Flash Memories: ISPP Renewal Theory and Flash Design Tradeoffs

In the write process of multilevel per cell (MLC) flash memories, an iterative approach is used to mitigate the monotonicity problem. The monotonicity in programming is considered to be the major restriction in MLC flash. To solve this issue, an iterative approach called incremental step pulse programming (ISPP) is used to concurrently program lots of cells in small steps. In this paper, we are mostly concerned with deriving a mathematical model for iterative programming using the framework of renewal theory . We obtain a closed-form approximation for the probability distribution of the number of steps required in the ISPP process. We also bound the maximal error between the true distribution and our approximation. Moreover, the results obtained help to accurately analyze the effect of inter-cell interference in this type of memory. Finally, we devise an adaptive step size approach for write process to strike a balance between latency and lifetime under fixed bit error rate constraints or information rate constraints.