NANO LETTERS
Conductance, Surface Traps, and Passivation in Doped Silicon Nanowires
2006 Vol. 6, No. 12 2674-2678
M.-V. Ferna´ndez-Serra, Ch. Adessi, and X. Blase* Laboratoire de Physique de la Matiere Condensee et Nanostructures, UniVersite Lyon 1, UMR CNRS 5586, Domaine uniVersitaire de la Doua, F-69622 Villeurbanne, France Received June 21, 2006; Revised Manuscript Received September 19, 2006
ABSTRACT We perform ab initio calculations within the Landauer formalism to study the influence of doping on the conductance of surface-passivated silicon nanowires. It is shown that impurities located in the core of the wire induce a strong resonant backscattering at the impurity bound state energies. Surface dangling bond defects have hardly any direct effect on conductance, but they strongly trap both p- and n-type impurities, as evidenced in the case of H-passivated wires and Si/SiO2 interfaces. Upon surface trapping, impurities become transparent to transport, as they are electrically inactive and do not induce any resonant backscattering.
Progress in vapor-liquid-solid or related growth techniques has allowed the synthesis of a large variety of semiconducting nanowires with a diameter scaling down to a few nanometers. In particular, the production of well-characterized silicon nanowires (SiNWs) has been reported.1-3 Several SiNWbased transistors have been already demonstrated,4-7 and progress in their integration in existing large scale device technologies is being made.8-12 Further, novel SiNW-based applications, such as biomolecular sensors,13,14 have already been explored, even though much work is still needed to characterize their sensitivity and selectivity. Concerning the theoretical studies, important surface15-17 and core reconstructions18,19 have been shown to modify the structure and metallicity of surface-unpassivated SiNWs. In the case of surface passivation by hydrogen or oxidation, an evolution in the cross-section shape of small SiNWs has been predicted, 20 but the wires remain semiconducting with a band gap that depends on mean diameter, a confinement effect that has been studied with several semiempirical21-23 or ab initio formalisms,24-28 including a sophisticated firstprinciples GW approach27 or a tight-binding implementation including both “bulk“ self-energy effects and electron (or hole) interaction with its adiabatic surface image charge.23 The use of semiconducting wires in electronic devices is strongly conditioned by the presence of doping impurities able to displace the Fermi level close to the band edges. Various dopants have been introduced in SiNWs during growth, even though the exact concentration is still difficult to measure.9,29-32 Basic questions, such as the radial localization of impurities or the ionization energy of dopants as a function of SiNWs diameter and radial position, are still to be answered. 10.1021/nl0614258 CCC: $33.50 Published on Web 11/07/2006
© 2006 American Chemical Society
While ionized impurities significantly increase the density of carriers at the device’s working temperature, they also induce a strong drop of transmission for conducting channels close in energy to the impurity related bound state energies. This so-called resonant backscattering effect was clearly evidenced in the case of nanotubes for isolated substitutional impurities.33-37 As a result, it was shown within an efficient tight-binding Kubo formalism that the carriers mean free path in nanotubes would collapse very quickly with a random distribution of dopants exceeding a few percent.35-37 The same resonant backscattering effect was recently shown to dramatically affect the conductance of surface channels in unpassivated SiNWs. 38 In the more common case of surface-passivated wires, where only “bulk” channels play a role, the effect on conductance of band structure,39 surface roughness,40,41 and doping42-44 has been studied within several model approaches (effective mass approximation, Boltzmann theory, etc.), but there has been so far no ab initio study of impurity-induced limitations of conductance. In this Letter, we study by means of ab initio calculations, within an order (N) Green’s function approach, the conductance of doped SiNWs. We consider several possible dopant locations along the NW transversal section. We show that dopants in the bulk induce a strong backscattering at the energy of the impurity levels. However, upon trapping by surface dangling bond defects, the impurity becomes transparent to incoming wavepackets that can propagate ballistically. This surface trapping is energetically favorable, as evidenced for several p- and n-type impurities in the case of hydrogen or SiO2 passivated SiNWs surfaces. The large surface to bulk ratio indicates that such a surface segregation
Figure 1. Symbolic representation of the wire used for transport calculations with an isodensity surface associated with (a) the top of the valence bands and (b) the bottom of the conduction bands. (c-e) Onsite potential 2D maps along transversal and longitudinal planes sectioning the wire: (c) P-impurity at the wire center, (d) an isolated DB surface site, and (e) the “P + DB” complex. (f) Profile of the onsite potential along a line in the longitudinal plane, for the P-impurity at the center (black circles) and “P + DB” complex (red diamonds).
is significant for nanowires with diameters up to several nanometers. We work within the density functional theory (DFT) in a generalized gradient approximation to the exchange and correlation functional.45 Pseudopotentials,46 combined with a basis set of strictly localized numerical atomic orbitals, are used.47 Structural relaxations, up to a tolerance of 0.04 eV/Å, and band structure calculations are performed with double-ζ polarized sets, while these are reduced to single-ζ polarized sets for transport calculations. The conductance studies are performed using the Tablier code, a recently developed O(N) ab initio implementation36 of the Landauer formalism. Our approach exploits the block tridiagonal form of the ground-state Hamiltonian (and overlap matrix) expressed on a strictly localized basis48 in order to calculate recursively the ΣL and ΣR self-energies associated with the left and right electrodes (semi-infinite Si wires in the present case) and the retarded (r) and advanced (a) central device Green’s function GDa,r. The energy resolved transmission can then be calculated: T() ) Tr(Γˆ LG ˆ DaΓˆ RG ˆ Dr) with, e.g., Γˆ L ) Im(Σˆ L). This approach is now standard and is similar, within the linear response, to other implementations using strictly localized basis48 or Wannier functions.49 Transport calculations are performed on a 13 Å diameter SiNW grown along the 〈110〉 direction (Figure 1a). The corresponding Kohn-Sham band structure around the forbidden gap is provided in Figure 2a. Our device consists of a supercell made of 12 wire sections (480 atoms for a length of 47.6 Å), repeated periodically. The on-site and hopping Hamiltonian blocks associated with the two left (right) most sections are used to reconstruct the semi-infinite left (right) electrode Hamiltonian. The remaining central part of the supercell defines the “channel”. In a first step, all surface Si atoms are passivated by hydrogen and we study phosphorus substitutional doping. Since phosphorus is a donor with Nano Lett., Vol. 6, No. 12, 2006
Figure 2. (a) Wire band structure around the gap. Band edges are at (0.7 eV (DFT value. The gap is not on-scale on the graph). (b) Conductance (in units of G0 ) 2e2/h) for (black) the undoped wire, (blue) P atom at wire center, (dashed violet) P atom at the surface (see text), and (red) P atom at a DB site (P + DB complex). (c) Density of states: (black) undoped wire and (blue) P atom in the center.
respect to silicon (n-type doping), we focus mainly on the conduction bands. The conductance and electronic density of states (eDOS) of the undoped wire are represented in parts b and c of Figure 2 (black lines). The eDOS, calculated from the trace of the density operator built from the scattering states, exhibits the expected van Hove singularities at band edges. The structure in plateaus of the transmission shows that our supercell is large enough to ensure that the two left most sections, used to build the infinite leads, are far enough from the impurity to recover the behavior of the perfect (undoped) SiNWs. Upon doping, with phosphorus substituting a central Si atom (blue lines) or a surface Si atom connected to an hydrogen (dashed violet line), we observe a clear drop of conductance related to the backscattering of incoming wavepackets by the potential well created by the impurity (Figure 1c,f). At specific energies on the first conduction plateau, the transmission goes even to zero; that is, the incoming propagating states are entirely backscattered. 2675
We plot in Figure 2c (blue) the impurity-related local density of states obtained by restricting the trace of the density operator to the phosphorus orbitals (P at the wire center). Noticeably, the peaks in the P-related eDOS correspond to the drop of conductance in Figure 2b. This is the clear signature of the resonant character of the interaction between the impurity-induced bound states and the propagating waves, an effect that can be easily interpreted in terms of first-order perturbation theory. The presence of two peaks on the first conduction plateau, a sharp one just below the second van Hove singularity and a broad one at lower an energy, is very similar to what was observed in nitrogendoped nanotubes33 with the presence of a large s-like state and a sharp p-like one. In the valence bands, the impurity located at the center (blue line) induces as well a drop of conductance, but with a smooth energy dependence, free from any resonant character. The same conclusion can be given concerning the projected eDOS. As mentioned above, phosphorus is a donor with respect to silicon and the related bound states are located in the conduction bands.50 The phosphorus impurity located on a surface silicon atom, and bonded to a passivating hydrogen, induces as well a strong drop of conductance, with a zero of transmission on the first conduction plateau, but with resonant energies shifted as compared to the central wire substitutional position (violet dashed line in Figure 2b). The effects of hydrogen and confinement can certainly explain this radial dependence of the transmission peak structure. It demonstrates in particular that care should be taken when building a model scattering potential for semiempirical transport studies whenever the impurities come close to the wire surface. The large shift in energy at which the transmission cancels, upon moving the impurity from the wire center to the surface, indicates that a broad drop of conduction on a large energy window is to be expected for a random distribution of dopants. We turn now to the study of wires in the presence of surface dangling bond (DB) defects, that is in the presence of undercoordinated surface Si atoms. The large surface to bulk aspect ratio in nanowires enhances the importance of such defects in SiNWs as compared to standard bulk devices. It has already been experimentally confirmed51 that interfacial DB defects are notably enhanced in SiO2-coated SiNWs as compared to planar interfaces, stressing the importance of understanding their interaction with dopants. A simple estimate based on typical surface defects and bulk dopant concentrations38 allows the conclusion that there are as many dopants in the wire as surface DB for wires up to several nanometers in diameter. In the present work, we focus on the influence of such DB sites on transport. We find that DB defects alone have hardly any direct impact on the conductance; namely, the conductance of our wire is unaffected by removing one hydrogen atom, thus leaving an unpassivated surface Si atom. Such a result can be rationalized by analyzing in Figure 1 the evolution away from the defect or impurity site, of the on-site potential energy associated with Si s orbitals.52 The perturbation associated with a substitutional phosphorus atom in the bulk is found to be large and long ranged (Figure 1c,f), 2676
Figure 3. Band structure and corresponding eDOS of the large SiNW with a DB at the surface: (a) model of the large SiNW with and isodensity surface of charge associated to the DB in-gap band; (b) model of the Si/SiO2 interface with an isodensity surface of charge associated to the Pb in-gap band; (c) DB isolated, undoped wire; (d) eDOS projected onto the Si DB orbitals; (e) “P + DB” complex structure; (f) eDOS projected onto the P orbitals. Table 1. Segregation Energies (in eV, See Text)a
SiNW Si/SiO2 a
Bdoped
Aldoped
Pdoped
Asdoped
-0.69 -0.20
-1.21
-1.37 -1.47
-1.6
The energy reference is the bulk value.
explaining that the transmission of bulk states is significantly affected by the impurity as shown above. On the contrary, the perturbing potential generated by the DB defect at the surface is extremely short ranged (Figure 1d). As the states around band edges are mainly localized in the core of the wire (Figure 1a,b), they are hardly affected by the presence of the dangling bond. In the presence of dopants, however, the role of the DB defects becomes significant. It was shown in a recent work38 that P and B atoms tend to segregate to the surface at DB sites. We confirm that trend by extending this study to other type of dopants (namely, As and Al) and to a model Si/SiO2 interface with a Pb0 defect. Our total energy calculations are performed on a larger 16.7 Å diameter 〈110〉 wire (Figure 3a) using four cells along the axis direction (248 atoms) to avoid image dopant interactions. Our Si/SiO2 interface with its DB defect is represented in Figure 3b and is equivalent to that prepared by Rignanese et al. in ref 53, but with a larger Si slab (ten layers) in order to converge our surface to bulk impurity location difference of energy. Table 1 reports the surface to bulk energy difference for the surface positions, namely, the energy of the impurity at the DB site (labeled the “dopant + DB” complex) minus the energy of the DB at the surface with the dopant in the wire core. Our results indicate that no matter the dopant type, and the type of interface (H or SiO2 passivation), impurities will segregate at the surface, with larger segregation energies for n-type dopants. The transmission associated with the “P + DB” complex is shown in Figure 2b (red full line). Clearly, it is nearly indistinguishable from that of the perfect wire. Namely, and in great contrast with the case of phosphorus in the bulk, Nano Lett., Vol. 6, No. 12, 2006
the impurity is transparent to the incoming wavepackets and the transport is nearly ballistic. We emphasize that it is not just a geometric effect, as phosphorus located at the same surface site, but connected to an hydrogen, yields a significant drop of conductance as shown above (dashed violet line). The analysis of the on-site energy profile around the P + DB complex (Figure 1b,f) shows that the induced perturbation is weaker and shorter ranged as compared to the one associated with phosphorus in the core. In particular (Figure 1f), while the phosphorus on-site energies are ∼3.6 eV below that of unperturbed silicon when the dopant is at the center, they are only ∼2.1 eV below on the P + DB complex. Namely, the potential well associated with the P + DB complex is much shallower. To better understand this behavior, we have studied the electronic properties of the DB defect and the P + DB complex. The band structure of the SiNW with a DB defect at the surface is shown also in Figure 3c. As expected, the DB yields a half filled band deep into the forbidden gap, consistent with the findings of ref 28. With P in the core and in the presence of the DB, the extra electron fills the DB level which is now close to the VBM, a situation described in ref 54 in the case of hydrogenated silicon nanocrystals. This configuration is however energetically less favorable than having the dopant at the surface DB site (Table 1). Upon formation of the P + DB complex (Figure 3e), the occupied gap state forms a stable lone pair localized on the P atom, leaving the bulk Si wire unperturbed. The phosphorus relaxes in a sp3-like configuration with the three Si-P backbonds and the lone pair forming the tetrahedral environment.55 The stability of this lone pair can be further evidenced by analyzing the related projected density of states (Figure 3 and Figure 2c). The P + DB levels are now found to land mainly deep in the valence bands, a situation which is also reflected in the transmission profile with a drop of conductance no longer in the conduction bands, but on the second plateau in the valence bands (red line, Figure 2b). Similar results have been obtained in the case of p-type doping with the removal from the valence bands of any impurity character upon segregation into the surface DB sites. While the transparency to wavepackets propagation of the P + DB complex is a favorable situation, since the ballistic character of the transport in perfect wires is preserved, the removal of the impurity band away from the band gap means that the dopant is electronically neutralized, namely it cannot yield any free carrier, as the additional electron is now bound to the surface lone pair. The wire with its P+DB complex is a true semiconductor (Figure 3e) and hardly any free carrier can exist at room temperature. The impurity is thus completely neutralized upon segregation on the DB site, as it cannot be ionized and is transparent to propagating states. Recently, a detailed study of phosphorus-doped SiNWFETs with controlled dopant concentration56 revealed a surprising increase of conductance with increasing doping percentage, a result at odds with the present conclusions and also with what is observed in bulk silicon. This observation was interpreted in terms of a modification (lowering) of the conNano Lett., Vol. 6, No. 12, 2006
tact resistance upon doping. The importance of a possible Schottky barrier at the electrode/SiNWs interface was previously emphasized in ref 57. Whatever the impact of the contact resistance, one expects in the limit of large diameters that the intrinsic behavior of SiNWs will be similar to that of bulk Si. Our results lead to conclude however that below a few nanometers in diameter, a significant fraction of dopants will be neutralized by DB defects while bulk dopants will be very efficient in reducing the carrier mobility. Other strategies, such as doping of the shell in core/shell structures58 or the use of undoped Ge/SiNWs heterostructures59 have been proposed to reduce as much as possible the backscattering induced by dopants located in the conducting core. In conclusion, we have characterized the impact of dopants and surface dangling bond defects on the conductance of SiNWs. Dopants located in the wire core induce a strong resonant backscattering that significantly reduces the mobility of carriers at selected energies. The resonant energies depend on the radial location of the dopants, suggesting a drop of conductance on a large energy window upon random doping. However, surface dangling bond defects, the importance of which is enhanced by the large surface/bulk ratio in nanowires, are shown to trap the impurities and neutralize them. Namely, dopants are more stable when located on surface defects where they are transparent to transport. Such results could affect significantly the behavior of small diameter wires as compared to bulk silicon. Acknowledgment. The authors are indebted to Re´gion Rhoˆne-Alpes, CNRS, and the French ACI “Transnanofil” program for partial funding. Calculations have been performed at the French CNRS national supercomputing centers (IDRIS). The authors acknowledge G.-M. Rignanese and J.-C. Charlier for providing to them their model Si/SiO2 interface. References (1) Morales, A. M.; Lieber, C. M. Science 1998, 279, 208-211. (2) Ma, D. D. D.; Lee, C. S.; Au, F. C. K.; Tong, S. Y.; Lee, S. T. Science 2003, 299, 1874-1877. (3) Cui, Y.; Lauhon, L. J.; Gudiksen, M. S.;Wang, J.; Lieber, C. M. Appl. Phys. Lett. 2001, 68, 2214. (4) Huang, Y.; Duan, X.; Wei, Q.; Lieber, C. M. Science 2001, 291, 630-633. (5) Martensson, T.; Carlberg, P.; Borgstrom, M.; Montelius, L.; Seifert, W.; Samuelson, L. Nano Lett. 2004, 4, 699-702. (6) Jin, S.; Whang, D.; McAlpine, M. C.; Friedman, R. S.; Wu, Y.; Lieber, C. M. Nano Lett. 2004, 4, 915-919. (7) Friedman, R. S.; McAlpine, M. C.; Ricketts, D. S.; Ham, D.; Lieber, C. M. Nature 2005, 434, 1085. (8) Cui, Y.; Lieber, C. M. Science 2001, 291, 851-853. (9) Wang, D.; Sheriff, B.; Heath, J. R. Nano Lett. 2006, 6, 1096-1100. (10) Cui, Y.; Zhong, Z.; Wang, D.; Wang, W. U.; Lieber, C. M. Nano Lett. 2003, 3, 149-152. (11) Wu, Y.; Cui, Y.; Huynh, L.; Barrelet, C. J.; Bell, D. C.; Lieber, C. M. Nano Lett. 2004, 4, 433-436. (12) Duan, X.; Niu C.; Sahi, V.; Chen, J.; Wallace, P.; Empe-docles, S.; Goldman, J. L. Nature 2003, 425, 274-278. (13) Cui, Y.; Wei, Q.; Park, H.; Lieber, C. M. Science 2001, 293, 1289. (14) Wang, W.; et al. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 3208. (15) Ismail-Beigi, S.; Arias, T. Phys. ReV. B 1998, 57, 11923. (16) Kobayashi, K. Phys. ReV. B 2004, 69, 115338. (17) Rurali, R.; Lorente, N. Phys. ReV. Lett. 2005, 94, 026805. (18) Zhao, Y.; Yakobson, B. I. Phys. ReV. Lett. 2003, 91, 035501. (19) Kagimura, R.; Nunes, R. W.; Chacham, H. Phys. ReV. Lett. 2005, 95, 115502. 2677
(20) Chan, T.-L.; Ciobanu, C. V.; Chuang, F.-C.; Lu, N.; Wang, C.-Z.; Ho, K.-M. Nano Lett. 2006, 6, 277-281. (21) Bockelmann, U.; Bastard, G. Phys. ReV. B 1992, 45, 1688-1699. (22) Yeh, Chin-Yu; Zhang, S. B.; Zunger, A. Phys. ReV. B 1994, 50, 14405-14415. (23) Niquet, Y. M.; Lherbier, A.; Quang, N. H.; Fernandez-Serra, M. V.; Blase, X.; Delerue, C. Phys. ReV. B 2006, 73, 165319. (24) Read, A. J.; Needs, R. J.; Nash, K. J.; Canham, L. T.; Calcott, P. D. J.; Qteish, A. Phys. ReV. Lett. 1992, 69, 1232-1235. (25) Buda, F.; Kohanoff, J.; Parrinello, M. Phys. ReV. Lett. 1992, 69, 1272. (26) Delley, B.; Steigmeier, E. F. App. Phys. Lett. 1995, 67, 2370-2372. (27) Zhao, X. et al. Phys. ReV. Lett. 2004, 92, 236805. (28) Singh, A. K.; Kumar, V.; Note, R.; Kawazoe, Y. Nano Lett. 2006, 6, 920-925. (29) Cui, Y.; Duan, X.; Hu, J.; Lieber, C. M. J. Phys. Chem. B 2000, 104, 5213. (30) Ma, D.D.D.; Lee, C. S.; Lee, S. T. Appl. Phys. Lett. 2001, 79, 2468. (31) Lew, K.K. et al. Appl. Phys. Lett. 2004, 85, 3101. (32) Byon, K.; Tham, D.; Fisher, J. E.; Johnson, A. T. Appl. Phys. Lett. 2005, 87, 193104. (33) Choi, H. J.; Ihm, J.; Louie, S. G.; Cohen, M. L. Phys. ReV. Lett. 2000, 84, 2917. (34) Kaun, C.-C.; et al. Phys. ReV. B 2002, 65, 205416. (35) Latil, S.; Roche, S.; Mayou, D.; Charlier, J.-C. Phys. ReV. Lett. 2004, 92, 256805. (36) Adessi, Ch.; Roche, S.; Blase, X. Phys. ReV. B 2006, 73, 125414. (37) Avriller, R.; Latil, S.; Triozon, F.; Blase, X.; Roche, S. Phys. ReV. B 2006, 74, 121406(R). (38) Ferna´ndez-Serra, M. V.; Adessi, C.; Blase, X. Phys. ReV. Lett. 2006, 96, 166805. (39) Nehari, K.; Cavassilas, N.; Autran, J. L.; Bescond, M.; Munteanu, D.; Lannoo, M. Solid State Electron. 2006, 50, 716-721. (40) Sundaram, V. S.; Mizel, A. J. Phys.: Condens. Matter 2004, 16, 4697. (41) Wang, J.; Polizzi, E.; Ghosh, A.; Datta, S.; Lundstrom, M. Appl. Phys. Lett. 2005, 87, 043101.
2678
(42) Gold, A.; Ghazali, A. Phys. ReV. B 1990, 41, 7626. (43) Wang, J.; Polizzi, E.; Lundstrom, M. J. Appl. Phys. 2004, 96, 21922203. (44) Das Kunal, K.; Mizel, A. J. Phys.: Condens. Matter 2004, 19, 6675. (45) Perdew, J. P.; et al. Phys. ReV. Lett. 1996, 77, 3865. (46) Troullier, N.; Martins, J.-L. Phys. ReV. B 1991, 43, 1993. (47) Soler, J.-M.; et al. J. Phys. Condens. Matter 2002, 14, 2745. (48) Rocha, A. R.; Garcia-Suarez ,V.; Bailey; S.; Lambert; C.; Ferrer; J.; Sanvito; S. Phys. ReV. B 2006, 73, 085414. (49) Nardelli, M. B.; Fattebert, J.-L.; Bernholc, J. Phys. ReV. B 2001, 64, 245423. (50) In Figure 2, the P-induced donor in-gap levels cannot be seen, as the eDOS is calculated from the trace of the density matrix built from the propagating states. As in-gap states are strictly localized, not propagating, they cannot be seen in this “transport-related” density of states. This is not the case in Figure 3 where stationary Bloch states are used. (51) Baumer, R. P.: et al. Appl. Phys. Lett. 2004, 85, 943. Wang, R. P. Appl. Phys. Lett. 2006, 88, 142104. (52) Very similar results are obtained for the p orbitals on-site energies. Such on-site energies are directly extracted from the diagonal of the ab initio Hamiltonian. (53) Rignanese, G.-M.; Pasquarello, A.; Charlier, J.-C.; Gonze, X.; Car, R. Phys. ReV. Lett. 1997, 79, 5174. (54) Blomquist, T.; Kirczenow, G. Nano Lett. 2006, 6, 61-65. (55) In the case of p-type doping (B, Al), the impurity + DP complex adopts rather an sp2 configuration as the dangling bond is now completely empty. (56) Zheng, G.; Lu, W.; Jin, S.; Lieber, C. M. AdV. Mater. 2004, 15, 1890. (57) Landman, U.; Barnett, R.; Scherbakov, A. G.; Avouris, Ph. Phys. ReV. Lett. 2000, 85, 1958. (58) Zhong, J.; Stocks, G. M. Nano Lett. 2006, 6, 128-132. (59) Xiang, J.; Lu, W.; Hu, Y.; Yan, H.; Lieber, C. M. Nature 2006, 441, 489.
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Nano Lett., Vol. 6, No. 12, 2006
