Letter pubs.acs.org/JPCL
A Pathway to Type‑I Band Alignment in Ge/Si Core−Shell Nanowires Jongseob Kim,† Jung Hoon Lee,‡ and Ki-Ha Hong*,§ †
Samsung Advanced Institute of Technology, Samsung Electronics Co., Ltd. San 14, Nongseo-Dong, Giheung-Gu, Yongin-Si, Gyeonggi-Do, 446-712, Korea ‡ Spin Convergence Research Center, Korea Institute of Science and Technology, Seoul 136-791, Korea § Department of Materials Science and Engineering, Hanbat National University, Daejeon, 305-719, Korea ABSTRACT: We investigate the electronic band structures of Ge/Si core−shell nanowires (CSNWs) and devise a way to realize the electron quantum well at Ge core atoms with first-principles calculations. We reveal that the electronic band engineering by the quantum confinement and the lattice strain can induce the typeI/II band alignment transition, and the resulting type-I band alignment generates the electron quantum well in Ge/Si CSNWs. We also find that the type-I/II transition in Ge/Si CSNWs is highly related to the direct to indirect band gap transition through the analysis of charge density and band structures. In terms of the quantum confinement, for [100] and [111] directional Ge/Si CSNWs, the type-I/II transition can be obtained by decreasing the diameters, whereas a [110] directional CSNW preserves the type-II band alignment even at diameters as small as 1 nm. By applying a compressive strain on [110] CSNWs, the type-I band alignment can be formed. Our results suggest that Ge/Si CSNWs can have the type-I band alignment characteristics by the band structure engineering, which enables both n-type and ptype quantum-well transistors to be fabricated using Ge/Si CSNWs for high-speed logic applications. SECTION: Physical Processes in Nanomaterials and Nanostructures
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of nanoelectronic devices.23−25 Not only high-performance ptype nanowire quantum well transistors,26 but also 2 THz intrinsic operation speed of logic devices27 has already been reported along with theoretical estimation on the superior and unique performance of Ge/Si CSNW FETs.28−30 Up to now, Ge/Si CSNWs are applicable only to the p-type transistors to our knowledge. In order to make CMOS, which is a basic unit of logic circuits, n-type transistors should be also implemented together. Thus, heterogeneous materials such as silicon or III− V compound semiconductors should be implemented for ntype channel materials unless a new method for Ge to be used as the electron transport channel is developed. Heterogeneous CMOS integration using different n-type and p-type channel materials results in the increase of cost and process complexity. In this article, we investigate pathways to achieve n-type quantum well FETs with Ge/Si CSNWs through first-principles calculations. As shown in Figure 1, when a heterointerface between bulk Si and Ge is formed, the conduction band minimum (CBM) and the valence band maximum (VBM) of Ge are higher by 0.09 and 0.52 eV than those of Si, respectively, to form a type-II band alignment. In type-II band structures, the hole carriers are confined in the valence band quantum well, while the electrons are spread out into the conduction band of Si shell, inhibiting the use of Ge core as an n-type channel
emiconductor nanowires have been studied for their peculiar features and for their potential uses as new building blocks in the areas of nanoelectronic,1−3 optoelectronic,4,5 flexible electronics,6,7 and energy harvesting devices.8−11 The quantum confinement effect and large surface-tovolume ratio in nanodevices lead to novel electrical, optical, and magnetic properties over bulk materials.12−14 On the other hand, nanostructured materials can be easily affected by surface defects due to their large surface-to-volume ratio properties.15,16 As the surface is inherently defective and defect densities tend to increase as the size of nanowires becomes smaller,17 the performances of manufactured nanowire devices are considerably lower than theoretical values. Germanium (Ge) is considered one of the strongest alternatives to silicon (Si) in the field of electronic devices due to its superior electron and hole motilities to those of Si.18,19 Theoretical investigation demonstrated the promising performance of Ge nanowire field effect transistors (FETs).20 However, the surface passivation remains one of the major issues for Ge to be used as an efficient channel material for FETs due to the lack of a high-quality native oxide in contrast with the case of Si.21 Thus, the quantum well structures with Si shells have been investigated by many research groups. Given the advantages of nanostructures for device applications, Ge/Si core−shell nanowire (CSNWs) can be expected to be a good candidate as the base material for high-performance transistors. Since Lauhon et al. developed a prominent solution to make core−shell type nanowire structures,22 there have been many successful achievements to apply CSNWs to the various kinds © 2012 American Chemical Society
Received: November 29, 2012 Accepted: December 15, 2012 Published: December 15, 2012 121
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Figure 1. Schematic atomic and electronic band structures of (a,b) Ge/Si superlattice and (c,d) Ge/Si CSNW. Ge/Si superlattice has the type-II band alignment, whereas engineered Ge/Si CSNW has the type-I band alignment generating the electron quantum well.
material. This can be avoided by introducing a novel method to make a transition from the type-II band alignment of the Ge/Si interface into the type-I alignment. Two prospective methods are of particular interest, based on the general studies on the band structure engineering of Si and Ge nanowires. One is using the quantum confinement effect by shrinking the diameters. Because the band structure alternation in a Si nanowire induced by the quantum confinement is quite different from that of Ge,31 changing the diameters of the Ge/Si CSNW opens room for a type-I band alignment. The other method is by applying a lattice strain, which can modulate the electronic band structures and induce the band gap changes in Si12 and Ge nanowires.32 Density functional theory (DFT), as implemented in the VASP program package33,34 is used to analyze the electronic band structures of Ge/Si CSNWs. The plane wave basis expansions with an energy cutoff of 300 eV and the generalized gradient approximation (GGA) with the PBE exchangecorrelation functional are used. The core−valence interaction is described by the projector-augmented wave (PAW) method.35 The distance between neighboring wires should be greater than 10 Å in order to reduce the cell-to-cell interaction. We first obtained the bulk Si and Ge structures by applying Monkhorst-Pack sampling with a 6 × 6 × 6 k-point grid and then constructed a Ge/Si CSNW supercell with the resulting lattice constant. The axial lattice constants of CSNWs are reoptimized for each directional nanowires because the optimum lattice constants are severely influenced by the composition and growth direction. The atomic positions are relaxed until residual forces are less than 0.02 eV/Å. We begin by addressing the fact that type-I/II transition in Ge/Si CSNWs can be obtained for small nanowires induced by quantum confinement effect. [100], [110], and [111] directional hydrogen passivated CSNWs are analyzed, and the diameters are varied from 1 to 3 nm, which is the size limit of present DFT calculation for nanowires. Atomic structures of each directional nanowire are represented in Figure 2a−c, in
Figure 2. (a−c) Cross-sectional views of [100], [110], and [111] directional Ge/Si CSNWs, respectively. Yellow, pink, and white circles represent Ge, Si, and H atoms, respectively. (d−f) Electronic band structures (on the left figures), total DOS (blue lines on the right figures), and PDOS of Ge core atoms (red areas on the right figures) of [100], [110], and [111] directional CSNWs, respectively.
which the diameters of CSNWs are near 1.5 nm. The number of Ge/Si atoms in CSNWs with respect to the growth direction is 25/24 in [100] nanowires, 16/26 in [110] nanowires, and 38/36 in [111] nanowires, respectively. The resulting axial lengths of unit cells are 5.71 Å, 3.97 Å, and 9.83 Å, respectively. To determine whether the electron band structure of Ge/Si CSNW has the type-I or type-II band alignment along the radial direction of Ge/Si, quantitative criterion based on the projected density of states (PDOS) of Ge core atoms is used, which was successfully adopted in the previous studies.28,36 When the ratio of the PDOS of Ge core atoms to the total density of states (DOS) is larger than 0.75, we accept that the energy level originates from the Ge core. The electronic band structures, total DOS, and PDOS of Ge core atoms are shown in Figure 2d−f. When the electronic band structures of bulk Ge/Si superlattice are compared with those of [100] and [111] Ge/Si CSNWs, there is a major difference in the conduction band edge region. It can be observed that the DOSs near the CBM are mainly composed of Ge core atoms in the case of [100] and [111] CSNWs in contrast with the bulk Ge/Si case, which means that there is a transition in the band alignment from type-II to type-I. In our analysis, the conduction band edges of Ge core atoms for [100] and [111] CSNWs are lower by 0.33 and 0.25 eV than that of the Si shell, respectively. The calculation results show that the 122
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type-I transition of Ge/Si CSNWs can be achievable when [100] and [111] directional CSNWs are fabricated in nanometer scale. However, in the case of [110] CSNW, as shown in Figure 2e, the PDOS of Ge takes a relatively small fraction of the total DOS, and the type-II band alignment is preserved. Comparing the band structures represented in Figure 2, [100] and [111] directional CSNWs exhibit indirect band gap characteristics, but [110] CSNW shows a direct band gap feature. In our previous reports on the electronic band structures of Si nanowires (SiNWs),12 [100] and [110] SiNWs showed direct band gaps, and [111] SiNW exhibited an indirect band gap. The previous reports on the band structure changes of GeNWs showed that [110] GeNW has a direct band gap, while indirect band characteristics are found in the case of [100] and [111] GeNWs.37,38 Thus, it can be inferred that the indirect−direct band characteristics of Ge/Si CSNWs shown in Figure 2 follow those of GeNWs rather than SiNWs. Although the band gap underestimation of DFT calculation is a well-known issue, 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 nanocrystals and nanowires.12,39 We have also performed hybrid DFT calculations including Hartree−Fock exchange to confirm the reliability of our DFT calculations and were able to confirm that the change of band alignment can be successfully described by DFT calculations. Charge density profiles at CBM and VBM are plotted in Figure 3. For [100] and [111] CSNWs, Γ-point and X-point are selected to plot charge densities of VBM and CBM, respectively. For [110] CSNWs, Γ-point is used to obtain the charge density profiles for both CBM and VBM. Figure 3a−c shows the charge density profiles at VBM, which clearly present that the wave functions are strongly confined in Ge core atoms for all directional CSNWs. Large band mismatch in the valence band between Ge and Si and heavy hole mass help to preserve the valence band alignment similar to that of bulk interface even for the extremely small nanowires. For [100] and [111] CSNWs, charge densities at VBM and CBM mostly appears in Ge core atoms, which is the representative feature of type-I band alignment, whereas in the case of [110] CSNW, the charge density at CBM is located in Si shell atoms and the charge separation occurs between VBM and CBM. The dependences on the diameter and core−shell thickness ratio are studied by analyzing the electronic band structures of CSNWs having a diameter larger than 2 nm with one or two Si shell layers. Figure 4a−c shows the structure of Ge/Si CSNWs having only one Si shell layer, and Figure 4a′−c′ shows that for those with two Si shell layers. The PDOS and total DOS of 2 nm-sized CSNWs with one Si shell layer represent that the conduction band edges of [100] and [111] CSNWs mainly come from Ge core energy states, whereas [110] CSNW preserves the type-II band alignment as was the case for the small CSNWs shown in Figure 2. This trend can be more quantitatively represented by the ratio of Ge PDOS to total DOS shown in Figure 4d−f. The ratio shows that the CBM of Ge core atoms is lower by 0.5 eV than that of Si for [100] and [111] CSNWs. In the case of much larger CSNWs, a similar trend is observed. When we calculated the ratio for a [100] directional Ge/Si CSNW of which the effective diameter is 2.7 nm and the number of Ge/Si atoms is 121/48, the electronic band structure
Figure 3. Charge density profiles at (a−c) the VBM in red color and (d−f) the CBM in blue color for [100], [110], and [111] Ge/Si CSNWs.
still has an indirect band gap, and the energy level of CBM at the X-point is lower than that at the Γ-point by 0.14 eV. For [100] and [111] CSNWs having thicker Si shells shown in Figure 4a′−c′, the conduction band edges consist of an even mixture of Si and Ge wave functions. The electronic band structures of 2 nm-sized CSNWs are represented in Figure 5 with respect to the thickness of Si shells. When there is only one Si shell layer, the electron band structures are very similar to those when the diameter is about 1.5 nm as shown in Figure 2. [100] and [111] directional CSNWs exhibit indirect band gap characteristics and [110] CSNW shows a direct band gap feature. However, when the Si shell layer becomes thicker by one more layer, even [100] and [111] directional CSNWs change into the direct band gap nanowires. Considering the charge density characteristics of CSNWs in Figure 3, it can be deduced that the appearance of a CBM at the X-point originates from the energy states of Ge atoms, while the CBM at the Γ-point is composed of mixed states of Ge and Si atoms. Thus, the change in electronic band structures from the indirect band gap into the direct band gap results in the type-II band alignment from the type-I band alignment. On the structural aspects, the main difference between CSNWs with one Si shell layer and those with two Si shell layers is the lattice constant in the growth direction. Adding one more Si shell layer induces the decrease of axial lattice constant by about 1.9%, 1.6%, and 1.7% for [100], [110], and [111] CSNWs, respectively. The lattice strain in Ge/Si CSNWs is inevitable due to the difference in lattice constants. As a result, the Ge core is under compressive strain, while the Si shell is under tensile strain. The addition of more Si layers 123
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Figure 4. Atomic and electronic band structures of Ge/Si CSNWs having a diameter larger than 2 nm with one or two Si shell layers. (a− c) Cross-sectional views of [100], [110], and [111] Ge/Si CSNWs with one Si shell layer. The number of Ge/Si atoms is 49/32, 42/38, and 74/48, respectively. (a′−c′) Cross-sectional views of [100], [110], and [111] Ge/Si CSNWs with two Si shell layers. The number of Ge/ Si atoms is 25/56, 16/64, and 38/84, respectively. (d−f) PDOS of Ge core atoms shown as red areas and total DOS in blue lines of [100], [110], and [111] Ge/Si CSNWs with one Si shell layer. The ratios of PDOS of Ge core atoms to total DOS are plotted, and values can be read in the right y axis.
Figure 5. The electronic band structures of 2 nm sized Ge/Si CSNWs. The upper figures represent those of CSNWs with only one Si shell layer in the direction of (a) [100], (b) [110], and (c) [111], in which the number of Ge/Si atoms is 49/32, 42/38, 74/48, respectively. The lower figures represent those of CSNWs with two Si shell layers in the direction of (a′) [100], (b′) [110], and (c′) [111], in which the number of Ge/Si atoms is 25/56, 16/64, 38/84, respectively.
not linearly changed with Si/Ge composition change.41,42 They obtained band gap transitions of CSNWs according to the composition x = NGe /(NGe + NSi) by changing numbers of core and shell atoms in the unit cell for various sizes and band gap minima appears at x ∼ 0.2−0.5. As Ge core compositions change from 0.61/0.53/0.60 to 0.31/0.2/0.31 for [100], [110], and [111] CSNWs, respectively, band gaps do not increase for thicker Si shell CSNWs. The impact of Si shell layers on the axial lattice constant can be reduced by increasing the number of Ge core atoms. In the case of larger [100] CSNWs with an effective diameter of 2.7 nm and the number of Ge/Si = 81/88, the energy level of CBM at the X-point is almost the same as that at the Γ-point. Also, the wave function mixing becomes relatively stronger, and the ratio of Ge PDOS to total DOS is somewhat below our criterion of 0.75, but greater than 0.70. This suggests that the type-I band alignment can be achieved even for larger CSNWs with thicker Si shells by creating an indirect band gap through proper choice of band gap engineering. Adopting the direct-to-indirect band gap transition for a type-I/II band alignment transition could open a new possibility to modulate the band alignment. In previous work, we reported that the lattice strain engineering can be an efficient method to control the direct/indirect band gap for the SiNWs.12 Here, we will demonstrate that the strain engineering
results in the reduction of the tensile strain in the Si shell. As was previously reported, the change in strain in the nanowire naturally induces changes in band structure,12 resulting in a higher energy level of the X-band under tensile strain in Si nanowires. Under reduced tensile strain with an extra Si shell layer, the energy level of the X-band would be lower, making it unfavorable to form a type-I band alignment, which requires higher conduction band edge on the Si shell. In another previous report, the direct-to-indirect band gap transition in a Si-core/Ge-shell nanowire was successfully explained by considering the changes of intrinsic lattice strain in Si and Ge layers.40 It is necessary to note that the band gaps of thicker Si shell CSNWs (Figure 4a′−c′) are not bigger than those of thinner Si shell CSNWs (Figure 4a−c) even though Si concentration increases. The calculated band gaps change from 1.45/0.83/ 1.11 eV to 1.44/0.64/1.16 eV for [100], [110], and [111] CSNWs, respectively. As the band gap of Si is larger than Ge, one may expect that the increase of Si concentration makes larger band gap CSNWs and our results show the different trend to analysis based on bulk data. Previous calculation results of CSNWs already showed that the band gaps of CSNWs are 124
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can drive the type-I/II band alignment transition and generate the electron quantum well in Ge/Si CSNWs. Our results show that [100] and [111] Ge/Si CSNWs can have the type-I band alignment by shrinking their diameters due to the quantum confinement. In the case of [110] Ge/Si CSNWs, the type-II band alignment is strongly preserved even at diameters as small as 1 nm. The analysis of band structures and charge density profiles reveal that type-I/II transition in Ge/Si CSNWs is highly related to the direct/indirect band gap transition. Accordingly, we show that type-I/II transition can be manipulated by the lattice strain engineering. When a compressive strain is applied to a [110] directional CSNW, its band structure changes from the direct band gap into indirect band gap, which results in the type-I band alignment. We expect that this opens a new possibility to fabricate both n-type and p-type transistors with only Ge/Si CSNWs for highspeed logic applications.
on Ge/Si CSNWs can likewise induce the type-I/II band transition. As [110] directional CSNW does not show type-I/II transition due to a direct band gap character, we will try to generate type-I band alignment for [110] CSNWs by applying the lattice strain. In Figure 6a, the electronic band structure of a [110] directional CSNW is presented when compressive strain of 4%
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Dr. Sung-Hoon Lee (SAIT) for helpful discussions. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A1011302) and the research fund of Hanbat National University in 2012.
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