Numerical simulation of electron diffraction through a narrow constriction

We performed time-evolved numerical simulations of a two-dimensional electr on wave packet passing through a semicircular constriction (very short quan tum wire) by solving the time-dependent Schrodinger equation using the fini te difference method to understand the nature of electron diffraction pheno mena in semiconductors. By Fourier transformation, we calculated the time-e volved electron wave packet in wave number space, which shows the transitio n from the Gaussian distribution to the circular distribution having equal energy by entering constriction. The obtained results are compared with the results of our previous simulations of an electron wave packet passing thr ough a rectangular constriction. By analyzing the nature of diffracted subp eaks, the following results were obtained: (1) The intensity of the subpeak s diffracted by a semicircular constriction is higher than that by a rectan gular one. (2) The starting point of the diffracted subpeaks is the center position of the narrowest width in a constriction, while that for rectangul ar ones is the center of the constriction entrance. (3) The lateral wave nu mber of the diffracted subpeak increases with the number n, n being the num ber counted from the main (0th) peak which propagates straight through, alt hough it deviates negatively from the linear relationship obtained for rect angular ones with an increase in n. (4) There is a time delay in the diffra cted subpeaks similar to that for rectangular constrictions. The difference s between passing through a semicircular constriction and a rectangular one were interpreted as caused by the reflection on the inside wall of the con striction and the energy spread of each quantum level. (C) 1999 American In stitute of Physics. [S0021-8979(99)09122-7].