Gregory Breyta

Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance

The number of steps any classical computer requires in order to find the prime factors of an l-digit integer N increases exponentially with l, at least using algorithms known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes. Quantum computers, however, could factor integers in only polynomial time, using Shors quantum factoring algorithm. Although important for the study of quantum computers, experimental demonstration of this algorithm has proved elusive. Here we report an implementation of the simplest instance of Shors algorithm: factorization of N = 15 (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule as quantum bits, which can be manipulated with room temperature liquid-state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to systems containing many quantum bits, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects in our system.

Polymer self assembly in semiconductor microelectronics

Integration of polymer self assembly with semiconductor processing enables sub-lithographic patterning of integrated circuit (IC) device elements and offers a non-traditional pathway to performance improvements (Black, 2005). We discuss target applications including surface-roughening for on-chip decoupling capacitors (Black et al., 2004), patterning nanocrystal floating gates for FLASH devices (Guarini et al., 2003), and defining FET channel arrays (Black, 2005)

Experimental realization of an order-finding algorithm with an NMR quantum computer.

We report the realization of a nuclear magnetic resonance quantum computer which combines the quantum Fourier transform with exponentiated permutations, demonstrating a quantum algorithm for order finding. This algorithm has the same structure as Shors algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.

Implementation of a three-quantum-bit search algorithm

We report the experimental implementation of Grover’s quantum search algorithm on a quantum computer with three quantum bits. The computer consists of molecules of 13C-labeled CHFBr2, in which the three weakly coupled spin-1/2 nuclei behave as the bits and are initialized, manipulated, and read out using magnetic resonance techniques. This quantum computation is made possible by the introduction of two techniques which significantly reduce the complexity of the experiment and by the surprising degree of cancellation of systematic errors which have previously limited the total possible number of quantum gates.

Effect of resist components on image spreading during postexposure bake of chemically amplified resists

The ultimate feature size achievable using a chemically amplified resist is determined by chemical and physical processes occurring during the post-exposure bake process. Using a combined experimental-modelling procedure we previously have developed a physically accurate, predictive description of coupled deprotection and diffusion in poly(p- tert-butyloxycar-bonyloxystyrene) (PTBOCST) resist containing a diaryliodonium perfluorobutanesulfonate salt as photoacid generator (PAG). In the present work we extend that study to quantify the impact of anion size and of added base on resist reaction diffusion kinetics. Our results show that both short and long range mobility of the PAG anion influence image spreading; the small triflate counterion leads to acid diffusion larger by a factor of 9 - 70 than that observed with the larger perfluoro-butanesulfonate counterion. The addition of tetra-n-butylammonium hydroxide leads to an overall suppression of image spreading in the exposed resist. This effect can be analyzed quantitatively using a proportional neutralization model, which reveals that base addition can lead to an overall sharpening of the developable latent image of deprotection even in the absence of acid diffusion.

Polymer design for 157-nm chemically amplified resists

Based on UV measurements at 157nm of in-house fluoropolymers we have selected (alpha) -trifluoromethylacrylate and norbornene bearing a pendant hexafluoroisopropanol group as our building blocks for 157nm resist polymers. Polymers consisting of these repeat units have an optical density/micrometers of 3 or below at 157nm. We have found that the (alpha) -trifluoromethylacrylate derivatives conveniently undergo radical copolymerization with norornenes, which has provided a breakthrough in preparation of our 157nm resist polymers. This approach offers flexibility and versatility because an acidic moiety or acid-labile group can be placed in either acrylate or norbornene repeat unit. Other platforms of interest include all acrylic, all-norbornene, and acrylic-styrenic polymers.

Highly porous silicon membrane fabrication using polymer self-assembly

A combination of diblock copolymer self-assembly and state-of-the-art semiconductor device fabrication methods is used to create highly uniform suspended porous silicon membranes. Integration of these two processing techniques is key to realizing manufacturable high quality devices. Three different methods are shown for adjusting membrane pore dimensions between 10 and 35 nm, allowing device optimization for specific applications.

Development of 157 nm positive resists

For adequate transparency we have selected hexafluoroisopropanol as an acid group and an α-trifluoromethylacrylic moiety as a repeat unit of our 157 nm resist polymers. The hexafluoroalcohol group is bound to norbornene or styrene. Four platforms are currently available to us: (1) all-acrylic, (2) all-alicyclic, (3) acrylic-alicyclic, and (4) acrylic-aromatic systems. While the all-alicyclic (all-norbornene) polymers are synthesized by transition-metal-initiated addition polymerization, all other polymers involving α-trifluoromethylacrylic monomers are prepared by conventional radical copolymerization. Characterization of the polymers and preliminary lithographic evaluation are reported.

Aliphatic platforms for the design of 157-nm chemically amplified resists

Our primary platform for 157 nm positive resists is built on a copolymer of t-butyl 2-trifluoromethylacrylate (TBTFMA) and norbornene bearing hexafluoroisopropanol (NBHFA) as an acid group, which is prepared by radical copolymerization. The radical copolymerization of 2-trifluoromethylacrylic monomers with norbornene derivatives has been found through reactivity ratio determination and in situ 1H NMR analysis of kinetics to deviate from the terminal model but to follow the penultimate model. These copolymers typically contain >50 mol% TBTFMA, are lipophilic, and fail to provide good imaging due to poor wettability. Blending a homopolymer of NBHFA (optical density (OD)=1.7/micrometers at 157 nm) into the copolymers (OD=2.5-2.7/micrometers ) increases the hydrophilicity and reduces OD to 2.2-2.0/micrometers , providing high resolution images. Another platform we have identified is a copolymer of TBTFMA with vinyl ethers, which can be prepared by using a common radical initiator. Some of the vinyl ether copolymers are also homogeneously miscible with the NBHFA homopolymer and thus their OD and aqueous base development can be improved by blending.

Protecting groups for 193-nm photoresists

Two versions of 193-nm single layer resists based on acrylic polymer chemistry have been described previously. The version 1 resist is a tool-testing version and is based on a methacrylate terpolymer structure. Its etch resistance analogue (version 2 resist) contains alicyclic compounds attached to the acrylic backbone. Key to enabling the performance of version 2 resist are the use of steroid additives which behave principally as thermomechanical modifiers to improve the mechanical properties of these rigid polymers through plasticization. We used the tertiary-butyl ester protecting group in these resists for thermal stability and other considerations. This paper describes an investigation of the impact of acid-cleavable protecting group structure on the properties of a series of model acrylic polymers. In this investigation, factors such as thermochemical stability, reactivity to photogenerated acid, and dissolution properties of exposed films as a function of dose were examined. A new highly reactive protecting group is introduced in this study, the tetrahydrofuranyl ester (THF) of methacrylic acid. Additionally, we introduce a new polymer family (polynorbornenes) with superior etch resistance, significantly broadening the polymer chemistry available for the construction of new 193-nm photoresists.