Memory device, memory system, method of operating the memory device, and method of operating the memory system

1. A method of erasing a non-volatile memory device which includes a plurality of NAND strings, the method comprising:

applying a first voltage to each of a plurality of word lines for a corresponding effective erasing execution time, wherein an erase operation is performed on a plurality of memory cells connected to each of the word lines for the corresponding effective erasing execution time; and

applying a second voltage to each of at least some word lines among the word lines for a corresponding erasing-prohibited time after the corresponding effective erasing execution time elapses,

wherein a sum of the corresponding effective erasing execution time and the corresponding erasing-prohibited time for each of the at least some word lines is substantially equal to an erasure interval during which an erase operation is performed using the first voltage and the second voltage higher than the first voltage, and

wherein the plurality of word lines is stacked on a substrate.

2. The method of claim 1 ,

wherein the applying of the first voltage comprises:

applying the first voltage to a first word line adjacent to the substrate for a first effective erasing execution time and to a second word line above the first word line for a second effective erasing execution time which is longer than the first effective erasing execution time.

3. The method of claim 1 ,

wherein the applying of the first voltage comprises:

applying the first voltage to a first word line group including word lines adjacent to the substrate for a first effective erasing execution time and to a second word line group including word lines above the first word line group for a second effective erasing execution time which is longer than the first effective erasing execution time.

4. The method of claim 2 ,

wherein the applying of the second voltage comprises:

applying the second voltage to the first word line for a first erasing-prohibited time after the first effective erasing execution time and to the second word line for a second erasing-prohibited time after the second effective erasing execution time,

wherein the second erasing-prohibited time is shorter than the first erasing-prohibited time,

wherein a sum of the first effective erasing execution time and the first erasing-prohibited time is substantially equal to the erasure interval, and

wherein a sum of the second effective erasing execution time and the second erasing-prohibited time is substantially equal to the erasure interval.

5. The method of claim 3 ,

wherein the applying of the second voltage comprises:

applying the second voltage to the first word line group for a first erasing-prohibited time after the first effective erasing execution time, and to the second word line group for a second erasing-prohibited time after the second effective erasing execution time,

wherein the second erasing-prohibited time is shorter than the first erasing-prohibited time,

wherein a sum of the first effective erasing execution time and the first erasing-prohibited time is substantially equal to the erasure interval, and

wherein a sum of the second effective erasing execution time and the second erasing-prohibited time is substantially equal to the erasure interval.

6. The method of claim 1 ,

wherein the erase operation is performed using the first voltage and is substantially prohibited using the second voltage.

7. The method of claim 1 ,

wherein the applying of the first voltage and the applying of the second voltage are performed in a unit of at least one word line among the at least some word lines.

8. The method of claim 1 , further comprising:

generating an erase control signal by determining the corresponding effective erasing execution time in a unit of at least one word line, based on distances between the substrate and the word lines, and

wherein the applying of the first voltage and the applying of the second voltage are performed based on the erase control signal.

9. The method of claim 8 ,

wherein the erase control signal is generated such that the corresponding effective erasing execution time is increased when a program/erase cycle count is equal to or greater than a threshold value.

10. The method of claim 8 ,

wherein the erase control signal is generated such that the corresponding effective erasing execution time is decreased when a data retention time is equal to or greater than a threshold value.

11. A memory device comprising:

a memory cell array including a plurality of NAND strings,

each NAND string including plurality of memory cells and

each memory cell being connected to a corresponding word line of a plurality of word lines vertically stacked on a substrate; and

a control logic configured to generate an erase control signal to increase a voltage applied to each of the word lines at different time points according to distances between the substrate and word lines,

wherein the erase control signal is generated in a unit of at least one word line during an erase interval in which an erase operation is performed on the memory cells; and

wherein the control logic determines an effective erasing execution time in the unit of at least one word line based on distances between the substrate and the word lines, and generates the erase control signal according to the determined effective erasing execution time.

12. The memory device of claim 11 ,

wherein the control logic generates the erase control signal by determining the effective erasing execution time such that the effective erasing execution time increases when a program/erase cycle count is equal to or greater than a threshold value.

13. The memory device of claim 11 ,

wherein the control logic generates the erase control signal by determining the effective erasing execution time such that the effective erasing execution time decreases when a data retention time is equal to or greater than a threshold value.

14. The memory device of claim 11 ,

wherein a first effective erasing execution time is shorter than a second effective erasing execution time,

wherein a first voltage is applied to a first word line adjacent to the substrate for the first effective erasing execution time, and

wherein the first voltage is applied to a second word line above the first word line for the second effective erasing execution time.

15. A method of operating a non-volatile memory device, the method comprising:

applying a substrate voltage to a substrate in response to an erase command, wherein the substrate voltage is increased to a substrate erase voltage for a first erase interval and the substrate erase voltage is maintained for a second erase interval;

applying a first voltage to a first word line for a first effective erasing time after the first erase interval;

applying the first voltage to a second word line for a second effective erasing time after the first erase interval, wherein the second effective erasing time is longer than the first effective erasing time; and

applying a second voltage to the first word line for a first erasing-prohibited time after the first effective erasing time,

wherein the first word line and the second word line are vertically stacked on the substrate,

wherein the second word line is positioned above the first word line, and

wherein a sum of the first effective erasing time and the first erasing-prohibited time is substantially equal to the second effective erasing time.

16. The method of claim 15 , further comprising:

applying a third voltage to a third word line for a second erasing-prohibited time,

wherein the third word line is interposed between the first word line and the second word line, and

wherein the second erasing-prohibited time is shorter than the first erasing-prohibited time.

17. The method of claim 16 ,

wherein the second voltage and the third voltage are substantially the same.

18. The method of claim 15 ,

wherein a plurality of memory cells connected to the first word line is erased for the first effective erasing execution time using a voltage difference between the first voltage and the substrate erase voltage, and

wherein after the first effective erasing execution time, a voltage difference between the second voltage and the substrate erase voltage is applied to the plurality of memory cells connected to the first word line for the first erasing-prohibited time.

19. The method of claim 15 ,

wherein the sum of the first effective erasing time and the first erasing-prohibited time is substantially equal to the second erase interval.