Method of searching read voltage of nonvolatile memory device using regression analysis and method of reading data from nonvolatile memory device using the same

A method of reading data from a nonvolatile memory device that includes a plurality of memory cells that have a plurality of states, the method comprising:

• searching a plurality of read voltages that distinguish the plurality of states from each other;
• and
• reading the data stored in the plurality of memory cells based on the plurality of read voltages;
• wherein:
• the plurality of states include a first state and a consecutive second state that differ from each other,
• the plurality of read voltages include a first read voltage that distinguishes
• the first state and the second state, and
• searching the plurality of read voltages includes:
• determining a number n that represents a number of times a data read operation is performed, wherein n is an integer greater than or equal to two;
• selecting n first read voltage levels of the first read voltage wherein a number of first read voltage levels is equal to the number of times the data read operation is performed, wherein the n first read voltage levels differ from each other;
• generating n first cell count values by performing n data read operations on the plurality of memory cells using all of the n first read voltage levels;
• and
• determining a first optimal read voltage level of the first read voltage by performing a regression analysis based on a first-order polynomial using the n first read voltage levels and the n first cell count values.

A method of searching a read voltage of a nonvolatile memory device that includes a plurality of memory cells that have a first state and a second state that differ from each other, the method comprising:

• determining a number n that represents a number of times a data read operation is performed, wherein n is an integer greater than or equal to two;
• selecting a first read voltage level to an n-th read voltage level of the read voltage wherein a number of read voltage levels is equal to the number of times the data read operation is performed, wherein the first to n-th read voltage levels differ from each other;
• generating a first cell count value to an n-th cell count value by performing a first data read operation to an n-th data read operation on the plurality of memory cells using all of the first to n-th read voltage levels;
• obtaining a first variable to an (n−1)-th variable based on the first to n-th read voltage levels and the first to n-th cell count values, wherein each of the first to (n−1)-th variables includes an averaged read voltage level and a cell count change value;
• obtaining a first function by performing a regression analysis based on a first-order polynomial using the first to (n−1)-th variables, wherein the first function is estimated as a first-order polynomial;
• and
• calculating an optimal read voltage level of the read voltage based on the first function,
• wherein the optimal read voltage level of the read voltage is obtained based on Equation 1, Equation 2 and Equation 3, as follows:
• -
• b
• a
• =
• ∑
• X
• i
• 2
• ⁢
• ∑
• Y
• i
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• ∑
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• n
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• Y
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• ;
• Equation
• ⁢
• 1
• X
• i
• =
• (
• x
• i
• +
• x
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• +
• 1
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• /
• 2
• ;
• Equation
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• 2
• Y
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• =
• y
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• +
• 1
• -
• y
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• ,
• Equation
• ⁢
• 3
• wherein, in Equation 2, Xi denotes an (i+1)-th averaged read voltage level, i is an integer greater than or equal to zero and less than or equal to (n−2), and xi and xi+i denote an (i+1)-th read voltage level and an (i+2)-th read voltage level, respectively, and in Equation 3, Y1 denotes an (i+1)-th cell count change value, and yi and yi+1 denote an (i+1)-th cell count value and an (i+2)-th cell count value, respectively,
• wherein the read voltage distinguishes the first state and the second state.