Determination of Bond Wire Failure Probabilities in Microelectronic Packages

This work deals with the computation of industry-relevant bond wire failure probabilities in microelectronic packages. Under operating conditions, a package is subject to Joule heating that can lead to electrothermally induced failures. Manufacturing tolerances result, e.g., in uncertain bond wire geometries that often induce very small failure probabilities requiring a high number of Monte Carlo (MC) samples to be computed. Therefore, a hybrid MC sampling scheme that combines the use of an expensive computer model with a cheap surrogate is used. The fraction of surrogate evaluations is maximized using an iterative procedure, yielding accurate results at reduced cost. Moreover, the scheme is non-intrusive, i.e., existing code can be reused. The algorithm is used to compute the failure probability for an example package and the computational savings are assessed by performing a surrogate efficiency study.Comment: submitted to Therminic 2016, available at http://ieeexplore.ieee.org/document/7748645

Coupled Simulation of Transient Heat Flow and Electric Currents in Thin Wires: Application to Bond Wires in Microelectronic Chip Packaging

This work addresses the simulation of heat flow and electric currents in thin wires. An important application is the use of bond wires in microelectronic chip packaging. The heat distribution is modeled by an electrothermal coupled problem, which poses numerical challenges due to the presence of different geometric scales. The necessity of very fine grids is relaxed by solving and embedding a 1D sub-problem along the wire into the surrounding 3D geometry. The arising singularities are described using de Rham currents. It is shown that the problem is related to fluid flow in porous 3D media with 1D fractures [C. D'Angelo, SIAM Journal on Numerical Analysis 50.1, pp. 194-215, 2012]. A careful formulation of the 1D-3D coupling condition is essential to obtain a stable scheme that yields a physical solution. Elliptic model problems are used to investigate the numerical errors and the corresponding convergence rates. Additionally, the transient electrothermal simulation of a simplified microelectronic chip package as used in industrial applications is presented.Comment: all numerical results can be reproduced by the Matlab code openly available at https://github.com/tc88/ETwireSi

Automated Netlist Generation for 3D Electrothermal and Electromagnetic Field Problems

We present a method for the automatic generation of netlists describing general three-dimensional electrothermal and electromagnetic field problems. Using a pair of structured orthogonal grids as spatial discretisation, a one-to-one correspondence between grid objects and circuit elements is obtained by employing the finite integration technique. The resulting circuit can then be solved with any standard available circuit simulator, alleviating the need for the implementation of a custom time integrator. Additionally, the approach straightforwardly allows for field-circuit coupling simulations by appropriately stamping the circuit description of lumped devices. As the computational domain in wave propagation problems must be finite, stamps representing absorbing boundary conditions are developed as well. Representative numerical examples are used to validate the approach. The results obtained by circuit simulation on the generated netlists are compared with appropriate reference solutions.Comment: This is a pre-print of an article published in the Journal of Computational Electronics. The final authenticated version is available online at: https://dx.doi.org/10.1007/s10825-019-01368-6. All numerical results can be reproduced by the Matlab code openly available at https://github.com/tc88/ANTHE

Electrical model for characterizing CVD graphene

Due to its extremely small thickness (0.35 nm), graphene is an intrinsic 2D nanomaterial. As in many other nanomaterials, its unique properties are derived from its exceptional dimensions. One of these properties is its linear dispersion equation that implies charge carriers with extraordinary high mobility. Therefore, the electronic properties of the material can lead to a big improvement in the performance of known electronic devices, or even result in novel devices for a post-silicon era

Method for electrical evaluation of graphene using a GFET structure

n this work, we explain a method to characterize graphene using electrical measurements in graphene field-effect transistors (GFET) devices. Our goal is to obtain the material electronic properties from the output characteristics of one GFET device. For the previous purpose, we will need to apply a physical model that allows us to correlate the electronic behavior of a GFET with the material properties

Nanoelectronic COupled problems solutions - nanoCOPS: modelling, multirate, model order reduction, uncertainty quantification, fast fault simulation

The FP7 project nanoCOPS derives new methods for simulation during development of designs of integrated products. It covers advanced simulation techniques for electromagnetics with feedback couplings to electronic circuits, heat and stress. It is inspired by interest from semiconductor industry and by a simulation tool vendor in electronic design automation. The project is on-going and the paper presents the outcomes achieved after the first half of the project duration

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

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

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

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