Transition Property for α\alpha-Power Free Languages with α≥2\alpha\geq 2 and k≥3k\geq 3 Letters

In 1985, Restivo and Salemi presented a list of five problems concerning power free languages. Problem $4$ states: Given $\alpha$-power-free words $u$ and $v$, decide whether there is a transition from $u$ to $v$. Problem $5$ states: Given $\alpha$-power-free words $u$ and $v$, find a transition word $w$, if it exists. Let $\Sigma_k$ denote an alphabet with $k$ letters. Let $L_{k,\alpha}$ denote the $\alpha$-power free language over the alphabet $\Sigma_k$, where $\alpha$ is a rational number or a rational "number with $+$". If $\alpha$ is a "number with $+$" then suppose $k\geq 3$ and $\alpha\geq 2$. If $\alpha$ is "only" a number then suppose $k=3$ and $\alpha>2$ or $k>3$ and $\alpha\geq 2$. We show that: If $u\in L_{k,\alpha}$ is a right extendable word in $L_{k,\alpha}$ and $v\in L_{k,\alpha}$ is a left extendable word in $L_{k,\alpha}$ then there is a (transition) word $w$ such that $uwv\in L_{k,\alpha}$. We also show a construction of the word $w$

Terahertz testing of very large scale integrated circuits

Growing sophistication of electronics devices and circuits and, especially of VLSI and ULSIC, presents increasing demands on circuit testing and fault diagnosis. The conventional well-established technique of electric AC and DC testing is costly, does not assure a complete fault identification. This technique also presents an additional security problem making it possible to design faked circuits avoiding the identification by this testing.1 Fabrication of and even perception of faked VLSI capable of surreptitious performance has become an increasing problem often referred to as “trojan hardware”. Experimental techniques, such as laser scanning2and terahertz imaging 3-5 have a limited resolution signal-to-noise ratios and encounter difficulties in defect identification. A new approach of THz testing of Microwave Monolithic Integrated Circuits (MMICs)6, VLSI, and ULSIC is based on measuring the circuit responses at the pins or input/output leads and comparing these responses with etalon responses. 7, 8 This technique could augment or replace the electrical testing and/or laser and THz scanning testing for production testing, burn-in testing, high temperature testing, and infant mortality testing. It could also be extended for the fault diagnosis and identification and for the lifetime and reliability predictions. To this end it could be augmented by the low noise measurements. The number of the detected responses could be very large, since the permutations of the voltages between the pins and leads could be measured at the different positions of the scanning THz beam, different THz frequencies and polarizations, in the pulsed and/or CW mode, at the different modulation frequencies and at the different THz intensities. This technique could be used under or without bias. The processing of these responses forming multi-dimensional images in the excitation parameter space could be processed using artificial intelligence algorithms and machine learning approaches making this testing technique self-learning and self-improving. This testing could be further improved by designing for testability by THz responses at the pins. Acknowledgements The work at RPI was supported by the U.S. Army Research Laboratory Cooperative Research Agreement (Project Monitor Dr. Meredith Reed) and by the Office of Naval Research (Project Monitor Dr. Paul Maki). References 1. D. Hély; K. Rosenfeld; R. Karri, Security challenges during VLSI test, 2011 IEEE 9th International New Circuits and systems conference, DOI: 10.1109/NEWCAS.2011.5981325s 2. Boscaro, A., Jacquir, S., Melendez, K., Sanchez, K., Perdu, P., and Binczak, S. (2016). Automatic process for time-frequency scan of VLSI. Microelectronics Reliability, 64, 299–305. doi:10.1016/j.microrel.2016.07.052 3. K. Ahi, S. Shahbazmohamadi, and N. Asadizanjani, “Quality control and authentication of packaged integrated circuits using enhanced-spatial-resolution terahertz time-domain spectroscopy and imaging,” Optics and Lasers in Engineering, vol. 104, pp. 274–284, 2018 4. M. Nagel and H. Kurz, Terahertz imaging: Terahertz reflectometry images faults in silicon chips, Laser Focus World, 11/01/2011 5. M. Yamashita, K. Kawase, C. Otani, T. Kiwa, and M. Tonouchi, Testing of large-scale integrated circuits using laser terahertz emission microscopy,” Opt. Exp., vol. 13, no. 1, pp. 115–120, Jan. 2005 6. S. Rumyantsev, A. Muraviev, S. Rudin, G. Rupper, M. Reed, J. Suarez and M. Shur, Terahertz Beam Testing of Millimeter Wave Monolithic Integrated Circuits, IEEE Sensors Journal, IEEE Sensors J., Vol. 17, No. Sep. 1, pp. 5487-5490 (2017) 7. G. Rupper, J. Suarez, S. Rudin, M. Reed, M. Shur, Terahertz plasmonics for testing very large-scale integrated circuits under bias, Patent Application Publication, No.: US 2018/0238961 Al, Pub. Date: Aug. 23, 2018 8. M. Shur, S. Rudin, G. Rupper, M. Reed, and J. Suarez, Sub-Terahertz Testing of Millimeter Wave Monolithic and Very Large Scale Integrated Circuits, Solid State Electronics (2019), to be publishe

Plasma Instability and Amplified Mode Switching Effect in THz Field Effect Transistors with Grating Gate

We developed a theory of collective plasma oscillations in a dc current-biased field effect transistor with interdigitated dual grating gate and demonstrated a new mechanism of electron plasma instability in this structure. The instability in the plasmonic crystal formed in the transistor channel develops due to conversion of the kinetic energy carried by the drifting plasmons into electromagnetic energy. The conversion happens at the opposite sides of the gate fingers due to the asymmetry produced by the current flow and occurs through the gate finger fringing capacitances. The key feature of the proposed instability mechanism is the behavior of the plasma frequency peak and its width as functions of the dc current bias. At a certain critical value of the current, the plasma resonant peak with small instability increment experiencing redshift with increasing current changes to the blue shifting peak with large instability increment. This amplified mode switching (AMS) effect has been recently observed in graphene-interdigitated structures (S. Boubanga-Tombet et al., Phys. Rev. X 10, 031004 (2020)). The obtained theoretical results are in very good qualitative agreement with these experiments and can be used in future designs of the compact sources of THz EM radiation.Comment: 15 pages, 6 figure

Electromechanical coupling in free-standing AlGaN/GaN planar structures

The strain and electric fields present in free-standing AlGaN/GaN slabs are examined theoretically within the framework of fully-coupled continuum elastic and dielectric models. Simultaneous solutions for the electric field and strain components are obtained by minimizing the electric enthalpy. We apply constraints appropriate to pseudomorphic semiconductor epitaxial layers and obtain closed-form analytic expressions that take into account the wurtzite crystal anisotropy. It is shown that in the absence of free charges, the calculated strain and electric fields are substantially differently from those obtained using the standard model without electromechanical coupling. It is also shown, however, that when a two-dimensional electron gas is present at the AlGaN/GaN interface, a condition that is the basis for heterojunction field-effect transistors, the electromechanical coupling is screened and the decoupled model is once again a good approximation. Specific cases of these calculations corresponding to transistor and superlattice structures are discussed.Comment: revte

The effect of electromechanical coupling on the strain in AlGaN/GaN heterojunction field effect transistors

The strain in AlGaN/GaN heterojunction field-effect transistors (HFETs) is examined theoretically in the context of the fully-coupled equation of state for piezoelectric materials. Using a simple analytical model, it is shown that, in the absence of a two-dimensional electron gas (2DEG), the out-of-plane strain obtained without electromechanical coupling is in error by about 30% for an Al fraction of 0.3. This result has consequences for the calculation of quantities that depend directly on the strain tensor. These quantities include the eigenstates and electrostatic potential in AlGaN/GaN heterostructures. It is shown that for an HFET, the electromechanical coupling is screened by the 2DEG. Results for the electromechanical model, including the 2DEG, indicate that the standard (decoupled) strain model is a reasonable approximation for HFET calculataions. The analytical results are supported by a self-consistent Schr\"odinger-Poisson calculation that includes the fully-coupled equation of state together with the charge-balance equation.Comment: 6 figures, revte

Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure