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We extended the density-gradient (DG) model to include a second-order quantum correction (SOQC) term. The DG model has been widely used as a device simulation model capable of simulating quantum effects in efficient way. However, when only the first order quantum correction term is considered in the DG model, it is difficult to accurately describe device characteristics such as carrier density or potential fluctuation in the narrow region due to discrete charges such as dopants and interface traps. Thus, we extended the DG model to the SOQC, implemented it as a three-dimensional (3D) simulator, and compared the simulation results for sub-10-nm devices, which have a single point charge, in the DG model and the 3D Schrödinger-Poisson (SP) solver. Through this, we identified that the DG extended to SOQC well reproduces the SP simulation results in terms of both capacitance-voltage (C-V) and local fluctuation in electron density.

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