*Ab initio* simulations of p-type porous silicon nanostructures

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## Abstract

### Abstract

The morphology of porous silicon (p-Si) depends on several parameters such as the doping type and the carriers’ concentration of the crystalline silicon substrate. The electrolytes used in the p-Si fabrication also have an important role. The final structure determines if p-Si is luminescent or suitable for photonic applications. Experimental results on p-Si produced by electrochemical etching show that although the carriers are greatly reduced by the etching process, boron atoms remain in the bulk. The study of p-type porous silicon nanostructures by means of an *ab initio* computational simulation might help to understand how boron atoms influence the p-Si final structure. Here, we report electronic and topological properties of ten p-type porous silicon structures as an extension of our previous paper on p-type crystalline silicon. Our results suggest that the boron atoms can not remain bonded on the porous surface but do so in the bulk. The presence of impurities changes the bond distance of their neighbors within a radius of 5 Å. The energy of the models is essentially the same for all the boron positions in the silicon backbone. The high electronic density around the boron impurity could influence the trajectory of an HF ion entering a p-Si pore during the fabrication process.

## Keywords

Porous silicon Nanomaterials Computational simulations## Background

We have extensively studied porous silicon, both theoretically [1, 2, 3] and experimentally [4, 5], and successfully implemented different applications such as biosensors [6], luminescent structures [7], one-dimensional photonic crystals [5], mirrors for solar concentration devices [8], and filters [5]. These diverse applications are possible in varying the structure of the porous silicon samples by changing the crystalline silicon substrate and the electrochemical etching conditions.

In order to understand the role of boron in the structure of porous silicon (p-Si) fabricated from p-type silicon wafers, we have recently studied some properties of crystalline p-type silicon models by means of *ab initio* computational simulations [9]. This article is another step in this direction. Here, we simulate ten p-type porous silicon models (PSiHB), with the highest number of silicon atoms used until now on a periodic solid configuration by an *ab initio* code. Our models incorporate experimental conditions like the concentration of boron atoms (corresponding to the resistivity of the p-type silicon wafers used in the fabrication of p-Si for photonic applications (NR, JdR, and PPM, unpublished work)) and dangling bonds passivated with hydrogen. The technical features of the *ab initio* software employed in our work and the procedure used to generate the PSiHB models are described in the ‘Methods’ section. In the ‘Results and discussion’ section, we report the total radial distribution functions (RDFs), topological radius influence of boron atoms, plane angle distributions, and relative electronic densities (RelD(E)s) along planes which contain the first Si neighbors of the B impurities.

Our results suggest that boron atoms cannot remain bonded on the surface of the pore but are bound in the bulk. The boron impurities favor the crystallinity of the PSiHB models because they reduce the interatomic distances among second silicon neighbors. Also, we find a large electronic density around the boron atom with a short-range influence of about two atomic layers. We speculate that due to this electronic density, during the electrochemical fabrication of p-Si, the HF ion avoids the boron atoms. This ion movement could determine the p-Si final topology.

### Experimental facts

^{−3}

*Ω*cm

^{−1}) substrates, porous silicon shows a column-like structure, see Figure 2a, and photonic features (NR, JdR, and PPM, unpublished work). On the other hand, high-resistivity (10

*Ω*cm

^{−1}) substrates produce a sponge-like structure with luminescent properties, as can be observed in Figure 2b. Although, in our simulations, we do not include the applied electric field used to produce p-Si by electrochemical etching, it is possible to fabricate p-Si by chemical etching with HF without any electrical current. Figure 3 shows a porous sample obtained by electrochemical etching with 40 mA cm

^{−2}current in only 60 s and then chemically etched by the sample in the HF solution during 68 h without any current. As it can be observed, chemical etching is a very slow process but capable of growing porous in a silicon substrate.

## Results and discussion

In Figure 5b, we present the superposition of the PSiHB boron radii of influence (*r*_{B}) defined in the previous section, and we compare it with the effect of one B atom in a p-type silicon crystal. The value of the boron radii of influence is bigger than the 10% for the atoms that are at less than 5 Å from the B impurities. The boron radii of influence coincide with the approximate boron effect observed in the PSiHB RDFs and with the contractions of the first and second Si nearest neighbors toward the substitutional impurity calculated by [13, 16] and observed by [17].

^{2}, respectively. The height of the PSiHB RelD(E) model with the B atom on the pore surface is 1.77 electrons/Bohr

^{2}near the mean value of the RelD(E) height distribution; we have not observed any peculiarity in this RelD(E)s with respect to the RelD(E)s of the rest of the PSiHB models with impurity in the bulk. Considering the plane of the impurity of first neighbors, the presence of the B atom modifies the silicon electronic charge distribution in a range less than two atomic layers; this result agrees with [16].

## Conclusions

We conclude that the presence of boron atoms in the porous silicon samples favors crystallinity since it reduces the interatomic distance among its first silicon neighbors around 10% with respect to pure silicon increasing the short range order, which is observed through the sharp peaks in the RDFs. Also, the plane angle distribution around the impurity is close to the crystalline value. Another interesting result of our simulations is that boron atoms do not remain on the pore surface because of weak bonding to the silicon network. We find that boron atoms present a bigger electronic density than silicon atoms which could indicate that during chemical etching, the HF ions will tend to avoid the impurities at a distance of at least 5 Å (two atomic layers). This might be the reason why *p* and *p*+ porous silicon samples present different topologies. When more boron atoms are present, there are not many possible trajectories for the HF and a more regular structure is obtained, while when a small number of impurities are present, the etching could be in many directions, generating a sponge-like structure.

## Methods

We generated ten PSiHB models with 255 Si atoms, 154 hydrogen atoms, and one B atom. For nine of the ten models, the B atom is placed on different bulk locations, and for one of the models, B is on the pore surface. The PSiHB models have one central and regular pore along the *z*-axis of the supercell. The optimized structures were calculated using ABINIT that is an *ab initio* code based on total energy pseudopotential methods [19]. This code is based on the density functional theory [20, 21] and uses plane waves to expand the electronic wave functions.

- 1.
The diamond structure Si cell was replicated four times on each axis to obtain a crystalline supercell with 512 Si atoms, whose edge length is 21.72 Å, with a density of 2.33 g/cm

^{3}. - 2.
The central pore was constructed eliminating 50% of the silicon atoms and with a regular transverse section.

- 3.
The silicon dangling bonds were passivated with hydrogen atoms.

- 4.
For each PSiHB model, one Si atom was substituted by a B one. The position of the impurity is different for each model. Just one of the PSiHB structures has a B atom bonded on the inner pore surface, while the other structures have their impurities in the bulk (Figure 4a). In this step, the B atom is bonded to four atoms, but this is an artificial state because B has just three valence electrons.

- 5.
Once the PSiHB models have been constructed, an optimization of their geometries is implemented in the ABINIT code to obtain the lowest energy configuration. The VMD code was used to visualize the resulting optimized structures.

- 6.
The Si and H atoms were simulated with a local type Troullier-Martins pseudopotential; the B atoms, with Troullier-Martins-Fermi. The exchange-correlation energy functional used for the local density approximation was the one proposed by Goedecker et al. [22].

- 7.
For geometry optimization, a cutoff energy radius of 10 Ha and a tolerance force of 5×10

^{−5}Ha/Bohr were used. - 8.
To reproduce the doping level of the experimental p-type silicon wafers, the PSiHB resistivity (

*ρ*) was set as*ρ*=1×10^{−3}*Ω*cm^{−1}corresponding to a 1×10^{20}carriers/cm^{3}concentration [23].

*r*

_{B}) as follows:

*r*

_{PSiH}and

*r*

_{PSiHB}are the distance vectors of each Si atom from the B impurity, at the origin of the coordinate system, on a pure porous silicon structure passivated with hydrogen (PSiH) and on a PSiHB structure, respectively. To study the electronic behavior around the B impurity, we calculate the relative electronic densities (RelD(E)) of the PSiHB structures as follows:

where D(E)PSiHB is the electronic density of a PSiHB model, and D(E)PSiH is the electronic density of a pure porous silicon model passivated with hydrogen. We have obtained the RelD(E) of each PSiHB model on a plane determined by a B atom and two of its first Si atom neighbors. In order to visualize the local changes around the boron, we consider *r*_{B} > 1*%* and RelD(E) > 0.01 electrons/Bohr^{2}.

## Notes

### Acknowledgements

The authors thank Dr. Maria Beatriz de la Mora and Orlando Hernández Cristobal for the SEM and TEM images. Support from the National University of México (UNAM) through a Posdoctoral Grant to E. R. L. Loustau is acknowledged. We thank the Computing and Information Technology Division of UNAM and the National Supercomputing Center (CNS) for the computer resources. This work was supported in part by DGAPA-UNAM under grant PAPIIT IN109812.

## Supplementary material

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