Abstract
We fabricated a threedimensional (3D) stacked Si nanodisk (SiND) array with a high aspect ratio and uniform size by using our advanced topdown technology consisting of biotemplate and neutral beam etching processes. We found from conductive atomic microscope measurements that conductivity became higher as the arrangement was changed from a single SiND to twodimensional (2D) and 3D arrays with the same matrix of SiC, i.e., the coupling of wave functions was changed. Moreover, our theoretical calculations suggested that the formation of minibands enhanced tunneling current, which well supported our experimental results. Further analysis indicated that four or more SiNDs basically maximized the advantage of minibands in our structure. However, it appeared that differences in miniband widths between 2D and 3D SiND arrays did not affect the enhancement of the optical absorption coefficient. Hence, high photocurrent could be observed in our SiND array with high photoabsorption and carrier conductivity due to the formation of 3D minibands.
Keywords:
Si nanodisk; Aspect ratio; Photocurrent; MinibandBackground
Quantum dot superlattices (QDSLs) have attracted a great deal of interest from both physical scientists and device researchers. Electron wave functions diffuse and overlap, which merge discrete quantum levels into minibands, with quantum dots approaching and forming a quasicrystal structure. This band rearrangement has significant applications for many novel optoelectronic/electronic devices [115]. For example, quantum dot solar cells, the most exciting photovoltaic device with more than 63% conversion efficiency, have to utilize minibands for carrier transport and additional optical transitions.
Ideal QDSLs present a great challenge to current nanotechnologies. Several technologies (e.g., chemical solution methods and molecular beam epitaxy (MBE)) have convincingly been used to fabricate relatively uniform quantum dots; however, very few technologies can finitely arrange QDs to form a quasicrystal structure. The welldeveloped MBE technology can only achieve very limited control on the direction of growth, which induces a mixed state with the wetting layer. The most direct idea is to develop a topdown nanotechnology. However, nanometerorder sizes exceed most light/electron beam limitations, and suitable masks seem impossible to create. The neutral beam (NB) etching and ferritin biotemplate we developed have recently brought about a great breakthrough in that we successfully fabricated twodimensional (2D) array Si nanodisks (SiNDs) with sub10 nm, high density (>10^{11} cm^{2}), and quasihexagonal crystallization [1620].
Photovoltaic conversion efficiency was determined by light absorbance and carrier collection efficiency. Our previous work has proven that wave function coupling relaxes the selection rule to induce additional optical transitions [21,22]. We first observed enhanced conductivity in 2D and threedimensional (3D) array SiNDs with a SiC matrix in this study. Moreover, we calculated electronic structures and current transport, which theoretically suggested that minibands enhanced conductivity, within envelope function theory and the Anderson Hamiltonian method. These enhanced optical and electrical properties indicated a potential application for the highly efficient quantum dot solar cells.
Methods
The fabrication of the 3D SiND array was based on biotemplate and NB processes. Figure 1 schematically illustrates the fabrication flow, which started with (Figure 1a) a 2nmthick SiC film and 4nmthick polySi being deposited alternately four times on the ndoped Si substrate using a highvacuum sputtering system and electron beam evaporation. Then a 3nmthick SiO_{2} layer was fabricated as a surface oxide (called NBOSiO_{2} after this) by the NB oxidation process we developed at a low temperature of 300°C [16]. Figure 1b has a 2D array of biotemplate molecules (ListeriaDps) that was deposited on the surface of the NBOSiO_{2}. Figure 1c shows the biotemplate protein shell that was removed by annealing it in an oxygen atmosphere to obtain a 2D array of iron cores as a uniform mask for the etching process. Figure 1d shows the etching process that was carried out with nitrogen trifluoride gas/hydrogen radical treatment (NF_{3} treatment) to remove the surface SiO_{2}, which was carried out with NB etching to remove the polySi. Here we performed a onestep etching and found a wellaligned vertical etching profile due to high etching selectivity between the iron cores and etched material and the low selectivity of 1.3 between Si and SiC. The etching process has been detailed elsewhere [1719]. Figure 1e shows that the iron cores were then removed by HCl wet cleaning, and then the remaining surface SiO_{2} was removed by NF_{3} treatment. Figure 1f shows that the SiC was deposited between pillars, which were stacked SiNDs, by the sputtering system. The diameter, space between NDs, and average ND centertoND center distance corresponded to 6.4, 2.3, and 8.7 nm in the structure. The size distribution of the SiNDs was less than 10% for all samples [19,21]. We prepared three types of SiND arrangements, as seen in Figure 2: separated SiNDs as a single QD, a 2D array of SiNDs as a 2D QDSL, and a 3D array of SiNDs as a 3D QDSL. The electrical conductivity and optical absorption in QDSLs were methodically, experimentally, and theoretically investigated with these samples to study the effect of wave function coupling between QDs.
Figure 1. Schematic of the fabrication flow for 3D array of SiNDs with SiC interlayer. (a) Deposition of 2nmthick SiC, 4nmthick polySi, and 3nmthick SiO_{2} layers. (b) Arrangement of 2D array of biotemplate molecules on the surface. (c) Removal of biotemplate protein shell by annealing in oxygen atmosphere. (d) NF_{3 }treatment to remove surface SiO_{2 }and NB etching to remove surface multilayers of polySi and SiC. (e) Removal of iron cores with HCl and NF_{3} treatment to etch remaining surface SiO_{2}. (f) SiC deposition on SiNDs.
Figure 2. Schematics of the three types of SiND arrangements. (a) Separated SiNDs as single QD, (b) 2D array of SiNDs as 2D QDSL, and (c) 3D array of SiNDs as 3D QDSL.
Results and discussion
Conductive atomic force microscopy (cAFM) has been used to investigate conductivity, as seen in Figure 3. Changing the matrix from SiO_{2} to SiC greatly increases current (I) and decreases threshold voltage (V), according to comparisons of the 2D arrays of SiNDs. Although a primary factor should be macroconductivity differences between SiC and SiO_{2}, one cause is minibands that enhance conductivity, which was revealed in a later theoretical simulation. More significantly, conductivity became higher as the arrangement was changed from a single SiND to 2D and 3D arrays with the same matrix of SiC, i.e., the coupling of wave functions was changed. Note that conductivity in the 3D array was higher than that in the 2D array, even though the total thickness of the QDSL expanded. These results indicate that the formation of minibands both inplane and outofplane (vertically) might enhance carrier conductivity in QDSLs.
Figure 3. IV curves of single SiND, 2D, and 3D arrays of SiNDs measured by cAFM. Red, blue, and green lines plot results for the 3D array, 2D array, and single SiND with SiC matrix. Black line plots the results for 2D array SiNDs with SiO_{2 }matrix.
We considered resonant tunneling to be a theoretical mechanism that could explain our experimental results on the basis of these results. Therefore, we theoretically investigated enhanced conductivity due to the formation of minibands. Our developed topdown nanotechnology achieved great flexibility in designing parts for the quantum structure, such as the independently controllable diameter and thickness, high aspect ratio, and different matrix materials. The finite element method duly described the complex quantum structures. The electronic structure and wave function within envelope function theory are presented as.
Here we mainly took into consideration the matrix material, realistic geometry structure, and number of stacking layers. The results are presented in Figure 4. A distinct feature is that electron wave functions are more strongly confined in the SiNDs in the SiO_{2} matrix due to the higher band offset of the Si/SiO_{2} interface. Thus, they resulted in higher quantum levels. In addition, stronger confinement means weaker coupling of the wave function and narrower minibands in the same geometry alignment. By stacking our NDs from one layer to ten layers, the miniband in Figure 5 gradually broadens, and at around four to six layers, the miniband width seems to saturate. The probability of the wave function diffusing into the barrier exponentially reduces with distance, which indicates that wave function coupling exponentially saturates as the number of layers increases. Perhaps four or sixlayer NDs are sufficient to maximize the advantage of minibands.
Figure 4. Calculated results for electron spatial possibilities. In three lateral coupled NDs and miniband width in 2D array of SiNDs. Square wave functions and quantum levels of coupled NDs with (a) SiC matrix and (b) SiO_{2 }matrix.
Figure 5. Calculated results for miniband width in 3D array of SiNDs. Thickness, diameter, and space between NDs were assumed to correspond to 4.0, 6.4 and 2.0 nm.
Chang et al. [23] considered interdot coupling with the Anderson Hamiltonian model to deduce tunneling current density as
Here E(k_{xy}) is related to the energy discrepancy, t, due to inplane ND coupling E(k_{xy}) = 2t[cos(k_{x}R) + cos(k_{y}R)]. We simulated the IV properties of our structures with this. The results are in Figure 6. The calculated results also revealed that the wider minibands in the SiC matrix resulted in better transport properties than those in the SiO_{2} matrix. A simplified, but not too obscure, explanation is that the formation of minibands broadens the resonance levels to increase jointstate density. Carrier transport in this twobarrier structure mainly depends on resonant tunneling. Moreover, if the Coulomb blockade effect is neglected, the tunneling jointstate density in Equation 2 can be simplified as a parabola function with a resonant peak at ~E_{0}– E(k_{xy}). The formation of minibands broadens the resonant peak to allow more states to approach maximum, which results in enhanced current. Thus, wider minibands mean a higher current density and lower threshold voltage, as can be seen in the SiNDs in the SiC matrix. In addition, the 2D array of SiNDs in the SiC matrix has a lower miniband level, E_{0}, which also shifts the IV curves to a lower threshold voltage. This tendency closely matches that in our experimental results, and due to the larger tunneling resistance in the SiO_{2} interlayer (C_{t}), the threshold voltage (V) is further increased in realistic IV curves. Moreover, conductivity in the 2D and 3D arrays of SiNDs was enhanced due to the same mechanism that broadened the wave functions and formed wider minibands. As these were also very consistent with the trend in our experimental results, they clarified that the formation of minibands both inplane and outofplane could enhance carrier transport in QDSLs. Enhanced conductivity is very important for electronic/optoelectronic devices, which indicates high charge injection efficiency in lasers and carrier collection efficiency in solar cells.
Figure 6. Simulation results for IV properties of our sample structures. Red, blue, and green lines plot calculated results for 3D array, 2D array, and single SiND with SiC matrix. Black line plots results for 2D array SiNDs with SiO_{2 }matrix.
Optical absorption was then investigated by measuring the transmittance of samples using ultravioletvisiblenearinfrared spectroscopy. Our previous work demonstrated that the formation of minibands perpendicular to incident light could enhance photon absorption, i.e., 2D minibands could improve the absorption coefficient in the 2D array of SiNDs [21,22]. Therefore, we investigated what effect 3D minibands had on optical absorption in this study. Figure 7 shows the absorption coefficients in the 2D and 3D SiND array samples prepared on transparent quartz substrates. The absorption coefficient in the 3D array was almost the same as that in the 2D array, and the calculated bandgap energy of both samples was 2.2 eV. Moreover, the change in the miniband width between the samples should be 3.85 meV, as shown in Figure 5 (0.95 meV in single layer and 4.80 meV in four layers). Therefore, it seems that the change of 3.85 meV in the miniband width is not sufficiently large to affect photon absorption.
Figure 7. Absorption coefficients of 2D and 3D arrays of SiNDs with SiC matrix. Blue and red lines correspond to 2D and 3D arrays of SiNDs.
Finally, we fabricated a p^{++}in Si solar cell with a 3D array of SiNDs as an absorption layer, as shown in Figure 8, and measured the amount of possible photocurrent generated from the SiND layers where the high doping density (>10^{20} cm^{3}) of the p^{++}Si substrate prevented photocurrent from being generated inside the substrate itself. Here we found that the generated shortcircuit current density from the p^{++}in solar cell was 2 mA/cm^{2}, where the largest possible photocurrent generated in the SiND layers and nSi emitter was estimated to be 3.5 mA/cm^{2} for the former and 1.0 mA/cm^{2} for the latter [22]. Since 1 mA/cm^{2} is the highest possible value for photocurrent from the nSi emitter according to this estimate, the actual value should be lower than the calculated value. Therefore, we found that out of the total photocurrent of 2 mA/cm^{2}, much more of it (>1 mA/cm^{2}) was contributed to by SiND. This confirms that most of the observed photocurrent originated from the carrier generated at the SiND itself because of high photoabsorption and carrier conductivity due to the formation of 3D minibands in our SiND array.
Figure 8. IV characteristics of p^{++}in solar cell. Currentvoltage characteristics in dark (blue line) and under sunlight (red line).
Conclusions
We developed an advanced topdown technology to fabricate a stacked SiND array that had a high aspect ratio and was of uniform size. We found from cAFM measurements that conductivity increased as the arrangement was changed from a single SiND to 2D and 3D arrays with the same matrix of SiC. This enhancement was most likely due to the formation of minibands, as suggested by our theoretical calculations. Moreover, the change in outofplane minibands did not affect the absorption coefficient. This enhanced transport should work in the collection efficiency of high carriers in solar cells.
Abbreviations
cAFM: Conductive atomic force microscopy; IV: Currentvoltage; MBE: Molecular beam epitaxy; ND: Nanodisk; QDSL: Quantum dot superlattices.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
MI and SS conceived and designed the experiment, fabricated the silicon nanodisk samples, performed electrical and optical measurements, analyzed these data, and wrote the paper. MMR and NU fabricated the solar cell structures and analyzed the IV data. WH performed the theoretical calculations. All authors discussed the results, commented on the manuscript, and read and approved the final version.
Acknowledgements
This work is supported by the Japan Science and Technology Agency (JST CREST) and the GrantinAid for Japan Society for the Promotion of Science (JSPS) Fellows.
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