Quantum Confinement in Oxide Heterostructures:

Quantum Confinement in Oxide Heterostructures: Room-Temperature Intersubband Absorption in SrTiO 3 /LaAlO 3 Multiple Quantum Wells John Elliott Ortmann 1, Nishant Nookala 2,3, Qian He 4, Lingyuan Gao 1, Chungwei Lin 1,5, Agham Posadas 1, Albina Y. Borisevich 4, Mikhail A. Belkin 2,3, and Alexander A. Demkov 1 * * demkov@physics.utexas.edu 1

1 Department of Physics, The University of Texas, Austin, TX 78712, USA 2 Department of Electrical and Computer Engineering, The University of Texas, Austin 78712, TX, USA 3 Microelectronics Research Center, The University of Texas at Austin, Austin, TX 78758, USA 4 The Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 5 Mitsubishi Electric Research Laboratories, Cambridge, MA 02139, USA Supporting Information Section 1: Sample Design and Quantum Confinement A generalized sample schematic is presented in Figure S1. Here, we also show the conduction band alignment, where the zero-point energy is set as the bottom of the conduction band in the STO well layers (shaded blue) and an example scanning transmission electron microscopy (STEM) image of a SrTiO 3 /LaAlO 3 (STO/LAO) heterostructure. The electronic 2

wavefunctions of states confined within the STO conduction band, as calculated using a Poisson- Schrödinger solver, are also shown in the band alignment schematic. Note that, in analogy with traditional GaAs/Ga 1-x Al x As quantum well (QW) heterostructures, the confining potential is a result of the band offset between the two constituent materials (in this case, STO and LAO). Therefore, in contrast with previous reports of subband formation in STO/LAO heterostructures 1,2 and at the STO/vacuum interface, 3 the separation of confined levels is, to a good approximation, independent of temperature, doping and dielectric constant. Figure S1. Sample schematic, band alignment, and example STEM image. The central portion of the figure shows a generalized sample schematic, showing the LAO substrate, the 1%La-doped STO well layers and the LAO barrier layers. Typical well widths are between three and six unit cells (u.c.) while the barriers are kept constant at seven u.c. The left side of the figure shows the conduction band alignment between STO and LAO as well as the confined states, as computed using a Poisson-Schrödinger solver. The right side of the figure shows an example STEM image of one of our heterostructures. Section 2: Structural Quality of Heterostructures In order to ensure the epitaxial quality of the samples remains high throughout the long growth process, we must ensure the surface of each layer is smooth, allowing for a clean growth template for deposition of subsequent atomic layers. We used in situ reflection high-energy electron diffraction (RHEED) to monitor the quality of the sample surface during growth. As presented below in Figure S2, our RHEED images confirm the presence of a high-quality surface at various stages of sample growth. The RHEED patterns stay consistent throughout the growth, 3

indicating that the quality of the sample surface is independent of the total sample thickness. This finding is qualitatively consistent with wide-view STEM images presented in Figure 1b in the main text, showing no systematic change in sample quality as a function of thickness. Figure S2. RHEED images of sample surface at various stages of sample growth. Images presented are after 5 total periods (a and b), 10 total periods (c and d), 15 total periods (e and f) and 40 total periods (g). Images (a), (c), (e), and (g) were taken along the <110> azimuth while images (b), (d), and (f) were taken along the <100> azimuth. After completion of sample growth, we measured the samples with x-ray diffraction (XRD) to further understand their structural quality. Figure S3 below shows out-of-plane XRD θ/2θ scans around the (002) LAO substrate peak for a four-u.c. well sample with composition [(La 0.01 Sr 0.99 TiO 3 ) 4 /(LaAlO 3 ) 7 ] 20, and for a six-u.c. well sample with composition [(La 0.01 Sr 0.99 TiO 3 ) 6 /(LaAlO 3 ) 7 ] 20. Both spectra have been aligned to the (002) LAO substrate peak. Superlattice peaks are clearly visible out to 4 th -order, in line with previous reports of shortperiod oxide heterostructures. 4,5 The fact that superlattice peaks are visible all the way out to 4 th - order indicates excellent crystalline quality, uniformity, and minimal interfacial roughness. Notably, changing the nominal well width by only two u.c. leads to a significant change in position of the corresponding superlattice peaks, with the peaks from the six-u.c. well sample being more closely spaced than those from the four-u.c. well sample. This observation is critical for the current study. As we are attempting to distinguish intersubband absorption in samples whose nominal well widths vary by only one to two u.c., it is crucial to ensure that the period width of the as-grown structures scales in agreement with the nominal sample design. Using Bragg s Law and averaging over adjacent superlattice peaks, we have calculated a period width of 40.57 ± 0.57 Å for the nominally 4-u.c. well sample and 51.28 ± 1.67 Å for the nominally 6- u.c. well sample, in very good agreement with the design values of 42.4 Å and 50.3 Å, respectively. As the LAO barrier width remains constant between samples, we can ascribe this change in period width to changes in the STO well width. Such changes in well width should 4

manifest themselves as shifts in the energy of observed intersubband absorption, as we verify in the main text. Figure S3. Out-of-plane X-ray diffraction measurements of heterostructures. Out-ofplane XRD θ/2θ scans around the (002) LAO substrate peak for a four-u.c. well sample (blue) and a six-u.c. well sample (red). Both samples have 20 total well/barrier periods. Section 3: Analysis of Interfaces In Figure 2b in the main text, we present a binary image of a QW heterostructure where unit cells containing Sr are represented by black pixels and those containing La are represented by white pixels. In order to generate this image, we first computed the integrated intensity for 5

every La or Sr cation column in the STEM image presented in Figure 2a. From there, we can create a map of the A-site (Sr and La) intensities where each pixel is one unit cell. The A-site intensities map is presented below in Figure S4. To convert this image into the binary image presented in Figure 2b, we must select an appropriate threshold between unit cells with Sr and those with La. The thresholding procedure is shown below in Figure S5. The distribution of A- column intensities from the intensity map in Supporting Figure S4 is well-described by a sum of two Lorentzian peaks. The threshold between La and Sr is defined as the intersection of the two Lorentzians; this threshold value is used to create the binary map in Figure 2b in the main text. This value corresponds to the smallest standard deviation in the average well depth computed from the binary map in Figure 2b. Figure S4. A-site intensity map. Map of A-site intensities (La and Sr) generated from the large-scale image in Figure 2a in the main text. 6

Figure S5. Determination of the threshold for Sr/La column differentiation. The distribution of A column intensities from the intensity map in Supporting Figure S4 (black line) is well described by a sum (red line) of two Lorentzian peaks (green lines). Threshold between La and Sr is defined as the intersection of the two Lorentzians. To validate this analysis approach, we have conducted a series of state-of-the-art STEM image simulations of the LAO/STO interface at different degrees of intermixing using the µstem software package published by the University of Melbourne. 6,7 This software takes full account of the elastic, inelastic, and thermal diffuse scattering effects to generate a STEM image for the accurate probe parameters and detector settings of our microscope. We used a sample thickness of 20 nm for all these calculations. The simulated images are shown below in Figure S6. 7

Sharp interface 90% - 10% intermixed interface 80% - 20% intermixed interface 60% - 40% intermixed interface 50%-50% intermixed interface Figure S6. Simulation of STEM images with different levels of cation intermixing. A series of STEM image simulations done using µstem software show the simulated LaAlO 3 /SrTiO 3 interface for different degrees of intermixing. Probe parameters and detector geometry were chosen to match those of Nion US200 used for the experiments. As one can immediately observe, the interface position can be unambiguously identified in all the simulated images. If we quantitatively analyze the intensities of the columns in the simulated images (Figure S7), in analogy with the analysis we present for the experimental samples in the main manuscript, we can see that column intensity follows column composition quite accurately under these conditions. This supports the notion that our analysis is a valid approach for quantification. Scatter in the intensities of columns with identical compositions is also apparent in Figure S7; this is due to the stochastic nature of the scattering process, which is reflected in the image simulations. The experimental spread for the intensities is expected to be wider, due to surface roughness effects that were not included in the simulations (compare Figure S7 to Figure S5). 8

Count 25 La 20 15 10 5 Sr columns La content: 100% 90% 80% 60% 50% 40% 20% 10% 0% columns 0 10000 12000 14000 16000 18000 20000 Intensity (a.u) Figure S7. Quantitative analysis of intensities in simulated STEM images. Intensity distribution of the atomic columns in the simulated STEM images in Figure S6 as a function of composition. The spread in the intensities of the columns is due to the stochastic nature of the electron scattering process. 9

Section 4: In-plane Transport Measurements of Heterostructures Although we dope the STO well layers with La (an n-type dopant in STO) by design, it is important to experimentally confirm the presence of sufficient charge in the STO wells before we can hope to optically stimulate intersubband transitions. To that end, we conducted roomtemperature Hall and magnetoresistance measurements, the results of which are presented below in Figure S8. From the slope of the Hall resistance vs field plot, we can calculate the volume carrier density according to =, where e is the fundamental electric charge and t is the total thickness of the conducting layers in the heterostructure (in this case, only the STO layers). Inserting the appropriate values into the above expression, we extract a charge density n = 3.5 x 10 20 cm -3, corresponding to approximately 2.2% doping. Thus, the wells are doped beyond their design value of 1%. In the present context, however, the presence of charge beyond the design value in the STO wells is not a detriment. Rather, it should ensure a more thorough filling of the ground-state subband. The presence of extra charge is also not surprising, as several additional n-type doping mechanisms exist in the STO/LAO system besides the intentional La doping. For example, oxygen vacancies are n-type dopants in STO and are often reported in the growth of STO films. 8 10 Both oxygen and air annealing have been found to significantly reduce the carrier concentration in STO/LAO heterostructures 8,11 14 via the removal of oxygen vacancies. Our samples were neither air nor oxygen annealed post-growth, as we would like to ensure the existence of sufficient charge in the STO conduction band for the sake of exciting intersubband transitions. DFT studies have also shown that the charge density from the interfacial 2DEG extends several unit cells into the STO layers. 1 In our superlattices, this effect would introduce additional charge into the Ti d xy orbitals, 15 18 leading the additional charge from oxygen vacancies and La doping to begin populating the QW subbands more quickly than would otherwise be the case if the charge from the 2DEG were not present. 10

Figure S8. Room-temperature in-plane transport data. Room-temperature Hall (a) and longitudinal (b) resistance measurements as a function of magnetic field for STO/LAO heterostructure with nominally 1% La-doped STO wells. Panel b in Figure S8 presents room-temperature magnetoresistance measurements, from which we can extract the electron mobility µ according to =, where n s = n*t is the 2D carrier density extracted from the Hall measurements. Using this, we extract a room-temperature mobility of 6.3 cm 2 V -1 s -1, in line with previous reports of roomtemperature mobility in STO 14,19 22 and further supporting our claim of high-quality samples. In fact, this value of mobility is remarkable given how thin the STO well layers are in our heterostructures (~ 2 nm). Indeed, most previous reports of mobility in doped STO studied films of thicknesses exceeding 100 nm. 20 22 Therefore, the role of interface scattering is significantly enhanced in our films as compared to previous reports. This should result in the reduction of electron mobility in our samples as compared to that measured in thick films. Despite this, we measure an excellent room-temperature mobility, owing to the high quality of our heterostructures. 11

Section 5: Optical Characterization of Heterostructures Before optical characterization, the QW samples are coated with approximately 2 nm of titanium followed by 100 nm of gold using e-beam evaporation. The titanium layer is used to increase the adhesion of the gold to the sample surface. The gold acts as a reflective coating, confining light within the sample and resulting in multiple bounces throughout the interior of the sample (see Figure S10). After gold deposition, the edges of the sample are polished at 45 to create two facets for light to enter and exit the sample. Two photographs of a sample which has been prepared for optical characterization are presented in Figure S9. The angled facets are more clearly visible in the photograph on the left. Figure S9. Prepared sample photographs. Photographs of a QW sample that has been prepared for optical characterization. A schematic of the setup used for optical characterization is presented below in Figure S10. Light emitted from a mid-infrared/near-infrared (MIR/NIR) Fourier-transform infrared (FTIR) spectroscopy source is focused onto one of the facets of the QW sample by a BaF 2 lens. The polarization is controlled by a ZnSe linear polarizer (LP) placed between the first BaF 2 lens and the sample. Upon entering the sample, the light is reflected multiple times from the gold coating, resulting in several light-qw interactions. After exiting the sample, the light is refocused onto an IR responsive liquid-nitrogen cooled mercury-cadmium-telluride (MCT) detector using a second BaF 2 lens. 12

Figure S10. Schematic of experimental setup used for optical characterization. Light travels from the FTIR source (left), through a lens and linear polarizer (LP) and into the transition metal oxide (TMO) multiple quantum well (MQW) sample, before being refocused by a second lens onto an MCT detector. 13

Section 6: Description of background correction for FTIR spectra. As described in the main text, two measurements were taken for each sample: one with TE-polarized incident light, and one with TM-polarized light, with the discrimination occurring via employment of a zinc-selenide (ZnSe) linear polarizer placed between the first lens and the sample. A schematic of the experimental setup is presented above in Figure S10. As only light with a component of polarization normal to the QW growth direction is absorbed by the QWs (in this case, TM light), we normalized the TM transmission spectrum by subtracting the TE I transmission as a background component and considering the quantity log TM I TE, where I TM is the transmission spectrum of TM-polarized light, and I TE is the transmission spectrum of TE-polarized light. Further, as the IR sources in our FTIR system and our external mercurycadmium-telluride (MCT) detector may possess properties that are polarization sensitive, we accounted for this contribution to the intersubband absorption spectra by taking background TE and TM transmission measurements of our setup without any sample loaded. We then subtracted ITM, bkgd the quantity log I from measurements taken with the samples loaded. The TE, bkgd resulting absorption spectra, plotted in Figure 3a in the main text, account for absorptions present exclusively in the TM spectra and exclude any polarization dependence of the experimental optics. 14

Section 7: Description of absorption coefficient calculations from FTIR spectra. In the main text, we plot the absorption spectra in Figure 3a in terms of the absorption coefficient, α, given in units of cm -1. To calculate the absorption coefficient from the raw FTIR spectra, we employ the following procedure. At the QW/metal interface, the total electric field in the z direction is given by, =, +, = 2, where E 0 is the magnitude of the incident electric field and φ is the angle of incidence relative to the plane of the QWs: 45 in this case. The geometry of the system is outlined in Figure S11 below. The period of the resulting standing wave is given by = 350 880, where n QW is the refractive index of the STO/LAO QWs and is approximately 2. Because the period of the standing wave is significantly longer than the thickness of the QW region, we can approximate the optical field across the QW region as relatively constant, resulting in an optical intensity of, 4 across the QWs (i.e., in the z direction). The resulting absorption coefficient α in units of inverse length is given by I where log TM I =, TE ln 10 log = / ln 10 log, is the experimental quantity, as described in the section above. The normalizing quantity, L int is given by =, cos, where t QW,total is the total interaction length between the optical field and the QW region. That is,, =, where n b is the total number of bounces and t QW is the thickness of the QW region. 15

Figure S11. Schematic of light-sample interactions. Light s path through the sample (not to scale), as indicated by the black arrows oriented at 45 to the z-axis. The MQW layer is represented by the orange shading while the reflective Ti and Au layers are represented by yellow shading on the top and bottom of the sample. 16

Section 8: Peak fitting for three u.c.-well sample In the inset of Figure 3a in the main text, the absorption peak from the three-u.c. sample is fit using a Bi-Gaussian function in order to determine the absorption energy. The fitting function is given by = +, < = +,, where the independent variable y is the absorption and the dependent variable x is the energy. The parameters y 0, H, x c, w 1, and w 2 represent the background, the height of the function, the center energy, and the standard deviations of peak 1 and 2, respectively. The fit parameters and standard errors calculated from fitting the three-u.c. sample are given in the table below. Parameter Value Standard Error y 0-139.29 cm -1 16.01 cm -1 x c 649.75 mev 4.61 mev H 300.02 cm -1 15.45 cm -1 w 1 247.08 mev 8.86 mev w 2 102.02 mev 8.01 mev Table S1. Fit parameters and values from fitting three-u.c. QW absorption peak. Here, we make use of a phenomenological fit in order to properly fit the observed asymmetric absorption peak. Similar fit functions have been employed before for the fitting of intersubband absorption spectra. 23,24 Furthermore, it has been noted experimentally that the absorption peaks of QW heterostructures with a large number of well/barrier periods are significantly broadened and asymmetrical in comparison to single-well samples. 25 As our samples typically contain on the order of 40 well/barrier periods, the observation of broad and asymmetrical absorption, especially in the three u.c. sample, is in line with this result. By calculating the reflected and transmitted optical fields in a self-consistent manner, theory has been able to reproduce the asymmetrical nature of many-period QW heterostructure absorption peaks. 26 17

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