Henning Braunisch

Effects of random rough surface on absorption by conductors at microwave frequencies

The effects of a random rough surface on the absorption by a metallic surface at microwave frequencies are analyzed by using two methods: the analytic small perturbation method and the numerical method of moments method. The results show significant difference between absorption of a rough surface and that of a smooth surface. The absorption depends on the root mean square height, correlation length, and correlation function of the random rough surface. The similarities with and differences from Morgans classical result and the Hammerstad and Bekkadal formula are discussed. It is shown that for multiscale rough surfaces, saturation of absorption does not occur, or occurs at much higher frequencies.

A multiplicative regularization approach for deblurring problems

In this work, an iterative inversion algorithm for deblurring and deconvolution is considered. The algorithm is based on the conjugate gradient scheme and uses the so-called weighted L/sub 2/-norm regularizer to obtain a reliable solution. The regularizer is included as a multiplicative constraint. In this way, the appropriate regularization parameter will be controlled by the optimization process itself. In fact, the misfit in the error in the space of the blurring operator is the regularization parameter. Then, no a priori knowledge on the blurred data or image is needed. If noise is present, the misfit in the error consisting of the blurring operator will remain at a large value during the optimization process; therefore, the weight of the regularization factor will be more significant. Hence, the noise will, at all times, be suppressed in the reconstruction process. Although one may argue that, by including the regularization factor as a multiplicative constraint, the linearity of the problem has been lost, careful analysis shows that, under certain restrictions, no new local minima are introduced. Numerical testing shows that the proposed algorithm works effectively and efficiently in various practical applications.

Off-Chip Rough-Metal-Surface Propagation Loss Modeling and Correlation with Measurements

We discuss a small-perturbation method (SPM) for the prediction of the surface-roughness augmented propagation loss encountered on interconnects on high-speed packages and boards. In this methodology, rough surfaces are characterized by their power spectral density (PSD) that can be obtained from surface height profiles by the application of Fourier methods and averaging. Piecewise uniformly rough interconnect structures can be treated by localization of the SPM and assigning corresponding effective conductivities in an electromagnetic field solver. Quantitative surface imaging techniques for acquiring surface height maps include optical interferometry, scanning probe microscopy and scanning electron microscopy. Reactive ion etching is used to expose copper surfaces on post-lamination samples with organic dielectrics. For demonstration of the SPM through correlation with measurements, de-embedding of the transmission line loss is performed using a two-line method. Atomic force microscopy is employed to image the rough ground plane of the micro-strip interconnect and obtain its PSD. Good agreement between measured and predicted loss is shown.

Modeling Effects of Random Rough Interface on Power Absorption Between Dielectric and Conductive Medium in 3-D Problem

We study the effects of a random rough surface on the power absorption between a dielectric and conductive medium in a 3-D configuration where the surface height varies in both horizontal directions. The analytic small perturbation method of second order and numerical T-matrix method are used. The absorption depends on the root mean square height, correlation length, and correlation function of the random rough surface. A closed-form expression of power absorption enhancement factor is obtained from small perturbation method of second order. Results show that the T-matrix method agrees with the small perturbation method for rough surfaces with a small slope. We further compare the 3-D results to the previous 2-D results and show significant difference. The power absorption enhancement factor exhibits saturation for the Gaussian correlation function, but not for the exponential correlation function

Wave Propagation in a Randomly Rough Parallel-Plate Waveguide

We study the effects of random rough surface on electromagnetic wave propagation in a parallel-plate waveguide excited by a line source. The second-order small perturbation method is applied to derive a closed-form expression for the coherent wave propagation and the power loss. The derived result is expressed in terms of a double Sommerfeld integral. The double Sommerfeld integral is evaluated by direct numerical integration and by approximate methods. The results of the two methods are shown to be in good agreement with each other. Numerical results of coherent wave propagation and power loss are illustrated as a function of roughness characteristics and waveguide thickness. The enhancement factors are compared with previous results of plane-wave scattering. The waveguide model and the plane-wave model are in good agreement for moderate to large waveguide thicknesses. For small waveguide thickness, the waveguide model shows significantly different power loss as compared to the plane-wave model. Full-wave simulations by the finite-element method are used to validate the second-order small perturbation in waveguide model.

Random Rough Surface Effects on Wave Propagation in Interconnects

To address the rough surface effects in high-speed interconnects on printed circuit boards (PCBs) and microelectronic packages, we study the electromagnetic wave propagation in a rough surface environment. In our model, the rough surface is characterized by a stochastic random process with correlation function or spectral density. This paper reviews the analytical theory, numerical simulations and experimental results based on such a model. We describe the rough surface characterization and the extraction of roughness parameters from 3D profile measurements. Initially we study the 2D case with the rough surface height function varying in only one horizontal direction and consider the case of plane wave incidence. Analytic second-order small perturbation method (SPM2) was used to obtain simple closed-form expressions for the absorption enhancement factor. The numerical transfer matrix (T-matrix) method and the method of moments (MoM) were also used. We next consider the case of the 3D problem with the rough surface height varying in both horizontal directions. We also used SPM2 to obtain a simple closed form expression for the enhancement factor. In interconnect problems, electromagnetic (EM) waves propagate in a guided wave environment. Thus, we next considered a waveguide model to study the effects of random roughness on wave propagation and compare with results from the plane wave formulation. Analytic SPM2 and numerical finite element method (FEM) with mode matching were used to obtain the enhancement factor. We also describe experimental results and correlation with the theoretical models. Finally, we explain how the enhancement factor concept used throughout lends itself to direct inclusion of rough surface effects in a wide variety of modeling problems.

Estimation of Roughness-Induced Power Absorption From Measured Surface Profile Data

We present a methodology for extracting the 2D power spectral density of a statistically isotropic random rough surface from height measurements by utilizing fast Fourier-Bessel transform. We compute the additional propagation loss due to surface roughness by integrating the extracted spectral density via the formula of absorption enhancement factor. Results for a microstrip demonstrate good correlation between measured and estimated loss up to 20 GHz. It is also possible to choose a random rough surface model for the measured surface and use it to predict the roughness effect on power loss.

High-Speed Flex-Circuit Chip-to-Chip Interconnects

High-speed chip-to-chip interconnect utilizing flex-circuit technology is investigated for extending the lifetime of copper-based system-level channels. Proper construction of the flex ribbon is shown to improve the raw bandwidth over standard FR-4 boards by about three times. Active testing results from a 130-nm CMOS test vehicle show the potential of up to two times higher data rates. The next-generation test vehicle with 90-nm CMOS circuits gives improved voltage and timing margins at 20 Gb/s. In an interconnect limited case a channel with 36 in (91.4 cm) of flex runs at 18.2 Gb/s data rate at a bit-error ratio (BER) of better than 10-12. The channel includes two 90-nm CMOS test chips, two organic flip-chip package substrates, and two flex connectors; crosstalk is not included in this experiment. High-speed connector solutions, including results from a ldquosplit socketrdquo assembly test vehicle, are discussed in detail. The characterization of two top-side flex connector prototypes demonstrates their basic durability and good high-frequency performance. Samples survive 100 mating cycles at an average contact resistance of less than 30 mOmega, adequate for high-speed signaling. Measured differential insertion loss is less than 1.5 dB up to 10 GHz and less than 3.5 dB up to 20 GHz. Near-end and far-end crosstalk measurements indicate that the connectors exceed crosstalk specifications.

RF packaging and passives: design, fabrication, measurement, and validation of package embedded inductors

Design, modeling, and characterization of inductors embedded in a package substrate promising higher quality factor (Q) and lower cost than on-chip inductors is described. In addition to the problem of large conductor losses, on-die inductors with or without magnetic materials consume considerable die area and require the removal of the first-level interconnect bumps beneath them to maintain a reasonably high Q value. Moving inductors to the package eliminates the need for bump array depopulation and, thus, mitigates the potential reliability problems caused by voids in the epoxy underfill between the die and the substrate. Competency developed to design, fabricate, and characterize inductors based on standard organic flip-chip packaging technology is described. Physical design details along with measurement procedures and results are discussed. In addition, modeling techniques for achieving good correlation to measured data are included.

Optical I/O technology for digital VLSI

We describe the development of a high-speed, 12-channel (8-data, 2-clock and 2-alignment channels), parallel optical link with a unique packaging concept. The package is used to demonstrate the viability of chip-to-chip optical I/O in very large scale integration (VLSI) circuits. However, for implementation of optical systems in high performance computing applications, the cost of components and packaging has to come down significantly from the traditional optical communication distances. In the current work we attempted to realize such a system by using power efficient optical and electronic components together with a potentially low cost packaging solution compatible with the electronics industry. Vertical Cavity Surface Emitting Lasers (VCSEL), positive-intrinsic-negative (PIN) photodetectors, polymer waveguide arrays as well as CMOS transceiver chip were heterogeneously integrated on a standard microprocessor flip-chip pin grid array (FCPGA) substrate. The CMOS transceiver chip from 0.18μm processing technology contains VCSEL drivers, transimpedance and limiting amplifiers and on-chip self-testing circuits. A self-test circuit in such high-speed systems will be highly beneficial to reduce the testing cost in real products. For fully assembled packages we measured a 3 Gb/s optical eye for the transmitter (24Gb/s aggregate data rate) and a transmission over the complete link was achieved at 1 Gb/s (8Gb/s aggregate data rate).