Zohaib Mahmood

Resonant Body Transistors in IBM's 32 nm SOI CMOS Technology

This paper presents unreleased CMOS-integrated MEMS resonators fabricated at the transistor level of IBMs 32SOI technology and realized without the need for any postprocessing or packaging. In this technology, resonant body transistors (RBTs) are driven capacitively and sensed piezoresistively using an n-channel field effect transistor (FET). Acoustic Bragg Reflectors (ABRs) are used to localize acoustic vibrations in the unreleased resonators completely buried under the CMOS metal stack and surrounded by low-κ dielectric. FET sensing is analytically compared with alternative active and passive sensing mechanisms to benchmark CMOS-MEMS resonator performance with frequency scaling. Experimental results from the first generation hybrid CMOS-MEMS RBTs show RBTs operating above 11 GHz with Qs of 24-30 and footprints of 5 × 3 μm. Comparative behavior of devices with design variations is used to demonstrate the effect of ABRs on spurious mode suppression. In addition, the performance of the RBTs is compared with passive electrostatic resonators, which show no discernible peak. Finally, temperature stability of <;3 ppm/K due to complimentary materials in the CMOS stack is analytically and experimentally verified.

Passive reduced order modeling of multiport interconnects via semidefinite programming

In this paper we present a passive reduced order modeling algorithm for linear multiport interconnect structures. The proposed technique uses rational fitting via semidefinite programming to identify a passive transfer matrix from given frequency domain data samples. Numerical results are presented for a power distribution grid and an array of inductors, and the proposed approach is compared to two existing rational fitting techniques.

An efficient framework for passive compact dynamical modeling of multiport linear systems

We present an efficient and scalable framework for the generation of guaranteed passive compact dynamical models for multiport structures. The proposed algorithm enforces passivity using frequency independent linear matrix inequalities, as opposed to the existing optimization based algorithms which enforce passivity using computationally expensive frequency dependent constraints. We have tested our algorithm for various multiport structures. An excellent match between the given samples and our passive model was achieved.

Efficient Localization Methods for Passivity Enforcement of Linear Dynamical Models

This paper describes a novel approach for passivity enforcement of compact dynamical models of electrical interconnects. The proposed approach is based on a parameterization of general state-space scattering models with fixed poles. We formulate the passivity constraints as a unitary boundedness condition on the H∞ norm of the system transfer function. When this condition is not verified, we use it as an explicit constraint within an iterative perturbation loop of the system state-space matrices. Since the resulting optimization framework is convex but nonsmooth, we solve it via localization based algorithms, such as the ellipsoid and the cutting plane methods. The proposed technique solves two critical bottleneck issues of the existing approaches for passivity enforcement of linear macromodels. Compared to quasi-optimal schemes based on singular value or Hamiltonian eigenvalue perturbation, we are able to guarantee convergence to the optimal solution. Compared to convex formulations based on direct Bounded Real Lemma constraints, we are able to reduce both memory and time requirements by orders of magnitude. We demonstrate the effectiveness of our approach on a number of cases for which existing algorithms either fail or exhibit very slow convergence.

General design approach and practical realization of decoupling matrices for parallel transmission coils

In a coupled parallel transmit (pTx) array, the power delivered to a channel is partially distributed to other channels because of coupling. This power is dissipated in circulators resulting in a significant reduction in power efficiency. In this study, a technique for designing robust decoupling matrices interfaced between the RF amplifiers and the coils is proposed. The decoupling matrices ensure that most forward power is delivered to the load without loss of encoding capabilities of the pTx array.

Optimal passivity enforcement of state-space models via localization methods

This work presents a novel approach for passivity enforcement of state-space macromodels, based on nonsmooth localization algorithms applied to a convex formulation of the passivity constraints. The main advantages of proposed scheme are guaranteed optimality and limited required computational resources. Compared to convex formulations based on a direct implementation of Bounded Real Lemma we are able to reduce both the memory and time requirements by orders of magnitude.

Resonant Body Transistors in IBM's 32nm SOI CMOS technology

This work presents an unreleased CMOS-integrated MEMS resonators fabricated at the transistor level of IBMs 32SOI technology and realized without the need for any post-processing or packaging. These Resonant Body Transistors (RBTs) are driven capacitively and sensed piezoresistively using an n-channel Field Effect Transistor (nFET). Acoustic Bragg Reflectors (ABRs) are used to localize acoustic vibrations in these resonators completely buried in the CMOS stack and surrounded by low-k dielectric. Experimental results from the first generation hybrid CMOS-MEMS show RBTs operating at 11.1-11.5 GHz with footprints <; 5μm × 3μm. The response of active resonators is shown to contrast with passive resonators showing no discernible peak. Comparative behavior of devices with design variations is used to demonstrate the effect of ABRs on spurious mode suppression. Temperature stability and TCF compensation due to complimentary materials in the CMOS stack are experimentally verified.

Resonant body transistors in standard CMOS technology

This work presents Si-based electromechanical resonators fabricated at the transistor level of a standard SOI CMOS technology and realized without the need for any postprocessing or packaging. These so-called Resonant Body Transistors (RBTs) are driven capacitively and sensed by piezoresistively modulating the drain current of a Field Effect Transistor (FET). First generation devices operating at 11.1-11.5 GHz with footprints of 3μm×5μm are demonstrated. These unreleased bulk acoustic resonators are completely buried within the CMOS stack and acoustic energy at resonance is confined using Acoustic Bragg Reflectors (ABRs). The complimentary TCE of Si/SiO2 in the resonator and the surrounding ABRs results in a temperature stability TCF of <;3 ppm/K. Comparative behavior of devices is also discussed to analyze the effect of fabrication variations and active sensing.