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Japanese Journal of Applied Physics

Quantum Mechanical Transmission and Reflection of Quasi-Particles at Arbitrary Potential Barriers in the Superconducting Base Transistor

Tetsuya Yamamoto, Hiroshi Suzuki, Tatsuro Usuki, Yorinobu Yoshisato, Shoichi Nakano

Published Dec 1, 1991• 9 citations
Publisher

Abstract

We propose a systematic method for calculating the quasi-particle transmission, T, and reflection, R, probabilities at the arbitrary potential barrier, by using multistep potential approximation. T and R were calculated from first principles using the Bogoliubov equations of motion. For the N/I/S emitter-base tunneling junction and base-collector heterojunction in the superconducting base transistor, T and R were computed as functions of quasi-particle energy, potential barrier height and width. In the case of the YBCO/n-InGaAs base-collector heterojunction with a Schottky barrier height of 70 meV, it was found that T was greater than 0.5. This suggests that a combination of YBCO and n-InGaAs is suitable for use in the base-collector heterojunction of a superconducting base transistor. We also show I-V curves for the N/I/S tunneling junction.

DOI
10.1143/jjap.30.3911

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We propose a systematic method for calculating the quasi-particle transmission, T, and reflection, R, probabilities at the arbitrary potential barrier, by using multistep potential approximation. T and R were calculated from first principles using the Bogoliubov equations of motion. For the N/I/S emitter-base tunneling junction and base-collector heterojunction in the superconducting base transistor, T and R were computed as functions of quasi-particle energy, potential barrier height and width. In the case of the YBCO/n-InGaAs base-collector heterojunction with a Schottky barrier height of 70 meV, it was found that T was greater than 0.5. This suggests that a combination of YBCO and n-InGaAs is suitable for use in the base-collector heterojunction of a superconducting base transistor. We also show I-V curves for the N/I/S tunneling junction.
Quantum tunneling is a phenomenon in quantum mechanics. In this phenomenon, Quantum particle can go through potential barrier that potential energy is higher than total energy of quantum particle. Physicists are interested in transmitted and reflected value of Quantum particle that is transmission and reflection probabilities. Then, Schrödinger equation is used to find transmission and reflection probabilities by directly solving. However, some potential barriers are too complex to solve directly. Then, we use another method to solve more complex problem. That method is called "quasilinearization''. Quasilinearization method (QLM) is a numerical method to solve nonlinear differential equations. In this thesis, we compare the quasilinearization method with the well-known WKB approximation method. The results show that the transmission and reflection probabilities calculated by the QLM and WKB approximation have the same trend as the transmission and reflection probabilities calculated from the exact solution.
A simle numerical method of calculating transmission coefficients across arbitrary potentials is presented by using the combination of a transfer matrix procedure and the solution of the wave functions in arbitrary potentials.This method is applied to a parabolic potential and a double barrier potential in an electric field.The transmission coefficients calculated are in agreement with those obtained using a multistep potential approximation.The wave functions at the resonant states are also given for the two examples.
At the turn of the twentieth century, the establishment of quantum theory propelled rapid advancements, particularly in the understanding of quantum tunnelling—a fundamental phenomenon in quantum mechanics crucial for various physical processes. The quantum phenomenon of particle passes through potential barriers is of great importance. In classical physics, when the energy of a particle is less than the height of a double barrier structure, it is impossible for it to pass through. However, quantum mechanics allows a particle to penetrate the barrier and emerge on the other side. This paper explores the quantum tunnelling effect, focusing on the single potential barrier model in one dimension and subsequently extending to the double potential barrier model. The Schrödinger equation provides the foundational framework for elucidating the motion of microscopic particles, emphasizing wave-particle duality inherent in quantum mechanics. The analysis of the single potential barrier model involves solving the Schrödinger equation in different regions, determining wave functions and coefficients through boundary conditions. The transmission coefficient is derived, representing the probability of a particle passing through a barrier. In the case of a “thick” barrier, an approximate form for transmission coefficient is provided, demonstrating the exponential decrease in transmission probability with increasing barrier thickness.
According to classical physics theories, a moving particle cannot move to an environment with greater potential energy than its total energy during movement. But according to quantum theories, this event is well known. This event is called tunneling. Tunneling is a probability, and it is measured by a transmission coefficient. Correct calculation of this coefficient is very important because very sensitive and important instruments have been developed based on this event, and many events in nature can be explained by tunneling. This coefficient is generally calculated by semi-classical approaches (WKB) and the known formula is an approximate formula. In previous publications, the general transmission coefficient of a potential barrier with arbitrary form is calculated by a simple method without any approximation. The results are applied to calculate the half-life values of the nuclei that emit alpha particles. The half-life values obtained from our calculations and the classical method (WKB) have been compared, and it has been found that the new half-life values are exactly consistent with the experimental values. In this article, this general transmission coefficient is applied to calculate transmission coefficient for an arbitrary form external electrical field barrier (cold emission by the metal). The values obtained from our calculations and those of classical method (WKB) have been compared.
The working principle of a large number of modern scientific equipment has been applied to the quantum tunneling effect. Although the explanations for the relevant principles of this effect are clarified, the calculation process is very complex and difficult to understand. Previous studies combine specific applications without theoretical model references. This study adopts the method of using the time-independent Schrodinger equation to solve the wave function, which is more convenient to obtain the expression of transmission probability. Then, one discusses the relationship between transmission probability and potential barrier width, potential barrier spacing, and incident particle energy. The experimental results show that the transmission probability decreases exponentially from 1 to 0 as the potential barrier width gradually increases. As the potential barrier width increases, the transmission probability exhibits a clear periodic oscillation relationship, the oscillation period remains unchanged, and this paper derives the relationship between the oscillation period and the potential barrier width. As the incident energy of particles gradually increases, the transmission probability exhibits periodic changes, and the minimum value of transmission probability increases with the periodic changes. Based on the analysis, the smaller the potential barrier width, the greater the incident energy, and the more likely quantum tunneling occurs.
The integration of ferroelectric barriers into high-temperature Josephson junctions offers a pathway to tunable superconducting quantum devices. Here, we demonstrate robust Josephson coupling in YBa2Cu3O7-x (YBCO)/Bi0.5Na0.5TiO3 (BNT)/YBCO trilayer junctions incorporating a 40 nm ferroelectric BNT barrier. Epitaxial trilayers were fabricated by pulsed laser deposition on SrTiO3 substrates and investigated under broadband terahertz (THz) irradiation (0.5-2.5 THz). At 1.5 THz, close to the Josephson plasma resonance, the BNT polarization increased from 33.4 to 46.4 uC/cm2 at 30 K, enhancing superconducting transport. The junctions exhibited a well-defined zero-voltage supercurrent branch, with the critical current Ic(T) remaining nearly constant up to 60 K and reaching 468.2 uA under 1.5 THz excitation, evidencing strong phase coherence. Scanning tunneling spectroscopy revealed an enhanced superconducting gap in YBCO/BNT/YBCO (Delta = 1.3 meV) compared with pure YBCO (Delta = 1.05 meV), while optical conductivity measurements showed a reduction in conductivity and gap with increasing temperature, consistent with BCS theory under THz excitation. Atomic force microscopy and X-ray reflectivity confirmed uniform morphology and sharp interfaces, excluding defect-mediated transport. Magnetic field modulation of Ic(B) exhibited a canonical Fraunhofer interference pattern, and resistance mapping revealed alternating lobes of high and low dissipation, indicating coherent Josephson tunneling. These results establish that Josephson coupling is intrinsic to the YBCO/BNT/YBCO junctions, enabled by the dipolar character and dynamic THz response of the BNT barrier. This study identifies BNT as a viable, tunable barrier material for next-generation high-Tc superconducting quantum devices.