Characterization of Si-doped GaAs cross-sectional surfaces via ab initio simulations

Si-doped (110) GaAs cross-sectional surfaces are investigated using first principles calculations with the aim of identifying simple configurations compatible with experimentally detected scanning tunneling microscopy (STM) images characterized by bright signals at negative bias and strongly attenuated when the bias is reversed. Since Si-donor is the most common defect in Si-doped GaAs, we study mainly several Si-donor based configurations, from the isolated impurity to extended defect configurations, up to the limit of an entire embedded donor interlayer. We consider also donor-acceptor configurations, stimulated by the experimental evidence of self-compensation effects in particular in highly doped samples. The systematic study of simulated cross-sectional STM images for all these and other configurations allows not only to identify the self-compensated donor-acceptor configurations as the simplest ones which are compatible with those experimental observations, but also to exclude most of the other candidates.

Figure 1

Clean (110) GaAs surface. Top and middle panels: ball and stick model of the relaxed surface, side (top panel), and top view (middle panel). The unrelaxed surface position is indicated by a solid line in the topmost panel. In the side view we indicate the bond lengths values; in the top view we indicate the surface-projected values of the bond lengths. Bottom panel: density of states (arbitrary units) of the surface atoms (solid line) and of bulk GaAs (dotted line).

Figure 2

A neutral single substitutional surface ${\mathrm{Si}}_{\mathrm{Ga}}$ impurity. Top panels: see Fig. 1 for caption. The long-dashed lines in the top-view ball and stick model indicate the cell used to simulate the XSTM image of the defected region, which is superimposed to the image of the otherwise perfect clean surface for a better visual rendering. Middle panels: corresponding simulated XSTM images at bias voltages of $-1\mathrm{eV}$ (left) and $+1\mathrm{eV}$ (right). Bottom panels: density of states of surface atoms belonging to the simulation cell with the defect (solid line); Ga and As surface atoms far from the defect but belonging to the simulation cell, for alignment with the density of states of the clean surface (dashed line); clean surface, from Fig. 1, for comparison (dotted line). The midgap peak in the DOS of the doped cell is originated by the impurity.

Figure 3

A single substitutional surface ${\mathrm{Si}}_{\mathrm{Ga}}$ impurity with different charge states. Top panels: STM images at bias voltages of $+1\mathrm{eV}$ [a1), b1), c1) panels] and $-1\mathrm{eV}$ [a2), b2), c2) panels] for negatively ($-1$ electron per defect; left panels), neutral (central panels), and positively charged samples ($-1$ electron per defect; right panels). Bottom panel: corresponding surface density of states aligned with respect to the band gap edges of the clean surface: negatively (long-dashed), neutral (solid), and positively (dotted) charged cases. Corresponding calculated Fermi energies are also indicated.

Figure 4

A row of ${\mathrm{Si}}_{\mathrm{Ga}}$ donors on the surface. For this figure and the following ones, see Fig. 2 for caption, if not differently indicated.

Figure 5

A row of ${\mathrm{Si}}_{\mathrm{Ga}}$ donors subsurface.

Figure 6

1 ML of ${\mathrm{Si}}_{\mathrm{Ga}}$ embedded in GaAs along the (001) direction, with the (110) cleavage plane containing ${\mathrm{Si}}_{\mathrm{Ga}}$ and As sites (case A in the text).

Figure 7

1 ML of ${\mathrm{Si}}_{\mathrm{Ga}}$ embedded in GaAs along the (001) direction, with the (110) cleavage plane containing unperturbed Ga and As sites only (case B in the text).

Figure 8

${\mathrm{Si}}_{\mathrm{As}}-{\mathrm{Si}}_{\mathrm{Ga}}$ dimer on the surface (dimer A in the text).

Figure 9

${\mathrm{Si}}_{\mathrm{As}}-{\mathrm{Si}}_{\mathrm{Ga}}$ dimer with ${\mathrm{Si}}_{\mathrm{Ga}}$ and ${\mathrm{Si}}_{\mathrm{As}}$ both subsurface (dimer B in the text).

Figure 10

${\mathrm{Si}}_{\mathrm{As}}-{\mathrm{Si}}_{\mathrm{Ga}}$ dimer with only ${\mathrm{Si}}_{\mathrm{Ga}}$ on the surface and ${\mathrm{Si}}_{\mathrm{As}}$ subsurface (dimer C in the text).

Figure 11

${\mathrm{Si}}_{\mathrm{As}}-{\mathrm{Si}}_{\mathrm{Ga}}$ dimer with only ${\mathrm{Si}}_{\mathrm{As}}$ on the surface and ${\mathrm{Si}}_{\mathrm{Ga}}$ subsurface (dimer D in the text).

Figure 12

Si bilayer with ${\mathrm{Si}}_{\mathrm{As}}$ and ${\mathrm{Si}}_{\mathrm{Ga}}$ on the surface (case A in the text).

Figure 13

Si bilayer with ${\mathrm{Si}}_{\mathrm{Ga}}$ and ${\mathrm{Si}}_{\mathrm{As}}$ both subsurface (case B in the text).

Figure 14

Si bilayer with only ${\mathrm{Si}}_{\mathrm{Ga}}$ on the surface and ${\mathrm{Si}}_{\mathrm{As}}$ subsurface (case C in the text).

Figure 15

Si bilayer with only ${\mathrm{Si}}_{\mathrm{As}}$ on the surface and ${\mathrm{Si}}_{\mathrm{Ga}}$ subsurface (case D in the text).

Figure 16

Donor-vacancy complex: both ${\mathrm{Si}}_{\mathrm{Ga}}$ and $V_{\mathrm{Ga}}$ on the surface.

Figure 17

Donor-vacancy complex: ${\mathrm{Si}}_{\mathrm{Ga}}$ subsurface and $V_{\mathrm{Ga}}$ on the surface.

Figure 18

Donor-vacancy complex: both ${\mathrm{Si}}_{\mathrm{Ga}}$ and $V_{\mathrm{As}}$ on the surface.

Figure 19

Donor-vacancy complex: ${\mathrm{Si}}_{\mathrm{Ga}}$ subsurface and $V_{\mathrm{As}}$ on the surface.

Figure 20

Isolated $V_{\mathrm{Ga}}$ on the surface.

Figure 21

Isolated $V_{\mathrm{As}}$ on the surface.

Figure 22

Isolated $V_{\mathrm{As}}$ on the surface with different charge state ($-1$, 0, and $+1$ electron for defect). See Fig. 3 for caption.

Figure 23

${\mathrm{As}}_{\mathrm{Ga}}$ antisite on the surface.

Figure 24

${\mathrm{Ga}}_{\mathrm{As}}$ antisite on the surface.