A Model for Interlevel Coupling Noise in Multilevel Interconnect Structures

In multilevel interconnect structures, the interconnect layers are practically always perpendicular to each other. Because of the capacitive coupling between adjacent layers, the switching activity in one layer produces noise in the other. This paper analyses the interlevel coupling noise present at the far end of a victim line when a large number of perpendicular attackers are randomly switching. Each attacker is modeled as a Markov chain and the victim is modeled as an RLC transmission line. The result is a novel closed-form expression for the power spectral density of the interlevel coupling noise. Introduction Interconnect noise has traditionally been and continues to be a significant issue for the design of high-performance microprocessors. Typically, it is addressed by determining the worst possible capacitive coupling noise that can be induced on a victim line by its parallel neighbors. In [1], the worstcase noise is simulated using an RC transmission line model that includes the timing of the attackers. In [2], inductance is taken into account and an expression for the peak crosstalk voltage between interconnects on the same layer is derived. In both cases, the conductors in layers adjacent to the victim’s layer are assumed quiet. Each adjacent layer is treated as a virtual ground plane. The problem with assuming that all interconnects perpendicular to the victim are quiet is that it underestimates the noise. Conversely, it is extremely pessimistic to assume that all conductors in the adjacent layers are simultaneously switching in the same direction. A better way to represent the interlevel coupling noise is to consider that the individual conductors in the adjacent layers are switching independently. A realistic noise model is sometimes very desirable, in particular for the design of clock distribution networks or the performance analysis of integrated antennas [5]. This paper analyses the interlevel coupling noise present at the far end of the victim line shown in Fig. 1 when a large number of perpendicular attackers are randomly switching. Each attacker is modeled as a Markov chain and the victim is modeled as an RLC transmission line. A closed-form expression for the power spectral density of the noise is derived for the first time. Finally, the noise characteristics are discussed for a typical 130-nm interconnect structure. Interlevel Coupling Noise Modeling The effect of a particular attacker on the noise at the far end of the victim is modeled as shown in Fig. 2. The capacitance between the attacker and the victim is CA. The source resistance RS represents the effective resistance of the circuit driving the victim and CT is the load capacitance that terminates it. The unit-length resistance, inductance, and capacitance of the victim line are r, l, and c. The length of the victim line is L and p is the position of the attacker. The pitch of each attacker (i.e. its width and space) is λ. The victim line is modeled as a linear system with multiple inputs (one per attacker) and one output. The power spectral density of the noise at V2 is obtained in three steps. First, the power spectral density of an individual attacker switching randomly at V0 is analyzed. Then, its transfer function H between V0 and V2 is derived. Since the system has multiple inputs, each attacker has its own transfer function. Given the power spectral density of the attacker at V0 and the transfer function corresponding to its position, its Metal (M 1) Metal M Metal (M + 1) Fig. 1: Multilevel interconnect structure.