1008 IEICE TRANS. ELECTRON., VOL.E94–C, NO.6 JUNE 2011 PAPER Special Section on Analog Circuits and Related SoC Integration Technologies Eigenmode Analysis of Propagation Constant for a Microstrip Line with Dummy Fills on a Si CMOS Substrate Yuya ONO †a) , Student Member, Takuichi HIRANO † , Kenichi OKADA † , Jiro HIROKAWA † , Members, and Makoto ANDO † , Fellow SUMMARY In this paper we present eigenmode analysis of the prop- agation constant for a microstrip line with dummy fills on a Si CMOS substrate. The effect of dummy fills is not negligible, particularly in the millimeter-wave band, although it has been ignored below frequencies of a few GHz. The propagation constant of a microstrip line with a periodic structure on a Si CMOS substrate is analyzed by eigenmode analysis for one period of the line. The calculated propagation constant and character- istic impedance were compared with measured values for a chip fabricated by the 0.18 μm CMOS process. The agreement between the analysis and measurement was very good. The dependence of loss on the arrangement of dummy fills was also investigated by eigenmode analysis. It was found that the transmission loss becomes large when dummy fills are arranged at places where the electromagnetic field is strong. key words: silicon CMOS, microstrip line, propagation constant, dummy fill, eigenmode analysis, periodic structure, millimeter wave 1. Introduction Millimeter-wave CMOS RF circuits have received substan- tial attention in recent years, motivated by advances in the CMOS process [1]–[3]. The integration of digital and RF circuits on a CMOS chip will enable cost reduction in the production of consumer applications. The recent miniatur- ization of the CMOS process has led to the realization of field-effect transistors (FETs) with a high cutoff frequency ( f T ) and maximum frequency of oscillation ( f max ), which enables the realization of active RF circuits such as ampli- fiers, oscillators, and so forth. However, there are many difficulties in realizing RF circuits using the present CMOS process for digital cir- cuits. CMOS circuits consist of several metal layers and vias above the surface of a silicon substrate. There are also many strict design rules. For example, the metal filling rate, usu- ally 25% to 75%, must be satisfied owing to the restriction imposed by the chemical mechanical polishing (CMP) pro- cess [4]. To satisfy the metal filling rate, square regions of dummy fills of side 2 μm to 10 μm are usually used [5]. The effect of dummy fills cannot be neglected in the millimeter- wave band, although it has been ignored below frequencies of a few GHz. It is very important to characterize transmission lines with dummy fills by simulation for the efficient develop- ment of CMOS RF circuits. The easiest way to simulate Manuscript received October 5, 2010. Manuscript revised January 18, 2011. † The authors are with Tokyo Institute of Technology, Tokyo, 152-8552 Japan. a) E-mail: ono yuya@antenna.ee.titech.ac.jp DOI: 10.1587/transele.E94.C.1008 transmission lines with dummy fills is to analyze a trans- mission line with a finite length. However, it is necessary to eliminate the finite truncation effect by using the thru- reflect-line (TRL) [6] or other calibration techniques, which require two or three patterns. This results in an increase in the computational cost of simulation. To overcome this problem and to extract the basic ef- fects of dummy load, in this paper we present a method of analyzing the propagation constant for an infinite guided mi- crostrip line on a Si CMOS substrate [7], [8] by applying eigenmode analysis to one period of a line to simulate a line with a dummy load [9], [10]. In Sect. 2 we describe the structure of a guided mi- crostrip line. The procedure of analysis is explained in Sect. 3. Numerical and measured results, as well as their comparison, are presented in Sect. 4. 2. Guided Microstrip Line on a Si CMOS Substrate A guided microstrip line on a Si CMOS substrate [7], [8] with dummy fills is shown in Fig. 1. The transmission line consists of several metal (aluminum; Al) layers and vias that connect them. Square regions of dummy fills of side 2 μm Fig. 1 Guided microstrip line on a Si substrate. Copyright c  2011 The Institute of Electronics, Information and Communication Engineers