Daniel A. Andersson

Modelling of segmental dynamics in polymer electrolyte PPO-LiClO4, by surface fitting of quasi-elastic neutron scattering data

Abstract The structural dynamics of an amorphous model polymer electrolyte, poly(propylene oxide) (PPO) complexed with lithium perchlorate (LiClO 4 ), has been investigated using quasi-elastic neutron scattering (QENS). Pure PPO was investigated for reference. A combination of data from several analyser reflections, has enabled an investigation of a (Fourier) time range, wide enough to encompass parts of the segmental relaxation as well as the methyl group motion. The two processes have been identified and investigated by a simultaneous surface fit of the data from all the detectors and resolutions to a model where the segmental motion is represented by a stretched exponential relaxation function with relaxation times proportional to Q − ν , and the methyl group motion is represented by the three-fold jump rotation model. The dynamics of the pure polymer is well described by the model, using fitting parameters which are in good agreement with literature data, and we conclude that the surface fitting approach is a successful method for analysing the data. The results for the salt-containing polymer show that the segmental relaxation is strongly slowed down and more stretched, whereas no significant change was seen for the methyl group motion. The adequacy of the model in this case cannot be fully evaluated due to the still limited data on the segmental relaxation.

Diffusive dynamics in polymer gel electrolytes investigated by quasi-elastic neutron scattering

Abstract Quasi-elastic neutron scattering has been performed on a polymer gel electrolyte consisting of lithium perchlorate dissolved in ethylene carbonate/propylene carbonate and stabilized with poly(methyl methacrylate). Two relaxational processes are observed, and their momentum transfer dependencies are studied. From this we attribute the faster process to a rotational motion and the slower process to diffusive motion of the solvent. The diffusive process was modelled with a jump diffusion model, giving a diffusion constant of 1.6×10 −10 m 2 / s , a mean residence time of 34 ps and mean jump length of 1.8 A . A jump rotation model analysis of the rotational motion yields a rotation radius of 1.5 A , which is compatible with the size of the solvent molecules.

Supply voltage drop study considering on-chip self inductance of a 32-bit processor's power grid

Conventional IR drop analysis suggests that on-chip inductive effects can be neglected when estimating supply voltage drops. We present a supply voltage drop analysis for a commercial 32-bit application processor. Our power grid model uses a backbone RL extracted netlist of the processors power grid, complemented with capacitances from the processor design and a current signature defined by the worst-case switching test vector, located in the power-up sequence of the processor. Our circuit simulations show that on-chip self inductance makes the actual supply voltage drop deviate by more than 55% and 25% from the ∼6% and ∼8% drop, respectively, of nominal supply voltage that a conventional IR power grid model yields.

Structural investigations of polymer electrolyte poly(propylene oxide)-LiClO4 using diffraction experiments and reverse Monte Carlo simulation.

The structure of an amorphous polymer electrolyte, poly(propylene oxide) (PPO) complexed with LiClO4, has been studied using reverse Monte Carlo (RMC) simulations. The simulations require no force field but are based on experimental data only, in this case from x-ray and neutron diffraction experiments. Excellent agreement between the experimental data and the structures resulting from the RMC simulation is obtained. Samples with ether-oxygen to lithium concentrations (molar ratios) O:Li=16:1 and 5:1 were studied and compared to results of pure PPO from a previous study. We focus on the effects of the solvated salt on the structure of the polymer matrix, the spatial distribution of ions, and the correlations between the anions and the polymer chains. Analyzing the structures produced in the simulations, we find that for a concentration 16:1, the interchain distance is approximately the same as in pure PPO but more well defined. For a concentration 5:1, we find a larger and less well-defined interchain distance compared to the 16:1 concentration. This signifies that at the 16:1 salt concentration, there is enough free volume in the polymer host to accommodate the ions, and that the solvation of salt induces ordering of the polymer matrix. At the higher salt concentration 5:1, the polymer network must expand and become less ordered to host the ions. We also note, in accordance with previous studies, that the solvation of salt changes the conformation of the polymer chain towards more gauche states. The simulations furthermore reveal marked correlations between the polymer chains and the anions, which we suggest arise predominantly from an interaction mediated via cations, which can simultaneously coordinate both ether oxygens in the polymer chains and anions. Interanionic distances at 5 A, which are consistent with two or more anions being coordinated around the same cation, are also observed. On a larger scale, the RMC structure of PPO-LiClO4 16:1 clearly indicates the presence of salt-rich and salt-depleted domains having a length scale of <20 A. In view of such a heterogeneous structure of PPO-LiClO4 16:1, it is plausible that the increased ordering of the polymer matrix is due to rather well-defined structural arrangements within the salt-rich domains, and that the characteristic interchain distance in the salt-rich domains is similar to that of the pure polymer.

Noise-Aware On-Chip Power Grid Considerations Using a Statistical Approach

We analyze the correlation between different parameters of the on-chip power distribution grid and their impact on noise. By using factor analysis we are able to uncover correlations between power grid design variables and power supply noise. We derive the correlation between design variables and noise from an analysis of 300 different grids in a 65-nm process technology, and manage to find the impact that a change in power grid design variables will have on noise. The results from this analysis can be used as guidelines when designing a robust power distribution grid.

Diffusive solvent dynamics in a polymer gel electrolyte studied by quasielastic neutron scattering

A quasielastic neutron scattering study has been performed on a polymer gel electrolyte consisting of lithium perchlorate dissolved in ethylene carbonate/propylene carbonate and stabilized with poly(methyl methacrylate). The dynamics of the solvent, which is crucial for the ion conduction in this system, was probed using the hydrogen/deuterium contrast variation method with nondeuterated solvent and a deuterated polymer matrix. Two relaxation processes of the solvent were studied in the 10-400 microeV range at different temperatures. From analysis of the momentum transfer dependence of the processes we conclude that the faster process ( approximately 100 microeV) is related to rotational diffusion of the solvent and the slower process ( approximately 10 microeV) to translational diffusion of the solvent. The translational diffusion is found to be similar to the diffusion in the corresponding liquid electrolyte at short distances, but geometrically constrained by the polymer matrix at distances beyond approximately 5 A. The study indicates that the hindered diffusion of the solvent on a length scale of the polymer network interchain distance ( approximately 5-20 A) is sufficient to explain the reduced macroscopic diffusivity and ion conductivity of the gel electrolyte compared to the liquid electrolyte.

Interconnect Characterization Flow for Minimal-Segment Model Selection

We present a new method to find minimal-complexity interconnect models that obey a certain specified accuracy in relation to the true waveform. The method can be described as an interconnect characterization flow that defines simple rules for finding the minimal number of segments and required segment type, RC or RLC, by regarding interconnect resistance, driver source resistance, interconnect characteristic impedance and load capacitance. To show the application of the method, segment selection rules are derived for a case with a waveform discrepancy constraint of 5%

On Skin Effect in On-Chip Interconnects

We investigate the influence of skin effect on the propagation delays of on-chip interconnects. For long wires, designed in the LC regime, on the top metal layer in a contemporary process, we find that the skin effect causes an extra delay by 10%. The impact of the skin effect on delay is furthermore rapidly increasing with increased interconnect width.

Toward a systematic sensitivity analysis of on-chip power grids using factor analysis

We present a systematic way of performing sensitivity analysis on on-chip power distribution grids. By using factor analysis we are able to uncover correlations between power grid design variables and power supply noise. From our analysis of 300 different grids in a 65-nm process, we can identify which power grid design variables have both high correlation to and high impact on noise; the most important one being supply rail width.

Accounting for the skin effect during repeater insertion

Since the skin effect will increase the propagation delay in an interconnect, it will also affect how to optimally select the number and size of the buffers. Failing to include the skin effect during buffer design may result in as much as 35% extra delay compared to the optimal repeater chain. We present a new method with closed-form expressions for repeater insertion where we take into account the skin effect and also the relationship between interconnect resistance, capacitance and inductance that are determined from the geometrical parameters. We also investigate the skin-effect influence on power dissipation for an optimally designed repeater chain, and find that the increase is at most 10% of the dynamic power dissipation.