Abstract. Most attempts to unify general relativity with the standard model of particle physics predict violations of the equivalence principle associated in some way with the composition of the test masses. We test this idea by using observational uncertainties in the positions and motions of solar-system bodies to set upper limits on the relative difference ∆ between gravitational and inertial mass for each body. For suitable pairs of objects, it is possible to constrain three different linear combinations of ∆ using Kepler's third law, the migration of stable Lagrange points, and orbital polarization (the Nordtvedt effect). Limits of order 10 −10 − 10 −6 on ∆ for individual bodies can then be derived from planetary and lunar ephemerides, Cassini observations of the Saturn system, and observations of Jupiter's Trojan asteroids as well as recently discovered Trojan companions around the Earth, Mars, Neptune, and Saturnian moons. These results can be combined with models for elemental abundances in each body to test for composition-dependent violations of the universality of free fall in the solar system. The resulting limits are weaker than those from laboratory experiments, but span a larger volume in composition space.PACS numbers: 04.80. Cc, 95.30.Sf
Gallium nitride is a promising wide bandgap material for demanding applications such as hightemperature and high-power electronics, as well as for space applications where its higher resistance to high fluxes of proton and electron radiation compared to Si represents an important advantage [1]. Electron irradiation of GaN is believed to create both N and Ga vacancies, as well as to induce threading dislocation glide. Typically, the creation or modification of structural defects in GaN are studied in a scanning electron microscope (SEM) retrofitted with cathodoluminescence (CL) or electron beam induced current (EBIC) tools, which identify locations of high defect concentration as dark regions due to increased (non-radiative) recombination rates. Unfortunately, the spatial resolution of these methods is limited due to the relatively large interaction volumes generated by primary electrons. While scanning transmission electron microscopy (STEM) enables the requisite spatial resolution necessary to understand the mechanisms of how defects are created and/or propagated under electron beam irradiation, it is still rarely combined with CL or EBIC, which can identify electronically active defects. Here we report the first STEM based EBIC characterization of Schottky diodes consisting of Ni contacts to free-standing hydride vapor phase epitaxy (HVPE) grown GaN with a threading dislocation density of ~10 5 /cm 2 .Our sample consists of a high purity single crystal n-type GaN substrate (275 µm thick) grown by HVPE with a nickel Schottky contact as well as an indium ohmic contact. Specimen preparation for this sample was unconventional because we did not thin the sample as is typically done in TEM sample preparation. As can be seen from Figure 1a), the Schottky contact remains intact after mounting the sample to the Nanofactory holder. The Ni contact can be seen in both the optical micrograph as well as the energy dispersive x-ray spectroscopy (EDS) map in Figure 1b) and c). The bright field STEM image in the inset of Figure 2a) shows the outline of the GaN and Au wire but does not show any features, as expected due to the specimen thickness. However, the EBIC image only shows areas where charge carriers are measurably excited and separated, i.e. the Ni pad, Ag epoxy, and Au wire. Furthermore, there is no difference in the EBIC signal on or off the GaN, which indicates this is a true EBIC signal and not just a specimen current from e.g. secondary electrons.In order to quantitatively interpret EBIC contrast, consideration of the beam/sample interaction is especially critical. During EBIC, the high energy electron beam excites electron-hole pairs in the material and, in the presence of an electric field, these charge carriers will separate and generate a current detectable with an ammeter [2]. In STEM, the interaction volume of the beam with a thick sample can be extremely large and thus decrease the resolution of the signal. We have begun Monte Carlo simulations to better understand our specific samples and plan to thin the ...
Gallium nitride is currently being investigated for demanding applications such as high-temperature and high-power electronics as well as space-based or other high radiation exposure applications. It has a wide bandgap and is more resistant than Si to high fluxes of proton and electron radiation [1]. Electron irradiation of GaN is believed to create both N and Ga vacancies, as well as to induce threading dislocation glide. These defects can act as recombination centers which reduce the overall minority carrier lifetime and mobility. Measurements of the minority carrier diffusion length in GaN can be studied using cathodoluminescence (CL) or electron beam induced current (EBIC) in a scanning electron microscope (SEM). However, as recently reported in Yakimov et. al. [2], the EBIC planar geometry in SEM often leads to an over estimation of the minority carrier diffusion length in n-type GaN. This over estimation is attributed to the interaction volume in SEM, which is on the order of hundreds of nanometers to a few microns and overlaps with the measured minority carrier diffusion length of n-GaN, reported to be between a few tens of nanometers to a few microns [2].Here we report on scanning transmission electron microscopy (STEM) EBIC characterization of Schottky diodes consisting of hydride vapor phase epitaxy (HPVE) grown n-GaN and patterned Ni contacts. We demonstrate that by using a bulk STEM EBIC technique, the minority carrier diffusion length, Ld, can be separated from the interaction volume diameter, R. An accelerating voltage of 100 kV or 200 kV in STEM gives a much larger interaction volume than an accelerating voltage of 5 to 30 kV does in SEM. We have shown previously [3] that the interaction volume is approx. 4 µm for 100 kV and 14 µm for 200 kV, which are both much larger than the expected diffusion length, Ld for n-type GaN. Since the length scales for R and Ld are quite different, we can separate the exponential decay of the interaction volume from the exponential decay of the diffusion length. This allows accurate measurement of diffusion lengths in a convenient planar geometry while avoiding the pitfalls of planar geometry in SEM EBIC.Our sample consists of a high purity single crystal n-type GaN substrate (275 µm thick) grown by HVPE with a threading dislocation density of ~10 6 /cm 2 and patterned with a nickel Schottky contact as well as an indium ohmic contact. As can be seen in Fig. 1b, the GaN sample is patterned with a Ni contact and wired with Ag epoxy to an Au wire. Since the EBIC image only shows areas where charge carriers are measurably excited and separated, only the Ni pad and some of the Ag epoxy is visible. Fig. 2a shows the line profile EBIC signal as a function of distance, which was taken from the inset of 2a. As can be seen, is a short, fast decay and a long, slow decay. These two exponential decays can be fit and two different decay lengths can be solved for, shown in Fig. 2b. Initial measurements show the minority carrier length for n-type GaN to be 265 ± 27 nm, which is co...
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