N. Rinaldi

On the modeling of the transient thermal behavior of semiconductor devices

A mathematical model of the transient temperature response of integrated devices is presented which takes into account the three-dimensional (3-D) nature of heat flow and the physical structure of the device. Simple analytical relations for the transient thermal impedance and thermal time constants are derived for the first time. The impact of device geometry on the transient thermal response curve is discussed, and simple guidelines for the thermal design of solid-state devices operated in transient or pulsed regime are given.

A back-wafer contacted silicon-on-glass integrated bipolar process. Part II. A novel analysis of thermal breakdown

Analytical expressions for the electrothermal parameters governing thermal instability in bipolar transistors, i.e., thermal resistance R/sub TH/, critical temperature T/sub crit/ and critical current J/sub C,crit/, are established and verified by measurements on silicon-on-glass bipolar NPNs. A minimum junction temperature increase above ambient due to selfheating that can cause thermal breakdown is identified and verified to be as low as 10-20/spl deg/C. The influence of internal and external series resistances and the thermal resistance explicitly included in the expressions for T/sub crit/ and J/sub C,crit/ becomes clear. The use of the derived expressions for determining the safe operating area of a device and for extracting the thermal resistance is demonstrated.

A critical review of thermal models for electro-thermal simulation

Abstract This paper discusses some limitations in the approaches commonly adopted for device and circuit electro-thermal simulation. Thermal models for circuit simulation assume a simple geometry for the region where power dissipation occurs. Available models are compared. The impact of model parameters and bias condition on simulation accuracy is discussed. A new approach for calculating the temperature distribution under both steady-state and transient conditions is also proposed. The accuracy of two-dimensional (2D) electro-thermal device simulations is then investigated. It is shown that 2D simulations can lead to markedly inaccurate results. Possible approaches to overcome these limitations are discussed.

Thermal analysis of solid-state devices and circuits: an analytical approach

Abstract An analytical model of the temperature distribution in integrated circuits is presented. The solution is based on a classic method of electrostatics: the integration of the temperature field produced by a point source. Using this approach, the temperature distribution is expressed by a closed-form analytical relation, while previous approaches involve the summation of a slowly convergent series (Fourier series method) or a numerical integration procedure (Fourier transform method). Therefore, the present approach is much more computationally effective, and is particularly suitable for being incorporated into electro-thermal simulation codes. Another significant advantage of the proposed analytical formulation is that a more clear understanding of the influence of geometric and layout parameters on the thermal behavior can be gained. The analysis applies to arbitrarily located surface or volume heat sources. Boundary conditions are properly taken into account using the method of images. Finally, an accurate analytical expression for the thermal resistance of an integrated device is derived, which accounts for all relevant geometric parameters. This result may be a useful guideline in the early stages of layout optimization.

Small-signal operation of semiconductor devices including self-heating, with application to thermal characterization and instability analysis

A rigorous mathematical treatment of dynamic self-heating in semiconductor devices is presented. Two formulations for the admittance parameters are given. The thermal behavior of the device is referred to device temperature in the first formulation, and to ambient temperature in the second. Contrary to previous work, nonlinear thermal effects are included. An analytical model for the thermal resistance is derived which confirms the relevance of these effects. Applications of the above results to device modeling and thermal characterization are studied in detail by means of numerical simulations. Possible sources of inaccuracies are evidenced. Finally, it is shown that the differential analysis of thermal feedback provides a general and rigorous means to determine the conditions for the onset of thermally-induced instabilities.

Theory of electrothermal behavior of bipolar transistors: Part I -single-finger devices

A detailed theoretical and numerical analysis of the electrothermal behavior of single-finger bipolar transistors is proposed. Two models of different complexities are introduced to investigate self-heating effects in bipolar junction transistors (BJTs) and heterojunction bipolar transistors (HBTs) biased with a constant base-emitter voltage source or with a constant base current source. In the constant base-emitter voltage case, simple relations are derived for determining the onset of the flyback behavior in the output characteristics which defines the boundary of the safe operating region. The model indicates that the flyback behavior disappears at high V/sub BE/ values, and predicts a thermal hysteresis phenomenon at high currents. It is also shown that at high current levels the electrothermal behavior is dominated by ohmic base pushout. If a constant base current is applied, the model shows that both BJTs and HBTs are unconditionally thermally stable. The transient behavior is also considered, and the temperature evolution is investigated for different bias conditions. The model shows that, if the device is biased in the thermally unstable region, thermal breakdown occurs within a finite time instant in the limit case of a zero ballast resistance. Finally, the reduction in the safe operating area due to avalanche effects and to the temperature dependence of thermal conductivity is discussed, and a simplified model is proposed.

Analytical model for thermal instability of low voltage power MOS and SOA in pulse operation

Thermal instability presented by some high current power MOS has been shown to limit significantly the SOA capability. In this paper, we present a new analytical model to explain this type of instability in transient operation, based on an analytical formulation for both the positive temperature coefficient of the drain current and for the thermal resistance. The model is capable of predicting the onset of thermal instability for a given device structure and layout, and can be used both to define the allowed SOA of the device and as a design guide to design more rugged devices.

Thermal instabilities in high current power MOS devices: experimental evidence, electro-thermal simulations and analytical modeling

The phenomenon of the thermal instability presented by some high current power MOS has been intensively investigated, both by experimental means and by numerical simulations. An analytical expression for the positive temperature coefficient of the Drain current has been developed and a model for the thermal instability in transient operation has been proposed. The results explain the main causes of the thermal instability and give some rules to evaluate the possible failure occurrence for a given device.

Restabilizing mechanisms after the onset of thermal instability in bipolar transistors

The electrothermal behavior of single- and two-finger bipolar transistors at medium- and high-current operations is studied through theoretical modeling, experimental measurements, and computer simulations. Bias conditions that border thermally stable and unstable operation regimes are described by novel analytical formulations, which for the first time include simultaneously all relevant parameters that weaken the electrothermal feedback at high currents such as ballasting resistors, current dependence of the base-emitter-voltage temperature coefficient, and high-injection effects. Hence, besides giving a correct description of thermal instability mechanisms, the developed formulations also allow the prediction and physical understanding of restabilization phenomena. The models are supported by measurements on silicon-on-glass n-p-n bipolar junction transistors and by simulation results from a novel SPICE-based electrothermal macromodel for bipolar transistors. Furthermore, the models are employed to analyze the influence of the germanium percentage in the base of SiGe heterojunction bipolar transistors on the thermal ruggedness of the device.

FAst Novel Thermal Analysis Simulation Tool for Integrated Circuits (FANTASTIC)

This work describes a Fast novel thermal analysis simulation tool for integrated circuits (FANTASTIC), which is fully automated and relies on an enhanced version of the Multi-Point Moment Matching algorithm. The tool provides a novel equivalent network suitable for use in SPICE-like circuit simulators to perform efficient thermal and electrothermal analyses. FANTASTIC requires much less CPU time and memory storage compared to commercial simulators. The thermal behavior of a state-of-the-art four-finger GaAs HBT is investigated as a case-study.