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Small metal-oxide-metal (MOM) capacitors are essential to energy-efficient mixed-signal integrated circuit design. However, only few reports discuss their matching properties based on large sets of measured data. In this paper, we report matching properties of femtofarad and sub-femtofarad MOM vertical-field parallel-plate capacitors and lateral-field fringing capacitors. We study the effect of both the finger-length and finger-spacing on the mismatch of lateral-field capacitors. In addition, we compare the matching properties and the area efficiency of vertical-field and lateral-field capacitors. We use direct mismatch measurement technique, and we illustrate its feasibility using experimental measurements and Monte Carlo simulations. The test-chips are fabricated in a 0.18 μm CMOS process. A large number of test structures is characterized (4800 test structures), which improves the statistical reliability of the extracted mismatch information. Despite conventional wisdom, extensive measurements show that vertical-field and lateral-field MOM capacitors have the same matching properties when the actual capacitor area is considered. Measurements show that the mismatch depends on the capacitor area but not on the spacing; thus, for a given mismatch specification, the lateral-field MOM capacitor can have arbitrarily small capacitance by increasing the spacing between the capacitor fingers, at the expense of increased chip area. Index Terms-Analog-to-digital converter (ADC), capacitanceto-digital converter (CDC), capacitive digital-to-analog converter (CapDAC), capacitor mismatch, energy-efficient circuits, metaloxide-metal (MOM) capacitors, mismatch characterization, programmable capacitor array (PCA). I. INTRODUCTION C APACITANCE sets a fundamental limit for the energy consumed in electronic circuitry. The energy required to charge a capacitor (C) to a voltage (V) is given by CV 2 ; thus, the smaller the capacitance the smaller the energy consumed. Energy efficiency of digital circuitry has been steadily Manuscript

The inevitable variability within electronic devices causes strict constraints on operation, reliability and scalability of the circuit design. However, when a compromise arises among the different performance metrics, area, time and energy, variability then loosens the tight requirements and allows for further savings in an alternative design scope. To that end, unconventional computing approaches are revived in the form of approximate computing, particularly tuned for resource-constrained mobile computing. In this paper, a proof-of-concept of the approximate computing paradigm using memristors is demonstrated. Stochastic memristors are used as the main building block of probabilistic logic gates. As will be shown in this paper, the stochasticity of memristors’ switching characteristics is tightly bound to the supply voltage and hence to power consumption. By scaling of the supply voltage to appropriate levels stochasticity gets increased. In order to guide the design process of approximate circuits based on memristors a realistic device model needs to be elaborated with explicit emphasis of the probabilistic switching behavior. Theoretical formulation, probabilistic analysis, and simulation of the underlying logic circuits and operations are introduced. Moreover, the expected output behavior is verified with the experimental measurements of valence change memory cells. Hence, it is shown how the precision of the output is varied for the sake of the attainable gains at different levels of available design metrics. This approach represents the first proposition along with physical verification and mapping to real devices that combines stochastic memristors into unconventional computing approaches.

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