A modern analog placer often needs to consider various geometrical constraints to generate desired layouts. To handle general constraints simultaneously, current state-of-the-art works adopt simulated annealing based on topological representations, due to their smaller solution spaces and higher efficiency. However, no published work achieves the optimal time complexity for general geometrical constraint handling and module packing. Besides, only limited constraints are considered and handled in each work. To remedy these insufficiencies, we present a new hybrid representation of a quadtree and B*-trees (QB-tree, for short) to handle general geometrical constraints while achieving linear, lower-bound time complexity of module packing and constraint handling. Experimental results based on real industrial designs with various constraints show that our placer outperforms the leading published works in both runtime and solution quality.

Layout-dependent effects (LDEs) have become a critical issue in modern analog and mixed-signal circuit designs. The three major sources of LDEs, well proximity, length of oxide diffusion, and oxide-to-oxide spacing, significantly affect the threshold voltage and mobility of devices in advanced technology nodes. In this paper, we propose the first work to consider the three major sources of LDEs during analog placement. We first transform the three LDE models into nonlinear analytical placement models. Then an LDE-aware analytical analog placement algorithm is presented to mitigate the influence of the LDEs while improving circuit performance. Experimental results show that our placement algorithm can effectively and efficiently reduce the LDE-induced variations and improve circuit performance.

Self-aligned double patterning (SADP) with complementary e-beam lithography (EBL) is one of the most promising hybrid-lithography techniques for sub-20nm designs. The complementary EBL mitigates the deficiencies of using a single cut mask in SADP. However, the low throughput and negative side effects of EBL might significantly increase the manufacturing costs and damage the symmetry properties in analog circuits. In this paper, we present the first work that considers SADP with EBL during analog placement to simultaneously optimize the area, wirelength, overlay errors, and e-beam shots. We first propose an overlay and cut conflict-aware SADP decomposition algorithm to optimize the overlay errors and e-beam shots in a layout. Then, a dynamic programming based module shifting technique is developed based on a symmetry-feasible slicing tree formulation to further minimize the differences of overlay errors and e-beam shots between symmetry modules during analog placement. To explore and obtain a desired placement, an analog placement flow is also presented. Experimental results show that our flow can effectively and efficiently reduce area, overlay errors, and e-beam shots while satisfying the symmetry constraints for analog placement.

Layout-dependent effects (LDEs) have become a critical issue in modern analog and mixed-signal circuit designs. The three major sources of LDEs, well proximity, length of oxide diffusion, and oxide-to-oxide spacing, significantly affect the threshold voltage and mobility of devices. In this paper, we propose the first work to consider the three major sources of LDEs during analog placement. We first transform the three LDE models into nonlinear analytical placement models. Then an LDE-aware analytical analog placement algorithm is presented to mitigate the influence of the LDEs while improving circuit performance. Experimental results show that our placement algorithm can effectively and efficiently reduce the LDE-induced variations and improve circuit performance.

Capacitance-ratio mismatch in a switched-capacitor circuit could significantly degrade circuit performance. In the nanometer era, the parasitic effects and lengths of interconnects both have significant impacts on the capacitance ratio. This paper presents the first routing work for the problem of coupling-aware length-ratio-matching routing for capacitor arrays in analog integrated circuits. The router adopts a two-stage approach of topology generation followed by detailed routing to route unit capacitors such that the coupling-aware wire length ratio can match the desired capacitance ratio. Given a length ratio, in particular, the length-ratio-matching routing problem can be handled by transforming the problem into an easier classical wirelength minimization one. Experimental results show that our algorithm can solve the addressed problem with substantially smaller costs.

Symmetry, common-centroid, topology-matching, and length-matching constraints are four major routing considerations to improve the performance of an analog circuit. Symmetry constraints are specified to route matched nets symmetrically with respect to some common axes. Common-centroid constraints are also specified to route matched net symmetrically with respect to some common centers. Topology-matching constraints are commonly imposed on critical yet asymmetry nets with the same number of bends, vias, and wirelength. Length-matching constraints are specified to route the nets which have limited resources with the same wirelength. These four constraints can reduce current mismatches and unwanted electrical effects between two critical nets. In this paper, we propose the first work to simultaneously consider the four constraints for analog routing while minimizing total wirelength, bend numbers, via counts, and coupling noise at the same time. We first present a basic integer linear programming (ILP) formulation to simultaneously consider the four constraints for analog routing. Then, a prioritized-constraint-aware routing algorithm is proposed to assist analog designers for assigning the four matching constraints and optimizing routing topologies. Effective reduction techniques are also employed to reduce the numbers of ILP variables and constraints for the two routing algorithms. To further enhance the routing performance, a nonuniform multilevel routing framework is presented and integrated into our routing algorithms. Experimental results show that our approach can obtain better routing results and satisfy all specified routing constraints while optimizing circuit performance.

Double patterning lithography (DPL) is one of the most promising solutions for the 28nm technology node and beyond. The main idea of DPL is to decompose the layout into two sub-patterns and manufacture the layout by two masks. In addition to traditional analog design constraints, the pre-coloring constraint should also be considered, in which patterns of critical or sensitive modules have predefined masks before layout decomposition to reduce mismatches. In this paper, we present the first work that considers DPL during analog placement and simultaneously minimizes area, wirelength, and DPL conflicts. We first propose an extended conflict graph (ECG) to represent the relation between patterns of analog modules and apply an integer linear programming (ILP) formulation to determine the orientation of each module and the color of each pattern for conflict minimization. ILP reduction schemes are proposed to further reduce the runtime. Finally, we present a three-stage flow and DPL-aware perturbations to obtain desired solutions. Experimental results show that the proposed flow can effectively and efficiently reduce area, wirelength, and DPL conflicts.

Capacitance-ratio mismatch in a switched-capacitor circuit could significantly degrade circuit performance. In the nanometer era, the parasitic effects and lengths of interconnects both have significant impacts on the capacitance ratio. This paper presents the first routing work for the problem of coupling-aware length-ratio-matching routing for capacitor arrays in analog integrated circuits. The router adopts a two-stage approach of topology generation followed by detailed routing to route unit capacitors such that the coupling-aware wire length ratio can match the desired capacitance ratio. Given a length ratio, in particular, the length-ratio-matching routing problem can be handled by transforming the problem into an easier classical wirelength minimization one. Experimental results show that our algorithm can solve the addressed problem with substantially smaller costs.

Current-flow and current-density are two major considerations for placement and routing of analog layout synthesis. The current-flow constraints are specified to the critical nets with monotonic current/signal paths to reduce parasitic impacts. The current-density constraints are usually specified on the nets with variable wire widths to avoid the IR-drop and electromigration problems. In this paper, we propose the first work to simultaneously consider current-flow and current-density constraints while placing and routing the analog circuits with minimized chip area, routed wirelength, bend numbers, via counts, and coupling noise at the same time. We first present an enhanced B*-tree representation to simultaneously model modules and interconnects for an analog circuit. Then a simultaneous placement and routing algorithm is presented to generate a layout while satisfying the current-flow and current-density constraints with minimized chip area, routed wire-length, bend numbers, via counts, and coupling noise. Experimental results show that our approach can obtain better layout results and satisfy all specified constraints while optimizing circuit performance.

Symmetry, topology-matching, and length-matching constraints are three major routing considerations to improve the performance of an analog circuit. Symmetry constraints are specified to route matched nets symmetrically with respect to some common axes. Topology-matching constraints are commonly imposed on critical yet asymmetry nets with the same number of bends, vias, and wirelength. Length-matching constraints are specified to route the nets which have limited resources with the same wirelength. These three constraints can reduce current mismatches and unwanted electrical effects between two critical nets. In this paper, we propose the first work to simultaneously consider the three constraints for analog routing while minimizing total wirelength, bend numbers, via counts, and coupling noise at the same time. We first present an integer linear programming (ILP) formulation to simultaneously consider the three constraints for analog routing, and employ effective reduction techniques to further reduce the numbers of ILP variables and constraints. Then, a non-uniform multilevel routing framework is presented to enhance the performance of our routing algorithm. Experimental results show that our approach can obtain better routing results and satisfy all specified routing constraints while optimizing circuit performance.

Symmetry constraints and regular structures are two major considerations for expert analog layout designers. Symmetry constraints are specified to place matched modules symmetrically with respect to some common axes to reduce unwanted electrical effects. Regular structures are commonly followed by experienced designers to enhance routability and suppress parasitics induced by extra bends of wires and via cost. In this paper, we propose a heterogeneous B*-tree representation to consider symmetry and regularity simultaneously. Corresponding moves and a new regularity cost modelling for the representation are also presented. Experimental results show that our approach can efficiently generate regularly structured placement satisfying all symmetry constraints. For example, our placer achieves a 18X runtime speedup, 28% smaller area, and 68% shorter wirelength than the previous work, based on placement results, and 60% fewer overflows, 39% fewer vias, and 86% shorter routed wirelength, based on global routing results.