A Scanned Perturbation Technique For Imaging Electromagnetic Standing Wave Patterns of Microwave Cavities

We have developed a method to measure the electric field standing wave distributions in a microwave resonator using a scanned perturbation technique. Fast and reliable solutions to the Helmholtz equation (and to the Schrodinger equation for two dimensional systems) with arbitrarily-shaped boundaries are obtained. We use a pin perturbation to image primarily the microwave electric field amplitude, and we demonstrate the ability to image broken time-reversal symmetry standing wave patterns produced with a magnetized ferrite in the cavity. The whole cavity, including areas very close to the walls, can be imaged using this technique with high spatial resolution over a broad range of frequencies.Comment: To be published in Review of Scientific Instruments,September, 199

Activation Energy of Metastable Amorphous Ge2Sb2Te5 from Room Temperature to Melt

Resistivity of metastable amorphous Ge2Sb2Te5 (GST) measured at device level show an exponential decline with temperature matching with the steady-state thin-film resistivity measured at 858 K (melting temperature). This suggests that the free carrier activation mechanisms form a continuum in a large temperature scale (300 K - 858 K) and the metastable amorphous phase can be treated as a super-cooled liquid. The effective activation energy calculated using the resistivity versus temperature data follow a parabolic behavior, with a room temperature value of 333 meV, peaking to ~377 meV at ~465 K and reaching zero at ~930 K, using a reference activation energy of 111 meV (3kBT/2) at melt. Amorphous GST is expected to behave as a p-type semiconductor at Tmelt ~ 858 K and transitions from the semiconducting-liquid phase to the metallic-liquid phase at ~ 930 K at equilibrium. The simultaneous Seebeck (S) and resistivity versus temperature measurements of amorphous-fcc mixed-phase GST thin-films show linear S-T trends that meet S = 0 at 0 K, consistent with degenerate semiconductors, and the dS/dT and room temperature activation energy show a linear correlation. The single-crystal fcc is calculated to have dS/dT = 0.153 {\mu}V/K for an activation energy of zero and a Fermi level 0.16 eV below the valance band edge.Comment: 5 pages, 5 figure

Suppression of thermoelectric Thomson effect in silicon microwires under large electrical bias and implications for phase-change memory devices

We have observed how thermoelectric effects that result in asymmetric melting of silicon wires are suppressed for increasing electric current density (J). The experimental results are investigated using numerical modeling of the self-heating process, which elucidates the relative contributions of the asymmetric thermoelectric Thomson heat (∼J) and symmetric Joule heating (∼J2) that lead to symmetric heating for higher current levels. These results are applied in modeling of the self-heating process in phase-change memory devices. While, phase-change memory devices show a clearly preferred operation polarity due to thermoelectric effects, nearly symmetric operation can be achieved with higher amplitude and shorter current pulses, which can lead to design of improved polarity-invariant memory circuitry. © 2014 AIP Publishing LLC

First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard

We report on first experimental signatures for chaos-assisted tunneling in a two-dimensional annular billiard. Measurements of microwave spectra from a superconducting cavity with high frequency resolution are combined with electromagnetic field distributions experimentally determined from a normal conducting twin cavity with high spatial resolution to resolve eigenmodes with properly identified quantum numbers. Distributions of so-called quasi-doublet splittings serve as basic observables for the tunneling between whispering gallery type modes localized to congruent, but distinct tori which are coupled weakly to irregular eigenstates associated with the chaotic region in phase space.Comment: 5 pages RevTex, 5 low-resolution figures (high-resolution figures: http://linac.ikp.physik.tu-darmstadt.de/heiko/chaospub.html, to be published in Phys. Rev. Let

Extracting the temperature distribution on a phase-change memory cell during crystallization

Phase-change memory (PCM) devices are enabled by amorphization- and crystallization-induced changes in the devices' electrical resistances. Amorphization is achieved by melting and quenching the active volume using short duration electrical pulses (∼ns). The crystallization (set) pulse duration, however, is much longer and depends on the cell temperature reached during the pulse. Hence, the temperature-dependent crystallization process of the phase-change materials at the device level has to be well characterized to achieve fast PCM operations. A main challenge is determining the cell temperature during crystallization. Here, we report extraction of the temperature distribution on a lateral PCM cell during a set pulse using measured voltage-current characteristics and thermal modelling. The effect of the thermal properties of materials on the extracted cell temperature is also studied, and a better cell design is proposed for more accurate temperature extraction. The demonstrated study provides promising results for characterization of the temperature-dependent crystallization process within a cell. � 2016 Author(s)

Influence of diffraction on the spectrum and wavefunctions of an open system

In this paper, we demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge of the system are found to have a strong influence on the transmission spectrum of the system, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.Comment: 27 pages, 29 figures, and 3 tables. Submitted to Physical Review E. A copy with higher resolution figures is available at http://monsoon.harvard.edu/~hersch/papers.htm

Single-Atom Gating of Quantum State Superpositions

The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space--or Hilbert space--is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hilbert space, determining an angle of rotation equivalent to quantum phase. Here we show that an individual atom inside a designed quantum corral can control this angle, producing arbitrary coherent superpositions of spatial quantum states. Using scanning tunnelling microscopy and nanostructures assembled atom-by-atom we demonstrate how single spins and quantum mirages can be harnessed to image the superposition of two electronic states. We also present a straightforward method to determine the atom path enacting phase rotations between any desired state vectors. A single atom thus becomes a real space handle for an abstract Hilbert space, providing a simple technique for coherent quantum state manipulation at the spatial limit of condensed matter.Comment: Published online 6 April 2008 in Nature Physics; 17 page manuscript (including 4 figures) + 3 page supplement (including 2 figures); supplementary movies available at http://mota.stanford.ed

Measurement of Wave Chaotic Eigenfunctions in the Time-Reversal Symmetry-Breaking Crossover Regime

We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a two-dimensional microwave resonator are analyzed as a function of an experimentally determined time-reversal symmetry-breaking parameter. We test four theories of onepoint eigenfunction statistics and introduce a new theory relating the one-point and two-point statistical properties in the crossover regime. We also find a universal correlation between the one-point and twopoint statistical parameters for the crossover eigenfunctions. PACS numbers: 05.45. Mt, 03.65.Sq, 11.30.Er, 84.40.Az Many complex quantum systems whose underlying classical behavior is chaotic can be described by treating their Hamiltonian matrix elements as random numbers which fluctuate around zero with a Gaussian distribution. There are universal statistical properties of the eigenvalues and eigenfunctions of these random matrices which depend only on the symmetries of the Hamiltonian. For instance, random matrix theory has been shown to be consistent with the statistical properties of nuclei [1], molecules [2], and two-dimensional quantum dots When time-reversal symmetry is present, wave chaotic systems have statistical properties described by a Gaussian orthogonal ensemble (GOE) of random matrices Here we address the evolution of eigenfunctions of semiclassical wave chaotic systems from the TRS to the TRSB limits. A considerable theoretical literature has developed proposing detailed descriptions of eigenvector statistics in the crossover regime, although little experimental data are available to test these theories. These theories treat only the evolution of the one-point statistical property of eigenfunction distribution, P͑jCj 2 ͒, which quantifies the degree of probability density, jCj 2 , fluctuations in the eigenfunctions The experimental arrangement used to create and measure the wave chaotic eigenfunctions has been described previously We have found that the nonreciprocal property of the ferrite, hence the degree of TRSB, is a function of frequency of the eigenmode in a relatively narrow range of frequency 2482 0031-9007͞00͞85(12)͞2482(4)$15.0

Operation dynamics in phase-change memory cells and the role of access devices

A detailed physical model of the heating and amorphization profiles in phase-change memory elements is applied to illustrate the effects of loads and pulse rise times on the reset operation of phase-change memory cells. Finite element modeling of the electrical and thermal transport is used for a mushroom phase-change memory element - including temperature dependent materials parameters, thermoelectric terms and thermal boundary resistance between different materials - and integrated idealized circuit models are used for the access devices (MOSFET and diode, with a separate series resistance). The results show certain windows of loads and transient times that lead to successful reset operation without excessive wasted power, for the particular PCM cells and programming conditions simulated