Full-wave Simulation of Transmission Line Structures in Microwave Monolithic Integrated Circuits

Future Si-based analog and digital highly integrated Microwave Monolithic Integrated Circuits (MMIC) are expected to operate at frequencies up into the millimeter-wave range. Further reduction of circuit dimensions will require multilayered wiring and transmission line structures with cross-sectional dimensions of the conductors in the order of micrometers. In order to achieve further reduction in conductor losses copper is also considered for internal wiring. The exact modelling of the transmission properties of the line structures requires full-wave modelling of the electromagnetic field in the semiconductor and insulator regions as well as within the conductors. In this paper various transmission line structures have been analyzed using the Mode Matching (MM) approach. Based on the numerical simulation transmission an equivalent network-oriented circuits are extracted. INTRODUCTION The application of copper as conductor material and the use of damascene technology is a promising way for future realization of highly integrated MMICs for frequencies of operation up to several 10 GHz. Compared to aluminium copper exhibits significantly lower electro-migration and better electrical and thermal conductivity [1, 2]. The higher possible current density in copper transmission lines allows a decrease in the cross-section of the conductors. Damascene technology allows one to reduce the size of transmission lines to 2.5 μm width and 0.4 μm height. The dimensions of the conductors are comparable with the skin depth, therefore an accurate simulation and optimization of the structures of the transmission lines requires full-wave modelling of the electromagnetic field inside the conductors as well. Figure 1: Schematic view of the simulated multilayered geometry. TECHNOLOGY In damascene technology trenches for the transmission lines and vias are first etched into the substrate (SiO 2). A very thin insulating layer of TiN or TaN is then deposited as a barrier between the substrate and copper to avoid diffusion of the copper into the SiO2 layer. A thin copper film is evaporated and all trenches and holes for vias are filled at once in a galvanic process (dual damascene process). The surplus copper on the surface of the wafer is removed afterwards by chemical-mechanical polishing, then the surface is covered by etching stopper (Si 3N4). After this a further SiO2 layer can be placed on top and these steps may be repeated up to 6 times. The result is a multilayered structure with various transmission line structures, i.e. coplanar waveguide (CPW), stripline, microstrip line, conductor backed CPW (see Fig. 1). THE MODE MATCHING APPROACH In transmission lines with strip width and height in the skin depth’s order of magnitude conductor loss influences the propagation characteristics severely. One of the most efficient methods for numerical simulation of such homogeneous two-dimensional structures is the mode matching method [4, 3]. The field inside the conductors, playing an important role, is completely taken into consideration. In the MM method the structure is subdivided into homogeneous subdomains. At the boundaries of the subdomains the tangential field components of the partial waves are matched. The method of moments is used to determinate the amplitudes of the partial waves. Truncating the complete set of eigenmodes numerical results depend on the set of testing functions used in the method of moments. SIMULATIONS RESULTS Various types of transmission lines are considered. From various investigations it turned out that the coplanar waveguides are advantageous compared to other line types in respect of the attenuation caused mainly by the conductor loss. For example, microstrip lines always show higher attenuation due to the thickness of the SiO 2 layer which is fixed by technological reasons. Two 50Ω CPWs of different dimensions are simulated. The simulations are performed with following material parameters: εSi = 11:9; σSi = 5:5 10 4 S=m, εSiO2 = 3:9, tanδSiO2 = 10 4, σCu = 5:9 107 S=m, vertical dimensions: TSi = 380 μm, T I SiO2 = 4.9 μm, T I M = 0.6 μm, T II SiO2 = 4.15 μm, TSiN = 0.55 μm. The first CPW (CPW1) has the dimensions: W = 7.5 μm, S = 2.5 μm; the size of the second CPW (CPW2) is twice as large: W = 15 μm, S = 5 μm. In Fig. 2 the numerical results for the characteristic impedance of two CPWs are shown in dependance of the number n 0 20 40 60 80 100 48 50 52 54 56 58 60 62 frequency [GHz] R e Z w [Ω ] CPW2, n = 10