DFT Calculations

The density functional theory (DFT) calculations presented in the following rely on the full-potential linearized augmented plane-wave method (FLAPW) as utilized in the FLEUR code [139]. In order to simulate the Fe/GaAs(110) interface, a slab of 9 ML GaAs(110) covered with 2 ML Fe on one side [see Figure 5.1] and 1 ML of hydrogen for passivation on the other side of the GaAs (not shown in Figure 5.1) has been taken as structural model [120].

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Figure 5.1: Slab of 9 layers GaAs and 2 layers Fe used for the DFT calculations. The passivating hydrogen layer on the left side of the GaAs film is not shown.

The resulting LDOS for the first 7 GaAs layers at the interface is shown in the upper pan-els in Figure 5.2(b). The plots show the sum of spin-up and spin-down density of states of the 𝑛𝑛th GaAs layer off the interface. The 4th, 5th, and 6th GaAs layers off the interface clearly exhibit a band gap with zero LDOS. The Fermi energy is located at the valence band edge. Approaching the interface, states in the band gap arise starting in the 3rd layer off the interface. These gap states become more and more prominent in the layers closer to the interface and reach a maximum LDOS in the interface layer. Furthermore, the asymmetric behavior of the gap states’ decay lengths, with slightly larger lengths on the conduction band side, is in good agreement with the high-resolution 𝑑𝑑𝐼𝐼/𝑑𝑑𝑉𝑉 spectra of the MIGS shown in Figure 3.12 from section 3.2.3.

In section 4.3, the variation of the interface LDOS with respect to the free surface has been investigated. Similarly, from the DFT data an LDOS variation at the interface can be extracted by substracting the LDOS of the reference “bulk” layer (𝑛𝑛= 6) from the LDOS of the 𝑛𝑛th layer. The result for each GaAs layer is plotted in the lower panels in Figure 5.2(b). In the first few GaAs layers at the interface the DFT data exhibit a sharp decrease in LDOS (transparent red area) with respect to the “bulk” at an energy of 0.35 eV below the valence band edge which is indicated by the horizontal dashed black line. The strong-est drop in LDOS is observed in the interface layer. The drop in LDOS decreases with each layer further away from the interface. The data from STS measurements across the p-type interface presented in section 4.3 exhibit essentially the same behavior: at the in-terface the LDOS also decreases abruptly with respect to the free surface at 0.35 eV be-low the valence band edge [see Figure 5.2(a)]. Thus, the DFT calculations are in good agreement with both the experimental observation of MIGS and the surplus positive charge deep inside the valence band for the p-type interface.

Here it should be mentioned that the DFT calculations describe a bulk interface whereas in the STS experiment the interface is investigated in a cross-sectional surface geome-try.¹³ However, the cross-sectional STS approach yields an LDOS variation map that is stunningly similar to DFT predictions (see Figure 5.2). Therefore, the combination of

13 At the end of section 4.1.4 it has been shown that the electrostatic effect resulting from the surface geome-try is small.

5.1 DFT Calculations

69 cross-sectional STS and complementary DFT calculations offers an excellent probe to explore the microscopic origin of the metal-semiconductor interface dipole.

Figure 5.2: (a) Variation of the LDOS inside the valence band obtained from the STS data set for the p-type interface from Figure 4.10 (interface is located at 𝑥𝑥= 0 nm). The white dashed line indicates the valence band maximum 𝐸𝐸𝑉𝑉 [121]. (b) Density functional calculations for the ideal Fe/GaAs(110) interface: (upper panels) The total (sum of spinup and -down) density of states of the 𝑛𝑛th GaAs layer off the interface. The Fermi energy is locat-ed at the valence band locat-edge. (lower panels) Variation of the LDOS in the 𝑛𝑛th GaAs layer with respect to the 6th layer. At 0.35 eV below the valence band edge (horizontal dashed line) the DFT calculations show a sharp drop in ∆LDOS (transparent red area) [121].

In order to obtain a better understanding of the origin of the surplus positive charge deep inside the valence band observed for the p-type interface, the DFT data are analyzed with respect to the LDOS at individual atomic sites. This analysis yields the plots in Figure 5.3. They show the (left) majority and (right) minority LDOS for the Fe interface layer and for the As atomic sites in the first 4 layers at the interface. The DFT data exhibit a strong hybridization between the majority states of Fe and As at the immediate interface (see left panels in Figure 5.3). The hybridization between Fe and As takes place over a broad energy range and extends also into the valence band. The sharp drop in LDOS with respect to the bulk layers is observed in the same energy range and can therefore be re-garded as a direct consequence of the Fe-As hybridization. Here it also should be pointed out that from the strong hybridization between solely the majority states of Fe and As a spin-polarization in the GaAs interface layer is expected.

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Figure 5.3: Calculated LDOS for Fe (upper panel, red solid line) and As for four different interface layers I to I-3 (black solid lines) for the majority states (left panels) and minority states (right panels). Gray shaded areas are the As local densities of states without Fe on-top of GaAs [120].

Moreover, one can also extract the Schottky barrier (SB) height from the DFT data. This is done by aligning the Fermi energies of the pure Fe monolayer and the clean uncovered GaAs(110) surface and adding the surface-dipole term. For the p-type Fe/GaAs(110) interface the DFT calculations yield a SB height of Φ_{𝑆𝑆𝑆𝑆}^𝑝𝑝 = 0.69 eV. The SB height ob-tained from XSTS measurements across an ideal p-type interface is Φ_{𝑆𝑆𝑆𝑆}^𝑝𝑝 = 0.78(2) eV (see section 4.2) which deviates only by around 12 % from the value predicted by DFT calculations. The MIGS-and-electronegativity model (see section 1.3) predicts a SB height of Φ_{𝑆𝑆𝑆𝑆}^𝑝𝑝 = 0.46 eV and therefore cannot explain the experimental value.

Thus, only a detailed atomic description of the interface in the sense of the bond polariza-tion model (see secpolariza-tion 1.5), which is realized by DFT calculapolariza-tions, can explain the ex-perimental p-type SB height and the variation of the LDOS inside the valence band. Fur-thermore, the DFT calculations also yield a realistic picture of the metal-induced states inside the semiconductor’s band gap.

Therefore, cross-sectional STS measurements and DFT calculations show that the Fe/p-GaAs(110) interface dipole essentially comprises of two different contributions: the first part is represented by metal-induced gap states and the second part originates from bond polarization. The influence of each part on the SB height will be discussed in section 5.2.

The overall interface dipole, i.e., the effective charge distribution at the interface, will also be of particular interest in the following section. Therefore, the effective charge across the interface is extracted from the DFT data.¹⁴ This is accomplished by obtaining

14 Since the DFT calculation does not take into consideration doping inside the semiconductor, the calculated effective charge does not include space charges from the space charge region.