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In this article, we first propose a deep reinforcement learning (RL)-based optimal decoupling capacitor (decap) design method for silicon interposer-based 2.5-D/3-D integrated circuits (ICs). The proposed method provides an optimal decap design that satisfies target impedance with a minimum area. Using deep RL algorithms based on reward feedback mechanisms, an optimal decap design guideline can be derived. For verification, the proposed method was applied to test power distribution networks (PDNs) and self-PDN impedance was compared with full search simulation results. We successfully verified by the full search simulation that the proposed method provides one of the solution sets. Conventional approaches are based on complex analytical models from power integrity (PI) domain expertise. However, the proposed method requires only specifications of the PDN structure and decap, along with a simple reward model, achieving fast and accurate data-driven results. Computing time of the proposed method was a few minutes, significantly reduced than that of the full search simulation, which took more than a month. Furthermore, the proposed deep RL method covered up to $10^{17}$ – $10^{18}$ cases, an approximately $10^{12}$ – $10^{13}$ order increase compared to the previous RL-based methods that did not utilize deep-learning techniques.

In this paper, we first propose power distribution network (PDN) model of the perforated power and ground (P/G) planes including substrate effects and multiarray through-silicon vias (TSVs) for a silicon interposer. Since it is almost impossible to simulate a high metal density perforated PDN structure, we first suggest a modeling methodology for P/G perforated planes to reduce simulation time significantly with a high accuracy. To obtain the PDN impedance of a silicon interposer faster, we convert the perforated planes to solid planes with a dielectric mixture. The capacitance (C) and conductance (G) component of perforated P/G planes are precisely estimated based on the conformal mapping method. From the estimated C and G, the physical dimension and material properties of the dielectric mixture of solid P/G planes are determined, respectively. Because silicon interposer PDN consists of a periodic structure, we design and analyze the unit cell of a PDN thoroughly. From the unit cell analysis, the electrical characteristic of an entire PDN for a silicon interposer is successfully estimated. The PDN impedance of the proposed solid and perforated P/G planes and simulation time to obtain each PDN impedance are compared and evaluated, respectively. The proposed methodology is validated by a full 3-D electromagnetic (EM) simulation in the frequency range from 0.01 to 20 GHz. We also proposed models of multiarray P/G TSVs that can be applied to the various P/G patterns for a silicon interposer. From the inductance matrix considering current directions, the self- and mutual inductances of TSVs are accurately calculated. Because quasi-transverse electromagnetic mode is propagated through TSVs and the substrate dielectric of a silicon interposer can be regarded as a uniform dielectric, the capacitance and conductance of TSVs can be calculated from the inductance matrix. The proposed model of multiarray TSVs is also analyzed and verified by EM simulations in the frequency range from 0.01 to 20 GHz with a high accuracy.

In this paper, we, for the first time, designed and analyzed differential high-speed serial links of the silicon interposer including differential through-silicon-via (TSV) channels for a high-bandwidth memory (HBM) graphic module. The meshed ground plane and various parameters were considered in designing the silicon interposer. In addition, superior designs were proposed to improve signal integrity (SI) for the differential channels in the redistribution layer, TSVs, and the meshed ground. SI of the silicon interposer was successfully analyzed, and the corresponding results were verified based on a full 3-D electromagnetic solver and circuit simulations. A number of RLGC parameters were extracted and calculated, then adopted to verify the simulation results. The simulation results for the differential characteristic impedance and insertion loss were compared with those of the equivalent circuit. A mixed-mode conversion matrix was utilized to analyze differential-mode transmission. Moreover, a model for differential TSV channels was proposed to precisely analyze the electrical characteristics. The eye-diagram simulation was conducted to evaluate SI of the proposed designs in terms of an eye-opening voltage and timing jitter. The eye-opening voltage of the proposed design was 0.594 V, which is 45.69% of a peak-to-peak voltage of the assumed peripheral component interconnect (PCI)-express 4.0 interfaces. It is expected that the analysis and design methodologies of differential high-speed serial links for a silicon interposer could be widely adopted in the semiconductor industry.

This paper, for the first time, proposes and verifies a new coaxial silicone rubber socket for high-bandwidth and high-density package test using a fabricated sample. In addition, this paper also characterizes and verifies the coaxial silicone rubber socket. Because of the proposed coaxial socket’s novel coaxial structure, the proposed socket successfully achieves the electrical performance improvement. For verification, we compare the proposed socket and the previous noncoaxial socket in time domain. The proposed socket has greater eye height and eye width in the measured eye diagram than those of the noncoaxial socket. Moreover, the slope in the eye diagram is also improved in the case of the proposed socket. Therefore, the measured eye diagram for the coaxial socket shows the improvement in electrical performances. This paper also characterizes the equivalent RLGC model for the coaxial silicone rubber socket. In order to verify the RLGC model, we compare the insertion losses and eye diagrams from measurement, 3-D electromagnetic simulation, and the proposed RLGC model, respectively. Their insertion losses are comparable up to 20 GHz. Furthermore, the obtained eye diagrams are almost identical at the data rate of 9.6 Gb/s. In conclusion, this paper successfully proposes, verifies, and characterizes a new coaxial silicone rubber socket for the first time.

In this paper, for the first time, we designed and analyzed channels between a graphic processing unit and memory in a silicon interposer for a 3-D stacked high bandwidth memory (HBM). We thoroughly analyzed and verified the electrical characteristics of the silicon interposer considering various design parameters, such as the channel width and space, redistribution layer via, and under bump metallurgy pads. In particular, we also considered the meshed ground planes used for the proposed transmission lines, which are microstrip and strip lines. Signal integrity (SI) of the proposed channels in the silicon interposer was successfully analyzed and verified using a full 3-D electromagnetic solver and circuit simulations. Based on the extracted lumped circuit resistance, inductance, conductance and capacitance parameters, we thoroughly analyzed the channel characteristics and identified the parameters that dominantly affect SI in relation to each frequency range. From the analyzed insertion loss and far end crosstalk, we verified SI of the silicon interposer by eye-diagram simulations in terms of eye-height voltage and timing jitter in the time domain. In the worst case, the eye-height voltage and timing jitter of the proposed microstrip lines are 0.911 V and 36.8 ps, respectively, with 72 mV of signal coupling. The eye-height voltage and timing jitter of the proposed strip line are 0.887 V and 42.1 ps with 34 mV of single couplings. We show that the proposed channels of the silicon interposer can successfully transfer data at a 2-Gb/s data rate. Finally, we propose concepts and solutions for the next-generation HBM interface with higher data rates up to 8 Gb/s.

In this paper, we propose glass-interposer (GI) electromagnetic bandgap (EBG) structure with defected ground plane (DGP) for efficient and broadband suppression of power/ground noise coupling. We designed, fabricated, measured, and analyzed a GI-EBG structure with DGP for the first time. The proposed GI-EBG structure with DGP is thoroughly analyzed using the dispersion characteristics and estimated stopband edges, $f_{L}$ and $f_{U}$ . We experimentally verified that the proposed GI-EBG structure with DGP achieved power/ground noise isolation bandgap (below −30 dB) between $f_{L}$ of 5.7 GHz and $f_{U}$ of 11 GHz. Estimation of $f_{L}$ and $f_{U}$ using dispersion analysis, full 3-D electromagnetic (EM) simulation results, and measurement results achieved good correlation. Effectiveness of the proposed GI-EBG structure with DGP on suppression of the power/ground noise coupling to high-speed through glass via (TGV) channel is verified with 3-D EM simulation. As a result, the proposed EBG structure successfully and efficiently suppressed the power/ground noise coupling and improved the eye diagram of the TGV channel. Lastly, we embedded thin alumina film in the proposed EBG structure and achieved even broader power/ground noise suppression between 2.1 and 14.7 GHz.

As a demand for electrical systems with a wide data bandwidth has increased, high-performance packages ensuring high data rates, such as low power double data rate series, have become common. The need for high-performance test sockets has also emerged to test these packages. However, a conventional pogo pin socket has a limited test bandwidth due to the parasitic components arising from its spring. On the other hand, a silicone rubber socket satisfies the wide bandwidth requirement because it has low parasitic components due to high-density conductive metal powders in an elastic silicone rubber. In this paper, we propose an RLGC equivalent circuit model of a silicone rubber socket and first experimentally verify it. The proposed model is experimentally verified in the frequency domain by comparing the insertion loss obtained from the proposed model to the measurement up to 20 GHz. The proposed model is experimentally verified in the time domain by comparing the eye diagrams obtained from the proposed model to the measurement at a data rate of 12.5 Gb/s. Also, the insertion loss of the sockets with varied height, diameter, and pitch is analyzed using the proposed model. The proposed model provides physical insight of a silicone rubber socket, and it allows to determine whether a socket is reliable for testing high performance packages in a short time. It also gives us the idea how to design a high-performance test socket. Furthermore, we discuss the current capacity and life cycle of the silicone rubber socket in terms of signal integrity as well.