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Abstract
While the SrTiO3/LaAlO3 materials system has garnered intense research interest over the past decade owing to the discovery of a two-dimensional electron gas at the interface of these two band insulators, recent reports have focused on its optical properties. The silicon-compatibility of the SrTiO3/LaAlO3 system, together with its large conduction band offset and the ability to confine charge carriers in SrTiO3 quantum wells, makes it a potential candidate for use in a wide range of integrated photonics applications. Here, we present numerical simulations of the electrical, optical, and electro-optical performance of silicon-integrated SrTiO3/LaAlO3 electro-optical devices utilizing the quantum-confined Stark effect to electro-optically tune intersubband absorptions occurring at near-infrared optical wavelengths. We discuss optimal design parameters for the fabrication of experimentally realizable devices and attempt to minimize the energy consumption of a SrTiO3/LaAlO3 electro-optic modulator while maximizing performance. We predict modulation energies on the order of tens of pJ/bit for the proposed device. Our results indicate the feasibility of producing SrTiO3/LaAlO3-based integrated electro-optical devices using existing thin film growth and semiconductor processing techniques.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Transition metal oxide (TMO) thin films show immense promise for use in a multitude of applications owing to their widely tunable electronic, magnetic, structural and optical properties [1–3]. Much of the work on TMO thin films has focused on their use in oxide electronics [4], facilitated by the silicon-compatibility of many perovskite TMO thin films via an epitaxial SrTiO3 (STO) buffer layer [5,6]. Accordingly, TMO thin films have featured prominently in the search for new and improved dielectric gate materials for integrated electronics [7]. However, more complex device structures can also be envisioned for TMO thin film heterostructures owing to the plethora of emergent phenomena arising from strong electron correlation in these materials and the potential for band engineering [8,9].
One area in which TMO thin films are rapidly gaining prominence is integrated photonics. For decades, LiNbO3 (LNO) has been the workhorse material for electro-optic modulators in communications technologies owing to the presence of a robust linear electro-optic effect in LNO [10]. However, the integration of LNO with silicon substrates is not straightforward and the linear electro-optic coefficient of LNO is small relative to other Pockels-active materials. Accordingly, the fabrication of compact, integrated devices from LNO has been challenging, although progress has been made in this area [11–14]. Recently, the perovskite TMO BaTiO3 (BTO) has garnered significant research interest for integrated photonics applications owing to its dramatic Pockels response and its epitaxial compatibility with silicon substrates [15–21]. The existence of a direct epitaxial integration route for BTO significantly reduces the complexity of device fabrication relative to LNO-based integrated devices and is one of the fundamental advantages of perovskite TMO-based integrated photonics devices.
Among this class of silicon-compatible TMO thin film systems, the SrTiO3/LaAlO3 (STO/LAO) materials system has attracted special attention due to the discovery of a high-mobility two-dimensional electron gas at the interface of these two band insulators [22]. While a significant effort has been made to utilize the STO/LAO interface in oxide electronics [23–25], recent work has focused on the optical properties of the STO/LAO system arising from the large 2.4 eV conduction band offset and the resulting ability to confine charge carriers in STO quantum wells (QWs) [26–28]. In particular, the recent demonstration of room-temperature intersubband absorption in STO/LAO QW heterostructures at near-infrared wavelengths [28] suggests the potential for STO/LAO QW heterostructures to find use in a variety of integrated photonics devices, including light sources, detectors, and modulators.
Here, we simulate the performance of experimentally realizable STO/LAO electro-optical devices exploiting the quantum-confined Stark effect in intersubband absorption for electro-optic operation. We calculate the wave functions of confined electrons in STO QWs and determine the Stark shift for multiple QW geometries. We then consider a hybrid silicon-TMO waveguide design for the confinement of an optical mode and simulate the electrical, optical, and electro-optical performance of such a device. Calculated figures of merit include the extent of optical confinement in the electro-optically active TMO layer and the switching energy for modulator devices. Our results demonstrate the feasibility of utilizing the STO/LAO system for electro-optical devices integrated on silicon.
2. Methods
Electron wave functions in the STO QWs were calculated within the effective-mass approximation using a Poisson-Schrödinger solver. Optical absorption spectra were computed from the calculated wave functions according to the method detailed in [29].
Finite element simulations were conducted using COMSOL Multiphysics. The STO/LAO QW heterostructures were modeled as a single thin film of thickness tTMO with optical index of refraction and electrical permittivity given by the weighted average of the STO and LAO permittivities according to the relative thicknesses of the STO and LAO layers. We validated this approach for approximating the effective index of the QWs by comparing the results of our weighted average approach to the Maxwell Garnett approximation. We find agreement in the effective refractive indices calculated with the two methods to within 0.3%. Mode simulations were carried out utilizing the mode analysis method in the RF module of COMSOL. The perfect electrical conductor boundary condition was applied to the edges of the 2D simulation cell, a reasonable approximation given the tight confinement of the optical mode to the hybrid silicon-TMO waveguide. Electrical simulations were conducted using the AC/DC module with the charge conservation boundary condition applied to the boundaries of the 2D simulation cell.
3. Results and discussion
3.1 Quantum-confined Stark effect in STO/LAO QWs
Many electro-optical devices relying on intersubband transitions, including modulators [30,31], photodetectors [32], and lasers [33], have been studied using the GaAs/AlGaAs materials system. However, the small conduction band offset in this system limits the energy with which such intersubband transitions can occur to the mid- or far-infrared range. The large conduction band offset in the STO/LAO system, on the other hand, allows for operation at much shorter wavelengths, including those in the near-infrared utilized in communications technologies. Furthermore, the ease with which STO/LAO QW heterostructures can be integrated with silicon substrates via direct epitaxial deposition [34] supports the use of such devices in photonic integrated circuits. QW-based electro-optical devices may offer several advantages over traditional thermo-optic- and plasma-dispersion-based electro-optical devices, including reduced switching times due to the high-speed nature of the Stark effect and reduced power consumption owing to the fact that the Stark effect is purely electric field-driven and does not necessitate current flow.
The calculated electronic wave functions in an STO/LAO QW with a six-unit cell (u.c.) thick well layer (Fig. 1) show that the energy spacing between confined states can significantly exceed 1 eV and enter the near-infrared. The effect of an external electric field Eext on the wave functions can also be observed. As expected, the ground state wave function experiences the most significant change in energy ΔE1 ≈ 200 meV as a result of the quantum-confined Stark effect. The shift in energy of the confined states is also clearly seen in the near-infrared absorption spectra of the QW (Fig. 2). Notably, the ground state-to-third-excited state ($|{ 1 \rangle \to \; } |4 \rangle$) transition is predicted to occur near the common telecom wavelength of 1550 nm. It should be noted that we have considered the case where the QW is doped such as to only populate the ground state in the calculation of the absorption spectra in Fig. 2.
Fig. 1. Calculated wave functions in a six-u.c. STO QW without (solid lines) and with (dashed lines) an external electric field. The electric field is set to the large value of 5 × 108 V/m in order to more clearly observe the energy level shifts. The 0 of energy is set to the bottom of the STO conduction band. The energy level corresponding to each electronic wave function can be read from the intersection of the wave function with the vertical axes. An effective mass of m* = 1.02me is used for the calculations.
Fig. 2. Calculated near-infrared absorption spectra of a six-u.c. STO QW without (solid line) and with (dashed line) an external electric field. The electric field is set to the more realistic value of 1 × 108 V/m, corresponding to a bias of approximately 10 V across the QW superlattice (Fig. 4). The corresponding electron transitions are noted above the absorption peaks. Absorption values are reported for a single QW.
While a six-u.c. thick QW is predicted to produce intersubband transitions near 1550 nm, transitions near the other critical telecom wavelength of 1300 nm can likely also be realized by utilizing other QW geometries. For example, our calculations suggest a transition energy of approximately 1300 nm in a two-u.c. thick QW (Fig. 3(a)). Such a narrow well confines just two electronic states, leaving us with only the $|{ 1 \rangle \to } |2 \rangle $ transition. However, because the ground state wave function is pushed farther from the conduction band bottom as the well becomes narrower, the transition energy of the two-u.c. well experiences a smaller Stark shift than the six-u.c. well (Fig. 3(b)). As a result, the utility of such narrow structures in devices requiring electro-optic switching will be limited as the fields required for switching may become prohibitively large. In general, QW geometries with wider well layers will require smaller fields for Stark shifting, a point we discuss in more detail in Section 3.4 in relation to energy optimization.
Fig. 3. Calculated near-infrared absorption spectra of a two-u.c. STO QW without (solid line) and with (dashed line) an external electric field. The corresponding electron transition is noted next to the absorption peak. A large electric field of magnitude 5 × 108 V/m is needed here in order to sufficiently shift the absorption line owing to the very narrow well width (see main text). Absorption values are reported for a single QW. An effective mass of m* = 1.02me is used for the calculations. (b) Change of absorption wavelength Δλ of the $|1 \rangle $ $ \to |2 \rangle $ transition as a function of applied electric field for a six-u.c. QW (red squares) and a two-u.c. QW (blue circles).
It should be noted that there is some uncertainty in the predicted intersubband transition energies arising from uncertainty in the electron effective mass within the STO QW. The effective mass in STO can vary as a function of doping [35,36] and strain [37] and is also band-dependent [38]. However, our calculated values represent a good approximation to the expected intersubband transition energies as we have used an effective mass value in our calculations that is consistent with the latest theoretical and experimental results for strained, lightly-doped STO films [36].
3.2 Device concept
In order to utilize the near-infrared intersubband transitions in STO/LAO QWs in integrated electro-optical devices, any device concept must conform to a few design rules. Firstly, the device must allow an external electric field to be applied normal to the QW layers. Only components of the external electric field normal to the QW layers will alter the confining potential and lead to Stark shifts of intersubband transition energies. Secondly, the waveguide must support a transverse magnetic (TM) optical mode. Due to a polarization selection rule [29,39,40], intersubband transitions between confined states can only be induced by the component of the optical electric field that is normal to the plane of the QWs. Therefore, any devices hoping to make use of intersubband absorptions for operation, such as electro-optic modulators, switches, or photodetectors, require a TM optical mode.
Our proposed device structure (Fig. 4(a)) features an STO/LAO QW superlattice epitaxially integrated on lightly-doped silicon (Fig. 4(b)) to form a hybrid TMO-silicon waveguide. The lightly-doped silicon layer can then be used as an integrated bottom electrode, reducing the distance between the electrodes and thereby reducing the voltage required to realize a given electric field across the QWs. The resulting external electric field is normal to the QWs, allowing for the realization of quantum-confined Stark shifts. Furthermore, the hybrid TMO-silicon waveguide supports a TM mode (Fig. 5), allowing for the optical stimulation of intersubband transitions.
Fig. 4. (a) Proposed device structure for STO/LAO electro-optical devices. The lateral electrode spacing d and vertical electrode-to-waveguide distance S are indicated in the figure. Fabrication would begin from a silicon-on-insulator (SOI) wafer. The STO/LAO QW heterostructure would be epitaxially deposited on ion-implanted SOI and then etched to form the hybrid TMO-silicon waveguide shown. (b) Zoom-in of STO/LAO QW heterostructure integrated on silicon via an epitaxial STO buffer layer.
Fig. 5. Simulated fundamental TM mode in a hybrid TMO-silicon waveguide with waveguide width 1 µm, top silicon thickness 90 nm and TMO thickness 100 nm. The structure here corresponds to a zoom-in of that shown schematically in Fig. 4(a) (note the scale bars in the two figures). The direction of the optical electric field Eopt is given by the red arrow. Mode propagation occurs in the ± z direction (normal to the page). The color scale represents the z-component of the optical electric field. Green regions correspond to zero field, blue to negative field and red to positive field.
Although the proposed device structure requires several processing steps for fabrication, similar electro-optical devices have been successfully fabricated using cleaved LNO as the electro-optically active layer [11,12]. In our proposed device structure, STO/LAO QWs would form the electro-optically active layer. Such QW heterostructures can be grown via epitaxial deposition techniques such as molecular beam epitaxy [34,41], pulsed laser deposition [42], or atomic layer deposition [43]. Our proposed device would require additional processing steps from those summarized in [11] in order to etch the TMO layers and form the hybrid TMO-silicon waveguide depicted in Fig. 4(a). However, such a device should be experimentally realizable with focused processing efforts following the outline given by Chen et al. [11].
3.3 Electro-optic overlap and optical confinement
Two figures of merit are particularly important when evaluating the performance of an electro-optical device such as the one we have proposed: the electro-optic overlap integral ΓEO and the optical confinement in the electro-optically active TMO layer ΓTMO. The electro-optic overlap ΓEO is a normalized measure of the interaction between the optical mode confined in the waveguide and the external electric field and is defined as [44]
The TMO optical confinement ΓTMO is a normalized measure of the amount of the optical signal present in the electro-optically active TMO layer and is defined as
Both ΓEO and ΓTMO can be modified by changing the waveguide width wWG and the thickness of the top silicon layer tWG (Fig. 6). In general, there is a tradeoff between the two figures of merit, with ΓEO increasing and ΓTMO decreasing as the top silicon thickness is increased. This tradeoff can be easily explained by the changing mode shape associated with altering the waveguide dimensions. As the top silicon is made thicker, the optical mode is pulled more into the top silicon, decreasing ΓTMO. At the same time, the mode becomes more confined laterally due to the large index contrast between silicon and the surrounding materials, increasing the electro-optic overlap integral ΓEO. The lateral confinement of the mode also increases as the waveguide width decreases, resulting in the observed behavior of increasing ΓEO as wWG decreases for a given tWG. Our calculated values of ΓTMO are competitive with other TMO-based electro-optical devices (see, e.g., [21], reporting ΓTMO = 0.55 for devices utilizing the TM mode) while our calculated values of ΓEO are somewhat smaller (see, e.g., [45], reporting ΓEO between approximately 0.65 and 0.85). However, it should be noted that the exact values of ΓEO and ΓTMO are dependent on the specific device design one chooses, which may differ from that suggested in Fig. 4(a).
Fig. 6. (a) Electro-optic overlap integral ΓEO and (b) TMO optical confinement ΓTMO as a function of waveguide width wWG and top silicon thickness tWG for a hybrid TMO-silicon waveguide structure with total TMO thickness tTMO = 100 nm.
In addition to the waveguide dimensions, the thickness of the TMO heterostructure tTMO also impacts ΓTMO with thicker heterostructures resulting in increased optical confinement within the TMO layer (Fig. 7). In principle, the epitaxial deposition of STO/LAO QW heterostructures of arbitrary thickness should be possible [41], although the exploration of such structures on silicon substrates has only begun rather recently [34]. In any case, by controlling the waveguide dimensions and TMO thickness, one can control the device performance as characterized by the electro-optic overlap ΓEO and the TMO optical confinement ΓTMO.
Fig. 7. Simulated TMO optical confinement ΓTMO as a function of TMO thickness tTMO for a hybrid TMO-silicon waveguide with wWG = 1 µm and tWG = 90 nm.
3.4 Example application: electro-optic modulator
As a specific example of an electro-optical device exploiting the quantum-confined Stark effect in the STO/LAO system, we consider an electro-optic modulator utilizing the device geometry presented in Fig. 4(a). Such a modulator could operate in the near-infrared where the modulated signal is given by the electric field-induced change in optical absorption at a given wavelength, as calculated e.g. in Fig. 2 and Fig. 3(a). The quantum-confined Stark effect is an excellent mechanism for the construction of an electro-optic modulator due to the high-speed nature of the electric field-induced energy level shifts [46]. High-speed operation should therefore be possible in such a device.
The modulation energy E of an electro-optic modulator in units of J/bit is given by
where C is the device capacitance and VD is the drive voltage [47]. From Eq. (3), we can see that the energy consumption is most directly impacted by the electrode geometry insofar as the electrode geometry impacts the device capacitance and the needed drive voltage. For the device geometry in Fig. 4(a), VD is tied to the vertical waveguide-to-electrode distance S (see Fig. 4(a)), while C is related to both S and the lateral electrode-to-electrode spacing d. By appropriately tuning S and d, the modulation energy can be minimized (Fig. 8(a)). However, by bringing the electrodes closer to the waveguide, one may induce additional optical absorption Δβel due to the interaction between the optical mode and the metallic electrodes (Fig. 8(b)). In our simulations, the electrodes were assumed to be tungsten with optical index at 1550 nm wavelength given by nW = 2.23 + 4.83i [48].Fig. 8. (a) Calculated switching energy E of an STO/LAO electro-optic modulator as a function of lateral electrode-to-electrode spacing d and vertical waveguide-to-electrode distance S. Calculations assume a device length of 100 µm and an electric field of 1000 kV/cm across the STO/LAO layer for switching. (b) Calculated additional optical absorption due to the electrodes Δβel as a function of S for d = 0.45 µm (red circles) and d = 2.45 µm (blue squares).
The calculations in Fig. 8 suggest that the lateral electrode-to-electrode distance d should be made large when constructing an electro-optic modulator using the design shown in Fig. 4. A large value of d minimizes the capacitance between electrodes in the lateral direction, thereby reducing the switching energy. Furthermore, for S > 0.4 µm, a larger value of d corresponds to reduced optical absorption from the electrodes, while the optical absorption is dominated by the top electrode regardless of the lateral electrode spacing for S ≤ 0.4 µm.
While the exact values of switching energy are dependent on extrinsic factors, such as device length and electrode design, our calculations suggest switching energies on the order of pJ/bit are possible in the STO/LAO electro-optic modulators. This value is competitive with switching energies in some silicon Mach-Zehnder modulators [49,50], although recent reports of compact silicon ring modulators have reduced the switching energy considerably into the sub-fJ/bit range [51]. The switching energies in STO/LAO modulators are primarily impacted by the rather large electric fields needed to sufficiently modulate the optical absorption energy. By optimizing modulator design such that the voltage needed to reach the switching field can be reduced, the switching energy can be significantly reduced.
One consideration for switching energy minimization is the use of sufficiently wide QW layers. The ground-state Stark shift calculated from perturbation theory scales proportionally to the fourth power of the well width [29,52], indicating a significant reduction of the applied electric field magnitude needed to reach a given level of electro-optic modulation as the wells are made wider. Another possibility is the use of transparent electrodes, such as indium-tin-oxide [53], which can be integrated with the waveguides while inducing minimal additional optical losses, thereby reducing the vertical distance between electrodes.
The proposed STO/LAO electro-optic modulators also have the advantage that they could likely be fabricated with a relatively small device footprint. Lateral device sizes of approximately 3 µm should be possible, with the lateral electrode spacing and the waveguide width defining the critical feature sizes in the lateral direction. Additionally, only a single, straight waveguide is necessary for the operation of such a device. This contrasts with ring resonators or Mach-Zehnder interferometers in which the interference of optical signals between two or more waveguides is required, thereby increasing device footprint. The straight, narrow geometry of the proposed STO/LAO electro-optic modulators should therefore allow for dense device packing.
4. Summary and conclusions
In summary, we have presented calculations supporting the feasibility of producing integrated electro-optical devices operating at near-infrared optical wavelengths based on the STO/LAO materials system. Such devices achieve electro-optic operation by utilizing the quantum-confined Stark effect to modulate the energy of intersubband transitions in the STO conduction band and could be constructed using existing thin film growth and semiconductor processing techniques. As a specific example, we present calculations of the switching energy in an STO/LAO electro-optic modulator integrated on silicon. Such modulators have the potential for high-speed operation due to the short time scales needed for electronic energy level modulation by the quantum-confined Stark effect. Additionally, electro-optical devices based on the Stark effect can be engineered for low power operation because the Stark effect is electric field-driven and does not necessitate current flow for operation.
Our results suggest an interesting avenue of investigation for the discovery of new electro-optical devices capable of operating in the near-infrared spectral range by utilizing the quantum-confined Stark effect in TMO thin film QW heterostructutres. While work remains on the optimization of such devices before beginning fabrication, the silicon-compatibility of many TMO perovskites, combined with the opportunity for significant bang-engineering within this class of materials, indicates their likely utility in the design of future integrated electro-optical devices. The incorporation of TMO thin films and thin film heterostructures into electro-optical device architectures in order to take advantage of the multitude of emergent phenomena in such materials will likely open the door to a wide variety of next-generation electro-optical devices with advanced functionalities.
Funding
National Science Foundation (NSF) (DGE-1610403); Air Force Office of Scientific Research (AFOSR) (FA9550-12-10494, FA9550-18-1-0053).
Acknowledgments
The authors wish to thank Agham B. Posadas of the University of Texas at Austin for his careful review of the manuscript and thoughtful comments on the text as well as Matthew Butcher of Rice University for his contributions to the development of the Poisson-Schrödinger solver used in this work.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. C. H. Ahn, “Ferroelectricity at the Nanoscale: Local Polarization in Oxide Thin Films and Heterostructures,” Science 303(5657), 488–491 (2004). [CrossRef]
2. H. Y. Hwang, Y. Iwasa, M. Kawasaki, B. Keimer, N. Nagaosa, and Y. Tokura, “Emergent phenomena at oxide interfaces,” Nat. Mater. 11(2), 103–113 (2012). [CrossRef]
3. J. Chakhalian, J. W. Freeland, A. J. Millis, C. Panagopoulos, and J. M. Rondinelli, “Colloquium: Emergent properties in plane view: Strong correlations at oxide interfaces,” Rev. Mod. Phys. 86(4), 1189–1202 (2014). [CrossRef]
4. M. Lorenz, M. S. Ramachandra Rao, T. Venkatesan, E. Fortunato, P. Barquinha, R. Branquinho, D. Salgueiro, R. Martins, E. Carlos, A. Liu, F. K. Shan, M. Grundmann, H. Boschker, J. Mukherjee, M. Priyadarshini, N. DasGupta, D. J. Rogers, F. H. Teherani, E. V. Sandana, P. Bove, K. Rietwyk, A. Zaban, A. Veziridis, A. Weidenkaff, M. Muralidhar, M. Murakami, S. Abel, J. Fompeyrine, J. Zuniga-Perez, R. Ramesh, N. A. Spaldin, S. Ostanin, V. Borisov, I. Mertig, V. Lazenka, G. Srinivasan, W. Prellier, M. Uchida, M. Kawasaki, R. Pentcheva, P. Gegenwart, F. Miletto Granozio, J. Fontcuberta, and N. Pryds, “The 2016 oxide electronic materials and oxide interfaces roadmap,” J. Phys. D: Appl. Phys. 49(43), 433001 (2016). [CrossRef]
5. R. A. McKee, F. J. Walker, and M. F. Chisholm, “Crystalline Oxides on Silicon: The First Five Monolayers,” Phys. Rev. Lett. 81(14), 3014–3017 (1998). [CrossRef]
6. Z. Yu, J. Ramdani, J. A. Curless, J. M. Finder, C. D. Overgaard, R. Droopad, K. W. Eisenbeiser, J. A. Hallmark, W. J. Ooms, J. R. Conner, and V. S. Kaushik, “Epitaxial perovskite thin films grown on silicon by molecular beam epitaxy,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 18(3), 1653 (2000). [CrossRef]
7. J. Robertson, “High dielectric constant gate oxides for metal oxide Si transistors,” Rep. Prog. Phys. 69(2), 327–396 (2006). [CrossRef]
8. J. Robertson, “Band offsets of wide-band-gap oxides and implications for future electronic devices,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 18(3), 1785–1791 (2000). [CrossRef]
9. J. Robertson, K. Xiong, and S. J. Clark, “Band structure of functional oxides by screened exchange and the weighted density approximation,” Phys. Status Solidi B 243(9), 2054–2070 (2006). [CrossRef]
10. L. Arizmendi, “Photonic applications of lithium niobate crystals,” Phys. Status Solidi B 201(2), 253–283 (2004). [CrossRef]
11. L. Chen, M. G. Wood, and R. M. Reano, “12.5 pm/V hybrid silicon and lithium niobate optical microring resonator with integrated electrodes,” Opt. Express 21(22), 27003 (2013). [CrossRef]
12. L. Chen, Q. Xu, M. G. Wood, and R. M. Reano, “Hybrid silicon and lithium niobate electro-optical ring modulator,” Optica 1(2), 112 (2014). [CrossRef]
13. C. Wang, M. Zhang, B. Stern, M. Lipson, and M. Lončar, “Nanophotonic lithium niobate electro-optic modulators,” Opt. Express 26(2), 1547 (2018). [CrossRef]
14. C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature , 562, 101–104 (2018). [CrossRef]
15. S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013). [CrossRef]
16. C. Dubourdieu, J. Bruley, T. M. Arruda, A. Posadas, J. Jordan-Sweet, M. M. Frank, E. Cartier, D. J. Frank, S. V. Kalinin, A. A. Demkov, and V. Narayanan, “Switching of ferroelectric polarization in epitaxial BaTiO3 films on silicon without a conducting bottom electrode,” Nat. Nanotechnol. 8(10), 748–754 (2013). [CrossRef]
17. C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active Silicon Integrated Nanophotonics: Ferroelectric BaTiO3 Devices,” Nano Lett. 14(3), 1419–1425 (2014). [CrossRef]
18. S. Abel, T. Stoferle, C. Marchiori, D. Caimi, L. Czornomaz, M. Stuckelberger, M. Sousa, B. J. Offrein, and J. Fompeyrine, “A Hybrid Barium Titanate–Silicon Photonics Platform for Ultraefficient Electro-Optic Tuning,” J. Lightwave Technol. 34(8), 1688–1693 (2016). [CrossRef]
19. F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3–Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3(9), 1698–1703 (2016). [CrossRef]
20. F. Eltes, M. Kroh, D. Caimi, C. Mai, Y. Popoff, G. Winzer, D. Petousi, S. Lischke, J. E. Ortmann, L. Czornomaz, L. Zimmermann, J. Fompeyrine, and S. Abel, “A novel 25 Gbps electro-optic Pockels modulator integrated on an advanced Si photonic platform,” in 2017 IEEE International Electron Devices Meeting (IEDM) (IEEE, 2017), p. 24.5.1–24.5.4.
21. S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large Pockels effect in micro- and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019). [CrossRef]
22. A. Ohtomo and H. Y. Hwang, “A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface,” Nature 427(6973), 423–426 (2004). [CrossRef]
23. J. Park, D. Bogorin, C. Cen, D. Felker, Y. Zhang, C. Nelson, C. Bark, C. Folkman, X. Pan, M. Rzchowski, J. Levy, and C. Eom, “Creation of a two-dimensional electron gas at an oxide interface on silicon,” Nat. Commun. 1(1), 94 (2010). [CrossRef]
24. D. F. Bogorin, P. Irvin, C. Cen, and J. Levy, “LaAlO3/SrTiO3-based device concepts,” in Multifunctional Oxide Heterostructures (Oxford University Press, 2010), pp. 364–388.
25. L. Bjaalie, B. Himmetoglu, L. Weston, A. Janotti, and C. G. Van de Walle, “Oxide interfaces for novel electronic applications,” New J. Phys. 16(2), 025005 (2014). [CrossRef]
26. C. Lin, A. Posadas, M. Choi, and A. A. Demkov, “Optical properties of transition metal oxide quantum wells,” J. Appl. Phys. 117(3), 034304 (2015). [CrossRef]
27. M. Choi, C. Lin, M. Butcher, C. Rodriguez, Q. He, A. B. Posadas, A. Y. Borisevich, S. Zollner, and A. A. Demkov, “Quantum confinement in transition metal oxide quantum wells,” Appl. Phys. Lett. 106(19), 192902 (2015). [CrossRef]
28. J. E. Ortmann, N. Nookala, Q. He, L. Gao, C. Lin, A. B. Posadas, A. Y. Borisevich, M. A. Belkin, and A. A. Demkov, “Quantum Confinement in Oxide Heterostructures: Room-Temperature Intersubband Absorption in SrTiO3/LaAlO3 Multiple Quantum Wells,” ACS Nano 12(8), 7682–7689 (2018). [CrossRef]
29. M. Helm, “Chapter 1 The Basic Physics of Intersubband Transitions,” Semicond. Semimetals 62, 1–99 (1999). [CrossRef]
30. D. A. Holm and H. F. Taylor, “Infrared phase modulators with multiple quantum wells,” IEEE J. Quantum Electron. 25(11), 2266–2271 (1989). [CrossRef]
31. E. B. Dupont, D. Delacourt, and M. Papuchon, “Mid-infrared phase modulation via Stark effect on intersubband transitions in GaAs/GaAlAs quantum wells,” IEEE J. Quantum Electron. 29(8), 2313–2318 (1993). [CrossRef]
32. B. F. Levine, “Quantum-well infrared photodetectors,” J. Appl. Phys. 74(8), R1–R81 (1993). [CrossRef]
33. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science 264(5158), 553–556 (1994). [CrossRef]
34. J. E. Ortmann, S. Kwon, A. B. Posadas, M. J. Kim, and A. A. Demkov, “Monolithic integration of transition metal oxide multiple quantum wells on silicon (001),” J. Appl. Phys. 125(15), 155302 (2019). [CrossRef]
35. W. Wunderlich, H. Ohta, and K. Koumoto, “Enhanced effective mass in doped SrTiO3 and related perovskites,” Phys. B 404(16), 2202–2212 (2009). [CrossRef]
36. M. Choi, A. B. Posadas, C. A. Rodriguez, A. O’Hara, H. Seinige, A. J. Kellock, M. M. Frank, M. Tsoi, S. Zollner, V. Narayanan, and A. A. Demkov, “Structural, optical, and electrical properties of strained La-doped SrTiO3 films,” J. Appl. Phys. 116(4), 043705 (2014). [CrossRef]
37. A. Janotti, D. Steiauf, and C. G. Van de Walle, “Strain effects on the electronic structure of SrTiO3: Toward high electron mobilities,” Phys. Rev. B 84(20), 201304 (2011). [CrossRef]
38. A. F. Santander-Syro, O. Copie, T. Kondo, F. Fortuna, S. Pailhès, R. Weht, X. G. Qiu, F. Bertran, A. Nicolaou, A. Taleb-Ibrahimi, P. Le Fèvre, G. Herranz, M. Bibes, N. Reyren, Y. Apertet, P. Lecoeur, A. Barthélémy, and M. J. Rozenberg, “Two-dimensional electron gas with universal subbands at the surface of SrTiO3,” Nature 469(7329), 189–193 (2011). [CrossRef]
39. D. D. Coon and R. P. G. Karunasiri, “New mode of IR detection using quantum wells,” Appl. Phys. Lett. 45(6), 649–651 (1984). [CrossRef]
40. H. C. Liu, M. Buchanan, and Z. R. Wasilewski, “How good is the polarization selection rule for intersubband transitions?” Appl. Phys. Lett. 72(14), 1682–1684 (1998). [CrossRef]
41. J. E. Ortmann, A. B. Posadas, and A. A. Demkov, “The MBE growth of arbitrarily thick SrTiO3/LaAlO3 quantum well heterostructures for use in next-generation optoelectronic devices,” J. Appl. Phys. 124(1), 015301 (2018). [CrossRef]
42. N. Nakagawa, H. Y. Hwang, and D. A. Muller, “Why some interfaces cannot be sharp,” Nat. Mater. 5(3), 204–209 (2006). [CrossRef]
43. M. D. McDaniel, T. Q. Ngo, S. Hu, A. Posadas, A. A. Demkov, and J. G. Ekerdt, “Atomic layer deposition of perovskite oxides and their epitaxial integration with Si, Ge, and other semiconductors,” Appl. Phys. Rev. 2(4), 041301 (2015). [CrossRef]
44. C. M. Kim and R. V. Ramaswamy, “Overlap integral factors in integrated optic modulators and switches,” J. Lightwave Technol. 7(7), 1063–1070 (1989). [CrossRef]
45. M. Luo and D. Sun, “Ultra-efficient modulation of BaTiO3 crystal thin film waveguide with a two-dimensional optic-electric field matching scheme,” J. Appl. Phys. 123(3), 034503 (2018). [CrossRef]
46. D. S. Chemla, T. C. Damen, D. A. B. Miller, A. C. Gossard, and W. Wiegmann, “Electroabsorption by Stark effect on room-temperature excitons in GaAs/GaAlAs multiple quantum well structures,” Appl. Phys. Lett. 42(10), 864–866 (1983). [CrossRef]
47. D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express 20(S2), A293 (2012). [CrossRef]
48. M. A. Ordal, R. J. Bell, R. W. Alexander, L. A. Newquist, and M. R. Querry, “Optical properties of Al, Fe, Ti, Ta, W, and Mo at submillimeter wavelengths,” Appl. Opt. 27(6), 1203–1209 (1988). [CrossRef]
49. L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. D. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129 (2005). [CrossRef]
50. W. M. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15(25), 17106 (2007). [CrossRef]
51. E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. Shah Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5(1), 4008 (2014). [CrossRef]
52. G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Variational calculations on a quantum well in an electric field,” Phys. Rev. B 28(6), 3241–3245 (1983). [CrossRef]
53. Z. Ma, Z. Li, K. Liu, C. Ye, and V. J. Sorger, “Indium-Tin-Oxide for High-performance Electro-optic Modulation,” Nanophotonics 4(1), 198–213 (2015). [CrossRef]
