This paper describes group theoretical classification of superconducting states (SC) in the extended Hubbard model with on-site repulsion (U), nearest neighbor attraction (V) and nearest neighbour exchange interaction (J) on the two-dimensional square lattice using the mean field approach. By decomposing the pairing interaction into irreducible parts; A1g, B1g and Eu of D4h point symmetry, we have derived two singlet SCs (s-wave and d-wave) from A1g and B1g, eight triplet SCs from Eu. The first three types of triplet SC have pairing by electrons with antiparallel spin, the second two types have pairing by electrons with equal spin and the last three types are non-unitary and have pairing by only up-spin electrons. We showed that three non-unitary states have to be accompanied with a ferromagnetic order from the structure of the maximal little groups. We performed numerical studies for these SCs. For parameters and electron density favorable for the ferromagnetic order, a non-unitary SC coexistent with ferromagnetism is most stable.
In this paper, an electrical test method is proposed to detect and locate open defects occurring at interconnects between two dies in 3D ICs. The test method utilizes a test architecture based on IEEE 1149.1 standards to provide a test vector to a targeted interconnect. Also, a testable design method for the IC is proposed for our testing. In this paper, testability of the electrical testing is evaluated using a SPICE simulation. The simulation results show that a resistive open defect of 100 Ω can be detected at a test speed of 1 GHz. Also, the test circuit is implemented inside a prototype IC. It is experimentally examined whether open defects between the IC and a printed circuit board can be detected by the test method. They are detected at a speed of 10 MHz by the test method in the experiments. It promises that interconnect open defects in a 3D IC can be detected by the test method per an interconnect at a test speed of at least 10 MHz.
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