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At least 73 records · Page 4

High dopant activation in arsenic doped single-crystal CdTe thin films: Insights from MBE growth and rapid thermal processing

Single-crystal model systems are valuable tools to investigate fundamental material properties. In this work, we use molecular beam epitaxy to deposit in situ arsenic (As) doped single-crystal CdTe films on large area Si substrates to better understand As doping for photovoltaic applications. We found that As incorporation is highly temperature dependent: a substrate temperature difference of 50 °C can lead to several orders of magnitude difference in As concentration. Cd overpressure during in situ doping may limit out-diffusion of As but decrease As incorporation, especially at lower growth temperatures. Carrier concentrations greater than 10 16 cm −3 can be achieved with or without Cd overpressure when annealed at temperatures above 500 °C. However, unlike the low (∼1% to 5%) dopant activation commonly observed in polycrystalline CdTe, our films achieve significantly higher activation ratios—exceeding 50%, and in some cases approaching 80%. These values are consistent with or exceed prior reports in single-crystal CdTe systems. In addition to as-deposited arsenic concentrations, we also consider arsenic distribution after different rapid thermal processing temperatures. We propose a detailed definition and description of how arsenic incorporation is considered and calculated. Due to carrier concentration saturation, As incorporation also needs to be controlled to average levels of 10 17 cm −3 to achieve high activation. These findings suggest that higher annealing temperature regimes may be beneficial to polycrystalline CdTe based PV devices.

36 MATERIALS SCIENCE↗

Peeled film GaAs solar cell development

Thin-film, single-crystal gallium arsenide (GaAs) solar cells could exhibit a specific power approaching 700 W/kg including coverglass. A simple process has been described whereby epitaxial GaAs layers are peeled from a reusable substrate. This process takes advantage of the extreme selectivity of the etching rate of aluminum arsenide (AlAs) over GaAs in dilute hydrofluoric acid. The feasibility of using the peeled film technique to fabricate high-efficiency, low-mass GaAs solar cells is presently demonstrated. A peeled film GaAs solar cell was successfully produced. The device, although fractured and missing the aluminum gallium arsenide window and antireflective coating, had a Voc of 874 mV and a fill factor of 68 percent under AM0 illumination.

Wilt, D. M.↗

Patterned, Low-Temperature Growth of Transition Metal Dichalcogenides for Low Resistance Raised Contacts

Transition metal dichalcogenide (TMD) monolayers are promising channel materials for next-generation electronic devices. A challenge is the high contact resistance between monolayer TMDs and metal contacts, especially for holes. Here, in this regard, raised source/drain contacts are promising. However, the direct, patterned growth of raised contacts at CMOS-compatible temperatures remains largely unresolved. We present plasma-free selenization and sulfurization of metal oxides at substrate temperatures down to 400 °C, compatible with back-end-of-line thermal budgets. To achieve growth at such temperatures, gas-phase chalcogen precursors are first thermally activated at 950 °C. Films grown on single-crystal monolayer TMDs exhibit high crystal quality, as confirmed by transmission electron microscopy. Raised contacts on WSe 2 monolayers fabricated using this approach yield a low hole contact resistance of 0.3 kΩ·μm after chemical doping. This process is shown to be applicable to growing various TMDs, including WS 2 , MoSe 2 , MoS 2 , PtSe 2 , and NbS 2 .

contact engineering↗

Oxide-nitride heteroepitaxy for low-loss dielectrics in superconducting quantum circuits

Superconducting qubits show great promise for the realization of fault-tolerant quantum computing, but lossy, amorphous dielectrics limit current technology. Identifying highly crystalline and stoichiometric dielectrics with intrinsically low microwave loss is therefore a central materials challenge, yet experimentally validated platforms remain scarce. In this work, we integrate a crystalline dielectric into a heteroepitaxial TiN/$γ$-Al$_2$O$_3$/TiN trilayer grown via pulsed laser deposition. Correlative high-resolution imaging, diffraction, and spectroscopy measurements confirm the single-crystal quality and chemical integrity of all layers, with minimal defects and limited anion interdiffusion across the oxide-nitride interfaces. Using microwave lumped-element resonators with parallel-plate capacitors, we report the first direct measurement of the dielectric loss of epitaxial $γ$-Al$_2$O$_3$, for which we find a low intrinsic two-level system loss, $δ_{\text{TLS}}^0 = (2.8 \pm 0.1) \times 10^{-5}$. These results establish heteroepitaxial oxides on transition metal nitrides as an attractive materials platform for superconducting quantum circuits, particularly for integration into compact device architectures such as merged-element transmons and microwave kinetic inductance detectors.

Garcia-Wetten, David A. [Northwestern U.]↗

CARES/Life Used for Probabilistic Characterization of MEMS Pressure Sensor Membranes

Microelectromechanical systems (MEMS) devices are typically made from brittle materials such as silicon using traditional semiconductor manufacturing techniques. They can be etched (or micromachined) from larger structures or can be built up with material deposition processes. Maintaining dimensional control and consistent mechanical properties is considerably more difficult for MEMS because feature size is on the micrometer scale. Therefore, the application of probabilistic design methodology becomes necessary for MEMS. This was demonstrated at the NASA Glenn Research Center and Case Western Reserve University in an investigation that used the NASA-developed CARES/Life brittle material design program to study the probabilistic fracture strength behavior of single-crystal SiC, polycrystalline SiC, and amorphous Si3N4 pressurized 1-mm-square thin-film diaphragms. These materials are of interest because of their superior high-temperature characteristics, which are desirable for harsh environment applications such as turbine engine and rocket propulsion system hot sections.

Nemeth, Noel N.↗

Fast, Large-Area, Wide-Bandgap UV Photodetector for Cherenkov Light Detection

Due to limited resources available for power and space for payloads, miniaturizing and integrating instrumentation is a high priority for addressing the challenges of manned and unmanned deep space missions to high Earth orbit (HEO), near Earth objects (NEOs), Lunar and Martian orbits and surfaces, and outer planetary systems, as well as improvements to high-altitude aircraft safety. New, robust, and compact detectors allow future instrumentation packages more options in satisfying specific mission goals. A solid-state ultraviolet (UV) detector was developed with a theoretical fast response time and large detection area intended for application to Cherenkov detectors. The detector is based on the wide-bandgap semiconductor zinc oxide (ZnO), which in a bridge circuit can detect small, fast pulses of UV light like those required for Cherenkov detectors. The goal is to replace the role of photomultiplier tubes in Cherenkov detectors with these solid-state devices, saving on size, weight, and required power. For improving detection geometry, a spherical detector to measure high atomic number and energy (HZE) ions from any direction has been patented as part of a larger space radiation detector system. The detector will require the development of solid-state UV photodetectors fast enough (2 ns response time or better) to detect the shockwave of Cherenkov light emitted as the ions pass through a quartz, sapphire, or acrylic ball. The detector must be small enough to fit in the detector system structure, but have an active area large enough to capture enough Cherenkov light from the sphere. The detector is fabricated on bulk single-crystal undoped ZnO. Inter - digitated finger electrodes and contact pads are patterned via photolithography, and formed by sputtered metal of silver, platinum, or other high-conductivity metal.

Wrbanek, John D.↗

On the Ordering Mechanism of Cu + in 2D van der Waals Multiferroic CuCrP 2 S 6

CuCrP 2 S 6 is a van der Waals multiferroic where the tunable Cu + sublattice underpins its exceptional ferroelectric and electronic switching properties. Yet, the microscopic mechanism governing Cu + ordering has remained elusive. Here, we combine single-crystal X-ray and neutron diffraction with pair distribution function analysis to uncover a temperature-driven evolution of Cu + ordering, giving rise to an incommensurate quasi-antipolar phase between the paraelectric and antiferroelectric states. The modulation originates from correlated Cu + occupancy redistribution coupled to breathing distortion of surrounding S 3 triangles, establishing a symmetry-adapted lattice distortion mode. Diffuse scattering persisting over 35 K above the transition confirms that the structural instability follows an order-disorder mechanism. The spontaneous off-centering of Cu + positions CuCrP 2 S 6 as a model platform for correlated order-disorder phenomena in 2D layered ferroics, and provides design principles for next-generation memory and logic devices.

ferroelectrics↗

A Microseismometer for Terrestrial and Extraterrestrial Applications

The scientific and technical requirements of extraterrestrial seismology place severe demands on instrumentation. Performance in terms of sensitivity, stability, and frequency band must match that of the best terrestrial instruments, at a fraction of the size, mass, and power. In addition, this performance must be realized without operator intervention in harsh temperature, shock, and radiation environments. These constraints have forced us to examine some fundamental limits of accelerometer design in order to produce a small, rugged, sensitive seismometer. Silicon micromachined sensor technology offers techniques for the fabrication of monolithic, robust, compact, low-power and -mass accelerometers. However, currently available sensors offer inadequate sensitivity and bandwidth. Our implementation of an advanced silicon micro machined seismometer is based on principles developed at JPL for high-sensitivity position sensor technology. The use of silicon micro machining technology with these new principles should enable the fabrication of a 10(exp -11) g sensitivity seismometer with a bandwidth of at least 0.01 to 20 Hz. The low Q properties of pure single-crystal silicon are essential in order to minimize the Brownian thermal noise limitations generally characteristic of seismometers with small proof masses. A seismometer consists of a spring-supported proof mass and a transducer for measuring its motion. For long period motion a position sensor is generally used, for which the displacement is proportional to the ground acceleration. The mechanical sensitivity can be increased either by increasing the proof mass or decreasing the spring stiffness, neither of which is desirable for planetary applications. Our approach has been to use an ultra sensitive capacitive position sensor with a sensitivity of better than 10(exp -13) m/Hz(exp 1/2). This allows the use of a stiffer suspension and a smaller proof mass. We have built several prototypes using these principles, and tests show that these devices can exhibit performance comparable to state-of-the-art instruments.

Banerdt, W.↗

Infrared-Bolometer Arrays with Reflective Backshorts

Integrated circuits that incorporate square arrays of superconducting-transition- edge bolometers with optically reflective backshorts are being developed for use in image sensors in the spectral range from far infrared to millimeter wavelengths. To maximize the optical efficiency (and, thus, sensitivity) of such a sensor at a specific wavelength, resonant optical structures are created by placing the backshorts at a quarter wavelength behind the bolometer plane. The bolometer and backshort arrays are fabricated separately, then integrated to form a single unit denoted a backshort-under-grid (BUG) bolometer array. In a subsequent fabrication step, the BUG bolometer array is connected, by use of single-sided indium bump bonding, to a readout device that comprises mostly a superconducting quantum interference device (SQUID) multiplexer circuit. The resulting sensor unit comprising the BUG bolometer array and the readout device is operated at a temperature below 1 K. The concept of increasing optical efficiency by use of backshorts at a quarter wavelength behind the bolometers is not new. Instead, the novelty of the present development lies mainly in several features of the design of the BUG bolometer array and the fabrication sequence used to implement the design. Prior to joining with the backshort array, the bolometer array comprises, more specifically, a square grid of free-standing molybdenum/gold superconducting-transition-edge bolometer elements on a 1.4- m-thick top layer of silicon that is part of a silicon support frame made from a silicon-on-insulator wafer. The backshort array is fabricated separately as a frame structure that includes support beams and contains a correspond - ing grid of optically reflective patches on a single-crystal silicon substrate. The process used to fabricate the bolometer array includes standard patterning and etching steps that result in the formation of deep notches in the silicon support frame. These notches are designed to interlock with the support beams on the backshort-array structure to provide structural support and precise relative positioning. The backshort-array structure is inserted in the silicon support frame behind the bolometer array, and the notches in the frame serve to receive the support beams of the backshort-array structure and thus determine the distance between the backshort and bolometer planes. The depth of the notches and, thus, the distance between the backshort and bolometer planes, can be tailored to a value between 25 to 300 m adjusting only a few process steps. The backshort array is designed so as not to interfere with the placement of indium bumps for subsequent indium bump-bonding to the multiplexing readout circuitry

Miller, Timothy M.↗

Additively-manufactured monocrystalline YBCO superconductor

Abstract Single-crystal microstructures enable high-performance YBa 2 Cu 3 O 7-x superconductors which are however limited to simple shapes due to their brittleness. Additive manufacturing can fabricate YBa 2 Cu 3 O 7-x superconductor with complex shapes, albeit with a polycrystalline microstructure. Here, we demonstrate a route to grow single-crystals from 3D-ink-printed, polycrystalline, sintered superconducting YBa 2 Cu 3 O 7-x (YBCO or Y123) + Y 2 BaCuO 5 (Y211), manufacturing objects with complex architectures displaying both high critical current density (J c =2.1 × 10 4 A . cm –2 , 77 K) and high critical temperature (T c = 88-89.5 K). An ink containing precursor powders (Y 2 O 3 , BaCO 3 , and CuO) is 3D-extruded into complex geometries and then reaction-sintered to obtain polycrystalline Y123 + Y211. A seed is then utilized to transform these 3D-printed parts from polycrystal to monocrystal via the melt growth method. The geometric details of 3D-printed parts survive the process without slumping, sagging or collapse, despite the long-term presence of liquid above the peritectic temperature. Origami structures can be created by sheet folding after 3D-printing. This additive approach enables the facile fabrication of superconducting devices with complex shapes and architectures, such as advanced undulator magnets to generate synchrotron radiation and microwave cavities for dark-matter axion search. This work highlights the potential of additive manufacturing for producing monocrystalline cuprate superconductors and opens the door to additive manufacturing of other monocrystalline functional ceramic or semiconductor materials.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Electron-Deficient Phenazines: Synthesis, Structures, Redox, and Optoelectronic Properties in the Gas Phase, in Solution, and in the Solid State

High-temperature gas-phase reactions of 1,4-C4F8I2 with phenazine (PHNZ) afforded new thermally- and air-stable derivatives with cyclo-C4F8 substituents, viz. 1,2-PHNZ(C4F8), 2,3-PHNZ(C4F8), 1,2:6,7-PHNZ(C4F8)2, 1,2:7,8-PHNZ(C4F8)2, and 1,2:8,9-PHNZ(C4F8)2. Reactions in the presence of Cu powder resulted in reductive-defluorination/aromatization of some of the cyclo-C4F8 substituents to produce 2,3-PHNZ(C4F4), 2,3-PHNZ(C4HF3), and 1,2:6,7-PHNZ(C4F8)(C4F4), which are formally tri- or tetrafluoro derivatives of benzo[a]phenazine. Single-crystal X-ray diffraction structures of these compounds demonstrate the planarity of 2,3-PHNZ(C4F4) and 2,3-PHNZ(C4HF3) and ordered p-stacking in 1,2-PHNZ(C4HF3), 1,2-PHNZ(C4F4), 1,2-PHNZ(C4F8), and 2,3-PHNZ(C4F8). Low-temperature gas-phase photoelectron spectra of the PHNZ(C4F8)1,2 compounds show that they are strong electron acceptors, with the three PHNZ(C4F8)2 isomers having electron affinities exceeding that of C60. Cyclic voltammetry in acetonitrile show that the five PHNZ(C4F8)1,2 compounds exhibit reversible one-electron reductions with large positive shifts in their reduction potentials relative to unsubstituted PHNZ. Spectroelectrochemical absorption and EPR spectra of PHNZ(C4F8)1,2- • anion radicals and extensive DFT calculations revealed the significant role that the different substitution patterns have on determining the optoelectronic properties of the PHNZ(C4F8)1,2 derivatives and PHNZ(C4F8)1,2- • anion radicals. Time-resolved microwave conductivity measurements and photoluminescence spectra of blends of the PHNZ(C4F8)1,2 derivatives with the donor poly(3-hexylthiophene) (P3HT) were recorded to assess the possible use of the new compounds in optoelectronic devices.

Balser, Sebastian↗

Spectra-Orthogonal Optical Anisotropy in Wafer-Scale Molecular Crystal Monolayers

Controlling the spectral and polarization response of two-dimensional (2D) crystals is vital for developing ultrathin platforms for compact optoelectronic devices. However, independently tuning optical anisotropy and spectral response remains challenging in conventional semiconductors due to the intertwined nature of their lattice and electronic structures. Here, we report spectra-orthogonal optical anisotropy─where polarization anisotropy is tuned independently of spectral response─in wafer-scale, one-atom-thick 2D molecular crystal (2DMC) monolayers synthesized on monolayer transition-metal dichalcogenide (TMD) crystals. Utilizing the concomitant spectral consistency and structural tunability of perylene derivatives, we demonstrate tunable optical polarization anisotropy in 2DMCs with similar spectral profiles, as confirmed by room-temperature scanning tunneling microscopy and cross-polarized reflectance microscopy. Additional angle-dependent analysis of the single-crystal and polycrystalline molecular domains reveals an epitaxial relationship between the 2DMC and TMD. In conclusion, our results establish a scalable, molecule-based 2D crystalline platform for unique and tunable functionalities unattainable in covalent 2D solids.

2D materials↗

Epitaxial growth of conducting perovskite SrTiO3 on (0001) c-axis sapphire using a γ-Al2O3 intermediate layer

Epitaxial growth of complex oxides on large-area wafers, such as sapphire and silicon, represents a key step toward scalable oxide device production. Solid phase epitaxy allows the synthesis of γ-Al 2 O 3 on α-Al 2 O 3 and provides a template with a matched lattice constant and appropriate cubic symmetry for subsequent heteroepitaxial growth of perovskite complex oxides. Nb-doped SrTiO 3 thin films were deposited epitaxially on (111)-oriented γ-Al 2 O 3 intermediate layers on (0001) c-axis-oriented sapphire α-Al 2 O 3 crystals using pulsed laser deposition. The Nb:SrTiO 3 thin films with a thickness of 53 nm, grown at 700 °C on γ-Al 2 O 3 , reached fully relaxed lattice parameters and were epitaxially oriented with respect to the substrate. Nb:SrTiO 3 layers deposited using identical deposition conditions directly on α-Al 2 O 3 , without the γ-Al 2 O 3 intermediate layer, were polycrystalline. The sheet conductivity of Nb:SrTiO 3 grown on γ-Al 2 O 3 /α-Al 2 O 3 is more than ten times higher than that of Nb:SrTiO 3 grown directly on α-Al 2 O 3 without the γ-Al 2 O 3 layer. The results point to new directions for the integration of (111)-oriented pseudocubic perovskite complex oxides and the integration of epitaxial complex oxides over larger areas using α-Al 2 O 3 single-crystal substrates.

Atomic force microscopy↗

A loophole-free Bell's inequality experiment

The proof of Nature's nonlocality through Bell-type experiments is a topic of longstanding interest. Nevertheless, no experiments performed thus far have avoided the so-called 'detection loophole,' arising from low detector efficiencies and angular-correlation difficulties. In fact, most, if not all, of the systems employed to date can never close this loophole, even with perfect detectors. In addition, another loophole involving the non-rapid, non-random switching of various parameter settings exists in all past experiments. We discuss a proposal for a potentially loophole-free Bell's inequality experiment. The source of the EPR-correlated pairs consists of two simultaneously-pumped type-2 phase-matched nonlinear crystals and a polarizing beam splitter. The feasibility of such a scheme with current detector technology seems high, and will be discussed. We also present a single-crystal version, motivated by other work presented at this conference. In a separate experiment, we have measured the absolute detection efficiency and time response of four single-photon detectors. The highest observed efficiencies were 70.7 plus or minus 1.9 percent (at 633 nm, with a device from Rockwell International) and 76.4 plus or minus 2.3 percent (at 702 nm, with an EG&G counting module). Possible efficiencies as high as 90 percent were implied. The EG&G devices displayed sub-nanosecond time resolution.

Kwiat, Paul G.↗

Real-Time, Holographic, Dynamic Image-Storage Device

Solid-state device developed for high-speed acquisition, dynamic storage, and amplification of three-dimensional holographic images. Holograms generated via four-wave mixing in two or more photorefractive crystals (or subelements of single crystal) to create single-crystal or multicrystal oscillator. Apparatus provides dynamic storage of holographic image of object after electronic shutter closed to turn off object beam. Provides capability to store, amplify, process, and transmit time-varying, two-dimensional, spatial information. Developments include sensors, actuators, and optical computers operating at speeds on order of speed of light. Potential in applications in which need for high-speed acquisition and storage of three-dimensional holographic images.

Montgomery, Raymond C.↗

Atomically Flat Surfaces Developed for Improved Semiconductor Devices

New wide bandgap semiconductor materials are being developed to meet the diverse high temperature, -power, and -frequency demands of the aerospace industry. Two of the most promising emerging materials are silicon carbide (SiC) for high-temperature and high power applications and gallium nitride (GaN) for high-frequency and optical (blue-light-emitting diodes and lasers) applications. This past year Glenn scientists implemented a NASA-patented crystal growth process for producing arrays of device-size mesas whose tops are atomically flat (i.e., step-free). It is expected that these mesas can be used for fabricating SiC and GaN devices with major improvements in performance and lifetime. The promising new SiC and GaN devices are fabricated in thin-crystal films (known as epi films) that are grown on commercial single-crystal SiC wafers. At this time, no commercial GaN wafers exist. Crystal defects, known as screw defects and micropipes, that are present in the commercial SiC wafers propagate into the epi films and degrade the performance and lifetime of subsequently fabricated devices. The new technology isolates the screw defects in a small percentage of small device-size mesas on the surface of commercial SiC wafers. This enables atomically flat surfaces to be grown on the remaining defect-free mesas. We believe that the atomically flat mesas can also be used to grow GaN epi films with a much lower defect density than in the GaN epi films currently being grown. Much improved devices are expected from these improved low-defect epi films. Surface-sensitive SiC devices such as Schottky diodes and field effect transistors should benefit from atomically flat substrates. Also, we believe that the atomically flat SiC surface will be an ideal surface on which to fabricate nanoscale sensors and devices. The process for achieving atomically flat surfaces is illustrated. The surface steps present on the "as-received" commercial SiC wafer is also illustrated. because of the small tilt angle between the crystal "basal" plane and the polished wafer surface. These steps are used in normal SiC epi film growth in a process known as stepflow growth to produce material for device fabrication. In the new process, the first step is to etch an array of mesas on the SiC wafer top surface. Then, epi film growth is carried out in the step flow fashion until all steps have grown themselves out of existence on each defect-free mesa. If the size of the mesas is sufficiently small (about 0.1 by 0.1 mm), then only a small percentage of the mesas will contain an undesired screw defect. Mesas with screw defects supply steps during the growth process, allowing a rough surface with unwanted hillocks to form on the mesa. The improvement in SiC epi surface morphology achievable with the new technology is shown. An atomic force microscope image of a typical SiC commercial epilayer surface is also shown. A similar image of an SiC atomically flat epi surface grown in a Glenn laboratory is given. With the current screw defect density of commercial wafers (about 5000 defects/cm2), the yield of atomically free 0.1 by 0.l mm mesas is expected to be about 90 percent. This is large enough for many types of electronic and optical devices. The implementation of this new technology was recently published in Applied Physics Letters. This work was initially carried out in-house under a Director's Discretionary Fund project and is currently being further developed under the Information Technology Base Program.

Powell, J. Anthony↗

Wideband Single-Crystal Transducer for Bone Characterization

The microgravity conditions of space travel result in unique physiological demands on the human body. In particular, the absence of the continual mechanical stresses on the skeletal system that are present on Earth cause the bones to decalcify. Trabecular structure decreases in thickness and increases in spacing, resulting in decreased bone strength and increased risk of injury. Thus, monitoring bone health is a high priority for long-term space travel. A single probe covering all frequency bands of interest would be ideal for such measurements, and this would also minimize storage space and eliminate the complexity of integrating multiple probes. This invention is an ultrasound transducer for the structural characterization of bone. Such characterization measures features of reflected and transmitted ultrasound signals, and correlates these signals with bone structure metrics such as bone mineral density, trabecular spacing, and thickness, etc. The techniques used to determine these various metrics require measurements over a broad range of ultrasound frequencies, and therefore, complete characterization requires the use of several narrowband transducers. This is a single transducer capable of making these measurements in all the required frequency bands. The device achieves this capability through a unique combination of a broadband piezoelectric material; a design incorporating multiple resonator sizes with distinct, overlapping frequency spectra; and a micromachining process for producing the multiple-resonator pattern with common electrode surfaces between the resonators. This device consists of a pattern of resonator bars with common electrodes that is wrapped around a central mandrel such that the radiating faces of the resonators are coplanar and can be simultaneously applied to the sample to be measured. The device operates as both a source and receiver of acoustic energy. It is operated by connection to an electronic system capable of both providing an excitation signal to the transducer and amplifying the signal received from the transducer. The excitation signal may be either a wide-bandwidth signal to excite the transducer across its entire operational spectrum, or a narrow-bandwidth signal optimized for a particular measurement technique. The transducer face is applied to the skin covering the bone to be characterized, and may be operated in through transmission mode using two transducers, or in pulse-echo mode.

Liang, Yu↗