In a nonvolatile memory (NVM) cell, an injector having one or more layers of material with a lower potential barrier for holes is disposed between a charge storage stack and a source of holes (the gate for top injection, the substrate for bottom injection), to facilitate hole tunneling from the source of holes into the charge-storage layer of the charge storage stack. The injector has a barrier potential for holes which is less than an insulating layer of the charge-storage stack which is oriented towards the source of holes. A multi-layer crested barrier injector may have layers of increasing potential barriers for holes from the source to the charge-storage layer. Methods of operating NVM cells are disclosed. The NVM cell may be NROM, SONOS, or other oxide-nitride technology NVM cells such as SANOS, MANOS, TANOS.