The fabrication of advanced semiconductor dev·ices makes heavy demands on the simulation. The main directions for ongoing research are on the one hand the extension of the simulation tools to three spatial dimensions and on the other hand the development of more sophisticated physical models.

Through Silicon Via (TSV) is a lead topic in interconnects and 3D integration research, mainly due to numerous anticipated advantages. However, several challenges must still be overcome if large scale production is to be achieved. In this work, we have studied effects of Bosch scallops concerning mechanical reliability for a specific TSV technology. We identified that the presence of scallops on the TSV wall modifies the stress distribution. The achieved results support experiments and give a better insight into the influence of scallops in an open TSV.

The through Silicon Via (TSV) is a lead topic in interconnects and 3D integration research, mainly due to numerous anticipated advantages. However, several challenges must still be overcome if large scale production is to be achieved. In this work, we have studied the effects of Bosch scallops concerning mechanical reliability for a specific TSV technology. The presence of scallops on the TSV wall modifies the stress distribution along the via. By means of Finite Element Method (FEM) simulations, we assess this change in order to better understand the process. The achieved results support experiments and give further insight into the influence of scallops on the stress in an open TSV.

Through Silicon Via (TSV) is a lead topic in interconnects and 3D integration research, mainly due to numerous anticipated advantages. However, several challenges must still be overcome if large scale production is to be achieved. In this work, we have studied effects of Bosch scallops concerning mechanical reliability for a specific TSV technology. The presence of scallops on the TSV wall modifies the stress distribution along the via. By means of Finite Element Method (FEM) simulations, we could assess this change and understand the process. The achieved results support experiments and give a better insight into the influence of scallops on the stress in an open TSV.

We have studied the stress evolution in the tungsten film of a particular open TSV technology during the thermal processing cycle. The film is attached to the via's wall and some plasticity is expected in the metal due to the temperature variation. Our work introduces a stress model for thin-films utilizing the traditional mechanical FEM approach. The results reveal potential reliability issues and a specific evolution of the stress in the tungsten layer.

Thin film deposition is a widely used technique for the fabrication of MEMS (Micro-Electro-Mechanical Systems) devices. This technique is required to establish free-standing structures which can induce or sense a mechanical movement. During the deposition of new layers of thin films an intrinsic stress is generated. In subsequent process steps, a stressed layer, usually an important component part of the desired MEMS device, is left free-standing. As a consequence the process induced stress can relax and deform the layer in an undesirable way. For the investigation of stress effects during deposition we are focusing on the deposition of SiGe on the sacrificial layer. In our model we combine three stress generation mechanisms where each is related to one of three charachteristic phases of thin film growth and corresponding microstructure evolution. In the initial phase we assume the so-called Volmer-Weber growth which includes a build-up of a strong compressive stress components due to the Laplace pressure of isolated material islands [2]. It is followed by a tensile stress mechanism which operates during the island coalescence phase and thereafter [2]. The third phase introduces again compressive component but this time due to adatom insertion into the top of the grain boundaries (Figure 1). The basic feature of our approach is an introduction of the straingradient function ω(z, r) which depends on the grain size distribution function L(z) and material deposition rate r. L(z) can be obtained by using several different algorithms which simulate morphology evolution of the thin film microstructure according to the Van der Drift mechanism [3]. The first expression in (1) (ε(z, r)) represents the microstrain evolution in the direction of the film growth (Figure 1). It consists of the strain contribution from the first phase εt,1(zi, r), where zi is the film thickness after a coalescence, and an integral term relating to microstrain development in the second and the third phase (1),

We present a model for build-up of intrinsic stress during the deposition of thin metal films. The model assumes a three-phase stress generation mechanism which corresponds to three characteristic phases of microstructure evolution. The simulation results based on the model are successfully compared with experimental results for Poly-SiGe PECVD films. The impact of critical parameter variation on mechanical properties of thin film is discussed.

Residual mechanical stresses introduced during deposition of thin films and coatings have a significant impact on the reliability of electronic devices and structural components. The mechanical stress in thin metal films consists of a thermal component and an intrinsic component due to the evolution of the metal microstructure during film growth. Controlling of the intrinsic stress component has become one of the most important challenges in modern technology. In this work we introduce an intrinsic stress model which combines three stress generation mechanisms where each is related to one of the three characteristic phases of thin film growth and corresponding microstructure evolution. In the initial phase we assume the Volmer-Weber growth which includes a build-up of strong compressive stress components due to the Laplace pressure of isolated material islands [1]. It is followed by a tensile mechanism which operates during the island coalescence phase and thereafter [1]. The third phase introduces again a compressive component but this time due to adatom insertion into the top of the grain boundaries (Figure 1). The basic feature of our approach is an introduction of a strain gradient function which depends on grain the size distribution. This distribution can be obtained by using several different algorithms which simulate the morphology evolution according to the Van der Drift mechanism [2].

We presented a transient electro-thermal analysis with STAP considering self-heating. Thermo-mechanical simulators, e.g. FEDOS, are coupled to provide appropriated input data for electromigration analysis to obtain predictive results. The presented electro-thermal results depict the high temperature gradients close to heat sources and heat sinks. Further regions of high risk of electromigration are presented as results of thermo-mechanical simulations. The vias as well as edges and corners of interconnects in general are highly stressed regions due to the mismatch of thermal volume expansion coefficients and due to weak material adhesion of material interfaces

Investigations of state-of-the-art integrated circuit designs clearly show that the temperature in interconnect structures is becoming the dominant and straitening factor for system performance. In this work we combine three-dimensional transient electro-thermal simulations with a finite element formulation of the thermo-mechanical stress problem in order to study the evolution and development of mechanical stress in complex layered interconnect structures at different operating conditions.

We present a parallelization method based on message passing interface (MPI) for a Monte Carlo program for two-dimensional (2-D) and three-dimensional (3-D) simulation of ion implantations. We use a master-slave strategy where the master process synchronizes the slaves and performs the input-output operations, while the slaves perform the physical simulation. For this method the simulation domain is geometrically distributed among several CPU's which have to exchange only very little information during the simulation. Thereby, the communication overhead between the CPU's is kept so low that it has almost no influence on the performance gain even if a standard network of workstations is used instead of a massively parallel computer to perform the simulation. We have optimized the performance gain by identifying bottlenecks of this strategy when it is applied to arbitrary geometries consisting of various materials. This requires the application of different physical models within the simulation domain and makes it impossible to determine a reasonable domain distribution before starting the simulation. Due to a feedback between master and slaves by online performance measurements, we obtain an almost linear performance gain on a cluster of workstations with just slightly varying processor loads. Besides the increase in performance, the parallelization method also achieves a distribution of the required memory. This allows 3-D simulations on a cluster of workstations, where each single machines would not have enough memory to perform the simulation on its own.

As semiconductor technology continues to evolve, numerical modelling of the devices' electrical behaviour is becoming increasingly important. In this contribution, the model hierarchy which exists for the description of current flow in a semiconductor device is briefly reviewed. The strengths and restrictions of each model are critically examined. Presently, drift-diffusion based simulation programs are considered as the workhorse tools in engineering. However, an enormous research effort is going on, with the aim of improving alternatives such as the hydrodynamic model, the spherical harmonics expansion method and the Monte Carlo technique. Examples of recently proposed improvements in that field are described.

This contribution is intended to review the international state-of-the-art in three-dimensional process and device modeling. As one particular example, results for ion implantation into a three-dimensional trench are presented. Redistribution of dopants, interstitials and vacancies with fully coupled models is discussed. The recent refinements to carrier transport models in semiconductor devices are presented. As a particular example for three-dimensional device simulation the influence of the shape of the field-oxide in the width direction is discussed. Some remarks on the computational requirements are made.

We present a two-dimensional model of ion implantation which allows for position dependent lateral moments. The lateral standard deviation and the lateral kurtosis as a function of depth have been calculated by 2-D Monte-Carlo simulations for boron, phosphorus, arsenic, and antimony in silicon for energies in the range of 10–300 keV. The lateral moments as a function of depth and energy as well as the vertical moments as a function of energy have been fitted by simple formulae. We specify two types of distribution functions the parameters of which can be adjusted to given values of standard deviation and kurtosis. In this way the depth dependent lateral moments can be included into analytical distribution functions.

We present a numerical algorithm for the calculation of phase velocities of acoustic surface and bulk waves in anisotropic piezoelectric materials. The mathematical model is based on fundamental partial differential equations in three spatial dimensions which are the equations of motion and Poisson's equation. We present examples for LiNb03 and Quartz.

We present an ab initio transient analysis of acoustic wave generation in piezoelectric materials, which takes into account second-order effects (e.g., bulk wave generation and interaction between surface waves and bulk waves). The computer program we have developed for this purpose solves the fundamental differential equations in two space dimensions with the corresponding mechanical displacements and the electrical potential as dependent variables using a semi-implicit finite difference scheme rather than by wave approximations. This has become possible with acceptable usage of computer resources only by introducing a novel form of boundary conditions for the quasi-infinite sagittal plane to avoid reflection phenomena. We present numerical results for YX LiNbO3.

Abstract : In this paper we present an analysis of the fundamental one-dimensional semiconductor equations describing potential, carrier, and current density distributions in single-junction semiconductor devices when an external voltage is applied to the contacts. We reformulate the model equations by appropriate scaling as a singularly perturbed two point boundary value problem for a system of nonlinear ordinary differential equations. The right-hand side of the system has a jump discontinuity with respect to the independent variable (space-coordinate) representing the junction between differently doped sides of the device. The solution components are assumed to be continuous across this junction. (Author)

A selfconsistent numerical analysis of bulk-barrier diodes (BBD) is presented. The principal way of operation of a BBD is explained. A computer program which can accurately model second order effects is used to achieve basic understanding of the internal electric behaviour of a BBD. The distributions of the relevant physical quantities in the interior of a BBD are discussed. Measured and simulated characteristics which show good agreement, owing to the carefully modeled physical parameters, are compared. The sensitivity of electrical properties to minute variations of the doping profile is presented. This can only be done by a program simulating the characteristics of a BBD. The advantages and disadvantages of a BBD compared to a standard silicon diode and a Schottky diode are discussed.