next up previous contents
Next: 2. Circuit Equations Up: Dissertation Grasser Previous: List of Figures

1. Introduction

Over the last decades numerous powerful circuit simulation programs have been developed. Amongst those are general purpose programs which have been designed to cope with all different kinds of circuits and special purpose programs which provide highly optimized algorithms for, e.g., filter design. General purpose programs can be divided into two categories. Programs belonging to the first category provide the user with a general purpose modeling language which can be used to define fairly arbitrary dependencies between the circuit elements. The most prominent member of this category is ASTAP [33] which was developed by IBM in the 70-ties. To provide the user with a maximum of flexibility, ASTAP generates FORTRAN source files which need to be compiled before execution. The other category consists of programs which only allow for a predefined set of circuit elements and dependencies. Although the flexibility is strongly diminished, this approach allows for a much faster execution and a compact, highly optimized simulator kernel. The most prominent member of this category is SPICE which was developed at the University of Berkeley [43].

Circuit simulation programs have in common that the electrical behavior of the devices is modeled by means of a compact model, that is, analytical expressions describing the device behavior. Once a suitable compact model is found, it can be evaluated in a very efficient way. However, this task is far from being trivial and many complicated models have been developed. Even if the behavior of the device under consideration can be mapped onto one of the existing compact models, the parameters of this compact model need to be extracted. In the case of the BSIM2 model [60] for short-channel MOS transistors 300 parameters are available for calibration purposes the identification of which is obviously a cumbersome task. If the device design is known and not modified, these parameters need to be extracted only once and can be used for circuit design if the accuracy of the models is sufficient. When there is need to optimize a device using modified geometries and doping profiles the compact model parameters have to be extracted for each different layout as many of these parameters are mere fit parameters without any physical meaning.

The electrical behavior of the devices can either be measured or simulated. When performing a device optimization, fabricating and measuring each optimization step would be very expensive. Hence, device simulators became more and more popular, e.g., DESSIS [34], MEDICI [69], MINIMOS [58], and PISCES [47]. These device simulators solve the transport equations for a device with given doping profiles and a given geometry. The transport equations form a highly nonlinear partial differential equation system which cannot be solved analytically. Numerical methods have to be used to calculate a solution by discretizing the equations on a suitable simulation grid. The data obtained from these simulations can be used to extract the parameters of the compact model.

Altogether, this subsequent use of different simulators and extraction tools is cumbersome and error-prone. To overcome these problems several solutions have been published where a device simulator was coupled to SPICE [49,12,39]. This is again problematic when considering the communication between two completely different simulators. On the other hand some solutions were presented where circuit simulation capabilities were added to a device simulator [40]. However, the restrictions imposed were so severe that many examples published in this thesis could not be properly dealt with. For example, the number of distributed devices was limited to either one or only a few.

To overcome these shortcomings, the device simulator MINIMOS-NT has been equipped with full circuit simulation capabilities with the only limitation being the amount of computer resources available. MINIMOS-NT is a general purpose device simulator developed as the successor of MINIMOS [55]. Simulations in MINIMOS are restricted to rectangular MOS structures, a too severe limitation for state-of-the-art devices. MINIMOS-NT can cope with arbitrary device structures and geometries. An important prerequisite for accurate simulation of non-planar structures are triangular grids which have been introduced into MINIMOS-NT.

The traditional drift-diffusion equations can be augmented by the lattice heat flow equation to account for self-heating effects. To account for non-local effects a hydrodynamic equation set is available. These equations can be solved for static and transient problems.

As heterostructures are becoming more and more important, proper handling of all kinds of heterostructures has been a major design goal for MINIMOS-NT [15]. This is achieved by splitting the device into logical units, so-called segments which can consist of different materials. Furthermore, these segments form the basic units of model selection. Due to the flexible equation assembly it is, for instance, possible to use a drift-diffusion model on one segment, a hydrodynamic model on another segment, and to account for self-heating on even another segment.

MINIMOS-NT employs a powerful input deck language, enabling the user to customize the simulation in many details. The basic idea is that the input deck is not evaluated once at the beginning of the simulation, but is stored as a database which can be accessed at runtime. Since each keyword in this input deck can be an arbitrary complex and time dependent expression, fine-tuning can be done without the need of any predefined heuristic algorithms, e.g., increasing the number of allowed fill-ins into the sparse system matrix only for one bias point or time steps with large curvature of the input signals.

Different materials are treated in an abstracted way since all material properties are handled via a database which controls the model server. The only information needed in MINIMOS-NT is the so-called material class, e.g., semiconductor or insulator. For each material class a distinct set of models is supplied via this database. The model server provides a C++ like interpreter language [41] allowing the user to add new models in a simple fashion. This implies that any material can be added to the simulator by either providing proper parameters for the existing models or by adding completely new models. These models can be organized in libraries to extend the simulator at runtime whenever needed.

So far many different devices have been simulated with MINIMOS-NT demonstrating its wide applicability. Besides traditional MOSFETS [15,23,24], Charge-Coupled-Devices (CCDs) [50], Poly-Emitter-Bipolar transistors [19], Silicon-On-Insulator (SOI) devices [36], High-Electron-Mobility-Transistors (HEMTs) [61,15,4,62], Heterostructure-Bipolar-Transistors (HBTs) [46,21], and Ultra-Low-Power technologies [52] were investigated.

With the new mixed-mode capabilities at hand devices can be characterized by their performance in a circuit as a function of transport models, doping profiles, mobility models, etc. This is of fundamental importance when investigating the behavior of modern submicron devices and non-mainstream devices like HBTs or HEMTs where compact models are not readily available. Furthermore, when the devices are scaled down, non-local effects become more and more pronounced which can alter the device behavior completely. This cannot be handled by scaling the parameters of compact models.

next up previous contents
Next: 2. Circuit Equations Up: Dissertation Grasser Previous: List of Figures
Tibor Grasser