In this report we focus on some aspects related to modeling and formal verification of embedded systems. Many models have been proposed to represent embedded systems. These models encompass a broad range of styles, characteristics, and application do
mains and include the extensions of finite state machines, data flow graphs, communication processes and Petri nets. In this report, we have used a PRES+ model (Petri net based Representation for Embedded Systems) as an extension of classical Petri net model that captures concurrency, timing behaviour of embedded systems; it allows systems to be representative in different levels of abstraction and improves expressiveness by allowing the token to carry information. Modeling using PRES+, as discussed above, may be convenient for specifying the input behaviour because it supports concurrency. However, there is no equivalence checking method reported in the literature for PRES+ models to the best of our knowledge. In contrast, equivalence checking of FSMD models exist. As a first step, therefore, we seek to devise an algorithm to translate PRES+ models to FSMD models.
Since spin and charge are both carried by electrons (or holes) in a solid, it is natural to assume that charge and spin diffusion coefficients will be the same. Drift-diffusion models of spin transport typically assume so. Here, we show analytically
that the two diffusion coefficients can be vastly different in quantum wires. Although we do not consider quantum wells or bulk systems, it is likely that the two coefficients will be different in those systems as well. Thus, it is important to distinguish between them in transport models, particularly those applied to quantum wire based devices
We report measurement of the ensemble averaged transverse spin relaxation time (T2*) in bulk and few molecules of the organic semiconductor tris(8-hydroxyquinolinolato aluminum) or Alq3. This system exhibits two characteristic T2* times, the longer o
f which is temperature-independent and the shorter is temperature-dependent, indicating that the latter is most likely limited by spin-phonon interaction. Based on the measured data, we infer that the single particle T2 time is long enough to meet Knills criterion for fault tolerant quantum computing, even at room temperature. Alq3 is also an optically active organic and we propose a simple optical scheme for spin qubit read out. Moreover, we found that the temperature-dependent T2* time is considerably shorter in bulk Alq3 powder than in few molecules confined in 1-2 nm sized cavities, which is suggestive of a new type of ``phonon bottleneck effect. This is very intriguing for organic molecules where carriers are always localized over individual molecules but the phonons are delocalized.
Recent advances in manipulating single electron spins in quantum dots have brought us close to the realization of classical logic gates based on representing binary bits in spin polarizations of single electrons. Here, we show that a linear array of
three quantum dots, each containing a single spin polarized electron, and with nearest neighbor exchange coupling, acts as the universal NAND gate. The energy dissipated during switching this gate is the Landauer-Shannon limit of kTln(1/p) [T = ambient temperature and p = intrinsic gate error probability]. With present day technology, p = 1E-9 is achievable above 1 K temperature. Even with this small intrinsic error probability, the energy dissipated during switching the NAND gate is only ~ 21 kT, while todays nanoscale transistors dissipate about 40,000 - 50,000 kT when they switch.
We propose and analyze a novel dual-gate Spin Field Effect Transistor (SpinFET) with half-metallic ferromagnetic source and drain contacts. The transistor has two gate pads that can be biased independently. It can be switched ON or OFF with a few mV
change in the differential bias between the two pads, resulting in extremely low dynamic power dissipation during switching. The ratio of ON to OFF conductance remains fairly large (~ 60) up to a temperature of 10 K. This device also has excellent inverter characteristics, making it attractive for applications in low power and high density Boolean logic circuits.
We show that a Spin Field Effect Transistor, realized with a semiconductor quantum wire channel sandwiched between half-metallic ferromagnetic contacts, can have Fano resonances in the transmission spectrum. These resonances appear because the ferrom
agnets are half-metallic, so that the Fermi level can be placed above the majority but below the minority spin band. In that case, the majority spins will be propagating, but the minority spins will be evanescent. At low temperatures, the Fano resonances can be exploited to implement a digital binary switch that can be turned on or off with a very small gate voltage swing of few tens of microvolts, leading to extremely small dynamic power dissipation during switching. An array of 500,000 x 500,000 such transistors can detect ultrasmall changes in a magnetic field with a sensitivity of 1 femto-Tesla/sqrt{Hz}, if each transistor is biased near a Fano resonance.
