Si Core–Shell Nanowires

Article pubs.acs.org/JPCC

The Role of Atomic Hydrogen in Ge/Si Core−Shell Nanowires Jongseob Kim,† Kyung Yeon Kim,† Hyoung Joon Choi,‡ and Ki-Ha Hong*,§ †

Samsung Advanced Institute of Technology, Samsung Electronics Co., Ltd., Mt. 14-1, Nongseo-Dong, Giheung-Gu, Yongin-Si, Gyeonggi-Do, 446-712, Korea ‡ Department of Physics and IPAP, Yonsei University, Seoul 120-749, Republic of Korea § Department of Materials Science and Engineering, Hanbat National University, 125 Dongseo-daero, Yuseong-Gu, Daejeon, 305-719, Korea ABSTRACT: We investigate the role of atomic hydrogen in Ge/Si core−shell nanowires with first-principles calculations and present that the hole doping in the Ge/Si heterointerface is achievable through interstitial hydrogen mediated remote doping. This atomic hydrogen induced hole doping could generate onedimensional hole gas in Ge/Si core−shell nanowires. Hydrogen prefers to be incorporated in the Si shell due to the lattice strain effect. As the charge transition energy level of the interstitial hydrogen in Si is lower than the valence band maximum of the Ge band, the electrons in the Ge core prefer to move toward the Si shell and become trapped by the interstitial hydrogen. This unique hydrogen energy level in the Ge/Si heterostructure between the Ge and Si valence band edges drives the electron transfer from the Ge core and induces holes states in the Ge core through remote hole doping. We also perform a quantum transport simulation and show that a high conductive hole channel in the Ge core can be generated when hydrogen is incorporated into the Si shell. Our investigation on the role of atomic hydrogen in the Ge/Si core−shell nanowire opens the possibility of manipulating the hole concentration by tuning the process conditions.

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controlled.22,23 To surmount the surface defect issues in Ge nanowires, a prominent solution was devised by Lauhon et al.,24 who passivated Ge nanowires with Si atoms or Ge/Si core− shell type nanowire (CSNW) structures. Since their work, Ge/ Si CSNWs have been investigated by many research groups for prototype devices.11,25−27 Moreover, there have been theoretical estimations of their superior performance levels and electronic properties.28−31 High-performance p-type FETs25 and a 2-THz intrinsic operation speed of logic devices26 have been demonstrated. Prior successful fabrication efforts have shown that Ge/Si CSNWs can be a good candidate for the channel of high-performance p-type transistors. Moreover, our research group reported that Ge/Si CSNWs can be applied even to n-type transistors by band-structure engineering.32 Recently, direct observations of the unintentional formation of one-dimensional hole gas (1DHG) were reported even without any special dopants.33,34 Park et al. proposed a very interesting concept through first-principles calculations, suggesting that the 1DHG formation can be induced by surface dangling bonds of the Si surface and Au impurities in the Si shell.35 Although the experimentally measured unintentional hole doping concentration of 1DHG is greater than 1019/ cm3,33,34 the maximum Au concentration was seldom greater than 1017/cm3.22,36 If this large number of holes is induced by surface dangling bonds, these surface dangling bonds would

INTRODUCTION Semiconductor nanowires (NWs) are an attractive material platform for various emerging nanoelectronic and photoelectronic devices, such as light-emitting diodes,1−3 photovoltaic cells,4−6 sensors,7−10 field-effect transistors (FETs),11−13 and composite materials, for various applications.14 When considering NWs, special attention needs to be paid to their large surface-to-volume ratios, which can lead to different electrical, optical, and magnetic properties as compared to bulk materials.15−19 This can have advantageous effects, such as facilitating the realization of a large gate capacitance for electronic devices, a large absorbing area for photovoltaic devices, and a large sensing area for sensor devices. However, it can also cause issues such as increasing the vulnerability to surface defects. The surface is inherently defective such that the carriers can be scattered or trapped by surface defects, degrading the performance levels of devices. This limits the application of materials vulnerable to surface defects to nanowire platforms. Germanium (Ge) is a well-known surface defective material. Although Ge was considered as a strong candidate for an alternative to silicon (Si) in the field of electronic devices due to its superior electron and hole mobility,20,21 the use of Ge instead of Si as the basic channel material in transistors is hindered by numerous surface defects. Moreover, unlike Si, the lack of a high-quality native oxide prevents the fabrication of Ge-based transistors.20 Several reports have found that the doping status of Ge nanowires is severely affected by surface defects and that the electronic states cannot easily be © 2014 American Chemical Society

Received: July 7, 2014 Revised: August 11, 2014 Published: August 16, 2014 20710

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known that, when a heterointerface between Ge and Si is formed, the valence band maximum (VBM) and the conduction band minimum (CBM) of Ge are higher by 0.5 and 0.1 eV, respectively, than those of Si. This band offset induces the formation of the type-II band alignment at the Ge/ Si heterointerface.32 To generate a p-type doping state in a Ge core nanowire, one can consider an intrinsic defect with a lowenergy empty state. Considering the growth conditions of Ge/ Si nanowires, there is little possibility of doping by extrinsic dopants except by the catalyst Au.35 Instead, we focus on hydrogen (H) atoms, which are inevitably incorporated in large amounts during the growth processes of semiconductor materials. It is well-established that H can be a source for various doping phenomena in semiconductors.41,42 At the Ge/ Si interface, the energy levels of interfacial Si−Ge bonds are located between the VBMs of the Si and Ge bands. Our present work shows that, if there is hydrogen incorporated into the Ge/ Si interface, it energetically prefers to bind to a Si atom to create a Si−H chemical bond. This induces a partially empty Ge state that can be a source of 1DHG. As the diameters of fabricated Ge/Si CSNWs are larger than 10 nm, it is difficult to mimic the actual sizes of naowires with DFT calculations. Thus, we initially consider Ge/Si superlattices to represent the bulk-like characteristics of thick Ge/Si CSNWs and then study a few-nanometer-sized of nanowires to show the ultimate nanoscale features. We constructed a (110) Ge/Si superlattice, as shown in Figure 2b, which includes 72 Ge atoms and 144 Si atoms. For the Ge/Si superlattices, the lattice constants along the planar direction were set to those of the bulk Ge in order to reflect the large proportions of Ge in the experiment.25 In addition, lattice optimizations were conducted only in the growth direction (the z direction in Figure 2b). Panels (b) and (c) in Figure 2 correspondingly show the atomic structure and charge density profile at the energy levels denoted in Figure 2a when a H atom is incorporated into the tetrahedral interstitial (Td) site of Si near the Ge/Si interface. The charge density profiles clearly show that an interstitial H catalyzes a Ge−Si bond breaking at the interface (Figure 2b) and generating an extended hole state along the Ge core (Figure 2c). The energy level of a Si−H bond is 0.6 eV lower than the VBM. The density of states (DOS) of the Ge/Si superlattice with and without the H interstitial and the projected density of states (PDOS) of H are also presented in Figure 2a. The comparison of DOS with and without the H interstitial clearly shows that unoccupied hole states can be generated through remote doping induced by electron capturing at the interstitial H. Even when interstitial hydrogen atoms are present inside the Si shell away from the heterointerface, our result shows that hole states can also be generated by remote doping. The impact of the H location on the remote hole doping is examined by changing the position of H in the Si layer from the first to the fourth layer away from the Ge/Si interface. The atomic structures studied here are represented in Figure 3a−d, and their DOS profiles are given in Figure 3e. From the DOS profiles, it was found that, even when interstitial H atoms are located at the fourth Si layers, hole doping can be achieved. This induced remote hole doping in the Ge core can be explained in terms of the energy levels of interstitial hydrogens, which are lower than the VBM of the Ge band. The electron in the Ge core can move toward the interstitial hydrogen atom in the Si shell and become captured at the hydrogen. Through a population analysis, it is found that the Bader charge of

generate numerous interface defects between the dielectric and the active channel materials in the transistors, degrading the controllability of the gate.37 This manifests itself as a severe increase in the subthreshold slope. This implies that it is necessary to consider the roles of various intrinsic defects, which can be incorporated into the nanowires during the vapor−liquid−solid (VLS) growth procedure. In this report, we study the role of atomic hydrogen on the electrical properties of Ge/Si core−shell nanowires, which is abundant during VLS growth. We investigate the electronic band structures of the Ge/Si superlattices and Ge/Si CSNWs with first-principles calculations and show that atomic hydrogen can generate 1DHG within Ge/Si CSNWs.

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COMPUTATIONAL DETAILS To analyze the electronic band structures of Ge/Si heterostructures, spin-polarized density functional theory (DFT) calculations were carried out using the VASP program package.38,39 Electronic wave functions were expanded with plane waves with an energy cutoff of 350 eV. The core−valence interaction was described by the projector-augmented wave (PAW) method.40 As the conventional DFT calculation predicts a negative band gap for bulk Ge, hybrid density functional calculations were used for all Ge/Si superlattices and for the bulk Si or Ge. The screening and mixing parameters in HSE are set to 0.2 and 0.25, respectively. The calculated band gaps with k-points generated by 6 × 6 × 6 Monkhorst−Pack sampling were 0.62 eV for bulk Ge and 1.17 eV for bulk Si. The bulk bond lengths were predicted to be 2.468 Å for Ge and 2.353 Å for Si. Near the Ge/Si interface, the Ge−Ge, Si−Si, and Si−Ge bond lengths were 2.483, 2.427, and 2.420 Å, respectively. For Ge/Si CSNWs, we used the PBE-type generalized gradient approximation (GGA) for the exchangecorrelation functional.

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RESULTS AND DISCUSSION

Figure 1 shows a schematic and conceptual band diagram representing how hole states can be formed at the Ge/Si interface by intrinsic defects. As shown in Figure 1, it is well-

Figure 1. Schematic diagram showing how the partially occupied hole states are formed in the Ge/Si heterointerface by the interfacial hydrogen. The black line represents DOS without the H interstitial atom. Red and green areas represent occupied and unoccupied DOS areas, respectively, of a Ge/Si superlattice with a H interstitial atom. The inset shows the atomic structures at the interface between the Ge and Si layers with a interstitial hydrogen atom. Ge, Si, and H atoms are shown as yellow, gray, and white balls, respectively. A broken Si−Ge bond due to a H interstitial is presented in orange and red. 20711

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Figure 3. (a)−(d) Atomic structures of Ge/Si superlattices with respect to the position of the interstitial hydrogen atoms. (e) Density of states of Ge/Si superlattices for the atomic configurations (a)−(d). (f) Extended figure of the dotted rectangular region shown in (e). Figure 2. (a) Density of states (DOS) of a Ge/Si superlattice. The black line represents the DOS without a H interstitial atom. Red/pink and green/cyan areas represent occupied and unoccupied DOS areas, respectively, of a Ge/Si superlattice with a H interstitial atom. (b, c) Atomic structures and charge densities at the energy levels denoted in (a) of a Ge/Si superlattice including a interstitial hydrogen at the Td site. Ge, Si, and H atoms are represented as yellow, gray, and white balls, respectively.

Ge. Formation energies (Ef) were obtained with the following equation Ef = E HSC − (ESC + μH )

where EHSC and ESC are the total energy of the Ge/Si supercell with and without the H interstitial, respectively, and μH is the chemical potential of the hydrogen extracted from a hydrogen molecule. The formation energies of interstitial hydrogen in bulk Si, Ge/Si nanowires, and the Ge/Si superlattice with respect to the positions of hydrogen are listed in Table 1.

hydrogen in the first, second, and third layers of Ge/Si superlattices are −0.93, −0.86, and, −0.86, respectively, whereas that in Si bulk is −0.20. This reveals that the remote hole doping can occur when H atoms capture an electron from Ge. The charge state of the interstitial H at the Ge/Si superlattice can be inferred from the atomic structure. The local atomic configuration, in this case the bond angle, of H−Si−Si feasibly reflects the electrostatics of the chemical bonds. When the charge state of a H interstitial in bulk Si changes from a neutral state to a negatively charged state, the bond angle increases from 75 to 79°. This effect can be explained in terms of VSEPR (valence shell electron pair repulsion) rules, which state that negatively charged bonds tend to repel each other and increase the bond angle. In a Ge/Si superlattice, the H−Si−Si bond angle is much larger than that in Si bulk. The bond angle near the Ge/Si interface is 85°, and as a H atom moves away from the interface, the angle decreases. However, the H bond angle even at the fourth Si layer remains at 80°. This implies that the Si shell can provide sufficient sites for interstitial hydrogen to dope the Ge channel remotely. To confirm the thermodynamic stability of interstitial H in the Ge/Si superlattice, we compared the formation energies of neutral H in the Ge/Si superlattice with those in bulk Si and

Table 1. Formation Energies of a Hydrogen Interstitial in Bulk Si, Ge/Si Superlattice, and Ge/Si Nanowiresa interstitial hydrogen

formation energies (eV)

bulk Si Ge/Si superlattice at 1st Si layer Ge/Si superlattice at 2nd Si layer Ge/Si superlattice at 3rd Si layer Ge/Si superlattice at 4th Si layer Ge/Si core−shell nanowire (2.2 nm)

1.79 1.54 1.68 1.68 1.69 2.03

a

All formation energies are obtained using hybrid density functional calculations, except for the Ge/Si core−shell nanowire, which was obtained with PBE-GGA.

The differences in the formation energies reveal that a H interstitial in the Ge/Si superlattice is thermodynamically more stable than that in bulk Si and that the most stable position for a H interstitial in the Ge/Si superlattice is the Si layer close to the Ge/Si interface. This is attributed to the lattice strain effect and the charge transfer from the Ge, which resembles a hydrogen−boron pair. As the Si layer is under tensile stress caused by a lattice constant mismatch with Ge, a interstitial 20712

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Figure 4. Cross-sectional views of (a) [100], (b) [110], and (c) [111] directional hydrogen passivated Ge/Si CSNWs with a interstitial hydrogen at the first Si layer. Yellow, gray, and white atoms represent the Ge, Si, and H, respectively. (a’−c’) Total density of states of Ge/Si CSNWs with a interstitial hydrogen using PBE-DFT. Red and green areas denote occupied and unoccupied DOS areas, respectively.

hydrogen can more easily bond with Si atoms close to the Ge/ Si interface. We also analyzed the electronic band structures of [100], [110], and [111] directional H passivated Ge/Si CSNWs, as shown in Figure 4a−c, to confirm that our H-mediated remote hole doping concept can also be applied to nanowires. For Ge/ Si CSNWs, PBE-GGA calculations are conducted without considering hybrid density functional as the prior theoretical investigations,28,36 which presented that the negative band gap issue of the Ge band gap can be overcome for a few-nanometersized nanowires due to the quantum confinement effect. As shown in Figure 4a’−c’, the total DOS of Ge/Si CSNWs clearly show that hole states are generated through the H interstitial. The H energy levels are seldom affected by the growth direction of the nanowires. To study the scattering properties of holes generated by a single H interstitial impurity in Ge/Si CSNWs, we performed an electronic transport simulation using the first-principles scattering-state method for quantum conductance.43,44 We consider an infinitely long Ge/Si CSNW with a single H impurity in it, as shown in Figure 5a. The H impurity is at an interstitial site in the Si shell. We divide this H-doped CSNW into three regions conceptually: a scattering region, which is a region near the H impurity, and two perfect regions, which are semi-infinitely long undoped CSNWs. We consider only impurity-induced perturbations in the electron density and the electronic potential inside the scattering region and obtain

Figure 5. Transmission spectra T(E) through a (111) Ge/Si core− shell nanowire with a interstitial hydrogen. The energy of the valence band maximum of the undoped Ge/Si core−shell nanowire is set to zero. Only down spin-down T(E) is presented because there is no difference between those of spin-up and spin-down.

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the transmission spectra T(E) as a function of the electron energy E through a single H impurity in the CSNW. With multiple bands, we have T(E) = ∑n Tn(E), where Tn(E) is the transmission of an electron in the nth band. The details of the calculation method are described in the literature.28,44 Figure 5b shows the transmission spectrum of down spin as a function of the electron energy through [111] directional Ge/Si CSNWs with H interstitials. Comparing our transmission spectra of H-doped with those of B-doped CSNWs,28 remote H doping produces weaker scattering near the valence band edge than that by B doping despite the fact that H doping generates a broken bond. This shows that hole doping induced by a remote H inclusion can be an efficient way to produce relatively high-mobility hole gas in p-type quantum well transistors as compared to intentional doping such as that with B. Because there is no difference between the transmission spectra of up and down spin, only down spin is presented in Figure 5b. The negligible transmission difference between spin-up and spindown can be regarded as another evidence of the shallow doping level formation by atomic hydrogen. The remote doping induced by the H interstitial presents several implications with regard to the application of Ge/Si CSNWs. First, a highly conductive quantum well channel can be realized without the intentional incorporation of extrinsic dopants. A high-electron mobility transistor (HEMT) is a wellknown application that uses a quantum well. In an HEMT, the high mobility originates from a dopant-free channel. For conventional HEMTs, doping of the passivation layer above the quantum well is mandatory to obtain a highly conductive channel because the conductance of the channel is very low without external dopants. Therefore, a δ-doping layer is grown inside the passivation layer. Recent research on emerging transistors is focused on multigate structures for the enhancement of the gate controllability.45 In these structures, not only the region above the channel but also the side areas should act as remote dopant sources. However, the conventional δ-doping concept is not easy to implement with these types of threedimensional multigate structures, as the surface direction of the top surface has a different facet structure from that of the side surfaces and the growth speed varies with the surface direction. Moreover, ion implantation and diffusion are difficult to apply because these processes damage the epitaxial structures. Finally, the random dopant fluctuation issue cannot be avoided. As 1DHG induced by H impurities is not associated with such issues, it is an attractive way to obtain a high-mobility 3-D channel. The concentration of the 1DHG in the nanowire can also vary depending on the synthesis process. The hole concentration in the nanowire can be enhanced when nanowire growth is conducted under H-rich conditions. Annealing at high temperatures, in contrast, can annihilate H impurities and decrease hole concentrations in the Ge core. High-temperature processes and additional annealing for conventional semiconductor device processes do not allow large amounts of H into the Si shell due to the relatively small diffusion barrier of H. Thus, a low-temperature process is inevitable to obtain a highly conductive channel without an extrinsic doping process.

grown Ge/Si CSNWs. In Ge/Si heterostructures, the H interstitial energetically prefers to locate in the Si shell near the Ge/Si interface due to the strain effect. Moreover, as the energy level of the H interstitial in Si is lower than the VBM of the Ge band, the electron in the Ge core transfers toward the Si shell, resulting in hole states in the Ge core. A quantum electronic transport simulation shows that a highly conductive hole channel in the Ge core can be generated through hydrogen incorporation in the Si shell. Our investigation of hydrogen-mediated 1DHG in Ge/Si core−shell nanowires opens the possibility of manipulating the hole concentration by tuning the process conditions.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (K.-H.H.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A1011302). H.J.C. acknowledges support from NRF of Korea (Grant No. 2011-0018306).

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ABBREVIATIONS 1DHG, one-dimensional hole gas; NW, nanowire; CSNW, core−shell type nanowire; CBM, conduction band minimum; VBM, valence band maximum; HEMT, high electron mobility transistor; DOS, density of states

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REFERENCES

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CONCLUSION In conclusion, the role of atomic hydrogen incorporated into Ge/Si CSNWs was investigated using first-principles calculations. Our theoretical investigation shows that atomic hydrogen can be efficient hole doping sources for the VLS20714

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