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Low-Loss, High-Performance Chip-to-Chip Electrical Connectivity Using Air-Clad Copper Interconnects
Published in Lukas Chrostowski, Krzysztof Iniewski, High-Speed Photonics Interconnects, 2017
Rohit Sharma, Rajarshi Saha, Paul A. Kohl
Historically, interconnect technology used Al and SiO2 as the conductor–substrate pair. The transition from aluminum to copper as the interconnect conductor has been one of the most important technological advances in interconnect technology. The fundamental problem with Al-SiO2 interconnect includes the higher resistance and capacitance, and nonplanarity compared to copper and low dielectric constant interconnect (Cu-low k) technologies. The resistance-capacitance (RC) product represents the characteristic time constant of a series resistor–capacitor circuit. Typically, the bulk resistivity of Cu is less than that of Al, as shown in Table 2.1, although the actual resistivity of the Cu used is somewhat higher than the theoretical limit. This implementation of both Cu and low-k dielectrics results in up to 50% decrease in RC wiring delay compared to Al-SiO2 interconnect, as shown in Figure 2.2. Since Cu has lower resistivity the effect of line inductance is even more significant in Cu interconnect lines. At higher frequency, the inductive effect dominates causing signal overshoots and ringing and reflections due to impedance mismatch. Complex responses such as these generally require modeling of self and mutual inductance terms. Also, copper has 10 to 100 times higher electromigration resistance compared to aluminum making it a more reliable interconnect material.
Photodetectors
Published in Robert G. Hunsperger, Photonic Devices and Systems, 2017
To maximize the speed of response, the transit time needs to be minimized. This means making the active layer thin. By making the active region thin, the capacitance of the device is increased and the quantum efficiency of the device is decreased. The increasing capacitance causes the RC time constant to rise and the speed is slowed. To optimize the photodetector speed of response trade-offs must be made between transit time and RC considerations. These trade-offs have been modeled for InP/InGaAs/InP p-i-n devices and are plotted in Fig. 17 [13], where the device area, i-layer thickness, and active-area diameter are examined and frequency contours are established.
Transient Analysis
Published in John Okyere Attia, Circuits and Electronics, 2017
For the RC circuit, the time constant is given as τ = RC. The time constant determines the rate of charge or discharge of a capacitor. After τ seconds, the voltage will have decreased to e-1 (about 0.368) of its initial value. After 2τ seconds, it will have decreased to e-2 (0.135) its initial value, and after 5τ seconds, the voltage will have decreased to 0.0067 of the initial value. To allow the capacitor to charge to its maximum voltage, it is recommended that the period of the square wave should be far greater than five times the time constant. Example 3.1 shows how to use the Analog Discovery board to explore the behavior of an RC circuit.
Joint optimization of maintenance, buffers and machines in manufacturing lines
Published in Engineering Optimization, 2018
Nabil Nahas, Mustapha Nourelfath
Nahas and Nourelfath (2014) made an analogy between the acceptance function and the low-pass resistor–capacitor (RC) filter (Figure 2), which is a filter that passes only low-frequency signals by reducing the amplitude of signals with high frequencies. The capacitor blocks low-frequency signals, causing them to go through the load instead. At higher frequencies, the capacitor functions as a short circuit. The combination of resistance and capacitance gives the time constant of the filter τ = RC. The cut-off frequency (in hertz) is determined by the time constant f0 = 1/(2πRC). The transfer function of the low-pass RC filter, which describes the relationships between Vout and Vin in terms of frequency, is given by: where w represents the angular frequency (w = 2πf and w0 = 2πf0).