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Many applications in computational science and engineering require the computation of eigenvalues and vectors of dense symmetric or Hermitian matrices. For example, in DFT (density functional theory) calculations on modern supercomputers 10% to 30% of the eigenvalues and eigenvectors of huge dense matrices have to be calculated. Therefore, performance and parallel scaling of the used eigensolvers is of upmost interest. In this article different routines of the linear algebra packages ScaLAPACK and Elemental for parallel solution of the symmetric eigenvalue problem are compared concerning their performance on the BlueGene/P supercomputer. Parameters for performance optimization are adjusted for the different data distribution methods used in the two libraries. It is found that for all test cases the new library Elemental which uses a two-dimensional element by element distribution of the matrices to the processors shows better performance than the old ScaLAPACK library which uses a block-cyclic distribution.
A novel photoexcitation method for the light-addressable potentiometric sensor (LAPS) is proposed to achieve a higher spatial resolution of chemical images. The proposed method employs a combined light source that consists of a modulated light probe, which generates the alternating photocurrent signal, and a ring of constant illumination surrounding it. The constant illumination generates a sheath of carriers with increased concentration which suppresses the spread of photocarriers by enhanced recombination. A device simulation was carried out to verify the effect of constant illumination on the spatial resolution, which demonstrated that a higher spatial resolution can be obtained.
A novel photoexcitation method for the light-addressable potentiometric sensor (LAPS) realized a higher spatial resolution of chemical imaging. In this method, a modulated light probe, which generates the alternating photocurrent signal, is surrounded by a ring of constant light, which suppresses the lateral diffusion of photocarriers by enhancing recombination. A device simulation verified that a higher spatial resolution could be obtained by adjusting the gap between the modulated and constant light. It was also found that a higher intensity and a longer wavelength of constant light was more effective. However, there exists a tradeoff between the spatial resolution and the amplitude of the photocurrent, and thus, the signal-to-noise ratio. A tilted incidence of constant light was applied, which could achieve even higher resolution with a smaller loss of photocurrent.
As a semiconductor-based electrochemical sensor, the light-addressable potentiometric sensor (LAPS) can realize two dimensional visualization of (bio-)chemical reactions at the sensor surface addressed by localized illumination. Thanks to this imaging capability, various applications in biochemical and biomedical fields are expected, for which the spatial resolution is critically significant. In this study, therefore, the spatial resolution of the LAPS was investigated in detail based on the device simulation. By calculating the spatiotemporal change of the distributions of electrons and holes inside the semiconductor layer in response to a modulated illumination, the photocurrent response as well as the spatial resolution was obtained as a function of various parameters such as the thickness of the Si substrate, the doping concentration, the wavelength and the intensity of illumination.
The simulation results verified that both thinning the semiconductor substrate and increasing the doping concentration could improve the spatial resolution, which were in good agreement with known experimental results and theoretical analysis. More importantly, new findings of interests were also obtained. As for the dependence on the wavelength of illumination, it was found that the known dependence was not always the case. When the Si substrate was thick, a longer wavelength resulted in a higher spatial resolution which was known by experiments. When the Si substrate was thin, however, a longer wavelength of light resulted in a lower spatial resolution. This finding was explained as an effect of raised concentration of carriers, which reduced the thickness of the space charge region.
The device simulation was found to be helpful to understand the relationship between the spatial resolution and device parameters, to understand the physics behind it, and to optimize the device structure and measurement conditions for realizing higher performance of chemical imaging systems.