Three-dimensional (3D) memory products based on through silicon via (TSV) are widely developed to fulfill the ever-increasing demands of per unit area storage capacity. The yield is still one of the critical challenges for 3D memory. Redundancy technique is now widely used in industry to improve yield. How to reduce the overhead of redundancy by improving the utilization of redundancy is important to 3D memory. In this paper, we propose a row/column block-based mapping technique for 3D memory built-in self-repair scheme to improve the utilization of redundancy and low hardware overhead. Each row/column is divided into row/column block and the mapping can be performed at row/column-block level instead of the original row/column level. Therefore, more faulty cells can be clustered into the same row/column. Based on the proposed technology, a 3D-essential spare pivoting (ESP) algorithm is also proposed for the allocation of redundant rows and columns, and the area overhead of this algorithm is particularly low. The experimental results show that on an average the repair ratio of our proposed scheme is much better than the fault clustering technique by 12% and the redundancy-cost can reduce 23%.

In the study of the variety of nilpotent elements in a Lie algebra, Premet conjectured that this variety is irreducible for any finite dimensional restricted Lie algebra. In this paper, with the assumption that the ground field is algebraically closed of characteristic p > 3, we confirm this conjecture for the Lie algebras of Cartan type e S n and S n .Moreover, we show that the variety of nilpotent elements in S n is a complete intersection. Motivated by the proof of the irreducibility, we describe explicitly the ring of invariant polynomial functions on S n .

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Let G be a finite group scheme over an algebraically closed field k of characteristic char(k) = p ≥ 3. In generalization of the familiar notion from the modular representation theory of finite groups, we define the p-rank rkp(G) of G and determine the structure of those group schemes of p-rank 1, whose linearly reductive radical is trivial. The most difficult case concerns infinitesimal groups of height 1, which correspond to restricted Lie algebras. Our results show that group schemes of p-rank ≤ 1 are closely related to those being of finite or domestic representation type.

Let B0(G) ⊆ kG be the principal block algebra of the group algebra kG of an infinitesimal group scheme G over an algebraically closed field k of characteristic char(k) =: p ≥ 3. We calculate the restricted Lie algebra structure of the first Hochschild cohomology L := H 1 (B0(G), B0(G)) whenever B0(G) has finite representation type. As a consequence, we prove that the complexity of the trivial G-module k coincides with the maximal toral rank of L.