Polarization-balanced design of AlN/GaN heterostructures: Application to double-barrier structures

Inversion- and depletion-regions generally form at the interfaces between doped leads (cladding layers) and the active region of polar heterostructures like AlN/GaN and other nitride compounds. The band bending in the depletion region sets up a barrier which may seriously impede perpendicular electronic transport. This may ruin the performance of devices such as quantum-cascade lasers and resonant-tunneling diodes. Here we introduce the concepts of polarization balance and polarization-balanced designs: A structure is polarization balanced when the applied bias match the voltage drop arising from spontaneous and piezeolectric fields. Devices designed to operate at this bias have polarization-balanced designs. These concepts offer a systematic approach to avoid the formation of depletion regions. As a test case, we consider the design of AlN/GaN double barrier structures with Al$_{\tilde{x}}$Ga$_{1-\tilde{x}}$N leads. To guide our efforts, we derive a simple relation between the intrinsic voltage drop arising from polar effects, average alloy composition of the active region, and the alloy concentration of the leads. Polarization-balanced designs secure good filling of the ground state for unbiased structures, while for biased structures with efficient emptying of the active structure it removes the depletion barriers

Response of the Shockley surface state to an external electrical field: A density-functional theory study of Cu(111)

The response of the Cu(111) Shockley surface state to an external electrical field is characterized by combining a density-functional theory calculation for a slab geometry with an analysis of the Kohn-Sham wavefunctions. Our analysis is facilitated by a decoupling of the Kohn-Sham states via a rotation in Hilbert space. We find that the surface state displays isotropic dispersion, quadratic until the Fermi wave vector but with a significant quartic contribution beyond. We calculate the shift in energetic position and effective mass of the surface state for an electrical field perpendicular to the Cu(111) surface; the response is linear over a broad range of field strengths. We find that charge transfer occurs beyond the outermost copper atoms and that accumulation of electrons is responsible for a quarter of the screening of the electrical field. This allows us to provide well-converged determinations of the field-induced changes in the surface state for a moderate number of layers in the slab geometry.Comment: 11 pages, 6 figures, 4 tables; accepted for publication by Phys. Rev. B; changes from v1 in response to referee comments, esp. to Sections I and V.B (inc. Table 4), with many added references, but no change in results or conclusion

Math, Science, and Engineering Integration in a High School Engineering Course: A Qualitative Study

Engineering in K-12 classrooms has been receiving expanding emphasis in the United States. The integration of science, mathematics, and engineering is a benefit and goal of K-12 engineering; however, current empirical research on the efficacy of K-12 science, mathematics, and engineering integration is limited. This study adds to this growing field, using discourse analysis techniques to examine whether and why students integrate math and science concepts into their engineering design work. The study focuses on student work during a unit from a high school engineering course. Video data were collected during the unit and were used to identify episodes of students discussing math and science concepts. Using discourse analysis, the authors found that students successfully applied math and science concepts to their engineering design work without teacher prompting when the concepts were familiar. However, explicit teacher prompting and instruction regarding the integration of less familiar concepts did not seem to facilitate student use of those concepts. Possible explanations and implications are discussed

Enhancement of thermoelectric properties by energy filtering: Theoretical potential and experimental reality in nanostructured ZnSb

Energy filtering has been suggested by many authors as a means to improve thermoelectric properties. The idea is to filter away low-energy charge carriers in order to increase Seebeck coefficient without compromising electronic conductivity. This concept was investigated in the present paper for a specific material (ZnSb) by a combination of first-principles atomic-scale calculations, Boltzmann transport theory, and experimental studies of the same system. The potential of filtering in this material was first quantified, and it was as an example found that the power factor could be enhanced by an order of magnitude when the filter barrier height was 0.5~eV. Measured values of the Hall carrier concentration in bulk ZnSb were then used to calibrate the transport calculations, and nanostructured ZnSb with average grain size around 70~nm was processed to achieve filtering as suggested previously in the literature. Various scattering mechanisms were employed in the transport calculations and compared with the measured transport properties in nanostructured ZnSb as a function of temperature. Reasonable correspondence between theory and experiment could be achieved when a combination of constant lifetime scattering and energy filtering with a 0.25~eV barrier was employed. However, the difference between bulk and nanostructured samples was not sufficient to justify the introduction of an energy filtering mechanism. The reasons for this and possibilities to achieve filtering were discussed in the paper

Theory of Polar Corrections to Donor Binding

We calculate the optical phonon correction to the binding energy of electrons to donors in cubic materials. Previous theories calculated the Rydberg energy reduced by the effective mass and the static dielectric function. They omitted an important energy term from the long-range polarization of the ionized donor, which vanishes for the neutral donor. They also omitted the donor-phonon interaction. Including these terms yields a new formula for the donor binding energy

Temperature stability of intersubband transitions in AlN/GaN quantum wells

Temperature dependence of intersubband transitions in AlN/GaN multiple quantum wells grown with molecular beam epitaxy is investigated both by absorption studies at different temperatures and modeling of conduction-band electrons. For the absorption study, the sample is heated in increments up to $400^\circ$C. The self-consistent Schr\"odinger-Poisson modeling includes temperature effects of the band-gap and the influence of thermal expansion on the piezoelectric field. We find that the intersubband absorption energy decreases only by $\sim 6$ meV at $400^\circ$C relative to its room temperature value

Shallow impurity band in ZrNiSn

ZrNiSn and related half Heusler compounds are candidate materials for efficient thermoelectric energy conversion with a reported thermoelectric figure-of-merit of n-type ZrNiSn exceeding unity. Progress on p-type materials has been more limited, which has been attributed to the presence of an impurity band, possibly related to the presence of Ni interstitials in nominally vacant 4d position. The specific energetic position of this band, however, has not been resolved. Here, we report results of a concerted theory-experiment investigation for a nominally undoped ZrNiSn, based on measurements of electrical resistivity, Hall coefficient, Seebeck coefficient and Nernst coefficient, measured in a temperature range from 80 to 420 K. The results are analyzed with a semi-analytical model combining a density functional theory (DFT) description for ideal ZrNiSn, with a simple analytical correction for the impurity band. The model provides a good quantitative agreement with experiment, describing all salient features in the full temperature span for the Hall, conductivity, and Seebeck measurements, while also reproducing key trends in the Nernst results. This comparison pinpoints the impurity band edge to 40 meV below the conduction band edge, which agrees well with a separate DFT study of a supercell containing Ni interstitials. Moreover, we corroborate our result with a separate study of ZrNiSn0.9Pb0.1 sample showing similar agreement with an impurity band edge shifted to 32 meV below the conduction band

Benchmarking van der Waals Density Functionals with Experimental Data: Potential Energy Curves for H2 Molecules on Cu(111), (100), and (110) Surfaces

Detailed physisorption data from experiment for the H_2 molecule on low-index Cu surfaces challenge theory. Recently, density-functional theory (DFT) has been developed to account for nonlocal correlation effects, including van der Waals (dispersion) forces. We show that the functional vdW-DF2 gives a potential-energy curve, potential-well energy levels, and difference in lateral corrugation promisingly close to the results obtained by resonant elastic backscattering-diffraction experiments. The backscattering barrier is found selective for choice of exchange-functional approximation. Further, the DFT-D3 and TS-vdW corrections to traditional DFT formulations are also benchmarked, and deviations are analyzed.Comment: 15 pages, 9 figure