Enhanced Donor Binding Energy Close to a Semiconductor Surface

We measured the ionization threshold voltage of individual impurities close to a semiconductor-vacuum interface, where we use the STM tip to ionize individual donors. We observe a reversed order of ionization with depth below the surface, which proves that the binding energy is enhanced towards the surface. This is in contrast to the predicted reduction for a Coulombic impurity in the effective mass approach. We can estimate the binding energy from the ionization threshold and show experimentally that in the case of silicon doped gallium arsenide the binding energy gradually increases over the last 1.2 nm below the (110) surface.

Figure 1

(a)–(c) Voltage dependent $dI/dV$ maps obtained on the (110) surface of Si-GaAs showing the rings of ionization around the Si donors. All three images are of the same area of the sample. The image size is $48\times 48{\mathrm{nm}}^2$. The layer in which the donor is situated is indicated, counting the surface layer as 1. The rings of ionization clearly appear at lower voltages for donors deeper below the surface. (d) Schematic energy diagram including the TIBB in the homogeneous approach.

Figure 2

(a) $dI/dV$ map at 0.24 V. This measurement is obtained with a different tip than the one shown in Fig. 1. The numbers in brackets refer to the layer in which the donor is situated, counting the surface as 1. (b) Voltage dependence of the ring radius. The lines are added to guide the eye. (c) $V_{\mathrm{th}}$ (open red dots) and the onset of tunneling into the bulk CB (solid green dots) for $D_1$ to $D_5$, where the horizontal axis represents the depth of the donor below the surface.

Figure 3

(a) $V_{\mathrm{th}}$ relative to the flat band voltage ($V_{\mathrm{FB}}$), (b) the corresponding TIBB at the donor position and (c) the estimated binding energy (see text for details). The squares and stars refer to the measurement shown in Fig. 1, 2 respectively. The solid lines are added to guide the eye.

Figure 4

Comparison of a bare Coulomb potential (solid black line) with the TIBB (red dotted line), where the tip is located on top of the donor. The blue dash-dotted line represents the superposition of the Coulomb potential and the TIBB, which is shown in 3D in the inset.