Modeling of irregular shaped power distribution planes using transmission matrix method

Kim, Joong-Ho; Swaminathan, Madhavan

doi:10.1109/6040.938301

Cited by 127 publications

(5 citation statements)

References 10 publications

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“…Randomly rough surfaces are usually characterized by the root mean square height σ which represents the vertical scale and the correlation length τ which denotes the lateral scale. The autocovariance function of Gaussian distributed randomly rough surfaces is as follows [ 21 ]:

where

represents the height at position

is a spatial vector, and q denotes its magnitude.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Regime Map of the Effective Medium Approximation Modelling of Micro-Rough Surfaces in Ellipsometry

Huang,

Guo,

Jiang

2024

Sensors

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In this work, we discuss the precision of the effective medium approximation (EMA) model in the data analysis of spectroscopic ellipsometry (SE) for solid materials with micro-rough surfaces by drawing the regime map. The SE parameters ψ (amplitude ratio) and Δ (phase difference) of the EMA model were solved by rigorous coupled-wave analysis. The electromagnetic response of the actual surfaces with micro roughness was simulated by the finite-difference time-domain method, which was validated by the experimental results. The regime maps associated with the SE parameters and optical constants n (refractive index) and k (extinction coefficient) of the EMA model were drawn by a comparison of the actual values with the model values. We find that using EMA to model micro-rough surfaces with high absorption can result in a higher precision of the amplitude ratio and extinction coefficient. The precisions of ψ, Δ, n and k increase as the relative roughness σ/λ (σ: the root mean square roughness, λ: the incident wavelength) decreases. The precision of ψ has an influence on the precision of k and the precision of Δ affects the precision of n. Changing σ alone has little effect on the regime maps of the relative errors of SE parameters and optical constants. A superior advantage of drawing the regime map is that it enables the clear determination as to whether EMA is able to model the rough surfaces or not.

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where

represents the height at position

is a spatial vector, and q denotes its magnitude.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Regime Map of the Effective Medium Approximation Modelling of Micro-Rough Surfaces in Ellipsometry

Huang,

Guo,

Jiang

2024

Sensors

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“…To satisfy compression requirement, the power grid should be cut into N parts and the swtich transistors should be divided into N groups. To ensure that switched capacitance driven by each switch transistor group is less than C s_max , N should be no less than the ceiling of (C s_total /C s_max ) as shown in (3). Where C s_total is the total switched capacitance driven by all switch transistors, and it can be extracted from process files.…”

Section: Ecs Transactions 60 (1) 1215-1218 (2014)mentioning

confidence: 99%

“…As technology scaling, shorting the gate length of a transistor increases its power consumption due to the increased leakage current [1][2][3][4]. Power gating is a well-known way to reduce leakage power by turn off idle blocks.…”

Section: Introductionmentioning

confidence: 99%

Power Gating Method for Power Supply Noise Suppression

Song¹,

Ding²,

Wang³

et al. 2014

ECS Trans.

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As technology scaling down, power consumption of integrated circuits increases tremendously due to leakage current. Power gating is one of the most effective techniques to reduce leakage power by shutting off idle blocks from power supply. However, during a power-mode transition, an instantaneous charge current passes through the switch transistor, and creates current surge elsewhere. Because of the self-inductance of the off-chip bonding wires and parasitic inductance inherent to the on-chip power rails, these surges result in severe simultaneous switching noise (SSN), which results in function failure.Based on typical power delivery network, it is found that the magnitude of SSN would accumulate positively with Fcurrent = 1/(n + 1) Resonant, and the magnitude of SSN would accumulate negatively with Fcurrent = 1/(n + 1/2) Resonant. In this paper, a new method is proposed to suppress the power supply noise based on its periodic characteristic. By cutting power grid, partition of switch transistors and controlling their switching, smaller segmented charge current magnitude and controllable period can be provided into gated block for mitigating noise. The power supply noise produced by charge current can be suppressed through adjusting the delay of charge current and the magnitude of charge current which is verified by simulation. Compared to conventional power gating structures, this method can save decap area and is practical and flexible to embed in an optimization flow. A principle for controllable switch transistor chain is also given to simplify the high speed power delivery network design.

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“…Even small changes in these parameters cause considerable variations in nanostructured material properties. The optical constant and film thickness are the most important factors influencing the properties of nanostructured materials; therefore, accurate measurement of the optical constant and thickness of a thin film is crucial [6].…”

Section: Introductionmentioning

confidence: 99%

A Characterization Method of Thin Film Parameters Based on Adaptive Differential Evolution Algorithm

et al. 2021

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According to the transmission mode of polarized light in Mueller ellipsometry, a characterization method for the thickness and optical constants of isotropic nano films based on Self-Adaptive Differential Evolution algorithm (SADE) is proposed. By establishing the least square model of the output light intensity with respect to the Mueller matrix of the standard sample to be measured, the elements of the Mueller matrix are solved by using the Sade algorithm, and the Mueller spectral curve obtained by fitting is compared with that measured by DRC-MME, and the film thickness is calculated by using the transfer matrix. The SiO2 / Si standard samples with calibration values of 100.4 nm and 121.56 nm are simulated and calculated. The experiment shows that: when numbers of iterations accumulated to 65 and 80 respectively, the residual square sum of the light intensity of the objective function converges to the minimum values of 1.24 and 1.02. The calculated film thickness values are 101.25nm and 120.53nm respectively, and the relative errors are both less than 1%. It proves the characteristics of simple calculation, fast convergence and accurate global optimal solution.

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Modeling of irregular shaped power distribution planes using transmission matrix method

Cited by 127 publications

References 10 publications

Regime Map of the Effective Medium Approximation Modelling of Micro-Rough Surfaces in Ellipsometry

Regime Map of the Effective Medium Approximation Modelling of Micro-Rough Surfaces in Ellipsometry

Power Gating Method for Power Supply Noise Suppression

A Characterization Method of Thin Film Parameters Based on Adaptive Differential Evolution Algorithm

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