H. Pötzl

MINIMOS—A two-dimensional MOS transistor analyzer

We describe a user-oriented software tool-MINIMOS-for the two-dimensional numerical simulation of planar MOS transistors. The fundamental semiconductor equations are solved with sophisticated programming techniques to allow very low computer costs. The program is able to calculate the doping profiles from the technological parameters specified by the user. A new mobility model has been implemented which takes into account the dependence on the impurity concentration, electric field, temperature, and especially the distance to the Si-SiO 2 interface. The power of the program is shown by calculating the two-dimensional internal behavior of three MOSTs with 1-µm gate length differing in respect to the ion-implantation steps. In this way, the threshold voltage shift by a shallow implantation and the suppression of punchthrough by a deep implantation are demonstrated. By calculating the output characteristics without and with mobility reduction, the essential influence of this effect is shown. From the subthreshold characteristics, the suppression of short-channel effects by ion implantation becomes apparent. The MINIMOS program is available for everyone for just the handling costs.

Simulation of critical IC fabrication processes using advanced physical and numerical methods

Critical steps of IC fabrication are simulated by one- and two-dimensional computer programs using advanced physical models. Our codes deal with an arbitrary number of physical quantities such as concentrations of dopants, vacancies, interstitials and clusters, the electrostatic potential, and so on. Furthermore, they easily permit the exchange or variation of the physical models under consideration. As typical applications phenomena of coupled diffusion in one and two dimensions and dynamic arsenic clustering are investigated. The differences caused by the models of the zero space-charge approximation and the solution of the exact Poisson equation are studied by examples of As-B diffusion with various doping concentrations at different temperatures. A dynamic cluster model developed for the simulation of thermally annealed As implantations is compared to measured data of laser annealing experiments. A short outline of the mathematical and the numerical problems is given to show the amount of sophistication necessary for up-to-date process simulation.

Generalized Model for the Clustering of As Dopants in Si

A model for As clustering in single crystal silicon is presented that allows for the participation of arbitrary numbers of As ions, electrons, and arbitrarily charged vacancies. From this model the saturation behavior of the concentration of unclustered, electrically active As impurities is derived. It is shown that saturation (or electrical solubility) demands the participation of at least one negative charge in the formation of positively charged clusters, be it electron or negative vacancy. By analysis of our own experimental results and those by other authors, this general cluster model indicates that the participation of exactly one negative charge is the most likely case. In the course of this discussion the equilibrium saturation concentration of electrically active As is deduced from experiment as a function of temperature.

Simulation of Critical IC-Fabrication Steps

Due to the advances in device miniaturization it is often necessary to get a better understanding of the physical fabrication processes by applying advanced physical models. Since existing process modeling programs can handle only specific physical quantities, we have developed general purpose solvers for one and two space dimensions which are able to treat an arbitrary number of coupled partial differential equations for physical quantities. In the paper we will show the general formulation of the equations which can be solved. We deal with the user-interface of the programs and the numerical problems one has to face. To demonstrate the capabilities of the programs we will show typical applications.

A two-dimensional model of the avalanche effects in MOS transistors

Abstract A two-dimensional self consistent MOS transistor model accounting for the avalanche effect is described. The classical semiconductor equations—Poissons equation and the two carrier equations—are solved with the finite difference method. The pair production rate is evaluated at any mesh point and dominates the inhomogeneity term of the carrier continuity equations in case of avalanche. Calculated and measured current-voltage characteristics are in good agreement and thus support our model. For a 3 μm device the electrical potential, the carrier densities, and the generation rates are shown in quasi three-dimensional plots from which the avalanche generation in the pinch-off region becomes apparent. Furthermore, hole storage close to the interface is seen to take place in the channel up to the vicinity of the source region. The corresponding barrier lowering leads to increased electron injection from the source and enhanced avalanche. The barrier lowering is supported by the influence of the parasitic bulk resistance.

INVESTIGATION OF PARAMETER SENSITIVITY OF SHORT CHANNEL MOSFETS

Abstract A strategy to examine the sensitivity of electrical device parameters on geometrical and technological tolerances is described. An approach is offered to determine the limit of device miniaturzation for a given fabrication process and a desired operating condition. As a didactic example of practical relevance the minimum channel length for a modern silicon gate, double implant process due to threshold uncertainty is estimated. A method to calculate global sensitivity numbers for the reproducability of miniaturized devices is suggested. As an experimental determination of sensitivities is extremely difficult and expensive, numerical simulations are ideally suited for this purpose.

Analysis of Breakdown Phenomena in MOSFET's

An accurate two-dimensional self-consistent numerical model for MOS transistors which is able to predict avalanche behavior is presented. This model aims at a more principal understanding of the physical processes which arise from the avalanche effect and which eventually lead to breakdown. The system of the fundamental semiconductor equations with several generation/recombination mechanisms is solved. To improve the description of the ionization process, correction terms are introduced which account for the fact that the gate induced field does not cause ionization. Holes which are generated in the pinch-off region by impact ionization cause a bulk current; the voltage drop at the parasitic bulk resistance initiates an internal feedback mechanism. Thus a negative resistance branch of the drain current characteristic can arise. However, at high current levels, introduced by a high gate bias and/or a short channel, this snap-back effect is often counterbalanced by strong recombination. Snapback voltage can be estimated with this model.

MINIMOS - A Two-Dimensional MOS Transistor Analyzer

We describe a user-oriented software tool-MINIMOS-for the two-dimensional numerical simulation of planar MOS transistors. The fundamental semiconductor equations are solved with sophisticated programming techniques to allow very low computer costs. The program is able to calculate the doping profiles from the technological parameters specified by the user. A new mobility model has been implemented which takes into account the dependence on the impurity concentration, electric field, temperature, and especially the distance to the Si-SiO/sub 2/ interface. The power of the program is shown by calculating the two-dimensional internal behavior of three MOSTs with 1-/spl mu/m gate length differing in respect to the ion-implantation steps. In this way, the threshold voltage shift by a shallow implantation and the suppression of punch through by a deep implantation are demonstrated. By calculating the output characteristics without and with mobile reduction, the essential influence of this effect is shown. From the sub-threshold characteristics, the suppression of short-channel effects by ion implantation becomes apparent. The MINIMOS program is available for everyone for just the handling costs.

Simulation of critical IC-fabrication steps

Due to the advances in device miniaturization it is often necessary to get a better understanding of the physical fabrication processes by applying advanced physical models. Since existing process modeling programs can handle only specific physical quantities, we have developed general purpose solvers for one and two space dimensions which are able to treat an arbitrary number of coupled partial differential equations for physical quantities. In the paper we will show the general formulation of the equations which can be solved. We deal with the user-interface of the programs and the numerical problems one has to face. To demonstrate the capabilities of the programs we will show typical applications.

Analytical science for the development of microelectronic devices

ZusammenfassungDie neue technologische Revolution, nämlich Entwicklung und Einführung der Mikroelektronik, stellt für die Analytische Chemie eine der größten Herausforderungen dar: Die material- und prozeßbezogenen Fragestellungen beziehen sich nämlich in hohem Maße auf extrem kleine Konzentrationen und räumliche Dimensionen. Eine erfolgreiche Behandlung derartiger Fragestellungen ist nur durch Einsätz modernster, überwiegend auf der Physik basierender Hochleistungsanalytik („Analytische Wissenschaft“) möglich.In der vorliegenden Arbeit wird versucht, die Rolle dieser Analytischen Wissenschaft für die Entwicklung mikroelektronischer Bauelemente am Beispiel des höchstintegrierten Direct Random Access Memory (DRAM) darzustellen. Ausgehend von den verschiedenen Stufen der Herstellung eines solchen Bauelementes in MOS-Technologie werden die wichtigsten analytischen Fragestellungen und deren Behandlung mit analytischen Methoden diskutiert: Reinheit und chemische Oberflächenstruktur der Siliciumwafer, Verteilung und Reaktionen der Dotierungselemente während der Grundoperationen des MOS-Prozesses (Oxidation, Implantation, Ausheilung), chemische und physikalische Eigenschaften der Metallisierungsstrukturen und funktionelle sowie chemische Untersuchungen der Bauelemente. Besonders eingegangen wird auf die Dotierungselemente, welche die elektrischen Eigenschaften eines Bauelementes bestimmen. Es wird gezeigt, daß in erster Linie physikalische Methoden wie SIMS, NAA, RBS, TEM wichtige neue und quantitative Informationen über die bei der Herstellung eines Bauelementes im Halbleiter ablaufenden chemischen und physikalischen Prozesse liefern. Diese Informationen ermöglichen wesentliche Verbesserungen in der Modellierung dieser Prozesse. Dies ist wiederum eine wesentliche Grundlage für die Weiterentwicklung mikroelektronischer Bauelemente in Richtung höherer Integration und Komple-xität.SummaryThe new technical revolution, the development and introduction of microelectronics poses a great challenge for Analytical Chemistry: the material and process related analytical problems largely refer to extremely small concentrations and spatial dimensions. A successful treatment of such problems is only possible through the use of the most modern, mainly physical techniques, for which reason it seems appropriate to speak of “Analytical Science”.This paper tries to demonstrate the potential of Analytical Science for the development of sophisticated microelectronic devices, taking as an example the most highly integrated circuit, the Direct Random Access Memory (DRAM). Referring to the various steps of production of such a device in MOS. technology the most important analytical problems and their treatment with analytical methods are discussed: purity and chemical surface structure of silicon wafers, behaviour of dopant elements during the basic operations of MOS technology (oxidation, implantation, annealing), chemical and physical features of metallization layers, and functional and chemical investigation of devices. Special emphasis is placed on the behaviour of the dopant elements which are decisive for the electrical properties of a device. It is shown that mainly physical analytical techniques like SIMS, NAA, RBS, TEM provide valuable new and quantitative information about the chemical and physical processes occurring in the semiconductor material during production of a device. This information enables substantial progress in process modelling, which is an important basis for further development of devices towards higher integration and complexity.