1. INTRODUCTION Interconnection wiring is gaining a significant importance in speed of modern VLSI circuits. Since the wiring may cover up to eighty percent of nowdays chip area, special care must be devoted to this problem. A special case of two interconnection lines is considered in [3]. We generalized these results to any number of lines and gave the method for computing maximal deviation of signal caused by crosstalk effect. Simulation of Crosstalk between Several Interconnection Lines in CMOS Integrated Circuits Marko Petković undergraduate student of Faculty of Electronic Engineering, University of Niš, Serbia & Montenegro E-mail: dexter_of_nis@neobee.net

2. MODEL OF INTERCONNECTION LINES Thin film technology which is commonly used in modern CMOS circuits requires dealing with interconnection lines with distributed parameters. There exists capacitance between each pair of interconnections, i.e. there are N(N-1)/2 coupled capacitances. This number can be drastically reduced because many of these capacitances can be neglected. On higher frequencies the inductance of interconnections is not negligible and must be included in the model. We used electromagnetic simulator Maxwell Student Version, for computing required capacitances directly form the model. We obtained results for different values of N (5, 7, 9, 11 and 15).

3. Dimensions we used in our simulation: Fig. 1. Capacitance model of interconnections

4. For N ≥ 7 capacitances do not depend on N. Every conductor influences only two neighbor conductors on each side (for example, 4th conductor influences on 2nd, 3rd, 5th and 6th). So, we just need to consider three classes of capacitances:,, From the table 1 and for a sake of symmetry there should hold: First two values should be slightly different due to the boundary effects (differences are 16% and 5%) So for the description of first class capacitances, we require three values.

5. [pF/m] 1234567 113014.52.330000 214.511714.12.29000 32.3314.111613.92.2900 40 13.911413.92.290 500 13.911614.12.33 60002.2914.111714.5 700002.3314.5130 TABLE I. Capacitances for N = 7 conductors

6. Situation is similar in the second and third class. Also holds: and is about 3% greater. In the third class, it is sufficient to consider just one value of capacitance and as we will see later, this class can be also neglected. Finally for the circuit simulation we require just six values of capacitances. Calculated values in our example are:

7. Fig. 1a. Potential distribution around N=5 conductors

8. Fig. 2. Section of electrical model for crosstalk simulation between i th and j th line. Fig. 3. Equivalent electrical scheme of the simulated circuit for N=7 conductors CROSSTALK SIMULATION To simulate crosstalk, we used OrCad PSpice simulator. System of interconnection lines is modeled as cascade connection of multiport sections. An electrical circuit representing one section is shown on Figure 2.

9. All sources have same voltage V in = 5 V. On 4 th line we apply periodic trapezoidal waveform with the frequency of f = 25 MHz and rise and fall times 0.01 ns. All resistances are equal R p = 1 kΩ Maximal deviation of signal at lines 5 and 6 due to the crosstalk are 700 mV and 110 mV respectively. This is similar to the ratio between c 45 and c 46. Complete model of interconnections is formed by cascade connection of k = 15 sections. Inductive and resistive parameters were calculated using formulas from [2]. Obtained values are: We considered N = 7 lines made of aluminum placed on the same distance. Equivalent circuit is shown in Fig. 3.

10. Fig. 5. Output signal on 5 th line Fig. 4. Output signal on 4 th line Fig. 6. Output signal on 6 th line Fig. 7. Output signal on 4 th line when input signals on 2 nd, 3 rd, 5 th and 6 th lines are pulse

11. Let us modify the circuit, such that input signal on 2nd, 3rd, 5th and 6th line is pulse, and on 4th line is constant (5 V, as in the previous case). Waveform of the output signal on line 4 is shown on Fig. 7. Maximal deviation of the signal is now 1.9 V. In this work we considered crosstalk between several interconnections in modern CMOS VLSI circuits. Maximal signal deviation due to the crosstalk can be up to 41% and it determines lower bound for the noise margins of the logical elements. The author wishes to thank Professor Vančo Litovski, head of the Laboratory for Electronic Design Automation (LEDA) at the Faculty of Electronic Engineering, University of Niš for the oportunity of this research given, and to Milan Savić for usefull discussions. Acknowledgement CONCLUSION