Spin transport in dangling-bond wires on doped H-passivated Si(100)
Mikaël Kepenekian, Roberto Robles, Riccardo Rurali, Nicolás Lorente
SSpin transport in dangling-bond wires on dopedH-passivated Si(100)
Mika¨el Kepenekian , , Roberto Robles , , Riccardo Rurali ,Nicol´as Lorente , Institut des Sciences Chimiques de Rennes UMR 6226, CNRS - Universit´e deRennes 1, Rennes, France ICN2 - Institut Catala de Nanociencia i Nanotecnologia, Campus UAB, 08193Bellaterra (Barcelona), Spain CSIC - Consejo Superior de Investigaciones Cientificas, ICN2 Building, CampusUAB ,08193 Bellaterra (Barcelona), Spain Institut de Ci`encia de Materials de Barcelona (ICMAB-CSIC), Campus deBellaterra, 08193 Bellaterra (Barcelona), SpainE-mail: [email protected]
Abstract.
New advances in single-atom manipulation are leading to the creation ofatomic structures on H passivated Si surfaces with functionalities important for thedevelopment of atomic and molecular based technologies. We perform total-energy andelectron-transport calculations to reveal the properties and understand the features ofatomic wires crafted by H removal from the surface. The presence of dopants radicallychange the wire properties. Our calculations show that dopants have a tendency toapproach the dangling-bond wires, and in these conditions, transport is enhanced andspin selective. These results have important implications in the development of atomic-scale spintronics showing that boron, and to a lesser extent phosphorous, convert thewires in high-quality spin filters.PACS numbers: 73.63.Nm,73.20.-r,75.70.-i
Submitted to:
Nanotechnology a r X i v : . [ c ond - m a t . m t r l - s c i ] S e p pin transport in dangling-bond wires on doped H-passivated Si(100)
1. Introduction
The integration of semiconductors and magnetic materials is of great importance for thecreation of new technology in which digital data are encoded in the spin of electrons. [1]To this respect, the use of molecules that can become spin devices is a very interestingpossibility. [2] Indeed, molecular devices are very small, adaptable and easy to createusing chemical engineering. Their spin functionalities are also very interesting, and theyhave been deemed superior to more common spintronic strategies. [3, 4] As in molecularelectronics, [5, 6] the problem still comes from creating efficient atomic-size interconnectsto form complete circuits. [6, 7]Interconnects that can transport spin are then desirable for spintronic application.Promising candidates for surface interconnects can be found in carbon nanotubes(CNTs), [8, 9] as they present both easy synthesis and complex physics. In particular,the low Z of carbon, assures very small spin-orbit coupling and hence long spinlifetimes. However, an important issue with CNTs is that their properties are extremelysensitive to the topological structure of the tube. Other serious candidates emergefrom the variety of silicon nanowires (Si NWs) that can be grown and that happento present an easier control on their physical properties. [10, 11] A new type ofnanowires has been recently proposed with embedded phosphorous in a silicon crystal.The resulting 1-D system exhibits then a very low resistivity. [12] An alternativepath consists in using the scanning tunneling microscope (STM) to selectively removehydrogen atoms from a H-passivated Si(100) surface along the Si dimer row leadingto a dangling-bond (DB) wire. [13, 14, 15, 16, 17, 18, 19] At variance with isolatedDBs, which introduce localized mid-gap states, these wires give rise to dispersive bandswith a marked one-dimensional character. The stability and the transport propertiesof such wires have been extensively studied by tight-binding as well as ab intitiomethods [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] and several experimental proofs-of-concept have been reported. [15, 16, 32]. Spin lifetimes in silicon are known to belong, however DB wires present some problems for transport: ( i ) transport propertiesof simple 1-D wires are limited due to the appearance of an electronic gap, [31, 7] and( ii ) the coupling of the wire with the substrate due to the presence of dopants andimpurities leads to a leak of the electronic current in the bulk. [33]In the present work we focus on the effect of dopants, boron ( p -type) andphosphorous ( n -type), on the electronic transport properties of DB-wires with specialinterest in the spin transport properties. In a semiconductor, the density of carriers canbe tuned by adding dopants. In a conventional approach, DBs are undesired surfacedefects, because they introduce deep states in the band-gap that act as charge traps,reducing the conductivity. Here, we place ourselves in the opposite situation: DBconductive wires are engineered on a Si surface, for a specific purpose, e.g. transportingcharge and spin between two devices, and we focus on how dopants affect transport inthese wires. We start by analyzing the dopant segregation on the H-passivated Si(100)surface with and without DB wires, finding that dopants segregate at the surface. Next, pin transport in dangling-bond wires on doped H-passivated Si(100)
2. Computational details
First-principles calculations are based on density functional theory (DFT) asimplemented in the
Siesta package. [34, 35] Calculations have been carried out withthe GGA functional in the PBE form, [36] Troullier-Martins pseudopotentials, [37]and a basis set of finite-range numerical pseudoatomic orbitals for the valence wavefunctions. [38] Structures have been relaxed using a double- ζ polarized basis sets. [38]The surfaces were modeled using a slab geometry with eight silicon layers and a 4 × ×
1) surface. The extent of the cell allows one tolimit the direct interaction between dopants, but still leads to a very high concentrationof dopant with one Si atom out of 600 being substituted by a B or P atom. Theelectronic structure was converged using a 1 × × k -point sampling of the Brillouinzone. Conductances have been computed using a single- ζ polarized basis set, by meansof the TranSiesta method, [39] within the non-equilibrium Green’s function (NEGF)formalism. The following setup has been used: 4-dimer DB wires act as left and rightelectrodes, while a 8-dimer DB wire constitutes the scattering region. The current isevaluated following Landauer’s equation: [40] I = 2 eh (cid:90) ∞−∞ T ( E, V )[ f R ( E ) − f L ( E )] dE where T ( E, V ) is the transmission function for an electron of energy E when the biasbetween the two DB electrodes is V , and f R ( E ) ( f L ( E )) is the right- (left-) electrodeFermi occupation function. We further simplify the current I calculation using thezero-bias transmissions. In TranSiesta , bias between the electrodes is establishedby applying an electric field along the transport direction. Mobile charges inside theelectrodes screen the electric field, resulting in the usual electric potential profile (flatinside the electrodes, potential drop in the scattering region). Only electrodes thatare three-dimensional metals guarantee this kind of screening. In this configuration,however, it becomes very difficult to disentangle the contributions to the resistance ofthe electrode-semiconductor interface from those of the sub-surface dopant scattering.We believe that our simplified model gives a better insight into the physics of electrontransport through DB wires in presence of dopant, because all the observed effects(stabilization of a magnetic solution, leakage, . . . ) necessarily stem from the presenceof the impurities. The price to pay is that biased calculation cannot be performed forthe methodological reasons outlined above. In all cases, an energy cutoff of 200 Ry forreal-space mesh size has been used. pin transport in dangling-bond wires on doped H-passivated Si(100)
3. Results and discussion
The impact of dopants on the current carried by DB-wires depends critically on theirdistribution with respect to the surface. Hence, our first goal was studying the surfacesegregation of these defects. Broadly speaking, we find that in this system impuritiesprefer to be closer to the surface because the strain introduced can be more easilyreleased. This is a well-known behaviour in similar systems, like unpassivated Sisurfaces [41, 42] and in Si nanowires. [43, 44, 11] Our calculations show the same trendin the H-passivated Si(100) surface. For both B and P, nearly 150 meV are gained in themost stable surface position (see Figure 1(b) and Table 1). As the dopant gets closer tothe surface, the formation energy becomes much more site-specific. It appears that sitesD, E and F are favored with respect to sites A, B and C, respectively. These differencesvanish quickly moving away from the surface and are within the numerical accuracy ofthe calculation at 15 ˚A from the surface. In the following, we limit our discussion to thecase of a substitution at sites D, E and F which appears to be more stable than thoseat A, B and C sites.
Table 1.
Formation energies (in meV, see text) for sites D, E, and F with andwithout DB-wires. The notations X@H-passivated, X@NM and X@AFM stands for asystem with the dopant X (X=B, P) below a H-passivated surface, a NM and AFMwire, respectively.
D E FB@H-passivated 29 −
148 214B@NM − − − − − − − −
145 105P@NM − − − − − − i.e. to the strongest bond form between the dopant and its Si neighbours(see Figure 1(c)).Starting from the previous structures, DB-wires are drawn on the surface byremoving a row of Hydrogens along the [110] direction. In the absence of dopants,such wires are known to be unstable and relax following either a non-magnetic (NM)Peierls distortion or a spin-polarized solution that leads to antiferromagnetic (AFM)ordering. [20, 21, 23, 24, 25, 26, 27, 29, 30] The two solutions are very close in energywith the NM configuration more stable than the AFM one by 5 meV/DB. [30]Our results show that surface segregation is enhanced by the presence of such DB- pin transport in dangling-bond wires on doped H-passivated Si(100) Figure 1. (a) Side views of the H-passivated Si(100) surface, where the dimers formedon the surface can be seen on the upper part. Si and H atoms are depicted in yellowand white, respectively. The different lattice sites for B and P are indicated. Sites A,B and C are shifted with respect to the surface dimers, whereas sites D, E and F arepositioned below them (cf. right side). (b) Formation energies (meV) of boron in Siclose to the H-passivated Si(100) surface. At the bulk limit all the sites A, B, C, D, E,and F are equivalent. The corresponding formation energy is taken as a reference. Theformation energies become site-specific close to the surface. (c) Calculated Mullikennet charges of the boron and phosphorous impurities depending on the site substituted.Dashed lines are a guide to the eye. wires. Indeed, whatever the site of substitution for B or P is, the formation energy issmaller than in the bulk position (see Table 1). This is in agreement with previous resultson Si NWs, [43, 45] where dopants are found to form electrically inactive complexes withisolated DBs. Also here, the tendency to surface segregation is more pronounced withP, as observed in the case of Si NWs and unpassivated Si(100) surface. [43, 45]More interestingly, we have found that both B and P stabilize the magnetic solutionwith respect to the NM distorted one, regardless of the site of substitution (see Table 2).The destabilization of the NM wire is due to the increased distortion caused by thedopant. The shortening going from Si-Si to Si-B or Si-P bonds is conflicting with the pin transport in dangling-bond wires on doped H-passivated Si(100) Table 2.
Energy differences (in meV/DB) between NM and AFM configurations fortop sites D, E, and F. In the absence of dopant this difference is − B@D B@E B@F P@D P@E P@F10 22 16 20 15 21buckling imposed by the NM Peierls-like structure. As an example the buckling inthe non-doped NM structure gives differences of ∆ z =0.69 ˚A in the vertical directionbetween neighbour DBs. In a B-doped (P-doped) system, this height difference becomesas high as ∆ z =1.34 ˚A (∆ z =1.52 ˚A) close to the dopant. In the undistorted AFM wirethe deformation introduced by the dopant is much less: ∆ z of 0.16 ˚A and 0.24 ˚A for Band P, respectively. The geometry of the magnetic solution is preserved. Thus, in thepresence of dopants the AFM solution becomes the ground state, yielding a magneticordering that can be exploited for spin transport related applications.Dopants lead to an injection of hole or electrons. In the presence of DBs on H-passivated Si(100), the extra charges are trapped by these surface defects, leading to adecrease in the conductance. Here, however, where conduction is supposed to take placealong the DB-wires, this effect turns out to be positive by closing the electronic gap ofthe AFM wire and leading to a spin-specific quasi-metallicity.Figure 2 shows the band structure of (a) an undoped AFM wire, (b) an AFM wirewith a substitutional B atom in its most stable configuration (F site) and (c) an AFMwire with a substitutional P atom in its most stable configuration (E site). One cansee the expected shifting of the Fermi energy (dashed line) controlled by the amount ofextra charge/hole injected in the system through the dopant. The undoped AFM wire,Fig. 2 (a), shows two surface states leaving a surface-band gap of 0.56 eV. For eachsurfaces state, the bands corresponding to each spin overlap due to the AFM ordering.The B-doped system, Fig. 2 (b), displays a splitting of bands according to spin (red andblue for majority and minority spins). The splitting of bands is due to the introductionof an extra spin in an otherwise perfect AFM wire, leading to an unbalanced number ofspins. The increase of the DB charge, also caused by the dopant, produces the reductionof the surface-band gap to 0.05 eV. In the case of P doping, the extra spin also producesthe spin polarisation of bands and a 0.09-eV gap. Therefore, the presence of dopantsbrings the initial insulating system to a spin-polarized quasi-metallic state.Figure 3 shows the computed I-V curves for B- and P-doped AFM wires. In bothcases, the bias required to obtain a current response is below 0.1 V in agreement with theabove electronic gaps. In the case of P doping, the current contains a bulk contributionto the current. This leads to leakage current, i.e. a loss of surface current into the Sibulk. A previous study showed that this loss could represent as much as 30% of thetotal current for low biases (less than 0.5 V). [33] Figure 3 displays the current alongthe DB wire that does not contain the fraction of the current lost into the bulk. Thisexplains why the current is largely spin polarized despite having a larger number of bulk pin transport in dangling-bond wires on doped H-passivated Si(100) k [110] -5.2-5-4.8-4.6-4.4-4.2-4-3.8-3.6-3.4 E ( e V ) k [110] -5.2-5-4.8-4.6-4.4-4.2-4-3.8-3.6-3.4 k [110] -5.2-5-4.8-4.6-4.4-4.2-4-3.8-3.6-3.4 (a) (b) (c) Figure 2.
Electronic bands evaluated for a periodic magnetic nanowire with (a) apure Si substrate, (b) B-doped Si substrate, and (c) P-doped Si substrate. The redand blue circles indicate the weight of the DB in the majority and minority spin bands,respectively. The dashed lines indicate the position of the Fermi energy. bands, because the wire current is mainly due to the first band below the Fermi energy,which is a surface band and hence spin polarized.However, current leakage is negligible for B doping because there is no bulk bandsin the energy windows for low biases. Indeed, for biases between 0.05 and 0.18 Vthe current remains on the surface and the current leakage is strictly zero. The spin-polarisation for both dopings is the same, i.e. adding or subtracting one electron by thedopant will change the spin balance on the DB, but the majority spin will be the samespin. However, the surface current shows different spin-polarisations, Fig. 3. This is dueto the actual ordering of the DB bands, which changes under the dopant potential.By defining the spin polarisation like P = ( I ↑ − I ↓ ) / ( I ↑ + I ↓ ), we obtain that B-doped systems present a 100% polarisation for biases below 0.17 V, Fig. 4. Beyond thisbias the presence of bulk bands contribute to current leakage and to the loss of spinpolarisation. In the case of P-doped system, the bulk bands contribution starts as earlyas 0.09 eV, leading to a lower spin polarisation. Therefore, for biases lower than 0.17 V,the B-doped DB wire drawn on H-passivated Si(100) system is a perfect spin-filteringsurface interconnect thanks to the absence of current leakage and to the perfect spinpolarisation. pin transport in dangling-bond wires on doped H-passivated Si(100) I ( µ Α ) minoritymajority Bias (V) I ( µ Α ) (a) Boron(b) Phosphorous Figure 3.
I-V curve for the most stable B-doped (a) and P-doped (b) AFM dangling-bond wire. The doted black line indicates the bias at which bulk contributions to thecurrent starts. For larger biases, a part of the current is lost into the Si bulk (leakagecurrent). The non-doped AFM DB wire presents a gap larger than the bias windowconsidered here.
Bias (V) | P | BoronPhosphorous
Bias (V) | P | ( % ) BoronPhosphorous
Figure 4.
Spin polarisation for the B-doped system (black) and the P-doped one(red). The curves are not defined for biases below the band gaps, since the wires holdno current. B-doped systems show 100% polarisation for biases below 0.17 V. Beyondthis bias the presence of bulk bands contribute to current leakage and to the loss ofspin polarisation. In the case of P-doped system, the bulk bands contribution startsas early as 0.09 eV, leading to a lower spin polarisation. Therefore, for biases lowerthan 0.17 V, the B-doped DB wire drawn on H-passivated Si(100) system is a perfectnon-leaking spin-filtering surface interconnect. pin transport in dangling-bond wires on doped H-passivated Si(100)
4. Conclusion
In summary, we have shown that boron and phosphorous dopants segregates to theH-passivated Si(100) surface. This phenomenon is enhanced by the presence of of DBwires. The first effect of dopants is to stabilize the magnetic form of DB wires over thenon-magnetic Peierls distorted one. As observed in other doped Si systems, the extracharge brought by the dopant is captured by the DB wire. One consequence is theclosing of the electronic gap leading to quasi-metallicity of AFM DB wires. Moreover,the presence of dopants induce a total magnetic moment on the electronic bands closeto the Fermi energy, leading to spin-specific electron transport. In the case of B-dopedAFM DB wire, the current is not only free of leakage from the wire but also spin-specific.Therefore, B-doped DB wires are perfect spin-filtering surface interconnects.
Acknowledgments
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