United States

Abstract Body: The next generation of solid-state power electronics will increasingly utilize the AlxGa1-xN system, benefitting from its large and direct band gap, high switching speed, and high FOM. Formation of selective-area p-type regions is critical for field management and remains a significant challenge for higher-voltage next-generation architectures. Activation of the p-type dopant Mg, especially in the case of ion-implanted AlxGa1-xN, requires temperatures high enough to cause significant diffusion of the dopant, potentially distorting the doped region shape. Microwave annealing has been shown to induce both dopant activation and diffusion, especially for rapid drive-in of B in Si1 Diffusion dynamics induced by microwave annealing can diverge from those suggested by the bulk thermal condition of the sample. This has been attributed to interaction of the microwave beam with ionized defects and dopants in the material, permitting higher diffusion of electrically charged (ionized) species in the lower-temperature bulk2. This makes understanding Mg redistribution in GaN due to microwave annealing in both implanted and in-situ doped material of critical importance to the continued development of selective-area doping. In order to better understand this diffusion and activation behavior, a study was conducted of spatially resolved Mg distribution in in-situ doped and implanted GaN grown by metalorganic chemical vapor deposition (MOCVD) and annealed by gyrotron microwave beam. Annealing conditions between 1160–1410 °C were performed for durations between 30–65 s in total using a quasi-gaussian beam intensity profile and a 2.5 cm beam raster across the sample surface. Low-temperature PL spectra were measured and used as a proxy for acceptor activation before and after annealing of doped GaN. At the locations of PL measurements on samples, depth profiles of [Mg] were taken using dynamic secondary ion mass spectroscopy (D-SIMS). Beyond concentrations of around 1016 cm-3, the intensity of PL bands is not linearly related to the density of acceptors in the material3, however PL spectra have been shown to indicate the presence of conductivity type, provided initial knowledge of the growth condition. The as-implanted [Mg] profile of all samples shows a profile of 1×1019 cm-3 to a depth of 250 nm with a quasi-Gaussian tail. The in-situ doped as-grown [Mg] of 7×1019 cm-3 remains constant from the surface to the p-GaN layer depth of ~120 nm before annealing, and the profile does not appreciably change after annealing. After annealing implanted samples above 1350 °C, diffusion of Mg dopant is observed to vary spatially across the sample, correlating approximately with the beam shape and raster. To understand potential correlation of such diffusion with PL bands, measurements on the same location as SIMS measurement was performed. PL measurements show the characteristic near-band edge (NBE) luminescence at 3.47 eV and Mg-acceptor-related UVL at 3.27 eV in all spectra. In the 2.2–2.4 eV range, either the VN-related GL2 band or the CN-ON-related YL band is dominant. Relative intensity of these bands varies across the sample area, however no correlation of PL activity with Mg diffusion is observed. We show that while PL activity reflects the presence of MgGa and other optically active defects within the laser excitation depth (~92 nm), (anneal-induced) diffusion has no significant impact on [Mg] within this depth, and therefore that diffused Mg deeper in the sample (200–800 nm) does not necessarily impact PL activity. This may be due in part to the upper limit of PL sensitivity to acceptor concentration3. This work was funded by a grant from ARPA-E PNDIODES program, grant #DE-FOA-001691 under the direction of Dr. Isik C. Kizilyalli. [1] Kohli, P., et al. (2002). J. of Electron. Mat., 31(3), 214-219. [2] Booske, J. H., Cooper, R. F., &amp; Dobson, I. (1992). J. Mat. Research, 7(2), 495-501. [3] Reshchikov, M. A., et al. (2017). Scientific reports 7(1), 1-11.

EMC 2021

Microwave-Induced Annealing, Its Impact on Mg Diffusion and Photoluminescence Activity in Implanted and In Situ Doped GaN

p-gan

ion implantation

diffusion

sims

annealing

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EIPBN 2021

Abstract Body: The next generation of solid-state power electronics will increasingly utilize the AlxGa1-xN system, benefitting from its large and direct band gap, high switching speed, and high FOM. Formation of selective-area p-type regions is critical for field management and remains a significant challenge for higher-voltage next-generation architectures. Activation of the p-type dopant Mg, especially in the case of ion-implanted AlxGa1-xN, requires temperatures high enough to cause significant diffusion of the dopant, potentially distorting the doped region shape. Microwave annealing has been shown to induce both dopant activation and diffusion, especially for rapid drive-in of B in Si1 Diffusion dynamics induced by microwave annealing can diverge from those suggested by the bulk thermal condition of the sample. This has been attributed to interaction of the microwave beam with ionized defects and dopants in the material, permitting higher diffusion of electrically charged (ionized) species in the lower-temperature bulk2. This makes understanding Mg redistribution in GaN due to microwave annealing in both implanted and in-situ doped material of critical importance to the continued development of selective-area doping. In order to better understand this diffusion and activation behavior, a study was conducted of spatially resolved Mg distribution in in-situ doped and implanted GaN grown by metalorganic chemical vapor deposition (MOCVD) and annealed by gyrotron microwave beam. Annealing conditions between 1160–1410 °C were performed for durations between 30–65 s in total using a quasi-gaussian beam intensity profile and a 2.5 cm beam raster across the sample surface. Low-temperature PL spectra were measured and used as a proxy for acceptor activation before and after annealing of doped GaN. At the locations of PL measurements on samples, depth profiles of [Mg] were taken using dynamic secondary ion mass spectroscopy (D-SIMS). Beyond concentrations of around 1016 cm-3, the intensity of PL bands is not linearly related to the density of acceptors in the material3, however PL spectra have been shown to indicate the presence of conductivity type, provided initial knowledge of the growth condition. The as-implanted [Mg] profile of all samples shows a profile of 1×1019 cm-3 to a depth of 250 nm with a quasi-Gaussian tail. The in-situ doped as-grown [Mg] of 7×1019 cm-3 remains constant from the surface to the p-GaN layer depth of ~120 nm before annealing, and the profile does not appreciably change after annealing. After annealing implanted samples above 1350 °C, diffusion of Mg dopant is observed to vary spatially across the sample, correlating approximately with the beam shape and raster. To understand potential correlation of such diffusion with PL bands, measurements on the same location as SIMS measurement was performed. PL measurements show the characteristic near-band edge (NBE) luminescence at 3.47 eV and Mg-acceptor-related UVL at 3.27 eV in all spectra. In the 2.2–2.4 eV range, either the VN-related GL2 band or the CN-ON-related YL band is dominant. Relative intensity of these bands varies across the sample area, however no correlation of PL activity with Mg diffusion is observed. We show that while PL activity reflects the presence of MgGa and other optically active defects within the laser excitation depth (~92 nm), (anneal-induced) diffusion has no significant impact on [Mg] within this depth, and therefore that diffused Mg deeper in the sample (200–800 nm) does not necessarily impact PL activity. This may be due in part to the upper limit of PL sensitivity to acceptor concentration3. This work was funded by a grant from ARPA-E PNDIODES program, grant #DE-FOA-001691 under the direction of Dr. Isik C. Kizilyalli. [1] Kohli, P., et al. (2002). J. of Electron. Mat., 31(3), 214-219. [2] Booske, J. H., Cooper, R. F., & Dobson, I. (1992). J. Mat. Research, 7(2), 495-501. [3] Reshchikov, M. A., et al. (2017). Scientific reports 7(1), 1-11.

technical paper

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Abstract Body: For the last few decades, most of the advancement in electronic and optoelectronic devices have been relying on our ability to integrate dissimilar materials having different lattice constants. By combining multiple different materials to form a heterostructure, we could engineer a particular band structure for a specific purpose. Nowadays the advancement on the integration technology is also motivated by the rapidly-growing field of Si photonics which requires integration of advanced non-Si infrared (IR) devices into the Si platform. However, to grow such devices on Si, one needs to address crystallographic challenges associated with high threading dislocations density caused by lattice mismatch. We have developed a novel materials integration technique, called metal-catalyzed lateral epitaxy, that has showed promising results in the Ge on Si system which has a 4% lattice mismatch. This technique uses a metal catalyst to control the growth location and a PECVD-grown capping layer to ensure growth laterally. The lateral growth is dictated by the vapor-liquid-solid mechanism which has shown a promising potential in suppressing the nucleation of threading dislocations by the extension of misfit dislocations. The main advantages of this technique over others are that it is wafer-scale, grown directly on the Si substrate, and allows direct electrical connection of the grown films to the substrate. In this talk, recent results of our systematic studies on the kinetics and the mechanism of this unique integration technique will be presented based on the heteroepitaxy of Ge-Si and InP-Si systems. Both are crucial heterostructures in Si photonics for high-performance IR photodetector and light source, respectively.

Kinetics and Mechanism of Metal-Catalyzed Lateral Epitaxy for Growing Lattice-Mismatched Heterostructures via Vapor-Liquid-Solid

Abstract Body: Conductors having at least one dimension at the nanoscale have properties that differ substantially from their bulk counterparts. In particular, electrical resistivity increases significantly when size is reduced while thermal conductivity (κ) decreases. These factors present a critical technological barrier to miniaturization, since the former increases self-heating when current is driven while the latter limits dissipation of that heat from device-active regions. Despite the prominent role of metallic nanostructures in current and future electronics and photonics, large gaps exist in understanding the influence of “size effects” on thermal characteristics at small dimensions. In particular, there is a paucity of direct measurements of thermal conductivity for technologically-relevant materials. This study focuses on development and test of a method for directly measuring κ for conducting nanofilms and nanowires. We report on design, fabrication, test, and application of this approach to 50 and 100 nm thick evaporated gold structures with lateral dimensions ranging from 74 to 720 nm, thereby spanning the nano- to meso-scale. Measurements are carried out at ambient room and 100° C temperatures, i.e., in the standard operating range of low-power electronics. A decrease in κ is observed as gold thickness is reduced. At large lateral width, corresponding to the microscale and analogous to thin films, κ values are found to be 200 and 280 W/mK for thicknesses of 50 and 100 nm, respectively (room temperature). These are to be compared with the accepted value of 317 W/mK for κ of bulk gold. In addition, as the width is reduced, for either thickness, a dramatic decrease in κ is observed beginning at ~ 300 nm width. For the smallest nanowire investigated, 50 nm in thickness and 74 nm in width, a value of κ = 56 W/mK is obtained. At higher test temperature, the thermal conductivities are found to decrease, as expected. The decrease in κ with diminishing size are primarily attributed to grain boundary and surface/interface scattering of electrons—that conduct most of the heat in gold—and quantitatively interpreted using the Boltzmann Transport Equation (BTE).

Direct Measurement of Thermal Conductivity of Gold from Meso- to Nano-Scale

Abstract Body: A material with a high thermoelectric figure of merit plays an important role in the development of efficient thermoelectric devices. Modification of thermal transport in a crystal lattice is one of the most sought-after methods of developing novel thermoelectric materials. Increasing phonon scattering in a crystalline material to lower thermal transport is one way of achieving this objective. A fundamental understanding of the effects of structural features on the thermal properties is a significant first step towards enhanced thermoelectric properties of a material. Although certain quaternary chalcogenides have been examined for their applications as thermoelectric materials, fundamental research into altering the thermal conductivity of this large class of materials remains to be explored. This work contributes towards this area of research by investigating the thermal conductivity and heat capacity of select quaternary chalcogenides to analyze their structure-property relationships. Phenomenological models were utilized to examine the thermal conductivity, κ, and heat capacity, Cp, of BaCu2SnQ4 (Q = S, Se) and BaCdSnSe4. The Debye-Callaway model was employed to investigate the phonon scattering phenomena that occur in these materials. Our analyses indicate similar anharmonicity in all crystal lattices. Furthermore, highly distorted corner-sharing chalcogen tetrahedra encompassing Cu/Cd atoms give rise to large thermal parameters for Cu/Cd in these materials. Relatively high scattering from soft modes in BaCu2SnS2Se2 was identified, such dynamic disorder resulting in very low κ values. Additional disorder for BaCu2SnS2Se2 is due to alloying, causing the lowest κ among the quaternary chalcogenides. The Debye and Einstein temperatures from Cp data corroborated the results obtained from our analyses of the κ data. The large primitive cells with complex lattice vibrations these materials possess lead to an increase in optical modes that further suppress κ. These results and analyses, as well as further recent results on other quaternary chalcogenides, demonstrate the direct impact of complex structural features on phonon dynamics, enhancing our fundamental understanding of the thermal properties of these materials. With material property developments being a significant aspect of thermoelectrics research, our results will aid investigations of other quaternary chalcogenides of interest for thermoelectric applications, as will be described in this presentation.

A Fundamental Study of Structural Effects on Thermal Properties of Quaternary Chalcogenides

Abstract Body: Global fifth-generation (5G) coverage has the potential to underpin the internet-of-things (IoT) ecosystem. Radio frequency (RF) microelectromechanical system (MEMS) filters based on Al1-xScxN are replacing AlN-based devices because of the higher achievable bandwidths. [1] However, overheating of Al1-xScxN film bulk acoustic wave resonators (FBARs) used in RF MEMS filters limits power handling and thus the phone’s ability to operate in an increasingly congested RF environment while maintaining its maximum data transmission rate. Despite this, the factors limiting thermal transport within Al1-xScxN have not been examined. This work investigated the physics that govern the thermal transport within Al1-xScxN, a fundamental building block for 5G RF MEMS. The thermal conductivities of c-axis textured Al1-xScxN films were found to be one order of magnitude lower than similarly textured polycrystalline AlN films and two orders of magnitude lower than single crystal and/or bulk AlN. This abrupt reduction of thermal conductivity with incorporation of Sc atoms into the AlN crystal can be understood in terms of phonon-alloy/disorder scattering, in the context of the phonon gas theory. Increasing the Sc composition results in a further decrease in the thermal conductivity due to structural frustration and lattice softening, which is an effect absent in isomorphs such as Al1-xGaxN. [2] A relatively strong film thickness dependence of the thermal conductivity was observed for the Al1-xScxN films. However, thermal conductivity measurement at varying ambient temperatures exhibited a weak temperature dependence. The impact of abnormally oriented grains on the cross-plane thermal conductivity was found to be negligible for the piezoelectrically functional Al1-xScxN films tested in this work. Outcomes of this work support the electro-thermo-mechanical co-design of 5G Al1-xScxN-based RF acoustic filters. From a thermal standpoint, for Al1-xScxN-based bulk acoustic wave (BAW) filters, the solidly mounted resonator (SAW) configuration would be preferred over the FBAR (free-standing membrane) configuration due to the poor thermal conductivity of Al1-xScxN. The thermal property data set generated in this work reveals design trade-offs for (i) increasing the Sc composition of Al1-xScxN to maximize the electromechanical coupling factor, (ii) decreasing the film thickness to achieve higher GHz-range resonance frequencies, (iii) higher operating temperatures resulting from higher integration density and RF input powers. The thermal conductivity data will allow construction of multi-physics device models that will enable the design and development of Al1-xScxN RF filter technologies with enhanced device performance and improved lifetime. Acknowledgment: This material is based upon work supported by the National Science Foundation, as part of the Center for Dielectrics and Piezoelectrics under Grant Nos. IIP-1361571, IIP-1361503, IIP-1841453, and IIP-1841466. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. G.E. would like to gratefully thank Sara Dickens and Joseph Michael at Sandia for conducting the EBSD analysis. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration under contract DE-NA-0003525. The views expressed in the article do not necessarily represent the views of the U.S. DOE or the United States Government. References: [1] G. Piazza, V. Felmetsger, P. Muralt, R. H. Olsson III, R. Ruby, MRS Bull. 2012, 37, 1051. [2] K. R. Talley, S. L. Millican, J. Mangum, S. Siol, C. B. Musgrave, B. Gorman, A. M. Holder, A. Zakutayev, G. L. Brennecka, Phys. Rev. Mater. 2018, 2, 63802.

Thermal Conductivity of Al1-xScxN for 5G RF MEMS Filters

Abstract Body: As Moore's Law reaches its natural saturation, it has become crucial to investigate novel devices and materials for high-performance computing. One promising approach is to develop brain-like connected neuromorphic architectures composed of elemental devices capable of non-linear phenomena, such as spiking and potentiation. Much progress towards this end has been made using oxide materials like VO2 and NbO2, in which memristive behavior arises as a consequence of non-linear conductance mechanisms and of the inherent metal-insulator transition (MIT). However, much work remains to be done to correlate device properties, especially performance versus energy cost, to underlying materials properties like effective energy barriers and conductance changes across the MIT. In this work, we investigate these issues by developing a compact model for individual vanadium dioxide devices, so as to link complex dynamic behavior to underlying material and device properties. Using a combination of steady-state current-voltage sweeps, time-varying oscillations, and a novel thermoreflectance temperature-measuring technique, we extract thermal and electrical conductance and capacitance model parameters, and show that the model reproduces all observed device behavior. Finally, we exploit the link between dynamics and materials parameters embodied by the compact model to develop non-trivial device scaling laws, and also experimentally demonstrate a capacitance-controlled bifurcation from stable to unstable oscillating dynamics. This work lays the foundation for future studies allowing disparate memristive materials to be compared through the compact model framework, as well as to begin investigating the even more complex dynamical behaviors arising from couplings of pairs or networks of non-linear devices.

Characterization and Exploitation of Non-Linear Dynamics in Vanadium Dioxide Thermal Memristors

Abstract Body: Recently, α-Ga2O3 have been attracting great attentions as an ultra-wide bandgap semiconductor. However, the reason why meta-stable α-Ga2O3, which was originally synthesized at a pressure of 44 kbar and at a temperature of 1000 °C [1], is grown at around 500 °C under atmosphere by mist chemical vapor deposition (CVD) has not been elucidated yet. In this study, in order to analyze the growth mechanisms of mist CVD-grown α-Ga2O3, we investigated the growth processes at the initial stage. α-Ga2O3 with thickness (t) of 2.3, 4.7, 7.8, and 30 nm were grown on (0001) sapphire by the mist CVD method. The four samples were investigated by atomic force micrograph (AFM), transmission electron micrograph (TEM), and X-ray diffraction reciprocal space mapping (XRD RSM). High resolution (HR-) TEM images at the interface viewed along the [11-20] axis indicates that α-Ga2O3 is pseudomophically grown on sapphire for t=2.3 nm, however, relaxed for t=4.7, 7.8, and 30 nm. Therefore, we found that the critical thickness of mist CVD-grown α-Ga2O3 on (0001) sapphire is 2.3-4.7 nm. In addition, for t=4.7, 7.8, and 30 nm, α-Ga2O3 was successfully grown even after the lattice relaxation. In TEM images under two-beam diffraction condition of g=10-10 viewed along the [11-20] , dark and bright regions periodically introduced in the film near the interface are seen, but not of g=0001, for t=4.7, 7.8, and 30 nm. Thus, it is considered that regions strained along in-plane direction or/and misfit dislocations with the Burger’s vector parallel to the interface are periodically introduced near the interface after the α-Ga2O3 film relaxes. From the electron diffraction patterns and XRD RSM, it is confirmed that the films of t=4.7, 7.8, and 30 nm keep α-phase even after the lattice relaxation. XRD RSM also indicates that relaxation ratio gradually increases as the film thickness increases; for t=30 nm, the film is almost free standing. We also calculated the critical thickness based on the force-balance model and obtained the value of ~4.2 nm, which is consistent to the prediction (2.3-4.7 nm) derived from the HR-TEM. From the above coincidence, it is considered that the relaxation of mist CVD-grown α-Ga2O3 is caused by dislocations. On the other hand, by MBE, PLD, and MOCVD previously reported, the lattice relaxation is caused by phase transition from α to β [2,3], that is, the frustration of taking the α-phase causes the lattice relaxation so that the crystal structure changes from α to β. The lattice relaxation processes by mist CVD are different from those by other growth methods. This may be attributed to the low temperature growth and the association of water in the growth atmosphere. We will discuss the mechanism in more detail at the conference. [1] J. P. Remeika et al., Appl. Phys. Lett. 8, 87 (1966). [2] R. Schewski et al., Appl. Phys. Express 8, 011101 (2015). [3] Z. Cheng et al., Appl. Phys. Lett. 111, 162104 (2017).

On the Initial Growth Mechanisms of α-Phase Ga2O3 on c-Plane Sapphire by Mist CVD

Abstract Body: β-Ga2O3 is well known for its multidimensional functionality, such as deep-UV photodetector, high power electronic device, water splitting, CO2 reduction, gas sensor, etc. Here we are presenting a low cost pulsed laser deposition method to demonstrate nano-columnar β-Ga2O3 thin film on silicon substrate with an average crystallite size of ~9 nm. In-situ anisotropic thermal conductivity during the grow process facilitates the unidirectional columnar growth of β-Ga2O3 thin film, decorated with nanocrystalline surface morphology. With increasing substrate temperature, it shows blue shifting of band edge absorption with decreasing defect density. Luminescence spectra show drastic improvement in intensity (~30 times), which is beneficial for further optoelectronic application.

Realization of Self-Assisted Growth of Nano-Columnar β-Ga2O3 Thin Film on Silicon Substrate

Abstract Body: Digitally-grown AlInAsSb alloys have recently emerged as a platform for high performance short- avalanche photodiodes (APDs) with potential applications in chemical sensing, security, and LIDAR [1,2]. While the impact ionization of APDs grown with a single composition has been shown to be nearly perfectly electron-initiated [2,3], AlInAsSb also enables sophisticated bandgap engineering to create a “staircase” APDs – a solid-state analogue of the photomultiplier tube wherein impact ionization only occurs in spatially-localized, narrow-gap wells [4, 5]. Carrier trapping phenomena in the narrow-gap regions, coupled to non-radiative Shockley-Read-Hall recombination, can reduce the efficiency of impact ionization and reduce the maximum achievable gain in staircase APDs. Unfortunately, due to the miscibility gap associated with conventionally grown AlInAsSb, the carrier lifetime of AlInAsSb materials is largely unknown. Furthermore, the SWIR and MWIR spectral regions spanned by AlInAsSb remain an active area of research for high-performance unity-gain photodiodes and emitters for chemical sensing and security applications; high performance in either class of devices depends critically on the carrier recombination dynamics. Thus, there is a need to measure the carrier lifetime in digitally-grown AlInAsSb to foster improved staircase APD performance, as well as to evaluate AlInAsSb more broadly as a candidate material for SWIR and MWIR detection and emission. Here, we present an investigation of carrier recombination dynamics of SWIR and MWIR AlInAsSb digital alloys with alloy compositions ranging from 0% Al to 30% Al, at temperatures between 77K and room temperature. Bright photoluminescence was observed from all samples at all temperatures, spanning wavelengths from 1.8μm to 5μm. Minority carrier lifetimes were measured from time-resolved photoluminescence ranging from 75ns to 260ns at 77K, and 25ns to 75ns at room temperature. Samples containing more than 0% Al displayed a ‘U’ shaped dependence on the temperature, with the minima occurring around 200K and ranging from 20ns to 50ns. The minority carrier lifetime of the 0% Al sample, however, monotonically increased with decreased temperature. Further characterization and analysis will be presented at the conference. This work was supported by ARO (W911NF-17-1-0065), DARPA (HR0011-20-9-0087), and NSF (ECCS-1926187). [1] S.R. Bank et al., IEEE J. Sel. Top. Quantum Electron. 24, 3800407 (2018) [2] M. Ren et al., … J. C. Campbell, J. Light. Technol. 35, 2380 (2017) [3] Y. Yuan et al., … J. C. Campbell, IEEE Photon. Technol. Lett. 31, 315 (2019) [4] F. Capasso and G. F. Williams, IEEE Trans. Nucl. Sci. 30, 381 (1983) [5] M. Ren et al., … S. R. Bank, Appl. Phys. Lett. 108, 081101 (2016).

Minority-Carrier Lifetimes in Digitally-Grown AlInAsSb Alloys

Abstract Body: Dilute germanium carbides (Ge:C) are promising optical materials for active silicon photonics since they can be grown directly on Si at temperatures compatible with post-metal CMOS fabrication. Although Ge and diamond-lattice C both have an indirect bandgap, substitution of ~1% C into Ge creates a direct bandgap suitable for lasers and modulators. However, there is disagreement in the literature about whether C creates a true direct bandgap or merely a pseudo-direct bandgap in which symmetry prevents optical emission even at Gamma (k=0). In this work, we studied the effects of strain and defects on the optical properties of Ge:C using ab initio techniques. We find Ge:C is similar to other highly mismatched alloys such as GaAs1-xNx in many ways, but it also presents several curious differences. The Vienna Ab initio Simulation Package (VASP) was used to model 128 atom supercells of Ge:C with different periodicities, as well as 128 atom supercells with a single Ge vacancy. The use of HSE06 hybrid functionals provided good agreement with experiment in both the direct and indirect bandgaps in unstrained Ge. To study whether periodic boundary conditions artificially affected the results, supercell lattice vectors were varied; the center of each supercell might align with the face, edge, or vertex of the next supercell. This changed the spacing between C atoms in different directions, mimicking a random alloy at a far lower computational cost than doubling the supercell sizes. Other groups have reported that the new conduction band edge created by C is dominated by indirect (L) states. We found instead that the conduction band splits into two bands, E- and E+, that are similar to each other (consistent with band anticrossing, BAC) but retain a predominantly Ge Γ character. The optical transitions in Ge:C are comparable with those of the direct bandgap transition (Γ) in Ge. Spectral weights after band unfolding show comparable or more weight at Γ than L for both E+ and E- states. We also ran a few validation jobs with spin-orbit coupling, compressive strain, or harder Ge potentials, and these all showed similar results. In particular, the band-to-band optical transition strength in Ge:C is within a factor of 2 of that in Ge, and it is comparable with common III-V materials currently used for lasers. We found that the pressure dependence of the band structure can be highly misleading when trying to interpret band identities. In particular, the E- band shifts with strain almost identically with the Ge CB L valley, but this is pure coincidence. Instead, the slow shift with strain comes from a carbon “defect” state near EVB+0.79 eV that varies relatively slowly, more or less tracking the vacuum level rather than the conduction band edge, unlike traditional impurity states. Because the C “defect” state is so close to the native Ge direct bandgap (0.80 eV), the splitting in bands is very strong, driving the direct bandgap more than 0.2 meV below the indirect L valley. This agrees with the deep state model of Hjalmarson and Dow and BAC models near Γ. However, BAC fails to explain the bands away from k=0, and it also does not explain the appearance of a third CB state between the E+ and E- bands. In summary, these results strongly support the development of Ge:C as a strongly optically active material for silicon photonics, with a strongly direct bandgap and optical transitions comparable with III-V materials. Furthermore, these strain results offer a route to test the computational models against experiments, using a diamond anvil cell. These tests are currently underway.

Optical Properties and Band Structures of Strained Ge:C

Abstract Body: Investigation of new group IV alloys to find a direct bandgap material that can emit and detect light efficiently has been pursued by Si photonics in the past decades. The integration of optoelectronics on the electronics chips enables high-speed data transfers through emitters and detectors that are compatible with Si technology 1. Although GeSn has been shown as a group IV that can achieve the above-mentioned goals by different groups 2, other alloys of group IV have not been yet fully investigated due to technical challenges such as insolubility, lattice mismatch, unavailability of proper precursor, etc. Theoretical calculations show that SixSn1-x alloys can also be a direct bandgap material like GeSn with the difference of having a larger bandgap due to high direct band edge of Si at 3.2 eV (Γ-valley)3. However, the theoretical study of this material is not well developed. The estimation of Sn concentration needed to achieve direct bandgap varies in the range of 40-60% while the experimentalist are expecting that to be in the 25% range.3 In this paper we have studied both material properties as well as electronic band structure using density functional theory (DFT) calculations. We have adopted generalized gradient approximation- Perdew–Burke–Ernzerhof (GGA-PBE) 4 with Vienna Ab-initio Simulation Package (VASP).5 The 16-atom cubic supercells of Si and Sn, as well as the unit cell, were used in this modeling in order to find the atomic configurations and energetics. The supercells were relaxed for all the atoms with a residual force of less than 5 × 10−5 eV/Å for each atom. A (4×4×4) Monkhorst−Pack mesh of k-points for a periodic 16-atom supercell was adopted to generate the Brillouin zone. We calculated the lattice constant and its formation energy for all compositions using the GGA–PBE exchange-correlation potential considering the structural relaxation of an isotropic stress for the supercell. The change in the lattice follows the Vegard’s law and a slight bowing (=0. 05 Å) is observed across the full range which is close to previously reported values 0.02-0.084 Å 3, 6 . The lattice constants of Si and α-Sn were estimated to be 5.47 and 6.65 Å, respectively. These values are in close agreement with previously reported values of 5.47Å for Si7 and 6.65–6.74 Å for α-Sn 8 using a similar modeling method of GGA–PBE. It is noteworthy that compared to other group IV binary alloys such as SiGe and GeSn, the proposed bowing parameter is slightly lower. The band structure of all compositions of SixSn1-x is calculated for both unit cell and supercell of 16 atoms. The electronic properties of the alloys are affected by the displacement of Si1-xSnx atoms; therefore, structural relaxation of the structures plays an important role in the band structure. These structures were relaxed to a high extent as stated above. Since the GGA-PBE method underestimates the bandgap of SixSn1-x alloys, different methods have been applied to bring the calculations closer to the real bandgap. In our calculations, we have included the valence band offset of SixSn1-x alloys. The valence band offset is attributed to the electronic interaction between the occupied and unoccupied orbitals of Si1-xSnx. Therefore, by considering an Sn dependent valence band offset as well as heavy, light, and split-off hole bands, the calculations are closer to the real bandgaps. More details of the material properties along with the electronic band structure calculations will be presented at the conference. References [1] A. Atabaki et al., Nature 556, 349 2018 [2] A. Mosleh et al. J Electron Mater 43, 938 2014 [3] J. Tolle et al., Appl. Phys. Lett. 89, 231924 2006 [4] J. P. Perdew et al. Physical Review B 46, 6671 1992 [5] G. Kresse et al. Physical Review B 54, 11169 1996 [6] P. Yakibchuk et al. J Physical Studies 23, 2703 2019 [7] SQ Wang et al. J Physics: Cond. Matt. 15, L197 2003 [8] R. Pandey et al. Appl. Phys. Lett. 75, 4127 1999

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