Modulation Doping in Metastable Heterostructures via Kinetically

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Modulation Doping in Metastable Heterostructures via Kinetically Controlled Substitution Suzannah R Wood, Devin R. Merrill, Gavin Mitchson, Alexander C. Lygo, Sage R Bauers, Danielle M. Hamann, Duncan R. Sutherland, Jeffrey Ditto, and David C. Johnson Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b04688 • Publication Date (Web): 09 Dec 2016 Downloaded from http://pubs.acs.org on December 23, 2016

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Chemistry of Materials

Modulation Doping in Metastable Heterostructures via Kinetically Controlled Substitution Suzannah R. Wood, Devin R. Merrill, Gavin Mitchson, Alexander C. Lygo, Sage R. Bauers, Danielle M. Hamann, Duncan R. Sutherland, Jeffrey Ditto, David C. Johnson* Department of Chemistry, Materials Science Institute, University of Oregon, Eugene, Oregon 97403, United States ABSTRACT: Controlling carrier concentration is critical in many device applications and both chemical substitution and modulation doping have been used in industry. For most inorganic materials, very low doping efficiencies are observed as site occupancies depend on both thermodynamic and kinetic factors. We demonstrate that we can make kinetically controlled site-specific substitutions in a series of (BixSn1-xSe)1+δTiSe2 compounds using the modulated elemental reactants (MER) method. These compounds were characterized using a combination of X-ray diffraction, resistivity and Hall coefficient measurements, and high angle annular dark field scanning transmission electron microscopy (HAADF STEM). For small x, the doping efficiency is 0.7, close to that observed for B in silicon. For higher x values a structural distortion is observed in X-ray diffraction data in which the symmetry of the in-plane unit cell decreases. HAADF STEM data reveals the presence of antiphase boundaries (Bi-Bi pairs) in the BixSn1-xSe layers, which increasingly occur as x increases from 0.48 to 0.71. Electrical measurements show that doping efficiency decreases as x increases, correlated with the structural distortion and the formation of periodic antiphase boundaries containing Bi-Bi pairs.

Chemical substitution has often been used to control carrier concentration in semiconducting materials, yet these substitutions result in ionized impurity scattering and therefore a reduction in carrier mobility. Modulation doping, in which the substitution results in an inclusion or occurs within one constituent of a superlattice, can circumvent this scattering, resulting in improved mobility along semiconductor interfaces and control of carrier concentration due to charge injection from the nonconducting phase.1,2 This approach has been suggested as a means of improving the thermoelectric figure of merit (zT) by increasing the electrical conductivity in a material, and has been demonstrated in bulk composite materials3,4 and epitaxial superlattice structures.5,6 The resulting composite materials display increased power factors (S2σ), and have low thermal conductivities due to the presence of interfaces between phases, which effectively scatter heat-carrying phonons.

quence of the constituent layers is limited. Recently a method for preparing metastable variants of these compounds has been demonstrated. The method, known as modulated elemental reactants (MER), uses an amorphous layered precursor that, at relatively low annealing temperatures, nucleates and self-assembles into a targeted superstructure.13 Controlling the structure of the precursor enables the synthesis of a variety of layering schemes which are not accessible via standard synthesis approaches.14–16 Compounds synthesized via this route in the (PbSe)1+δ(TiSe2)n family with high n values have demonstrated promising S2σ values, suggesting the compounds in this family may be promising thermoelectric materials.17 Compounds synthesized using this technique are often referred to as ferecrystals due to the large extent of rotational disorder between the adjacent layers. This disorder is known as turbostratic disorder in the clay literature.

Misfit layer compounds are an interesting class of thermodynamically stable layered compounds which represent an extreme case of a layered composite structure on a sub-nanometer scale.7–9 Early reports of these compounds suggest that compounds based on TiX210 and NbX211 may be interesting for thermoelectric materials (X= S, Se, Te), with more recent work showing ZT values of 0.4 for the unoptimized (SnS)1.20(TiS2)2 compound.12 Challenges associated with standard high temperature synthesis methods makes optimization of these materials through controlled doping difficult, and the ability to design nanoarchitecture by varying the thickness or se-

Recently, a family of (PbxSn1-xSe)1+δTiSe2 compounds was synthesized, demonstrating that this low temperature synthesis approach is able to make kinetically controlled site-specific substitutions, with enhanced mobility found for alloy compositions.18 Here we report the synthesis and characterization of analogous (BixSn1-xSe)1+δTiSe2 compounds, which display systematic changes in carrier concentration and electrical properties as might be anticipated for the substitution of Bi for Sn. The structure of the BixSn1-xSe layer varies between the end members, which have two distinct MX structures, while the structure of the TiSe2 layers is unaffected by the substitution. Assum-

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ing a single rigid band model, the carrier concentration calculated from the Hall coefficient suggests that carriers can be added through the targeted substitution with minimal effect on mobility. However, the change in transport properties as a function of Bi content is not linear suggests the doping efficiency of Bi drops as x increases. Analysis of HAADF STEM images shows increased formation of Bi-Bi bonds as x increases, which reduces the extent of charge transfer and accounts for the observed reduction in doping efficiency. Experimental Precursor films were deposited using a custom-built physical vapor deposition system operating at pressures below 5 x 10-7 Torr. The sources are isolated from one another by a baffle system designed to simultaneously operate four sources, with the substrate sitting above a hole in the baffle architecture and exposed to a desired source via opening a shutter. The elemental layers were deposited in a Ti-Se-Bi-Sn-Se sequence using a PC-controlled LabVIEW program that controls the length of time each shutter is kept open, enabling the delivery of calibrated thicknesses of each element to the substrate. Se was deposited using an effusion cell, while Bi, Sn, and Ti were deposited using electron beam guns, at nominal rates of 0.1-0.3 Å/s maintained and monitored using quartz crystal microbalances. Films were deposited on Si for structural characterization and fused silica for electrical measurements. Fused silica substrates were masked during deposition to provide a cross geometry for the measurement. Annealing was conducted on a hot plate in a dry N2 environment ([O2,H2O] ≤ 0.8 ppm), at the specified temperatures for 30 minute duration. X-ray diffraction (XRD) experiments were conducting in both locked coupled and grazing incidence in-plane geometries using a Bruker D8 Discover and Rigaku SmartLab diffractometer, respectively (both using Cu Kα radiation). Electron microprobe analysis experiments (EPMA) were performed using a Cameca SX50, equipped with 4 spectrometers, using a method described elsewhere.19 Transport measurements were conducted under vacuum (10-6 Torr) using the van der Pauw method on a custom-built closed He cryostat system. Electrical contacts were made using pressed indium contacts. Hall Effect measurements were made with magnetic field varying from 0 to 16 kG.

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an FEI Helios 600 Ga+ focused ion beam. A procedure was employed similar to the Wedge Prep method described by Schaffer et al,20 with final thinning and polishing performed using 2 keV ions. High angle annular dark field scanning transmission electron microscopy (HAADF STEM) images were collected from the thinned lamellae at Pacific Northwest National Laboratory using a Cscorrected FEI Titan 80-300 S/TEM operating at 300 keV. Immediately prior to STEM imaging, the samples were cleaned for 20 seconds in a 23% O2 / 77% Ar plasma using a Fischione Instruments 1020 Plasma Cleaner. Results and discussion The synthetic approach used to prepare the compounds requires calibration of the precursor deposition parameters to achieve the composition and similar structural unit to the target superstructure. To prepare the parent systems, sets of samples were prepared to calibrate the precursor deposition parameters. First, the MX and TX2 components of the parent structures were calibrated separately, by preparing a set of films containing a fixed thickness of Se and different thicknesses of M and T, respectively. The EPMA measured compo sition ratio of (M/Se) [or (T/Se)] were plotted against the quartz crystal monitor thickness ratio (M/Se) [or (T/Se)] to determine the quartz crystal monitor thickness ratios required to obtain a 1/1 [or 1/2] ratio, respectively. A set of samples was then made varying the (M/Se) to (T/Se) ratio by scaling the thickness while keeping the composition of the M/Se and T/Se at the desired 1/1 and 1/2 ratios. The EPMA measured composition ratio of (M/Ti) was plotted against the quartz crystal monitor thickness ratio (M/Ti)] to determine the quartz crystal monitor thickness ratios required to obtain the desired misfit ratio. The total thickness of a M/Se/Ti/Se layer was then scaled keeping all the ratios the same, with the quality of the specular diffraction patterns of annealed samples used to optimize the total thickness. The alloys were synthesized by scaling the MX deposition parameters to match the targeted x value. Elemental layers were then adjusted slightly to account for varying sticking coefficients based on measured thickness and composition via XRR and EPMA, respectively. The quality of the specular diffraction patterns were the final judge of sample quality. The compositions and lattice parameters for the two end members and three alloy precursors are summarized in Table 1. The ratio of the measured rock salt cation compositions match closely with the targeted values.

Electron-transparent cross-sectional lamellae of the samples with x = 0.24, 0.48, and 0.71 were prepared using Table 1. Composition and lattice parameters of (BixSn1-xSe)1+δTiSe2 compounds Targeted x

Bi (at. %)

Sn (at. %)

Ti (at. %)

Se (at. %)

O (at. %)

Measured x

MX space group

MX a (nm)

MX b (nm)

a (nm)

Misfit Parameter

c-lattice parameter (nm)

0.0

0

22

18

59

4

0.0

p2gg

0.6094(3)

0.5974(4)

0.356(1)

1.21

1.204(1)

0.25

5

17

19

57

1

0.24

p2gg

0.6146(3)

0.6006(3)

0.356(2)

1.19

1.195(1)

0.50

11

12

19

56

3

0.48

p2gg

0.6153(3)

0.5990(3)

0.356(1)

1.19

1.188(1)

0.75

16

6

20

56

2

0.71

Pcmn

0.449(1)

0.436(1)

0.358(1)

1.16

1.185(1)

1.0

19

0

18

59

4

1.0

Pcmn

0.4562(2)

0.4242(1)

0.358(6)

1.15

1.177(1)


TiSe2

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Figure 1. Specular diffraction patterns of (Bi0.48Sn0.52Se)1+δTiSe2 collected after annealing a precursor to the indicated temperatures for 30 minutes. The indices of the reflections are shown above.

An annealing study was carried out on the x = 0.48 sample, assuming it would be most representative of the alloyed compounds, and the resulting 00l diffraction the 350°C pattern. Asterisks denote textured Bi2Se3 Bragg reflections, patterns are shown in Figure 1. The diffraction pattern of the as-deposited precursor contains reflections resulting from the repeating electron density in the precursor, suggesting the precursor is uniformly layered throughout the film and that considerable order develops while the sample is deposited. As the annealing temperature is increased, reflections consistent with the targeted superstructure narrow and intensify, consistent with the self-assembly of the designed compound. At 350°C, the reflections have maximum intensity and minimum full width at half maximum. Above 350°C, the reflections of the targeted superstructure are broader, less intense, and accompanied by the growth of reflections from impurity phases, most notably Bi2Se3. The reflections of (Bi0.48Sn0.52Se)1+δTiSe2 do not shift in position, suggesting phase segregation into Bi2Se3 and undetected Sn and Ti containing phases. Observing Bi2Se3 as a decomposition product suggests that it may be possible to form Bi2Se3containing superstructures using designed precursors containing less Se. 350°C was chosen as the optimum formation temperature for the targeted compounds and was used for the remaining samples in this study. The 00l diffraction scans for the five compounds prepared in this study are shown in Figure 2a. Each of the patterns can be indexed to the superstructure with no discernible impurity phases present. Figure 2b shows the (007) and (008) reflections, highlighting the systematic decrease in the c-axis lattice parameter as Bi replaces Sn. The c-axis lattice parameters for all of the samples are presented in Table 1. The c-axis lattice parameter varies linearly with composition of the as-deposited precursor between the end members, as expected from Vegard's

Figure 2. a) Specular diffraction patterns obtained for each of the different (BixSn1-xSe)1+δTiSe2 compounds after annealing precursors for 30 minutes at 350°C. The color for each x value is indicated and indices are shown above each of the different reflections. b) An expansion of the high angle portion of the diffraction patterns, showing the systematic shift in position reflecting the change in lattice parameters. Asterisks denote Si reflections from the substrate.

law. The variation is also consistent with the previously reported (BixSn1-xSe)1+δVSe2 compounds,21 changing from 1.204(1) nm for the Sn compound to 1.177(1) nm for the Bi compound. The contraction of the c-axis is consistent with the cations having different oxidation states, as the ionic radii of Sn2+ and Bi3+ are 118 and 103 pm, respectively, and is consistent with the electrical properties discussed later in this manuscript. The systematic decrease in the (007) reflection’s relative intensity as a function of x also suggests that the composition of the ferecrystal structure changes systematically as the targeted substitution occurs to a greater extent. The intensity changes, however, depend on both the changes in scattering power of the rock salt layer due to the substitution of Sn by Bi and small changes in the positions of the atomic planes in each of these compounds. In-plane X-ray diffraction scans (Figure 3) were collected to probe the structure of the individual constituents and how they evolve as a function of the extent of substitution. The x = 1.0 sample's reflections can be indexed as TiSe2 and BiSe as reported previously.22 Similarly, the x =



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sample in Table 1 were calculated using the symmetry of the SnSe end member, resulting in a larger a-axis lattice parameter than the 0.25 sample, but the difference between them is less than expected from Vegard's law. This results in a misfit parameter that is larger than expected from the trend in misfit parameters across the rest of the series of compounds. The structural evolution during the substitution is more complex than the linear trend observed in the (PbxSn1-xSe)1+δTiSe2 alloys previously reported.18

Figure 3. In-plane diffraction patterns obtained for each of the different (BixSn1-xSe)1+δTiSe2 compounds after annealing precursors for 30 minutes at 350°C. Indices for the different constituent layers are shown above each of the reflections in (BiSe)1+δTiSe2 and (SnSe)1+δTiSe2.

0.0 sample's reflections can be indexed as TiSe2 and SnSe as reported previously.18 The diffraction patterns of the alloys with small x values are consistent with adding Bi to the SnSe structure and for large x values are consistent with adding Sn to the BiSe structure. The x = 0.5 sample is more complicated. The non-overlapping 220 reflection for BixSn1-xSe in this sample, located at about 2.9 Å-1, is broader than that for the x = 0.0, and x = 0.25 samples, suggesting a rectangular basal plane distortion for the BixSn1-xSe constituent that cannot be resolved. The in-plane lattice parameters were calculated from a least squares method and are summarized in Table 1. The in-plane parameter for the TiSe2 constituent does not change within error for this family of compounds, varying slightly between 0.356(1) and 0.358(1) nm. This range is consistent with previous reports of TiSe2–based metastable intergrowths23 and close to that reported for the bulk compound.24 The other reflections in the patterns were assigned to the nominally rock salt structured layers and were indexed using the space groups expected from the structures previously reported. The SnSe layer of (SnSe)1+δTiSe2 was fit using the 2-D space group p2gg, with a = 0.6094(3) nm and b = 0.5974(3) nm.18 The BiSe layer of (BiSe)1+δTiSe2 was fit using the space group Pcmn with a = 0.4562(2) nm and b = 0.4242(1) nm.22 The (BixSn1xSe)1+δTiSe2 compound with x = 0.25 has the same in-plane structure as the SnSe end member, with slightly larger inplane lattice parameters that reflects the substitution of Bi for Sn. The (BixSn1-xSe)1+δTiSe2 compound with x = 0.75 has the same in-plane structure as the BiSe end member, with the smaller a-axis lattice parameters reflecting the substitution of Sn for Bi. The x = 0.48 sample displays a broad background around the (220) SnSe reflection, as well as a shifting and broadening of the (420) and (240) reflections. This could reflect different MSe layers having different x values and hence the two symmetry types are both present, or it could indicate that the layers maintain a constant x value with a lower symmetry structure than expected for SnSe. The lattice parameters for the x = 0.48

Figure 4 contains the measured resistivity as a function of temperature for the alloys and the parent compounds. The slight decrease in resistivity as temperature is decreased and the slight upturn at low temperatures for the Sn-rich compounds is similar to that observed for other materials synthesized from modulated elemental reactants.22,25 The small temperature dependence at high temperatures was previously attributed to the turbostratic disorder observed between the layers,26,27 which decreases electron-phonon interactions at higher temperatures, but it also might result from a large density of defects which dominate the scattering. The upturn in resistivity observed at low T has been attributed to carrier localization, and increases as a function of the magnitude of the resistivity, consistent with previous reports.25,28 To provide information about the carrier type and carrier concentration and mobility for the compounds, Hall coefficient measurements were made (Figure 5a). The measured Hall voltages for all of the samples studied were negative, indicating that electrons are the majority carriers, as was reported previously for TiX2 based MLCs and ferecrystals.12,17,18,26,29,30 Carrier concentrations were calculated from the Hall coefficients assuming a single rigid band was responsible for conduction (Figure 5b) in which case the Hall coefficient is inversely proportional to the carrier concentration. Carrier concentrations are found to decrease slightly as temperature is decreased. The compounds containing bismuth had smaller Hall coefficients, indicating an increase in carrier concentration as Bi is added to the structure. Interestingly, the change in carrier concentration is smaller than would be expected if each Bi atom donated a full electron. The temperature-

Figure 4. Temperature dependent resistivity values for the five compounds investigated in this study along with a previously measured sample of (SnSe)1.21TiSe2.


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Figure 6. Carrier mobility as a function of temperature calculated from the measured conductivity and Hall coefficients, assuming a single band model.

Figure 5. (a) Hall coefficients as a function of temperature and (b) the variation of the carrier concentration as a function of temperature determined from the measured Hall coefficients assuming a single band model.

dependent carrier concentration and resistivity for each sample was used to calculate mobility as a function of temperature (Figure 6). The mobility values are all very similar, with the x = 0.24 and x = 0.48 compounds having lower mobility than the x = 0.71 compound making substitutions on this scale. Mobility values typically vary by an order of magnitude or more between the pure and alloyed compounds in bulk materials.31 The slight decrease in mobility for the alloys suggests that the substitution in the MX layer only weakly affects the mean free path of carriers. This is consistent prior studies of TiX2 based materials, which indicated that conduction was dominated by a TiX2 based band.7–9,18

Figure 7. Carrier concentration per rock salt cation and the net increase in carrier concentration per bismuth cation over the carrier concentration of (SnSe)1.21TiSe2

Figure 7 shows the increase in the number of carriers per rocksalt cation relative to the carrier concentration found in (SnSe)1.21TiSe2 graphed as a function of x. It is clear from the decrease in the slope of the curve with increasing x that the doping efficiency of the Bi decreased doping efficiency inferred from the Hall coefficients.

turbostratic disorder is commonly observed in compounds prepared using the synthetic method employed inthis study. Although ion bombardment can lead to structural disordering,32 this effect is typically avoided by the protective cap33 and the use of low keV polishing.20 Furthermore, sample preparation-induced disorder would be expected to disrupt the layering sequence, which is not observed in the HAADF STEM images. Distinguishing between SnSe-type and BiSe-type structures in individual layers is challenging due to the small grain sizes and turbostratic disorder in the samples. The HAADF STEM images from the x = 0.48 sample suggests that the BixSn1-xSe layers have uniform composition and structure, but cannot rule out the possibility that different structure types may be present. Most of the observed intensity variation results from channeling effects as the layer-to-layer zone axis alignment changes.

HAADF STEM images were collected from the three samples with alloyed BixSn1-xSe layers to search for antiphase boundaries in the BixSn1-xSe layers. The images (Figure 8) confirm the layered structures indicated by XRD data. The samples contain alternating BixSn1-xSe (light) and TiSe2 (dark) layers crystallographically aligned to the substrate. Many different zone axis alignments are

The HAADF STEM images also indicate that Bi-Bi pairs are present in the BixSn1-xSe layers of the x = 0.48 and 0.71 samples. As discussed previously,26,34 Bi-Bi bonds are visible as adjacent Bi atomic columns in grains oriented along the [100] zone axis, assuming a Pcmn space group. Figure 9 shows two BixSn1-xSe grains from the x = 0.71 sample oriented along or close to the [100] zone axis of



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Figure 8. Representative HAADF STEM images from three samples with x = 0.24 (left), 0.48 (center), or 0.71 (right). The magnification is the same for all three images, and is indicated by the scale bar in the center image. BixSn1-xSe layers are marked with the light gray boxes with black borders, while TiSe2 layers are marked with the dark gray boxes with white borders. Selected grains for each constituent oriented along a zone axis have been labeled. Zone axes for the 0.48 samples are labeled assuming the 2D p2gg space group, while those for the x = 0.71 are labeled assuming the Pcmn space group.

odic adjacent Bi columns, marked in the figure with red arrows.

Figure 9. Two BixSn1-xSe grains from the x = 0.71 sample oriented along or close to the [100] zone axis of the Pcmn space group. The lower image shows periodic adjacent Bi columns, marked in the figure with red arrows.

the Pcmn space group. These regions were cropped from Figure 8, magnified, and bandpass filtered to reduce high frequency scan noise. The top oriented grain displays the expected zig-zag structure of bright spots expected for a rock salt structured compound, resulting from alternating Bi- and Se-containing atomic columns within each layer of the bilayer. The bottom oriented grain displays regions with the expected zig-zag structure, but also shows peri-

As mentioned in the discussion of the electrical data, the presence of Bi-Bi bonds might explain the decreased doping efficiency with increased concentration of Bi in the BixSn1-xSe layers. For x = 0.24, the electrical measurements suggested donation of nearly one electron per Bi atom. Consistent with this finding, no adjacent Bi-Bi columns were observed in the [110]-oriented grains (relative to p2gg space group) in any of the HAADF STEM images collected from this sample. Bi3+ cations are substituting for Sn2+ cations in the MSe layer, and the additional electron is transferred to the conduction band of the TiSe2 layer. For x = 0.48, about 13% of [110]-oriented grains showed adjacent Bi-Bi columns, and about 50% of [100]oriented grains (relative to Pcmn) in the images from the x = 0.71 film showed adjacent Bi-Bi columns. In a simplistic picture, the reduction in charge donation with x should be proportional to the percentage of Bi atoms involved in Bi-Bi bonds due to the decrease in average oxidation state of the Bi atoms. The observation of Bi-Bi bonds, however, is correlated with the change in the inplane structure of the BixSn1-xSe layers, complicating this simplistic picture. The structural distortion changes the bilayer band structure, which might influence the alignment of BixSn1-xSe bands with the TiSe2 conduction band and hence the amount of modulation doping that can occur.


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Conclusions A series of (BixSn1-xSe)1+δTiSe2 compounds were prepared with values of x ranging from 0 to 1.0. The compounds consist of bilayers of a distorted rock salt structure alternating with monolayers of CdI2-type TiSe2. The Sn-rich compounds had a distorted rock salt-like structure similar to SnSe in the (SnSe)1+δTiSe2 end member, while the Birich compounds had a different in-plane structure, similar to that of the BiSe constituent in (BiSe)1+δTiSe2 end member. The x = 0.48 compound's structure contains evidence for both distortions. The electrical transport data suggest that the Bi cations provide extra charge carriers, but the doping efficiency clearly reduces as the Bi content increases. The presence of an increase in the number of antiphase boundaries that contain Bi-Bi bonds in the BixSn1-xSe layers with increased Bi content may partially account for the reduction in doping efficiency, but does not adequately describe all of the reduction. The observed properties suggest that modulation doping via controlled site-specific substitutions can be a useful mechanism for modifying electrical properties in similar heterostructures. However, changes in the dopant layer structure might also lead to changes in the amount of charge donation that occurs. The resulting dopant efficiency is the sum of both effects.

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Bauers, S. R.; Merrill, D. R.; Moore, D. B.; Johnson, D. C. Carrier Dilution in TiSe2 Based Intergrowth Compounds for Enhanced Thermoelectric Performance. J. Mater. Chem. C 2015, 3, 10451–10458.

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Merrill, D. R.; Sutherland, D. R.; Ditto, J.; Bauers, S. R.; Falmbigl, M.; Medlin, D. L.; Johnson, D. C. Kinetically

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] Author Contributions All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors acknowledge the facilities in CAMCOR that enabled the XRD and FIB sample preparation of TEM samples. The authors acknowledge support from the National Science Foundation under grant DMR-1266217. We also acknowledge support through the Collaborative Access Team (CAT): Pooled Resources for Electron Microscopy Informatics, Education and Research (PREMIER) Network Program at Pacific Northwest National Laboratory (PNNL) and the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research at PNNL. PNNL is a multiprogram national laboratory operated by Battelle for DOE under Contract DE-AC05-76RL01830.

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Modulation Doping in Metastable Heterostructures via Kinetically

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