Given recent advances in the field of global optimization, we aim to make advances towards deterministic global optimization of some important engineering systems (namely, multilayer filters, lens systems, and semiconductors),. The design of these systems is an activity popularly regarded as an art, and it may potentially be turned into a science using the deterministic global optimization technique of branch-and-bound. The technique of branch-bound is briefly illustrated in Figure 1 below.

Figure 1: An illustration of the technique of branch-and-bound.

As Figure 1 shows, this methodology requires the cheap construction of tight bounds on the merit function defining each optimization problem. With the recent availability of extensively verified and parallelizable software for suppressing the dependency problem (using the technique of Taylor arithmetic) arising in attempts to bound explicit merit functions (of sufficient differentiability), we aim to identify the subset of the important classes of multilayer filters and lens systems accessible by rigorous global optimization. Given recent advances in mathematical theory for constructing parametric bounds on ODE solutions (in particular, suppressing the wrapping effect using the technique of generalized McCormick Relaxations), we have developed a mathematical methodology for constructing parametric bounds on semilinear parabolic PDE solutions. The specific long-term goal of the PDE work is rigorous global optimization of semiconductors. The project is presently in the supercomputing software development phase. Preliminary serial work in the domain of multilayer filters yielded an important broadband omnidirectional antireflection coating design for silicon solar cells. Work is in progress to experimentally demonstrate this design.

Photolithography’s accuracy and scalability have made it the method for sub-micron-scale definition of single-crystal semiconductor devices for over half a century. Unfortunately, organic semiconductor devices are chemically incompatible with the types of resists, solvents, and etchants traditionally used. This work investigates the use of an uncommonly used chemically inert resist method ^{[1] [2] [3] [4] [5]} that relies on physical phase changes for lift-off patterning of thin films of organic semiconductors and metals.

The resist gas is flowed over a cryogenically cooled substrate, where it freezes solid as schematically shown in Figure 1. This layer an be patterned by thermal excitation in a number of ways to define the areas where the desired thin film is to remain.  After the desired thin film or films are deposited, the substrate is brought up above the resist material’s sublimation point, leaving behind only the intended pattern. All the unwanted regions are lifted-off by the subliming resist.

Creating and defining the shadow mask on the surface of the substrate in this manner allow for patterning it with a stamp or roller with micron-scale features without changing the process conditions.  In this work, carbon dioxide is used as the sublimable mask material, and prototype stamps have been fabricated using SU-8 photoresist. A mask and the subsequent organic thin film are shown in Figure 2. This process may provide an alternative to shadow masks and provide a manufacturing solution for large area organic electronics.

1. W. Johnson, R. Laibowitz, and C. Tsuei, “Condensed gas, in situ lithography,” IBM Technical Disclosure Bulletin, vol. 20, no. 9, Feb. 1978.
2. A. Han, D. Vlassarev, J. Wang, J. A. Golovchenko, and D. Branton, “Ice lithography for nanodevices,” Nano Letters, vol. 10, no. 12, pp. 5056-5059, Dec. 2010.
3. D. Branton, J. A. Golovchenko, G. M. King, W. J. MoberlyChan, and G. M. Schürmann, “Lift-off Patterning Processing Employing Energetically-stimulated Local Removal of Solid-condensed-gas Layers,” U.S. Patent 752443 B1, April 28, 2009.
4. G. M. King, G. Schürmann, D. Branton, and J. A. Golovchenko, “Nanometer patterning with ice,” Nano Letters, vol. 5, no. 6, pp. 1157-1160, June 2005.
5. J. Cuomo, C. Guarnieri, K. Saenger, and D. Yee, “Selective deposition with ‘dry’ vaporizable lift-off mask,” IBM Technical Disclosure Bulletin, vol. 35, no. 1, June 1992.

Singlet fission, a process that converts a singlet exciton into two triplet excitons, has the potential to achieve a high-efficiency solar cell that exceeds the Shockley-Queisser limit ^[1] . Singlet fission has been previously employed to enhance the photovoltaic efficiency of organic nanostructured solar cells ^[2] , photodetectors ^[3] , and fission-sensitized quantum dot solar cells ^[4] . To obtain optimum efficiency from singlet fission, we need to understand the molecular factors that control its rate. Since singlet fission involves two neighboring chromophores, their intermolecular coupling is expected to play an essential role in determining the single fission rate. Here, we investigate how intermolecular interactions control singlet fission in pentacene, an archetypal molecule exhibiting singlet fission.

In this project, we examine the rate of singlet fission while modulating the intermolecular coupling by altering the side group of pentacene derivatives. We study unsubstituted pentacene and four other pentacene derivatives in thin-film states, 6,13-bis(triisopropyl-silylethynyl) pentacene (TIPS-pentacene), 6,13-diphenylpentacene (DP-pentacene), 6,13-di-biphenyl-4-yl-pentacene (DB-pentacene), and 6,13-di(2’-thienyl)pentacene (thienyl pentacene); see Figure 1 for their crystal structures. We characterize the intermolecular coupling by monitoring the ref shift and peak broadening in their absorption spectra when the molecules in solutions become solid-state thin films. Then, we compared the intermolecular coupling with the rate of singlet fission measured using femtosecond photoinduced absorption spectroscopy; see Figure 2. We also perform density-functional calculations to estimate the coupling between a singlet and two neighboring triplets. We expect our study to contribute to better understanding of the mechanism of singlet fission and rational designs of singlet-fission-based photovoltaic devices.

1. M. B. Smith and J. Michl, “Singlet fission,” Chemical Reviews, vol. 110, pp. 6891-6936, Nov. 2010.
2. P. J. Jadhav, A. Mohanty, J. Sussman, J. Lee, and M. A. Baldo, “Singlet exciton fission in nanostructured organic solar cells,” Nano Letters, vol. 11, pp. 1495-1498, Feb. 2011.
3. J. Lee, P. Jadhav, and M. A. Baldo, “High efficiency organic multilayer photodetectors based on singlet exciton fission,” Applied Physics Letters, vol. 95, p. 033301, 2009.
4. B. Ehrler, M. W. B. Wilson, A. Rao, R. H. Friend, and N. C. Greenham, “Singlet exciton fission-sensitized infrared quantum dot solar cells,” Nano Letters, vol. 12, pp. 1053-1057, Jan. 2012.

Organic solar cells and photodetectors that feature singlet exciton fission materials have two additional exciton processes that traditional organic solar cells do not: singlet fission and triplet doublet annihilation. To maximize the usable power of the photovoltaic cell, we must understand how to optimize the gain from singlet fission and minimize the loss from doublet annihilation. We focus on the former here.

An organic photodetector is composed of thin layers of pentacene and PTCBI stacked repeatedly, as in Figure 1. This device structure is designed to enhance exciton dissociation at the donor/acceptor interface. The rapid dissociation of the singlet exciton in the photodetector competes with the singlet fission process, which is the formation of two triplet excitons from one singlet, and has been shown to be very fast and efficient ^{[1] [2]} . Modulation of the singlet fission rate by application of an external magnetic field changes the photocurrent by reducing the singlet fission rate relative to the rate of singlet dissociation into a charge.  The high field asymptotic value of the change in photocurrent is proportional to the fission yield ^[2] .

We built photodetectors that utilize variably thick layers of pentacene to modulate the rate competing with singlet fission. The maximum the internal quantum efficiency (IQE) of 130% occurs for an 8-nm-thick pentacene layer. The trend in IQE is matched by the trend of an increasing change in photocurrent with applied magnetic field, as Figure 2 shows. We conclude that there is less competition between the singlet for performing fission and dissociating at the donor/acceptor interface.

The gain in IQE from the singlet fission process is largest for pentacene layers of 8 nm. The change in photocurrent suggests that the fission efficiency is even larger for thicker layers; however, we observe loss in IQE, which could be due to exciton diffusion.

1. M. W. B. Wilson, A. Rao, J. Clark, R. S. S. Kumar, D. Brida, G. Cerullo, and R. H. Friend, “Ultrafast dynamics of exciton fission in polycrystalline pentacene,” Journal of the American Chemical Society, vol. 133, no. 31, pp. 11830–11833, 2011
2. J. Lee, P. Jadhav, and M. A. Baldo, “High efficiency organic multilayer photodetectors based on singlet exciton fission,” Applied Physics Letters, vol. 95, p. 033301, 2009.

We are investigating the fabrication, material, and circuit properties of magnetic memory and logic devices.  The research is divided into two main subjects. The first is the study of 360° domain walls (360 DWs), which show novel characteristics under DC and AC applied magnetic fields and currents and are a promising data token in racetrack memory applications.  The second subject is designing and fabricating an instantiation of magnetic logic that has the potential to be more energy efficient than today’s transistors.

In 360 DWs, the magnetization makes a full in-plane 360° turn in a localized region of a magnetic wire, while the rest of the wire is magnetized parallel to its edges. Figure 1 shows a 360 DW in a Co nanowire ^[1] . Simulations ^[2] indicate that 360 DWs have a response to a current that is qualitatively different from the behavior of 180 DWs. The 360 DWs move at a velocity independent of applied magnetic fields and can be destroyed by a burst of applied current. The stability of the domain wall can be controlled by an externally applied field. These features make the 360 DW a data token candidate in novel domain wall logic and memory devices.

The heat dissipated per switching operation by logic transistors can potentially be greatly reduced by using a collective effect, such as the collective switching of magnetic moments.  Thus, we are researching a device that uses the current-induced switching of a 180 DW in a soft ferromagnet to perform logic.  The state of the logic gate is read out using a magnetic tunnel junction.  Modeling of the device performance shows its potential for beyond-CMOS: it is nonvolatile, it is compatible with CMOS, it has a fanout greater than one, a single device acts as a universal NAND gate, and the power dissipation per device operation scales well with device size ^[3] .  Figure 2 shows a device prototype, using NiFe as the soft ferromagnetic wire, with ends exchange biased with IrMn antiferromagnets to ensure a single 180 DW in the wire.

1. Y. Jang, S. R. Bowden, M. Mascaro, J. Unguris, and C.A. Ross, “Formation and structure of 360 and 540 degree domain walls in thin magnetic stripes,” Appl. Phys. Lett., vol. 100, p. 062407, 2012.
2. M. D. Mascaro and C. A. Ross, “AC and DC Current-Induced Motion of a 360˚ Domain Wall,” Phys. Rev. B vol. 82, p. 214411, 2010.
3. J. A. Currivan, Y. Jang, M. D. Mascaro, M. A. Baldo, and C. A. Ross, “Low energy magnetic domain wall logic in short, narrow ferromagnetic wires, IEEE Magnetics Letters, vol. 3, p. 3000104, 2012.

Collaborators

• T. Van Voorhis, MIT Dept of Chemistry
• T. Swager, MIT Dept of Chemistry
• C.A. Ross, MIT DMSE
• V. Bulović, MIT EECS

Graduate Students

• P. Reusswig, Research Assistant, EECS
• P. Jadhav, Research Assistant, EECS
• J. Lee, Research Assistant, EECS
• C.L. Mulder, Research Assistant, EECS
• N. Thompson, Research Assistant, DMSE
• M. Bahlke, Research Assistant, EECS
• J. Currivan, Research Assistant, Harvard Physics
• D. Congreve, Research Assistant, EECS
• T. Wu, Research Assistant, EECS

Postdoctoral Associates

• C. Rotschild
• S. Reineke

Support Staff

• C.M. Bourgeois

Publications

Orf, N.D., O. Shapira, F. Sorin, S. Danto, M.A. Baldo, J.D. Joannopoulos, and Y. Fink, “Fiber draw synthesis”, Proceedings of the National Academy of Sciences, 108, 4743-4747 (2011).

Jadhav, P.J., A. Mohanty, J. Sussman, and M.A. Baldo, “Singlet-fission-based alternative to multijunction organic solar cells,” Nano Letters 11, 1495–149 (2011).

Heidel, T.D., D. Hochbaum, M. Bahlke, I. Hiromi, J. Lee, and M.A. Baldo, “Reducing recombination losses in planar organic photovoltaic cells using multiple step charge separation,” Journal of Applied Physics, 109, 104502 (2011).

Rotschild, C., M. Tomes, H. Mendoza, T. L. Andrew, T. M. Swager, T. Carmon, and M.A. Baldo, “Efficient broad-band pumping of high-finesse, high quality-factor lasers,” Advanced Materials, 23, 3057-3060 (2011).

Currivan, J.A., Y.M. Jang, M. Mascaro, M.A. Baldo, and C.A. Ross,“Low energy magnetic domain wall logic”, IEEE Magnetics Letters, 3, 3000104 (2012).