Provided are a nonvolatile memory and related method of programming same. The nonvolatile memory includes a memory cell array with a plurality of nonvolatile memory cells and a write circuit. The write circuit is configured to write first logic state data to a first group of memory cells during a first program operation using a first internally generated step-up voltage, and second logic state data to a second group of memory cells during a second program operation using an externally supplied step-up voltage.