Within-Die Gate Delay Variability Measurement using Re-configurable Ring Oscillator

We report a circuit technique to measure the on-chip delay of an individual logic gate (both inverting and non-inverting) in its unmodified form using digitally reconfigurable ring oscillator (RO). Solving a system of linear equations with different configuration setting of the RO gives delay of an individual gate. Experimental results from a test chip in 65nm process node show the feasibility of measuring the delay of an individual inverter to within 1pS accuracy. Delay measurements of different nominally identical inverters in close physical proximity show variations of up to 26% indicating the large impact of local or within-die variations.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Within-Die Gate Delay Variability Measurement Using Reconfigurable Ring Oscillator

We report the design and characterization of a circuit technique to measure the on-chip delay of an individual logic gate (both inverting and noninverting) in its unmodified form. The test circuit comprises of digitally reconfigurable ring oscillator (RO). The gate under test is embedded in each stage of the ring oscillator. A system of linear equations is then formed with different configuration settings of the RO, relating the individual gate delay to the measured period of the RO, whose solution gives the delay of the individual gates. Experimental results from a test chip in 65-nm process node show the feasibility of measuring the delay of an individual inverter to within 1 ps accuracy. Delay measurements of different nominally identicall inverters in close physical proximity show variations of up to 28% indicating the large impact of local variations. As a demonstration of this technique, we have studied delay variation with poly-pitch, length of diffusion (LOD) and different orientations of layout in silicon. The proposed technique is quite suitable for early process characterization, monitoring mature process in manufacturing and correlating model-to-hardware.

Monolithic surface acoustic wave resonator oscillator

A monolithic surface acoustic wave (SAW) resonator operating at 156 MHz, in which the frequency controlling element is a Fabry–Perot type of SAW resonator and the gain element is a monolithic SAW amplifier (SiOx/InSb/SiOx structure located inside the SAW resonator cavity) is described and experimental details presented. Based on the existing experimental data, an uhf monolithic ring resonator oscillator is proposed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Monolithic surface acoustic wave resonator oscillator

A monolithic surface acoustic wave (SAW) resonator operating at 156 MHz, in which the frequency controlling element is a Fabry–Perot type of SAW resonator and the gain element is a monolithic SAW amplifier (SiOx/InSb/SiOx structure located inside the SAW resonator cavity) is described and experimental details presented. Based on the existing experimental data, an uhf monolithic ring resonator oscillator is proposed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Identity for harmonic oscillator brackets

An identity satisfied by the harmonic oscillator (Talmi-Moshinsky) brackets is derived from two equivalent methods for evaluating an integral often encountered in cluster model studies.

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.

Dissipative dynamics of a harmonic oscillator: A nonperturbative approach

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.

Highly stable oscillator for quartz crystal thickness monitor

A highly stable oscillator used in a quartz crystal thickness monitor for monitoring the rate of evaporation and total thickness of film during thin film deposition is reported. The design aspects of the oscillator and its long term stability, which enhances the reproducibility and the performance of the thickness monitor, are discussed. The stability of the oscillator at defined conditions is tested and compared with the conventional transistorized oscillator and the IC oscillator using inverters. The oscillator is coupled to the crystal monitor and its performance is studied in an evaporation system by evaporating different materials

Tuning the Conductance of Dirac Fermions on the Surface of a Topological Insulator

We study the transport properties of the Dirac fermions with a Fermi velocity v(F) on the surface of a topological insulator across a ferromagnetic strip providing an exchange field J over a region of width d. We show that the conductance of such a junction, in the clean limit and at low temperature, changes from oscillatory to a monotonically decreasing function of d beyond a critical J. This leads to the possible realization of a magnetic switch using these junctions. We also study the conductance of these Dirac fermions across a potential barrier of width d and potential V-0 in the presence of such a ferromagnetic strip and show that beyond a critical J, the criteria of conductance maxima changes from chi = eV(0)d/(h) over barv(F) = n pi to chi = (n + 1/2)pi for integer n. We point out that these novel phenomena have no analogs in graphene and suggest experiments which can probe them.

Simulation and implementation of a tunable C-band dielectric resonator oscillator

Microwave sources used in present day applications are either multiplied source derived from basic quartz crystals, or frequency synthesizers. The frequency multiplication method increases FM noise power considerably, and has very low efficiency in addition to being very complex and expensive. The complexity and cost involved demands a simple, compact and tunable microwave source. A tunable dielectric resonator oscillator(DRO) is an ideal choice for such applications. In this paper, the simulation, design and realization of a tunable DRO with a center frequency of 6250 MHz is presented. Simulation has been carried out on HP-Ees of CAD software. Mechanical and electronic tuning features are provided. The DRO operates over a frequency range of 6235 MHz to 6375 MHz. The output power is +5.33 dBm at centre frequency. The performance of the DRO is as per design with respect to phase noise, harmonic levels and tunability. and hence, can conveniently be used for the intended applications.