700 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 48, NO. 4, APRIL 2000 Modeling and Design Aspects of Millimeter-Wave and Submillimeter-Wave Schottky Diode Varactor Frequency Multipliers Jesús Grajal, Viktor Krozer, Member, IEEE, Emilio González, Francisco Maldonado, and Javier Gismero Abstract—Design and optimization of Schottky varactor diode frequency multipliers for millimeter and submillimeter wavelengths are generally performed using harmonic balance techniques together with equivalent-circuit models. Using this approach, it is difficult to design and optimize the device and mul- tiplier circuit simultaneously. The work presented in this paper avoids the need of equivalent circuits by integrating a numerical simulator for Schottky diodes into a circuit simulator. The good agreement between the calculated and published experimental data for the output power and conversion efficiency originates from the accurate physical model. The limiting effects of multi- plier performance such as breakdown, forward conduction, or saturation velocity are discussed in view of the optimum circuit conditions for multiplier operation including bias point, input power, and loads at different harmonics. It is shown that the onset of forward or reverse current flow is responsible for the limitation in the conversion efficiency. Index Terms—Frequency multipliers, harmonic balance technique, numerical modeling, Schottky diode modeling, semi- conductor simulation, submillimeter-wave multipliers. I. INTRODUCTION V ARACTOR frequency multipliers play a vital role in developing all-solid-state power sources at terahertz fre- quencies. The key points in the progress of the performance of Schottky varactor frequency multipliers have been the enhanced physical insight into and optimization of submillimeter-wave Schottky diode operation [1], the improvement in frequency multiplier analysis methods since the original work of Siegel and Kerr [2]–[5], and in physical analytical Schottky diode models [5]–[9], as well as numerical physical device models [4], [10]–[12]. The performance of active devices is defined not only by their inherent characteristics, but also by the embedding circuit. This coupling can be taken into account by including a numerical physical model into a circuit simulator [10], [11], [13]. The main problem in frequency varactor circuit design today is the inability to reproduce the experimental results Manuscript received March 4, 1999. This work was supported in part by the European Space Agency. The work of J. Grajal was supported by the Comunidad Autónoma de Madrid. The work of V. Krozer was supported by the Ministerio de Educación y Cultura Madrid, Spain, under the Programa Nacional de Formación de Personal Investigador. J. Grajal, E. González, F. Maldonado, and J. Gismero are with the ETSIT, Technical University of Madrid, 28040 Madrid, Spain. V. Krozer is with the Technical University of Chemnitz, D-09126 Chemnitz, Germany. Publisher Item Identifier S 0018-9480(00)02529-1. without additional empirical parameters. Furthermore, the limitations of multiplier operation at high powers and/or high frequencies is not well understood. Finally, a predictive design and circuit analysis tool is still missing, which is essential for the design of integrated frequency multipliers. The scope of this paper is to present a circuit analysis tool, which works without empirical parameters and is able to pre- dict the required device and circuit parameters of a frequency multiplier. We focus on the circuit design and operation aspects of frequency multipliers for millimeter and submillimeter bands. As a design tool, we employ the harmonic balance method (HBM) together with a physics-based drift-diffusion (DD) numerical device simulator. Our simulator incorporates accurate boundary and interface conditions for high forward as well as reverse bias, including impact ionization, nonconstant recombination velocity, self-consistent incorporation of the tunnelling, and image-force effects [11]. The validation of the numerical simulator has been performed by comparison of simulated device and circuit characteristics with experimental results obtained for submillimeter-wave Schottky diodes fabri- cated at the Technical University Darmstadt (TUD), Darmstadt, Germany, and the University of Virginia (UVa), Charlottesville, and for a number of multiplier circuits published in the litera- ture [4], [5]. The integration of numerical simulators for active devices into circuit simulators avoids the need of an equivalent-circuit model extraction. This new philosophy accounts for the de- vice–circuit interaction and provides another degree of freedom to improve the performance of circuits because they can be designed from both a device and circuit point-of-view. The simulation tool utilized in this paper and its implementa- tion are presented in Section II. The validation of the tool is out- lined in Section III, including a comparison of measured dc and RF performance characteristics with simulated values. In Sec- tion IV, an analysis of the performance of the frequency multi- pliers is presented together with an identification of the limiting mechanisms. Simulated results and a detailed discussion for the limiting mechanisms are provided in Section V, including break- down and velocity saturation effects. Based on these results, the synthesis of an optimum doubler and tripler circuit is dealt with in Section VI. The optimization of the device parameters such as doping concentration and profile, layer thicknesses, etc. are omitted in this paper, but will be dealt with in a future paper. This paper concludes with a summary of the results. 0018–9480/00$10.00 © 2000 IEEE