InAs is a low band gap semiconductor (Eg = 0.36 eV, compared to 1.42 eV for GaAs),
promising for applications in high-speed transistors, infrared detectors and lasers. The reconstructions of its (001) surface are similar to GaAs(001), but relatively simple and few
in number, with mainly As-rich (2×4) and In-rich (4×2) phases reported.2 The structure
and stoichiometry has been little investigated, with STM being the primary technique used so far. As with GaAs(001) reconstructions in the previous chapter, Xue offers a good review of the work performed on InAs(001) to date.3
The As-rich (2×4) surface may be prepared by decapping at 530 K or by annealing in As flux.4,5 Models proposed are very similar to those for GaAs(001)–(2×4), with STM results
to date being most consistent with a bilayer model as shown in figure 6.1.
Figure 6.1: Models for the As-rich InAs(001)–(2×4) reconstruction. As atoms are shown as red, In atoms as grey.
The In-rich (4×2) phase is readily prepared by annealing, IBA or MBE growth.6,7
Indications from STM are that the structure is consistent, by whichever method the surface is prepared, and is extremely well-ordered. It is believed to be a missing-row dimer structure, and three distinct models have been proposed; a two In dimer bilayer model (hereafter, 2DB) similar to that proposed for GaAs(001)8, a one In dimer bilayer model
(1DB)9 and a two In dimer model with perpendicular As dimerization (2DR)10. Each
model is shown in figure 6.2.
As with other III–V semiconductor surfaces, there is a related c(8×2) phase, derived from a shift in the In dimers, either in the top or the third layer.7 Although this phase was
Figure 6.2: Models for the In-rich InAs(001)–(4×2) reconstruction. (a) two-dimer bilayer model (2DB), (b) one-dimer bilayer model (1DB), (c) two-dimer rebonded-As model (2DR). As atoms are shown as red, In atoms as grey.
The observed contrast difference in the STM images of figure 6.3, along lines L1 and L2 (the direction) is relatively low indicating corrugation much less than the 3 Å which would be expected for the 1DB model, given the large gap between dimer chains. This suggests a two-dimer model is more likely. However, for both the 2DB and 1DB models, the In coverage is 0.75 ML, whilst the STM experimental results are more consistent with the 0.5 ML coverage of the 2DR model.
[
110]
Figure 6.3: Filled states STM images of the InAs(001)–(4×2) surface taken at bias voltages of (a) –2.2 V and (b) –1.6 V [from Xue et al10].
Models for all three (4×2) structures were created in VEGAS, and iterative simulations performed in order to determine the atomic positions of the dimerized atoms, following a similar pattern to that described in the previous chapter. The structural parameters varied
were the lengths and heights of the In dimers in the top and third layer as well as the positions of the As atoms in the second layer separating the dimer chains. As before, the limitation of the software to analysis of only three simultaneous parameters meant that variations had to be simulated cyclically.
After several iterations of simulation and model refinement, the structural parameters were examined. The R–factors for the best-fit 2DB model, shown in table 6.1, were noticeably worse than for the other two models. The structure itself was nonphysical, with a top layer dimer length of 1.12 Å, as shown in figure 6.4. This is consistent with the appraisal based on STM data, and therefore the 2DB model was discounted and not examined further.
In
[
111]
[
11¯ 1]
In[
111]
As[
11¯ 1]
As16.79 3.34 6.16 2.88
Table 6.1: Best-fit R–factors for the InAs(001)–(4×2) reconstruction, 2DB model.
Figure 6.4: Best-fit structural solution for the InAs(001)–(4×2) reconstruction, 2DB model. The top layer dimer length for this solution is 1.12 Å.
The 1DB model provided a much better fit to the data. However, the model was still not particularly physical, particularly in the value of as shown in figure 6.5. The structural parameters obtained are shown in table 6.2. The global best-fit simulations and MEIS data for the 1DB model are shown in figure 6.6. Whilst some dips, such as the dip at 115.24° in the As azimuth, are not well matched the overall closeness of the yield profile is good, with consistently reasonable R–factors, listed in table 6.3.
x
[
2¯ 33]
Figure 6.5: Best-fit structural solution for the InAs(001)–(4×2) reconstruction, 1DB model.
Scattering angle / ° Scattering angle / °
Yield Yield [111] In [111] As [111] In_ [111] As_ 100 110 120 130 2 2.5 3 3.5 4 100 110 120 130 1.5 2 2.5 3 3.5 100 110 120 130 1.5 2 2.5 3 3.5 100 110 120 130 1.5 2 2.5 3 3.5 4
y1 z1 y2 z2 x
2.45 1.35 2.29 1.82 2.13
Table 6.2: Structural parameters for the InAs(001)–(4×2) reconstruction, 1DB model. All figures are in Å, with an estimated error of 0.05 Å.
In
[
111]
[
11¯ 1]
In[
111]
As[
11¯ 1]
As4.81 2.49 4.80 3.81
Table 6.3: Global best-fit R–factors for the InAs(001)–(4×2) reconstruction, 1DB model.
The 2DR data again demonstrated that use of R–factors as a criterion of fit quality must be tempered by consideration that comparisons cannot be made across datasets, even within a single experiment. After a number of iterations, best-fits were obtained for In and As datasets. The best-fit for the different datasets was for different parametric variations of the model. In and As fits for the azimuth are shown in figure 6.7. The difference in the position of the second layer rebonded atom between these two fits was 0.7 Å, and the best-fit R–factors were , and . However, the best-fit for the As simulation fails to match a number of experimental peaks. For example, as with the 1DB model, the dip at 115.24° in the experimental data is not present in the simulation, whilst conversely a dip at around 112° is visible in the simulation but not in the data. Although the R–factor is almost twice as large for the In simulation, the matching of the peak locations is visibly better, and therefore it was used as the basis for further refinement.
[
11¯ 1]
RAs = 2.32 R In = 4.23
[
2¯ 33]
Scattering angle / ° Scattering angle / °
Yield [111] As_ [111] In_ 100 110 120 130 2 2.5 3 3.5 100 110 120 130 2 2.5 3 3.5 R = 4.23In R = 2.32As
The best-fit solution for the 2DR model is shown in figure 6.8 and structural parameters given in table 6.4. The simulation fits are shown in figure 6.9; the R–factors obtained are given in table 6.5. As can be seen by comparison with the R–factors for the 1DB model in table 6.3, this model is not dissimilar in terms of global quality of fit. However, whilst the individual is relatively poor, the overall parity in dip position, yield profile and
R–factors are much greater than for the 1DB model. Perhaps more pertinent though, is that the model is physical, with a structure consistent with the STM data already
reported.10 It is therefore proposed that the 2DR structural model for the InAs(001)–(4×2)
reconstruction, shown in figure 6.2(c), is the most consistent with the results of these MEIS experiments, with structural parameters as given in table 6.4.
RIn[111]
There is one caveat in this analysis, which is that more parameters needed to be varied in order to produce a solution for the 2DR model than for the 1DB. This gives a greater degree of freedom, and so more potential for a parametric (if nonphysical) solution to the data. Conversely though in this case, the 1DB model with fewer degrees of freedom produced a less physical model. This supports the 2DR as the most viable solution.
y x1 z1 x2 z2 x3 z3
2.35 0.51 1.03 1.16 1.28 0.35 1.60
Table 6.4: Structural parameters for the InAs(001)–(4×2) reconstruction, 2DR model. All figures are in Å, with an estimated error of 0.05 Å.
In
[
111]
[
11¯ 1]
In[
111]
As[
11¯ 1]
As7.49 3.87 3.79 3.44
Table 6.5: Best-fit R–factors for the InAs(001)–(4×2) reconstruction, 2DR model.
Scattering angle / ° Scattering angle / °
Yield Yield [111] In [111] As [111] In_ [111] As_ 100 110 120 130 2 2.5 3 3.5 4 100 110 120 130 2 2.5 3 3.5 4 100 110 120 130 1.5 2 2.5 3 3.5 4 100 110 120 130 1.5 2 2.5 3 3.5 4