NH3 molecular doping of silicon nanowires grown along the [112], [110], [001], and [111] orientations

The possibility that an adsorbed molecule could provide shallow electronic states that could be thermally excited has received less attention than substitutional impurities and could potentially have a high impact in the doping of silicon nanowires (SiNWs). We show that molecular-based ex-situ doping, where NH3 is adsorbed at the sidewall of the SiNW, can be an alternative path to n-type doping. By means of first-principle electronic structure calculations, we show that NH3 is a shallow donor regardless of the growth orientation of the SiNWs. Also, we discuss quantum confinement and its relation with the depth of the NH3 doping state, showing that the widening of the bandgap makes the molecular donor level deeper, thus more difficult to activate.


Background
Semiconductor nanowires exhibit a variety of unique material properties, including mechanical flexibility, sizedependent optical and electronic properties, and solution processability. In particular, silicon nanowires (SiNWs) have been explored and studied both theoretically [1] and experimentally [2] for a long time, and they have attracted much attention for many applications, such as bipolar and field-effect transistors [3][4][5], nanosensors [3,6], solar cells [7,8], and energy conversion devices [9,10], but controlled doping with electronic and magnetic impurities remains an important challenge [11][12][13][14]. While developing these applications, it is important to control the electrical and optical properties of nanowires (NWs), which strongly depend on the diameter as well as the crystallographic orientation [15] and defect structure of the NWs [16]. There are several ways that the electronic structure of SiNWs can be modified, for example, by changing the thickness, orientation, surface morphology, hydrogen concentration, and doping [1,2]. Reduced-dimensionality systems are *Correspondence: amiranda@icmab.es 1 Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus de Bellaterra, Bellaterra, Barcelona, 08193, Spain 3 Instituto Politécnico Nacional, ESIME-Culhuacan, Av. Santa Ana 1000, México D.F., 04430, México Full list of author information is available at the end of the article characterized by a large surface-to-bulk ratio and offer the possibility of doping through the external adsorption of molecules [17] rather than the incorporation of substitutional impurities [18].
The increase in graphene carrier mobility induced by absorbed gas molecules has been recently used as a highly sensitive solid-state sensor capable of detecting individual molecules [17,19]. This has motivated molecular doping calculations in graphene [20,21], where the vanishing bandgap makes it easier to find molecular adsorbates whose HOMO (LUMO) falls in the host conduction (valence) band. Also, adsorption of NH 3 and NO 2 has been predicted to occur in carbon nanotubes [22], where charge transfer and gas-induced charge fluctuations should affect significantly the transport properties of single-walled carbon nanotubes [23], in agreement with the experimental results of Kong [24].
In SiNWs, the possibility that an adsorbed molecule could provide shallow electronic states has received less attention, though some promising experimental results have been recently reported [25,26]. This is relevant because traditional substitutional dopants in Si have too large activation energies in thin SiNWs [27,28]. On the other hand, many experimental results have been obtained with mesoporous Si (meso-PSi) [29][30][31], where http://www.nanoscalereslett.com/content/7/1/308 electrochemical attack of a Si sample yields a disordered network of single-crystalline Si wires. In the work of Garrone et al. [32], n-and p-type doping was achieved by the exposure of meso-PSi to NH 3 and NO 2 , respectively. Some of us have recently studied the chemisorption of NH 3 and NO 2 on SiNWs [33], reporting n-and p-type doping of a SiNW with dangling bonds upon gas exposure. That work, however, was restricted to the {110} facet of a [111] SiNW. Focusing on NH 3 the present work will show that those conclusions can be extended to SiNWs grown along other low index orientations, with the molecule sticking to facets of any crystallographic orientation. We will also consider the effect of the diameter of the NW since it is not obvious whether the impurity state introduced by the dopant molecule will be subject to the effects of quantum confinement.

Methods
All of our ab initio calculations were performed with the SIESTA code [34], which implements density functional theory (DFT). We use norm-conserving pseudopotentials for the core electrons and expand the one-electron wane function of the valence electron with a double-ζ basis set plus polarization functions [35]. The exchange correlation energy is calculated within the generalized gradient approximation (GGA) in the parametrization of Perdew-Burke-Ernzerhof [36]. We consider silicon nanowires hydrogenated with a diameter of approximately  [37,38]. The geometrical structures of freestanding NWs are shown in Figure 1 and have been relaxed until all the forces were lower than 0.04 eV/Å. We study NH 3 molecular doping of silicon nanowires in the [ 112] , [ 110] , [ 001], and [111] directions, using supercells made of three, five, three, and two primitive cells, respectively, to allow neglecting the spurious interaction with the periodic image of the molecule and to obtain converged results of the total energies [39]. Also, we study the effect of quantum confinement of NH 3 chemisorbed on 1.0-, 1.5-, and 2.0-nm-thick [111] SiNWs, supercells made of three primitive cells. The Brillouin zone has been sampled with a 1 × 1 × 2 grid of k-points within the Monkhorst-Pack algorithm [40].

Results and discussion
We study NH 3 adsorption on 1.   We have found that all the adsorption processes considered are favored, with the N bonding the unpaired electron of the Si DB. Chemisorption energies are shown in Table 1, from which we see that NH 3 molecules will always bind to available dangling bonds. Subsequent desorption at room temperature will be substantially suppressed, as binding energies are, at least, of the order of 8k B T, with {110} facets being the ones providing the most stable binding.
In Figure 2, we plot the band structure corresponding to the adsorption of an NH 3 molecule at the DB of the {110} facet for all the growth orientation considered. The formation of the DB-molecule complex yields a shallow molecular state close to the conduction band edge, thus  resulting in n-type doping, similar to what we previously reported [33]. Therefore, NH 3 is found to be an efficient donor, with carriers that can be thermally excited into the conduction band. The efficiency of the doping process is, at first approach, independent on the wire growth orientation. Band structures of the less favored, but possible, adsorption mechanisms, i.e., at sidewalls other than the {110} facet (Figure 3), are shown in Figure 4. The conclusions are qualitatively the same, although in the cases shown, the molecular state is somewhat deeper than for the adsorption at {110} facets. Shallower states will be recovered at slightly larger diameters (see the discussion on quantum confinement below). These results suggest that NH 3 can act as a donor agent, a conclusion also corroborated by experimental results [32]. It should be kept in mind that SiNWs in this size range, for instance, have been shown to have calculated bandgaps within GGA that are 0.6 to 0.8 eV smaller than GW or DFT hybrid functional calculations [41,42], which are close to experimental results [37]. Also, as discussed recently by Niquet et al. [43], density functional calculations, at least within the local and semilocal approximations to the exchangecorrelation functionals, only allow a qualitative inspection of this kind of systems, and a many-body treatment is required for a quantitative estimation of the dopant binding energy. For these reasons, it cannot be guaranteed that the estimation of the molecular state depth is quantitatively accurate, and beyond DFT calculations are needed to clarify this point. Therefore, the results presented here should be taken to be qualitative.
Next, we study the effect of the wire diameter. For this, we have considered NH 3 adsorption on three different hydrogenated SiNWs with diameters of 1.0, 1.5, and 2.0 nm grown along the [111] orientation and bounded by {110} facets (see Figure 5). These small diameters yield a sizeable quantum confinement effect [41], which leads to the widening of the electronic bandgap. The electronic band structures of the adsorbed configurations of Figure 5 are shown in Figure 6. In the smaller diameter SiNW (Figure 5a), with a bigger bandgap, NH 3 adsorption yields a deep state, as illustrated by Figure 6a. On the other hand, we obtain for the 1.5-nm NW that the adsorbed molecule contributes with a localized shallow state close to the conduction band edge, where it pins the Fermi level (see Figure 6b), similar to the case of conventional substitutional dopants for bulk Si, such as P. In the limit of a large diameter SiNW, the NH 3 donor state falls at the conduction band edge, as shown in Figure 6c, thus confirming that in larger NWs, where the bandgap is smaller due to a reduced quantum confinement; this state is shallow enough to be an active electron donor.

Conclusions
In summary, we have reported electronic structure calculations of the adsorption of NH 3 [33], where only one specific adsorption configuration was considered. We have found that NH 3 is more strongly bound to {110} facets, regardless of the growth orientation of the SiNWs. On the other hand, quantum confinement effects turn the shallow impurity level into a deep one as the http://www.nanoscalereslett.com/content/7/1/308 SiNW diameter is decreased. All these observations suggest that NH 3 can be used as an active n-type dopant in thin SiNWs.