The Local Density of States at the Interface

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4.3 The Local Density of States at the Interface

As was already stated earlier in the introductory part of this thesis, up to the present day no experiment has been reported that yields a “complete” energetic and spatial map of the local density of states (LDOS) covering both the band gap region and the valence and conduction band at the interface. However, solely such a complete energetic and spatial LDOS map allows to check the validity of any proposed model. In chapter 3.2.3 highly resolved cross-sectional scanning tunneling spectroscopy (XSTS) at the ideal Fe/p-GaAs(110) interface has been applied to observe the continuum of interface-induced states in the band gap of the semiconductor. In this section it will be shown for the first time that XSTS in combination with 3D FEM simulations also allows to investigate the variation of the LDOS inside the valence and conduction band at the interface.

The experimental 𝐼𝐼-𝑉𝑉 spectra can be thought of as a superposition of an electrostatic part and an interface specific part. The electrostatic part contains both the band bending along the space charge region of the Schottky contact and the tip-induced band bending (TIBB).

Both are decribed by essentially the same physics and are included in electrostatic 3D FEM simulations described in section 4.1. However, the second component of the exper-imental 𝐼𝐼-𝑉𝑉 spectra, namely the interface specific contribution, is due to charge rear-rangements at the interface. These charge rearrangement are either due to MIGS (see section 3.2.3) or due to chemical bond effects energetically localized inside the valence band (see chapter 5). These interface specific contributions are not considered by the 3D FEM simulations. In the following it will be shown how the 3D FEM data is used to re-move the electrostatic contribution from the experimental 𝐼𝐼-𝑉𝑉 spectra revealing the charge rearrangement at the interface.

As a first example the experimental 𝐼𝐼-𝑉𝑉 spectra along the n-doped sample from Figure 4.7(b) is taken. In the upper panel in Figure 4.9 the same data set is shown. In a first step the best fit between the tunnel current isoline deep inside the conduction band (black dots starting at a bias voltage of 𝑉𝑉_{𝑏𝑏𝑖𝑖𝑣𝑣𝑠𝑠}= +0.9 V) and the Φ_{𝑉𝑉𝑇𝑇} isoline (solid light blue line) from the 3D FEM simulation is found in the same way as described in section 4.2. The best fit is obtained for a Schottky barrier height of Φ_{𝑆𝑆𝑆𝑆}^𝑛𝑛 = 0.94(3) eV and a contact po-tential difference of 𝑉𝑉_CPD^𝑛𝑛 = 0.0 V. For a first visualization of deviations between experi-ment and simulation, several isolines at different starting voltages are plotted as depicted in the upper panel in Figure 4.9. The starting energy of Φ_{𝑇𝑇𝑆𝑆} for the simulated Φ_{𝑉𝑉𝑇𝑇} iso-lines is shifted by the same amount as the starting voltage of the corresponding tunnel current isolines is shifted. In this example the first 𝐼𝐼_𝑇𝑇 isoline starts at a sample bias volt-age of 𝑉𝑉_𝑠𝑠 = +0.9 V whereas the second 𝐼𝐼_𝑇𝑇 isoline starts at 𝑉𝑉_𝑠𝑠= +0.8 V. Therefore, the starting value of Φ_{𝑇𝑇𝑆𝑆} for the second corresponding Φ_{𝑉𝑉𝑇𝑇} isoline is also decreased by 0.1 eV. The same applies to all other isolines as well. In this way an explicit energetic relation between the experimental data and the simulated data is established. The solid yellow Φ_{𝑉𝑉𝑇𝑇} isoline represents the conduction band edge in the electrostatic rigid band model. Anything below this band edge isoline is located inside the band gap. The voltage where the tunnel currentfrom the tip into the conduction band sets in is measured on the

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free GaAs(110) surface far away from the interface. In this case the onset voltage is at 𝑉𝑉_𝑠𝑠= +0.25 V and therefore the band edge isoline starts also at this voltage.

By plotting several Φ_{𝑉𝑉𝑇𝑇} isolines over the corresponding tunnel current isolines one can get a first impression on deviations between experiment and simulation on a broader en-ergetic range. The overall progression of the experimentally observed space charge region is reproduced quite nicely by the simulated isolines. However, a rather large deviation between experiment and simulation is found at 𝑥𝑥 ≈ −32 nm. This deviation is due to an STM tip modification and therefore of no further relevance. Furthermore, smaller devia-tions between experimental and simulated isolines can be observed directly at the inter-face with the tendency that the tunnel current isolines lay energetically below the Φ_{𝑉𝑉𝑇𝑇} isolines. Also important to note is that at the interface a small additional tunnel current inside the band gap (below the yellow band edge isoline) is observed. At the band edge this additional tunnel current extends about 2 nm from the interface.

Figure 4.9: (upper panel) Color-coded plot of log (|𝐼𝐼_𝑇𝑇|) for positive voltages of 250 topog-raphy-normalized 𝐼𝐼-𝑉𝑉 spectra taken along the 𝑥𝑥 direction across an ideal n-type Fe/GaAs(110) interface at set-point values of 𝐼𝐼_𝑇𝑇= 100 pA and 𝑉𝑉_𝑠𝑠= +2 V [121]. The inter-face is located at 𝑥𝑥= 0 nm. Data was taken at room temperature [47]. The black dots represent isolines of constant tunnel current. The solid light blue and yellow lines are Φ_{𝑉𝑉𝑇𝑇} isolines from 3D finite element simulations. The yellow isoline represents the conduction band edge in the rigid band model. (lower panel) Variation of the LDOS inside the con-duction band for the n-type junction extracted from the STS data set above. The dashed black line indicates the conduction band minimum 𝐸𝐸_𝐶𝐶.

4.3 The Local Density of States at the Interface

65 So far solely tunnel current isolines and Φ_{𝑉𝑉𝑇𝑇} isolines have been compared. In a next step the variation of the LDOS will be discussed. To obtain the LDOS variation the following algorithm is applied to the 𝐼𝐼-𝑉𝑉 spectra:

• First of all, Φ_{𝑉𝑉𝑇𝑇} isolines as in the upper panel of Figure 4.9 are extracted from the 3D FEM simulation. However, this time a larger amount of isolines (~100) is ex-tracted for starting voltage values between 𝑉𝑉_𝑠𝑠= 0.0 V and 𝑉𝑉_𝑠𝑠 = +1.0 V.

• In a next step the experimental tunnel current data is read out along these Φ_{𝑉𝑉𝑇𝑇} isolines. In this way electrostatic effects (band bending of the space charge region and TIBB) are removed from the 𝐼𝐼-𝑉𝑉 data.

• Subsequently, the read out tunnel current data is differentiated along the energy axis (𝑑𝑑𝐼𝐼/𝑑𝑑𝑉𝑉) yielding a measure for the LDOS.

• Finally, the average LDOS offset far away from the interface (on the free surface) is substracted from the data yielding the LDOS variation ∆LDOS at the interface with respect to the free surface.

By applying this algorithm to the STS data, one obtains the lower panel of Figure 4.9.

One finds the same tendencies as in the upper panel. A rather slight increase of LDOS is observed inside the conduction band directly at the interface with respect to the free sur-face. There is also a slight increase in LDOS deep inside the conduction band between 𝑥𝑥 ≈ −25 nm and 𝑥𝑥 ≈ −5 nm. A more pronounced increase of LDOS in the order of sev-eral pA/V is observed at 𝑥𝑥 ≈ −32 nm which is due to the measurement artefact men-tioned above.

The data for the ideal p-type Fe/GaAs(110) interface is shown in Figure 4.10. In the upper panel, the bump on the tunnel current isolines at 𝑥𝑥 ≈ −11 nm can be attributed to a charged acceptor in proximity. Clearly, the p-type junction exhibits stronger deviations between the experimental tunnel current isolines and the simulated Φ_{𝑉𝑉𝑇𝑇} isolines than the n-type junction. The largest deviation between simulated and experimental isolines is found directly at the interface. The spectra clearly show an additional tunnel current in-side the band gap. At the band edge (solid yellow isoline) this additional tunnel current extends around 5 nm into the band gap, nicely showing the diverging character of the gap states at the band edge as described by the MIGS model (see section 1.3).

The lower panel in Figure 4.10 shows the corresponding LDOS variation with respect to the free surface for the p-type junction. The map exhibits two very prominent features:

first of all, there is a very sharp decrease in LDOS deep inside the valence band directly at the interface (red color). This LDOS decrease with respect to the free surface is in the order of several hundred pA/V. The sharp decrease in LDOS sets in at ~0.35 eV below the valence band maximum 𝐸𝐸_𝑉𝑉. The second prominent feature is the increase in LDOS at the valence band edge. This LDOS increase with respect to the free surface is rather smeared out and extends around 5 nm from the interface into the semiconductor. The slight LDOS increase further inside the semiconductor can be attributed to the charged

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acceptor at 𝑥𝑥 ≈ −11 nm. It should be pointed out here that while the very small LDOS variation of only a few pA/V in the n-type case can be attributed to noise, for the p-type case a clear signal of the LDOS variation is observed being about 100 times stronger than for the n-type case.

Figure 4.10: (upper panel) Color-coded plot of log (|𝐼𝐼_𝑇𝑇|) for positive voltages of 250 topog-raphy-normalized 𝐼𝐼-𝑉𝑉 spectra taken along the 𝑥𝑥 direction across an ideal p-type Fe/GaAs(110) interface at set-point values of 𝐼𝐼_𝑇𝑇 = 150 pA and 𝑉𝑉_𝑠𝑠=−1.5 V [121, 125].

The interface is located at 𝑥𝑥= 0 nm. Data was taken at 𝑇𝑇= 6 K. The black dots represent isolines of constant tunnel current. The solid light blue and yellow lines are Φ_{𝑉𝑉𝑇𝑇} isolines from 3D finite element simulations. The yellow isoline represents the valence band edge in the rigid band model. (lower panel) Variation of the LDOS inside the valence band for the p-type junction extracted from the STS data set above. The upper dashed black line indicates the valence band edge 𝐸𝐸_𝑉𝑉. The lower dashed black line indicates the energetic position where a sharp decrease of the LDOS at the interface sets in [121].

In conclusion, in this section a new approach to analyze 𝐼𝐼-𝑉𝑉 spectra along the space charge region of a metal-semiconductor interface is presented. This approach based on 3D FEM simulation data allows to visualize the LDOS variation with respect to the free surface inside the conduction and valence band for n-type and p-type junctions, respec-tively. For the n-type interface a rather slight increase in conduction band LDOS is ob-served directly at the interface whereas the p-type case exhibits a strong decrease of LDOS deep inside the valence band. How this relates to the experimentally obtained Schottky barrier height will be discussed in chapter 5 after a short presentation of density functional calculations of the ideal Fe/GaAs(110) interface.

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