML}∕\mathrm{Ga}\mathrm{As}$ (110) homojunction (see text).

Figure 10

Contour plot of the probability density $\rho$ in the (110) plane and the planar average $\left(\overline{\rho }\right)$ along the [100] direction of some states in the $\mathrm{Ga}\mathrm{As}∕2\mathrm{Si}\mathrm{MLs}∕\mathrm{Ga}\mathrm{As}$ (100) heterostructure. (a) $\mathrm{Ga}{\mathrm{As}}^d$ As-derived $s$ state at $\overline{J}$. (b) $\mathrm{Si}-\mathrm{Si}$-derived $s$ state with lowest energy at $\overline{J}$. (c) ${\mathrm{Si}}^d$-derived $s$ state at $\overline{K}$. (d) ${\mathrm{Si}}^d$-derived $s$ state at $\overline{K}$. The probability density for the above states in atomic planes other than the ones considered is a small fraction of the one shown.

Figure 11

Left: Contour plot of the probability density $\rho$ in the (110) plane and the planar average $\left(\overline{\rho }\right)$ along the [100] direction of two states in the (100) $\mathrm{Ga}\mathrm{As}∕2\mathrm{Si}\mathrm{MLs}∕\mathrm{Ga}\mathrm{As}$ heterostructure. Right: Contour plot of the same states in the (100) plane indicated by the dashed line. (a) $s\text{−}\mathrm{Ga}$- and $p\text{−}\mathrm{Si}$-derived state at $\overline{J}$. (b) $sp\text{−}\mathrm{As}$- and Si-derived state at $\overline{K}$. The probability density for the above states in atomic planes other than the ones considered is a small fraction of the one shown.

Figure 12

Contour plot of the probability density $\rho$ in the (110) plane and the planar average $\left(\overline{\rho }\right)$ along the [100] direction of some states in the (100) $\mathrm{Ga}\mathrm{As}∕2\mathrm{Si}\mathrm{MLs}∕\mathrm{Ga}\mathrm{As}$ heterostructure. (a) $\mathrm{Ga}{\mathrm{As}}^d$ As- and ${\mathrm{Si}}^d$-derived $p$ state at $\overline{J}$. (b) Si-derived $p$ state at $\overline{J}$. (c) $\mathrm{Ga}{\mathrm{As}}^u$ Ga- and Si-derived $p$ state at $\overline{J}$. (d) ${\mathrm{Si}}^d$-derived antibonding $sp$ state at $\overline{J}$. The probability density for the above states in atomic planes other than the ones considered is a small fraction of the one shown.

Figure 13

Resonant $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ interface states in the abrupt $\mathrm{Al}∕6\mathrm{Si}\mathrm{MLs}∕\mathrm{Ga}\mathrm{As}$ (100) junctions with As-terminated (left) and Ga-terminated (right) GaAs (100) at the $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (100) interface. (a) Dispersion of the interface states along the high symmetry directions of the 2DBZ (solid line); the gray area corresponds to the projected bulk band structure of GaAs. The zero of energy corresponds to the GaAs valence band maximum. (b) Probability density of the resonant states at the $\overline{\Gamma }$ point. The contour plots are shown in (010) planes, including the $\mathrm{As}-\mathrm{Si}-\mathrm{As}$ (left) and $\mathrm{Ga}-\mathrm{Si}-\mathrm{Ga}$ (right) bonds at the $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ interface. Solid (dotted) circles and lines indicate atoms and bonds which are in (out) of the plane. The planar average of the density is shown below the contour plots.

Figure 14

Schematic description of the interface-creation procedure discussed in the text.

Figure 15

Wave-vector resolved density of states (DOS) of bulk Si and GaAs for the four high-symmetry points of the (110) 2DBZ and integrated along a line in $k$ space parallel to the [110] crystallographic direction. The two DOS are aligned using the calculated valence band offset of $0.14\mathrm{eV}$ at the $\mathrm{Si}∕\mathrm{Ga}\mathrm{As}$ (110) interface. The volume of normalization is the GaAs unit-cell volume. The degeneracies of the Si (GaAs) valence-band DOS features, given in order of increasing energy, are 1 (1, 1) at $\overline{\Gamma }$, 2, 2 (1, 1, 2) at $\overline{X}$ and $\overline{M}$, and 1, 1, 2 (1, 1, 2) at ${\overline{X}}^{\prime }$.