Boosting to control programming of non-volatile memory

A method for programming non-volatile storage, comprising:

• applying a program voltage pulse to a selected word line associated with a set of non-volatile storage elements, the non-volatile storage elements are provided in a set of NAND strings, each NAND string includes a select gate and is associated with a bit line, and the program voltage pulse extends during a time period;
• during a first interval of the time period, for at least one of the NAND strings, opening the associated select gate, and providing a voltage on the associated bit line which allows discharging of a channel of the at least one of the NAND strings;
• during a second interval of the time period which follows the first interval, closing the associated select gate;
• and
• during a third interval of the time period which follows the second interval, opening the associated select gate, and providing a voltage on the associated bit line which at least partially inhibits discharging of the channel.

A non-volatile storage system, comprising:

• a NAND string comprising a selected non-volatile storage element and a control gate for coupling the NAND string to a bit line;
• and
• at least one control circuit associated with the NAND string, the at least one control circuit:
• a) applies a program voltage pulse to a control gate of the selected non-volatile storage element, the program voltage pulse extending during a time period, b) during a first interval of the time period, controls the select gate so that the NAND string communicates with the bit line, and provides a voltage on the bit line which allows discharging of a channel of the NAND string, c) during a second interval of the time period which follows the first interval, controls the select gate so that the NAND string does not communicate with the bit line, and d) during a third interval of the time period which follows the second interval, controls the select gate so that the NAND string communicates with the bit line, and provides a voltage on the bit line which at least partially inhibits discharging of the channel.