Analytical Modeling of 3D NAND Flash Cell With a Gaussian Doping Profile

The incessantly increasing demand for highly dense storage medium in this era of big-data has led to the development of 3D NAND Flash memories. 3D NAND Flash based SSDs have revolutionized edge storage and become an integral part of the data warehouses and the cloud storage systems. The conventional 3D NAND flash memory with greater than hundred stacked word-line (WL) layers suffer from channel tapering and non-uniformity in the threshold voltage of cells in different WL layers which necessitates the use of different programming voltages for different WL layers and a complex error-correction circuitry. A non-uniform vertical (Gaussian) channel doping profile alleviates the threshold voltage non-uniformity and leads to a significant reduction in the complexity of the error-correction circuitry and a simple (uniform) programming scheme for all WLs. Although behavioral models have been proposed to utilize 3D NAND flash memory for circuit and system-level applications, an analytical model is important to understand the intricate details of the device physics and propose design guidelines for efficient cell design. To this end, in this paper, for the first time, we have proposed an analytical model for the characteristic length, surface potential and inner potential of the Macaroni-body 3D NAND flash cell with vertical Gaussian doping profile. A strong agreement between the analytical model and the TCAD simulations for different gate lengths (down to 25 nm), inner and outer radius, channel and oxide thickness of the 3D NAND flash cell validates the efficacy of the developed model.