Application of a scanning tunneling microscopy (STM) and an atomic force microscopy (AFM) to electron devices and an optical device are introduced in this paper. Using STM tip/AFM cantilever as a cathode, surfaces of a metal or a semiconductor are oxidized to form a few tens of nanometers-wide oxidized metal line or an oxidized semiconductor line, which works as an energy barrier for an electron. A single-electron transistor (SET), a photoconductive switch, and a high-electron mobility transistor (HEMT) are fabricated using this fabrication process. The fabricated SET operates even at high room temperatures and shows the large Coulomb gap and staircase of 200-mV periods and the large Coulomb oscillation periods of 406 mV. The fabricated photoconductive switch shows a ultra-fast response time, i.e., a full-width at half-maximum response of 380 fs at a bias voltage of 10 V. The drain current of HEMT was controlled by the oxidized semiconductor wire on the channel region formed by this fabrication process.

This paper shows that the multicommodity flow problem on a class of planar undirected graphs can be reduced to another famous combinatorial problem, the weighted matching problem. Assume that in a given planar graph G all the sources can be joined to the corresponding sinks without destroying the planarity. Then we show that the feasibility of multicommodity flows can be tested simply by solving, once, the weighted matching problem on a certain graph constructed from G, and that the multicommodity flows of given demands can be found by solving the matching problem $O(n)$ times if G has n vertices. Efficient algorithms are also given for detecting negative and minimum cycles in planar undirected graphs.

This paper presents an efficient algorithm for finding multicommodity flows in planar graphs. Suppose that G is an undirected planar graph with all sources and sinks on the boundary of the outer face and that a real-valued demand is given for each source–sink pair. The algorithm decides whether G has multicommodity flows, each from a source to a sink and of a given demand, and actually finds them if G has. It spends $O(kn + n^2 (\log n)^{1/2} )$ time and $O(kn)$ space if G has n vertices and k source–sink pairs.