Electrothermal Field and Circuit Simulation of Thin Wires and Evaluation of Failure Probabilities

• Main Author: Casper, Thorben
• Format: Others
• Language: en
• Published: 2019
• Online Access: https://tuprints.ulb.tu-darmstadt.de/8959/1/2019-07-04_Casper_Thorben.pdf; Casper, Thorben <http://tuprints.ulb.tu-darmstadt.de/view/person/Casper=3AThorben=3A=3A.html> : Electrothermal Field and Circuit Simulation of Thin Wires and Evaluation of Failure Probabilities. Technische Universität, Darmstadt [Ph.D. Thesis], (2019)

This thesis deals with the electrothermal 3D field and circuit simulation of structures containing thin wires to evaluate their failure probability. Failure probabilities of wires in chip packages from the field of micro- and nanoelectronics are considered as an example. The failure model used in this thesis is based on the temperature of the bond wires under electric operating conditions. Since bond wires are very thin compared to the size of the surrounding chip package, the different geometric scales rise numerical challenges. Instead of locally applying very fine grids, a 1D–3D coupling approach is introduced. For a consistent discretization, the singular wire contributions are modeled by the powerful framework of de Rham currents. Particular focus lies on a consistent 1D–3D coupling condition to ensure a physical solution. In such a setting, the wires act as solution-dependent singular line sources resulting in a deteriorated convergence rate of the numerical method. It is demonstrated that a graded 3D grid and a non- zero coupling radius result in a recovered convergence rate. Furthermore, it is shown that this kind of problem is closely related to fluid flow in porous 3D media with 1D fractures. Apart from the calculation of electromagnetic fields, circuit simulation has been successfully integrated into many workflows. To realize circuit designs in an efficient way, a method to automatically generate netlists describing general discretized field problems is presented. Using a pair of orthogonal grids, a one-to-one correspondence between grid objects and circuit elements is obtained. The resulting circuit can then be solved with any state-of-the-art circuit simulator, circumventing the need for handling the nonlinearities or for a custom time integration scheme. Moreover, the approach allows a straightforward field-circuit coupling by adding any additional circuit elements to the generated netlist that represents the field problem. Often, circuit simulators provide interfaces to other useful software packages that may be exploited thanks to the obtained circuit description. One example is given by the interface between Xyce and Dakota to allow for uncertainty quantification methods. The proposed techniques are verified using numerical test examples. Driven by the goals of the nanoCOPS project, a possible industrial application of the outcomes of this thesis is demonstrated by the computation of the system failure probability of a chip package. The system failure probability is evaluated based on the failure probabilities of the individual bond wires of uncertain geometry. For small failure probabilities, classical Monte Carlo techniques require a very high number of samples. As a remedy, a hybrid iterative sampling scheme combines the accurate 3D field model with a cheap polynomial surrogate model, yielding accurate results at a low computational cost.