There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Quantum Computation and Quantum Information

Current research into semiconductor clusters is focused on the properties of quantum dots-fragments of semiconductor consisting of hundreds to many thousands of atoms-with the bulk bonding geometry and with surface states eliminated by enclosure in a material that has a larger band gap. Quantum dots exhibit strongly size-dependent optical and electrical properties. The ability to join the dots into complex assemblies creates many opportunities for scientific discovery.

Semiconductor Clusters, Nanocrystals, and Quantum Dots

Recent years have witnessed many breakthroughs in research on graphene (the first two-dimensional atomic crystal) as well as a significant advance in the mass production of this material. This one-atom-thick fabric of carbon uniquely combines extreme mechanical strength, exceptionally high electronic and thermal conductivities, impermeability to gases, as well as many other supreme properties, all of which make it highly attractive for numerous applications. Here we review recent progress in graphene research and in the development of production methods, and critically analyse the feasibility of various graphene applications.

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A roadmap for graphene

We examine the current performance and future demands of interconnects to and on silicon chips. We compare electrical and optical interconnects and project the requirements for optoelectronic and optical devices if optics is to solve the major problems of interconnects for future high-performance silicon chips. Optics has potential benefits in interconnect density, energy, and timing. The necessity of low interconnect energy imposes low limits especially on the energy of the optical output devices, with a ~ 10 fJ/bit device energy target emerging. Some optical modulators and radical laser approaches may meet this requirement. Low (e.g., a few femtofarads or less) photodetector capacitance is important. Very compact wavelength splitters are essential for connecting the information to fibers. Dense waveguides are necessary on-chip or on boards for guided wave optical approaches, especially if very high clock rates or dense wavelength-division multiplexing (WDM) is to be avoided. Free-space optics potentially can handle the necessary bandwidths even without fast clocks or WDM. With such technology, however, optics may enable the continued scaling of interconnect capacity required by future chips.

Device Requirements for Optical Interconnects to Silicon Chips

We report experiments and theory on the effects of electric fields on the optical absorption near the band edge in GaAs/AlGaAs quantum-well structures. We find distinct physical effects for fields parallel and perpendicular to the quantum-well layers. In both cases, we observe large changes in the absorption near the exciton peaks. In the parallel-field case, the excitons broaden with field, disappearing at fields \ensuremath{\sim}${10}^{4}$ V/cm; this behavior is in qualitative agreement with previous theory and in order-of-magnitude agreement with direct theoretical calculations of field ionization rates reported in this paper. This behavior is also qualitatively similar to that seen with three-dimensional semiconductors. For the perpendicular-field case, we see shifts of the exciton peaks to lower energies by up to 2.5 times the zero-field binding energy with the excitons remaining resolved at up to \ensuremath{\sim}${10}^{5}$ V/cm: This behavior is qualitatively different from that of bulk semiconductors and is explained through a mechanism previously briefly described by us [D. A. B. Miller et al., Phys. Rev. Lett. 53, 2173 (1984)] called the quantum-confined Stark effect. In this mechanism the quantum confinement of carriers inhibits the exciton field ionization. To support this mechanism we present detailed calculations of the shift of exciton peaks including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations of exciton binding energy in a field. We also calculate the tunneling lifetimes of particles in the wells to check the inhibition of field ionization. The calculations are performed using both the 85:15 split of band-gap discontinuity between conduction and valence bands and the recently proposed 57:43 split. Although the detailed calculations differ in the two cases, the overall shift of the exciton peaks is not very sensitive to split ratio. We find excellent agreement with experiment with no fitted parameters.

Electric field dependence of optical absorption near the band gap of quantum-well structures.

We present theory and extended experimental results for the large shift in optical absorption in GaAs-AlGaAs quantum well structures with electric field perpendicular to the layers. In contrast to the Stark effect on atoms or on excitons in bulk semiconductors, the exciton resonances remain resolved even for shifts much larger than the zero-field binding energy and fields g 50 times the classical ionization field. The model explains these results as a consequence of the quantum confinement of carriers.

Band-Edge Electroabsorption in Quantum Well Structures: The Quantum-Confined Stark Effect

The various arguments for introducing optical interconnections to silicon CMOS chips are summarized, and the challenges for optical, optoelectronic, and integration technologies are discussed. Optics could solve many physical problems of interconnects, including precise clock distribution, system synchronization (allowing larger synchronous zones, both on-chip and between chips), bandwidth and density of long interconnections, and reduction of power dissipation. Optics may relieve a broad range of design problems, such as crosstalk, voltage isolation, wave reflection, impedence matching, and pin inductance. It may allow continued scaling of existing architectures and enable novel highly interconnected or high-bandwidth architectures. No physical breakthrough is required to implement dense optical interconnects to silicon chips, though substantial technological work remains. Cost is a significant barrier to practical introduction, though revolutionary approaches exist that might achieve economies of scale. An Appendix analyzes scaling of on-chop global electrical interconnects, including line inductance and the skin effect, both of which impose significant additional constraints on future interconnects.

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Rationale and challenges for optical interconnects to electronic chips

We analyze theoretically the optical properties of ideal semiconductor crystallites so small that they show quantum confinement in all three dimensions [quantum dots (QD's)]. In the limit of a QD much smaller than the bulk exciton size, the linear spectrum will be a series of lines, and we consider the phonon broadening of these lines. The lowest interband transition will saturate like a two-level system, without exchange and Coulomb screening. Depending on the broadening, the absorption and the changes in absorption and refractive index resulting from saturation can become very large, and the local-field effects can become so strong as to give optical bistability without external feedback. The small QD limit is more readily achieved with narrow-band-gap semiconductors.

David A. B. Miller

Papers

Device Requirements for Optical Interconnects to Silicon Chips

Electric field dependence of optical absorption near the band gap of quantum-well structures.

Band-Edge Electroabsorption in Quantum Well Structures: The Quantum-Confined Stark Effect

Rationale and challenges for optical interconnects to electronic chips

Theory of the linear and nonlinear optical properties of semiconductor microcrystallites