pubs.acs.org/NanoLett
Asymmetric Doping in Silicon Nanostructures: The Impact of Surface Dangling Bonds Ki-Ha Hong,*,† Jongseob Kim,*,† Jung Hoon Lee,‡ Jaikwang Shin,† and U-In Chung† †
Samsung Advanced Institute of Technology, Mt. 14, Nongseo-Dong, Giheung-Gu, Yongin-Si, Gyeonggi-Do 446-712, Korea, and ‡ Nano Convergence Device Center, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang, Seoul 130-650, Korea ABSTRACT We investigate peculiar dopant deactivation behaviors of Si nanostrucures with first principle calculations and reveal that surface dangling bonds (SDBs) on Si nanostructures could be fundamental obstacles in nanoscale doping. In contrast to bulk Si, as the size of Si becomes smaller, SDBs on Si nanostructures prefer to be charged and asymmetrically deactivate n- and p-type doping. The asymmetric dopant deactivation in Si nanostructures is ascribed to the preference for negatively charged SDBs as a result of a larger quantum confinement effect on the conduction band. On the basis of our results, we show that the control of the growth direction of silicon nanowire as well as surface passivation is very important in preventing dopant deactivation. KEYWORDS Silicon nanostructure, silicon nanowire, silicon nanocrystal, surface dangling bond, trap, dopant deactivation, asymmetric doping, doping
R
SiNC’s are larger than several tens of nanometers. Previous theoretical studies ascribed this asymmetric doping behavior to the surface segregation energy differences between boron and phosphorus21-23 or dopant pair defects,24 which are enhanced for n-type SiNW’s. This asymmetric doping behavior is also observed in the sub-10-nm regime. Recently our colleagues made n-type and p-type FETs using Si nanowires with diameters ranging from 1 to 11 nm and found that the conductance degradation of n-type NWs is still valid for small SiNW’s.25 Moreover, an additional unique feature of nanoscale doping was reported: as the diameter decreases, the subthreshold swing (SS) of the SiNW FET increases and SS values of the n-type SiNW FET become worse than those of the p-type FET. This asymmetric performance of SS with respect to dopant type was attributed to different interface trap generation between n- and p-type doped SiNW FETs, which cannot be explained with dopant segregation and the dopant pair defects model. (A detailed description can be found in the Supporting Information.) On the basis of this experimental evidence, we conjecture that surface or interface traps that form half-filled states within the band gap can play a critical role in the doping of sub-10-nm nanostructures26 and induce asymmetric doping properties in SiNC’s and SiNW’s. In this letter, we study the characteristics of surface dangling bonds (SDBs) in nanoscale Si through a first principles calculation to investigate the asymmetric dopant deactivation in Si nanostructures. We will begin by introducing the stability of charged SDBs in SiNC’s and SiNW’s in terms of the formation energy and will compare with that in bulk Si. Then we will show that asymmetric doping is induced by charged SDBs on Si nanostructures and will further investigate this effect as the size of the nanostructure
ecent progress in nanotechnology has enabled the development of various kinds of electrical devices based on nanocrystals (NCs)1,2 and nanowires 3 (NWs) such as lasers,4,5 photovoltaic cells,6-8 sensors,9-11 and field-effect transistors (FETs).12,13 These nanodevices exhibit unique behaviors of nanoscale materials, one of which is nanoscale doping. Doping is an essential step in modulating the conductivity in electronic devices. However, as the size of a semiconducting material shrinks to the nanometer scale, the doping of NCs and NWs is thermodynamically prohibited by self-purification.14 To overcome this limitation, the concept of kinetic doping has been introduced into the doping of nanocrystals.15 Si nanostructures such as silicon nanocrystals (SiNC’s) and nanowires (SiNW’s) share similar nanoscale doping issues. In the case of SiNW’s, the electrical resistance is inversely proportional to the diameter. Hence, heavier doping is needed for SiNW’s with small diameters to achieve the same level of conductance as that of bulk Si.16 Theoretical studies on the conductance of SiNW’s revealed that the ionization energy of dopants in SiNW’s increases with decreasing nanowire size because of the dielectric confinement resulting in lower conductance.17,18 Another intriguing issue is the asymmetric doping efficiencies between n-type and p-type doped Si nanostructures. Cui et al. reported that the conductance of p-type doped SiNW’s is higher than that of n-type doped SiNW’s,19 which is contrary to what happens in bulk Si. This asymmetric doping can also be observed in SiNC’s.20 In these experiments, the diameters of SiNW’s and * Corresponding author. (K-H.H) Phone: +82-31-280-8352. Fax: +82-31-2809308. E-mail:
[email protected]. (J.K.) E-mail:
[email protected]. Received for review: 12/29/2009 Published on Web: 04/08/2010 © 2010 American Chemical Society
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bond is formed by removing one hydrogen atom from a surface Si atom bonded to three neighboring Si atoms in order to mimic Pb centers. We do not incorporate extrinsic dopants in our calculations to focus on the role of charged defects. The shortest Si-Si distances of a 1.8-nm-diameter SiNC are 2.373-2.375 Å in the core region and 2.353-2.357 Å on the surface but 2.364 Å in bulk Si. When one hydrogen atom is removed from the surface and an SDB is formed, the remaining three Si-Si bond lengths on the surface decrease to 2.339-2.342 Å for neutral-state NC. The trap densities in our model systems are consistent with experimental values. For the case of a 2-nm-diameter SiNC/SiNW with a single SDB, the density of SDB is about 8 × 1012/3 × 1013 cm-2. This agrees well with the reported value of the surface trap density of 6 × 1012 cm-2 eV-1 for a 24-nm-diameter SiNW with increasing trap density as the diameter decreases.16 To elucidate the effect of surface dangling bonds of Si nanostructures on dopant activation, we calculate the dangling bond formation energies (Eqf ) and the charge transition energy levels of SiNC’s and SiNW’s with charge states q using the following expression
FIGURE 1. Structure of (a) a 1.8-nm-diameter silicon nanocrystal. Pale blue and white balls represent silicon and hydrogen atoms, respectively, and a red ball represents the hydrogen atom that is removed when a surface dangling bond is considered. (b) Formation energies of a surface hydrogen dangling bond on 1.8-nm-diameter SiNC with respect to the Fermi energy. The range of the x axis is determined by the band gap calculated via GGA. The vertical dashed line indicates the Kohn-Sham eigenvalue of the neutral dangling bond state. (c) Relationship between the formation-energy diagram of the SDB of SiNC’s and the interface trap density.
q 0 Efq ) ESDB - ESiNS + µH + q(εVBM + εF)
q 0 and ESiNS are the total energy of q-charged Si where ESDB nanostructures with surface dangling bonds and uncharged Si nanostructures without dangling bonds, respectively. εF is the Fermi energy level relative to the valence band maximum (εVBM). εVBM values are corrected by comparing the electrostatic potential between neutral and charged Si nanostructures at the farthest point from the defect site.32 µH is the chemical potential of a hydrogen atom extracted from a H2 molecule. It is not obvious how to set the reference of the chemical potential, which can be varied with chemical species and significantly affects the formation energy. Thus, our discussion will be focused on the relative variation between charged and uncharged states. The formation energies (Efq) of SDBs on 1.8-nm-diameter SiNC’s are represented in Figure 1b. The range of the x axis corresponds to the calculated band gap. In Figure 1b, there are three lines with positive, negative, and zero slopes that represent the formation energies with respect to εF for positively charged (+), negatively charged (-), and neutral (0) SDBs on SiNC’s, respectively. The transition from negatively charged to neutral SDB occurs at ε(-/0), which is 0.54 eV below the conduction band minimum, whereas ε(+/0) is 0.13 eV above the valence band maximum of the SiNC. This implies that the ability to capture an electron from the conduction band of an n-type SiNC is much stronger than that required to capture a hole from the valence band of p-type SiNC. If the density of charged SDBs follows the Boltzmann distribution, then it increases exponentially as
varies. Our results will show that SDBs can be fundamental obstacles in the nanoscale doping of Si. To obtain the formation energy of SDBs, we performed density functional theory (DFT) calculations using the VASP program package.27 Plane wave basis expansions with an energy cutoff of 240 eV and the generalized gradient approximation (GGA) with the PW91 exchangecorrelation functional are used. The core-valence interaction is described by the projector-augmented wave (PAW) method.28 We first obtained the bulk Si structure by applying Monkhorst-Pack sampling with a 4 × 4 × 4 k-point grid and then constructed a nanocrystal supercell with the resulting lattice constant and a 1 × 1 × 1 k-point grid for SiNC. The distance between neighboring nanocrystals is set to be greater than 10 Å in order to reduce the cell-to-cell interaction. We fully optimized the atomic configurations of SiNC’s. All of the atomic positions were optimized until the residual forces on each atom were less than 0.02 eV/Å. The optimized atomic structure of 1.8nm-diameter SiNC is presented in Figure 1a. It is well known that interface traps of Si/SiO2 are related to the Pb resonance centers.29 Pb centers are one of the main sources of interface trap states,30 corresponding to trivalent Si atoms bonded to three other Si atoms. Thus, the interface traps can be thought of as dangling bonds at the Si surface.31 As a feasible candidate for interface traps in Si nanostructures, we considered surface Si dangling bonds. A dangling © 2010 American Chemical Society
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the formation energy decreases, as shown schematically in Figure 1c. It suggests that SDBs of SiNC can strongly deactivate an n-type dopant such as P or As by capturing mobile electrons with which form localized states but has less tendency to do so with p-type dopants. This is in good agreement with the experimental results on the asymmetric doping behavior of SiNC’s.20 Although it is well known that DFT underestimates the band gap energy, DFT results have proven to be useful in the prediction of trends, as shown by the numerous studies on the band gap of hydrogen-passivated nanocrystals33 and nanowires.34,35 We have also performed hybrid density functional theory calculations including Hartree-Fock exchange for small SiNC’s to confirm the reliability of our DFT calculations and have summarized the results in Figure S1 (Supporting Information). Although DFT calculations tend to underestimate the band gap, we were able to confirm that the general trend of the SDB formation can be obtained with DFT calculations. To clarify the difference between nanoscale doping and bulk doping, we also calculated the formation energies of SDBs on bulk Si(110) and bulk Si(111) surfaces. The Si(100) surface is not considered in this study because the 2 × 1 reconstructed (100) surface of bulk Si is quite different from the dihydrogenated surface configurations of SiNW’s.36 We construct slab structures having (110) and (111) surfaces with thicknesses larger than 1.5 and 1.9 nm, respectively. To minimize the interaction between charged SDBs, the distance between the defects is set to be larger than 1.1 nm. The atomic positions of the layers below the middle of the system are fixed during structure optimization to mimic bulk surfaces. The formation-energy diagrams of SDBs on (110) and (111) bulk surfaces, as shown in Figure 2a,b, are quite different from those of SiNC’s. Unlike SiNC’s, there is no stable energy region for negatively or positively charged SDBs in bulk Si because the formation energy of a neutral SDB is lower than that of charged SDBs within the entire band gap. This indicates that an SDB in bulk Si prefers to be in a neutral charge state and does not affect the doping ability. Despite the differences in the overall energy diagram, the formation energies of neutral SDBs in bulk Si are very similar to those on SiNC’s. The formation energies of neutral SDBs in Si(110) and Si(111) surfaces and in 1.8-nm-diameter SiNC’s are 1.14, 1.15, and 1.18 eV, respectively. Therefore, the difference in charge-transition levels, ε(+/0) and ε(-/0), between SiNC’s and bulk Si is not from the change in the formation energy of neutral SDBs but from that of positively and negatively charged SDBs of SiNC’s. We also studied the formation energies of SDBs on SiNW’s. Both [110]SiNW and [111]SiNW show lower formation energies for negatively charged SDBs as shown in Figure 2c,d, which implies a higher deactivation of n-type dopants as seen in the case of SiNC’s. From Figure 2, it can be found that the dopant deactivation due to SDBs is asymmetric © 2010 American Chemical Society
FIGURE 2. Formation energies of surface hydrogen dangling bonds on (a) (110) and (b) (111) surfaces of silicon slabs. The band gap energy of a thin slab (Eg,slab) is larger than that of bulk Si (Eg,bulk) because of the finite system size. The vertical dashed lines in plots a and b indicate the calculated band gap energy of bulk Si. Formation energies of surface hydrogen dangling bonds of (c) a (111) facet of [110]SiNW and (d) a (110) facet of [111]SiNW, of which the diameter is 1.1 nm. For a clear comparison, the x axis of the formation-energy graph of [110]SiNW is extended to the band gap of [111]SiNW. The vertical dashed lines in plots c and d indicate the Kohn-Sham eigenvalue of the neutral dangling bond state.
between donor- and acceptor-like SDBs and is significantly dependent upon the growth direction of SiNW’s by comparing the ε(-/0) and ε(+/0) transition-energy levels. In the case of [111]SiNW, ε(+/0) is located only 0.23 eV above the valence band whereas ε(-/0) is 0.99 eV below the conduction band. In the case of [110]SiNW’s, the ε(+/0) transition point does not exist within the band gap and the ε(-/0) level is shallower than the [111]SiNW’s. This feature makes the formation-energy graph of [110]SiNW’s much closer to that of bulk Si. The calculated band gap of [110]SiNW’s is 1.33 eV, which is smaller than that of [111]SiNW’s having the same diameter, 2.17 eV. This implies that the formation of charged SDBs might be related to the quantum confinement effect. To characterize the dependence of the formation energies of charged SDBs on the diameter of SiNC’s and SiNW’s, we repeated the calculation for various sizes of SiNC’s and [111]SiNW’s. The phase diagrams obtained from the formation energies for varying diameters are shown in Figure 3. The acceptor/donor region in Figure 3 represents the energy region where the formation energy of a negatively/positively charged SDB is lower than that of a neutral SDB. For example, the region between ε(-/0) and the conduction band edge in Figure 1b is represented as an acceptor region of 1.8 nm SiNC in Figure 3a. The general trends in charging behavior in SiNC’s and SiNW’s are very similar. As the diameter decreases, both the donor region and the acceptor region become wider, which suggests a higher charged SDB density. Moreover, the acceptor region is consistently larger than the donor region. 1673
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FIGURE 4. Schematic representation of the relationship between the formation energy of SDB’s and trap generation due to quantum confinement effect as the size of the Si nanostructures decreases. See the text for details.
Finally, the quantum confinement effect plays a critical role in driving the asymmetric doping behavior. As shown in Figure 3, the variation of ε(+/0) and ε(-/0) charge transition levels is smaller than that of the conduction or valence band edges with varying diameters. Because quantum confinement makes a stronger impact on the conduction band than on the valence band in the case of Si,38,39 the stable energy region of the negatively charged SDBs appears prior to that of positively charged ones as the size of the Si nanostructures becomes smaller. The above descriptions are summarized in Figure 4. As the size of SiNC’s or SiNW’s shrinks, the change in the conduction band edge due to the quantum confinement (∆Ec) is larger than that of the valence band (∆Ev)38,39 and ε(+/-) is aligned at same energy level. The increase in charging energy is inversely proportional to the radius of nanowires or nanocrystals, whereas the band gap is proportional to the inverse square of the radius.38,39 Thus, the increment in the band gap energy induced by quantum confinement is larger than the change in charging energy with the decreasing size of the Si nanostructure. This results in the stabilization of charged SDBs for smaller SiNW’s and SiNC’s and a preference for the negatively charged states over the positively charged states. This works to hinder n-type doping in these structures because mobile electrons will likely be captured by an SDB and will form a negatively charged SDB. This charge compensation phenomenon by forming SDBs in SiNC’s was recently demonstrated by an electron paramagnetic resonance experiment.40 This stabilization of charged SDBs has important implications in understanding the carrier transport behaviors on SiNW-based field-effect transistors (FET). The first is the dependence of the conductance on dopant types in SiNW FETs. Although the complex between neutral DB and the dopant does not affect the ballistic transport behavior in SiNW’s,22 negatively or positively charged SDBs degrade the conductance of SiNW’s because of coulombic scattering. On the basis of our results, the negatively charged n-type SiNW is more stable than the positively charged p-type SiNW. Thus, we can expect that the n-type SiNW experiences a
FIGURE 3. Charging characteristic of SDBs of (a) SiNC’s and (b) [111]SiNW’s with respect to diameter. Ec and Ev represent the conduction band minimum and the valence band maximum, respectively.
We also carried out the same calculation with hybrid density function theory with Hartree-Fock exchange for smalldiameter SiNC’s and found a similar trend as shown in Figure S2 (Supporting Information). A similar trend between SiNC’s (Figure 3a) and SiNW’s (Figure 3b) suggests that the asymmetrical dependence of dopant deactivation and trap generation on dopant species can be a common phenomena in Si nanostructures. We attribute this similarity to three factors. The first one is the difference in atomic relaxation of surface dangling bonds depending on its charged state. In the case of [111]SiNW, a positively charged SDB exhibits sp2-like planar bonding character in which the Si-Si bond length is 2.32 Å and the bonding angle 118°. In contrast, a negatively charged SDB has sp3-type bonds with a lone-pair bond, and the bond length and angle are 2.38 Å and 100°, respectively. The difference in the bonding character affects the stability of charged states of SDBs. The preference for the sp3 bond type causes the formation energy of negatively charged SDBs to be lower than that of positively charged ones. Thus, the charge transition level ε(+/-) is shifted toward the valence band. The second factor is the charge transition energy level ε(+/-) of dangling hydrogen that stays nearly the same regardless of diameter variation as shown in Figure 3. This is consistent with Kagimura et al.’s suggestion that the charge transition levels of SDBs could be a reference energy level among Si, Ge, and Ge/Si nanowires in which the small coupling between the SDB and the underlying bulk states was attributed to the origin of the alignment.37 © 2010 American Chemical Society
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more significant degradation of conductance than does the p-type SiNW. These results are in good agreement with previous experimental results on the conductance asymmetry between n-type and p-type SiNW’s19,25 in which the conductance of n-type SiNW’s is reported to be lower than that of p-type. The second is the degradation of subthreshold swing (SS) of n-type SiNWFET.25 When a positive gate bias voltage is applied to SiNW’s with SDBs, the Fermi energy level of SiNW’s moves toward the conduction band. This corresponds to modulation doping in that the bias voltage controls the Fermi level instead of chemical dopants. In this case, SDBs prefer to be negatively charged as shown in Figure 4 and attract mobile electrons more strongly and screen the gate voltage effectively. Thus, the amount of electron carrier and drain current induced by the gate voltage is reduced and makes SS larger according to eq S.2 (Supporting Information) because of the increase in the density of interface traps. To overcome the nanoscale doping limitation due to SDBs and keep the doping efficiency in Si nanostructures, the formation of charged dangling bonds needs to be suppressed. [110]SiNW is the best candidate for suppressing the generation of surface defects because of its smaller band gap over that of other directional nanowires. Moreover, it has been reported that [110]SiNW’s would also be the best for making defect-free SiNW’s.41,42 In the case of SiNC’s, it can be suggested that other passivation materials having higher binding energies should be used. Because the chemical treatment can modify the electronic structures of SiNC’s,43,44 passivation materials should be carefully chosen according to SiNC applications. For SiNC memory, the binding energy of the passivation material is worth considering because the larger band gap of SiNC’s is not relevant for enhancing the performance of NC memory and in terms of the reliability of devices a lower band gap is preferred. In this study, we considered the hydrogen-passivated Si nanostructures to be model systems whereas real SiNC’s and SiNW’s are usually passivated with dielectric materials such as SiO2 and annealed with H2 for defect curing. If a charged SDB is generated between Si and SiO2, then neighboring atoms around the defect move to compensate for the broken charge neutrality. This deformation makes the trap energy level deeper and the formation energy lower than estimated values in this report. Thus, even though considering the effect of surrounding material will be another challenging issue for the analysis of dopant deactivation and trap-level generation, this will not alter our conclusions. In summary, we investigated the characteristics of surface dangling bonds on Si nanostructures and their effects on the asymmetric doping of SiNC’s and SiNW’s using a first principles calculation. In contrast to bulk Si, charged surface dangling bonds (SDBs) in Si nanostructures, which can be interpreted as traps for mobile carriers, become more stable as the size of the nanostructures decreased because of the © 2010 American Chemical Society
quantum confinement effect. This result implies that the charged SDBs on SiNC’s and SiNW’s can be fundamental obstacles in nanoscale doping, and this dopant deactivation becomes stronger as they become smaller. On the basis of these results, the asymmetric doping efficiency between p-type and n-type doped Si nanostructure is attributed to the preference for negatively charged acceptor-like SDBs over positively charged donor-like ones owing to a larger quantum confinement effect in the conduction band compared to that in the valence band. Our calculation results explain experimental results such as the conductance drop in n-type doped SiNW’s and subthreshold swing (SS) degradation in SiNW FETs. Acknowledgment. We thank Dr. Sung-Hoon Lee, Dr. Hyuk Soon Choi, Dr. Young-Gu Jin, Mr. Sung Dae Suk, and Mr. Kyoung Hwan Yeo for helpful discussions. Supporting Information Available. The relationship between the subthreshold swing of FET and interface traps, a formation-energy calculation with hybrid density functional theory for a 1.1-nm-diameter silicon nanocrystal, and charging characteristic of SDBs of SiNC’s with hybrid density functional theory. This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES AND NOTES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19)
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