Patent Publication Number: US-9406394-B2

Title: Flash memory device using adaptive program verification scheme and related method of operation

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a continuation of U.S. application Ser. No. 13/841,503, filed Mar. 15, 2013, which is a continuation of U.S. non-provisional application No. 12/963,867, filed Dec. 9, 2010, which claims priority under 35 U.S.C. §119 to Korean Patent Application No. 10-2010-0012894 filed on Feb. 11, 2010, the disclosure of which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Embodiments of the inventive concept relate generally to semiconductor memory devices. More particularly, embodiments of the inventive concept relate to flash memory devices using adaptive program verification schemes and related methods of operation. 
     Semiconductor memories play an important role in a wide variety of modern electronic devices, ranging from satellites to consumer products. Consequently, advances in semiconductor memory technology can lead to significant improvements in a broad range of technical applications. 
     Semiconductor memory devices can be roughly divided into two categories based on whether they retain stored data when disconnected from power. These categories include volatile semiconductor memory devices, which lose stored data when disconnected from power, and nonvolatile semiconductor memory devices, which retain stored data when disconnected from power. Examples of volatile memory devices include static random access memory (SRAM) devices and dynamic random access memory (DRAM) devices. Examples of nonvolatile memory devices include various types of read only memory (ROM), such as MROM, PROM, EPROM, and EEPROM. 
     Flash memory is a form of EEPROM that has achieved popularity in recent years. Flash memory tends to be relatively inexpensive and can provide high performance and data storage capacity compared with other forms of nonvolatile memory. In addition, flash memory is resistant to physical shock, making it especially popular for use in portable devices, such as cellular phones, digital cameras, netbook computers, and so on. 
     Flash memories have two common configurations, including a NOR configuration, and a NAND configuration. Flash memories having these configurations are referred to as NOR flash memories and NAND flash memories, respectively. NOR flash memories tend to provide faster access speed, but lower storage capacity, compared with NAND flash memories. Accordingly, NOR flash memories are often used to store information requiring fast access, such as code, while NAND flash memories are generally used to provide mass data storage capability for information such as multimedia information, data files, and so on. 
     Some flash memories are designed to store more than one bit of data per memory cell. Flash memories that store more than one bit of data per memory cell are referred to as multi-level cell (MLC) flash memories. 
     MLC flash memories are commonly programmed using a technique known as incremental step pulse programming (ISPP). In incremental step pulse programming, selected memory cells are programmed by a plurality of program loops, where each program loop comprises a programming execution section where program voltage is applied to a selected memory cell to modify its state, and a verification section where a verification voltage is applied to the selected memory cell to determine whether it has reached a target state. By performing program loops in this manner, selected memory cells are programmed gradually and can avoid certain types of programming errors such as over-programming. 
     SUMMARY 
     Embodiments of the inventive concept provide flash memory devices using adaptive program verification schemes, and methods of operating the flash memory devices. 
     According to one embodiment of the inventive concept, a method of programming a flash memory device comprises (a) programming selected memory cells, (b) performing a verification operation to determine whether threshold voltages of the selected memory cells have reached verification levels corresponding to target program states, (c) determining a verification start point for at least one of the target program states according to a parameter associated with a detection of an initial pass bit in the selected memory cells, and (d) determining a verification end point for at least one of the target program states according to a parameter associated with a detection of successful programming of multiple selected memory cells to a lowest one of the target program states. 
     In certain embodiments, the parameter associated with the detection of the initial pass bit is a program voltage used to program the selected memory cells in a program loop where the initial pass bit is detected. 
     In certain embodiments, the verification start point is a verification start loop. 
     In certain embodiments, the verification start point is varied according to a margin between a first threshold voltage distribution corresponding to an initial program state and a second threshold voltage distribution corresponding to the at least one target program state. 
     In certain embodiments, the verification start point is varied according to whether the first and second threshold voltage distributions overlap. 
     In certain embodiments, the verification start point is increased where the first and second threshold voltage distributions overlap. 
     In certain embodiments, the verification start point is decreased where the first and second threshold voltage distributions do not overlap. 
     In certain embodiments, the parameter associated with the detection of successful programming of multiple selected memory cells to the lowest one of the target program states comprises a program voltage used in a program loop where the multiple selected memory cells are detected to be successfully programmed to the lowest one of the target program states. 
     In certain embodiments, determining the verification end point comprises predicting a pass point for at least one of the target program states, and subtracting an offset value from the predicted pass point. 
     In certain embodiments, the same offset value is subtracted from predicted pass points of a plurality of the target program states to determine verification end points for the plurality of the target program states. 
     In certain embodiments, different offset values are subtracted from predicted pass points of a plurality of the target program states to determine verification end points for the plurality of the target program states. 
     According to an embodiment of the inventive concept, a method of programming a flash memory device comprises programming selected memory cells, performing a verification operation to determine whether threshold voltages of the selected memory cells have reached verification levels of target program states, and determining a verification start point to be used for each of the target program states in the verification operation according to a programming characteristic associated with an initial pass bit detected during programming of an initial program state in the selected memory cells. 
     In certain embodiments, each of the selected memory cells stores multi-level data. 
     In certain embodiments, programming the selected memory cells and performing the verification operation constitute a program loop, and the verification start point of each target program state is an iteration of the program loop in which the verification operation is first performed with respect to the target program state. 
     In certain embodiments, the programming characteristic associated with the initial pass bit is a programming voltage of a program loop in which the initial pass bit occurs. 
     In certain embodiments, the verification start points are varied according to a relationship between the target program states and the initial program state. 
     In certain embodiments, the relationship between the target program states and the initial program state is a margin between a first threshold voltage distribution corresponding to one of the target program states and a second threshold voltage distribution corresponding to the initial program state. 
     In certain embodiments, the verification start point of the one of the target program states is increased where the first and second threshold voltage distributions overlap. 
     In certain embodiments, the verification start point of the one of the target program states is decreased where the first and second threshold voltage distributions do not overlap. 
     In certain embodiments, information indicating the programming characteristic associated with the initial pass bit is provided to the flash memory device from an external source. 
     According to another embodiment of the inventive concept, a method is provided for determining verification start points for target program states of selected memory cells in a flash memory device. The method comprises detecting whether at least one of the selected memory cells has reached a lowest verification level among verification levels of the target program states, and variably determining verification start points of the target program states corresponding to remaining verification levels other than the lowest verification level according to a relationship between the target program states and initial states of the selected memory cells, according to a result of the detection. 
     In certain embodiments, the method further comprises storing the result of the detection. 
     In certain embodiments, the stored result of the detection is used to determine verification start points of final target program states in a reprogramming operation of each of the selected memory cells. 
     In certain embodiments, the verification start points of the target program states are varied by decreasing a verification start point of a target program state where the target program state has an overlapping threshold voltage distribution with an initial state. 
     In certain embodiments, the method further comprises providing the result of the detection to a device external to the flash memory device. 
     In certain embodiments, the result of the detection is used to determine verification start points for a subsequent programming operation of the selected memory cells. 
     According to one embodiment of the inventive concept, a flash memory device comprises a memory cell array comprising a plurality of memory cells connected to a plurality of word lines and bit lines, and a control logic controlling a programming operation of selected memory cells connected to a selected word line. The control logic determines whether threshold voltages of the selected memory cells are greater than or equal to verification levels of target program states during a verification operation, and determines a verification start point to be used for each of the target program states in the verification operation according to a programming characteristic associated with an initial pass bit detected during programming of an initial program state in the selected memory cells. 
     In certain embodiments, the control logic adjusts the verification start points of the verification operations associated with the target program states according to relationships between the target program states and corresponding initial states. 
     In certain embodiments, the verification start points of the target program states are varied by varied by decreasing a verification start point of a target program state where the target program state has an overlapping threshold voltage distribution with an initial state. 
     In certain embodiments, the programming characteristic is provided from a device external to the flash memory device. 
     According to another embodiment of the inventive concept, a method of programming a flash memory device comprises programming multi-bit data in selected memory cells of the flash memory device, and performing verification operations to determine whether the selected memory cells are programmed to target program states corresponding to the multi-bit data. Performing the verification operations comprises predicting a verification end point for an upper target program state among the target program states according to a pass point of a lower target program state among the target program states. 
     In certain embodiments, predicting the verification end point comprises predicting a pass point for the upper target program state according to the pass point of the lower target program state, and subtracting a predetermined offset value from the predicted pass point. 
     In certain embodiments, the predicted pass point corresponds to a particular programming loop or programming voltage. 
     In certain embodiments, the same offset value is used to predict verification end points for more than one of the target program states. 
     In certain embodiments, different offset values are used to predict verification end points for more than one of the target program states. 
     In certain embodiments, performing the verification operations further comprises sequentially performing the verification operations for each of the target program states other than the lower target program state. 
     In certain embodiments, verification operations are discontinued for the target program states other than the lower target program state upon reaching corresponding verification end points. 
     In certain embodiments, the lower target program state has a lowest threshold voltage distribution among the target program states. 
     In certain embodiments, target program states are divided into a plurality of groups, and verification end points of target program states in each group are predicted on the basis of a pass point of a lowest program state in the group. 
     In certain embodiments, verification end points are predicted for each group only after all of the target program states in lower groups are passed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings illustrate selected embodiments of the inventive concept. In the drawings, like reference numbers indicate like features. In addition, the relative sizes of certain elements may be exaggerated for clarity. 
         FIG. 1  is a block diagram illustrating a flash memory device according to an embodiment of the inventive concept. 
         FIG. 2  is a diagram illustrating a flash memory device comprising a memory cell array with memory blocks having an all bitline architecture or an odd-even bitline architecture. 
         FIGS. 3A through 3C  are diagrams illustrating threshold voltage distributions of memory cells storing different numbers of bits. 
         FIG. 4  is a diagram illustrating a series of programming pulses used to program memory cells connected to a selected wordline. 
         FIGS. 5A through 5C  are threshold voltage diagrams illustrating a method of programming a flash memory device according to an embodiment of the inventive concept. 
         FIGS. 6 and 7  are diagrams illustrating a method of verifying a programming operation of  FIG. 5A . 
         FIGS. 8 and 9  are diagrams illustrating a method of verifying a programming operation of  FIG. 5B . 
         FIGS. 10 and 11  are diagrams illustrating a method of verifying a programming operation of  FIG. 5C . 
         FIGS. 12A through 12C  are voltage diagrams showing program voltages and verification voltages for the methods of  FIGS. 5A through 5C . 
         FIG. 13  is a diagram illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
         FIG. 14  is a diagram illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
         FIG. 15  is a diagram illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
         FIG. 16  is a flowchart illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
         FIG. 17  is a threshold voltage diagram for memory cells storing multi-bit data. 
         FIG. 18  is a diagram illustrating a verification scheme used in the method of  FIG. 16  according to an embodiment of the inventive concept. 
         FIG. 19  is a diagram illustrating a verification scheme used in the method of  FIG. 16  according to another embodiment of the inventive concept. 
         FIG. 20  is a flowchart illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
         FIG. 21  is a diagram illustrating a verification scheme used in the method of  FIG. 20  according to an embodiment of the inventive concept. 
         FIG. 22  is a block diagram illustrating a flash memory device capable of performing the method of  FIG. 20 . 
         FIGS. 23A and 23B  are flowcharts illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
         FIGS. 24A and 24B  are flowcharts illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
         FIGS. 25A and 25B  are flowcharts illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
         FIGS. 26A and 26B  are flowcharts illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
         FIG. 27  is a flowchart illustrating a method of programming a flash memory device according to yet another embodiment of the inventive concept. 
         FIG. 28  is a diagram illustrating a verification scheme used in the method of  FIG. 27  according to an embodiment of the inventive concept. 
         FIG. 29  is a flowchart illustrating a method of programming a flash memory device according to yet another embodiment of the inventive concept. 
         FIG. 30  is a flowchart illustrating a method of programming a flash memory device according to yet another embodiment of the inventive concept. 
         FIG. 31  is a diagram illustrating a verification scheme used in the method of  FIG. 30  according to an embodiment of the inventive concept. 
         FIG. 32  is a flowchart illustrating a method of programming a flash memory device according to yet another embodiment of the inventive concept. 
         FIG. 33  is a block diagram illustrating an integrated circuit card comprising a flash memory device according to an embodiment of the inventive concept. 
         FIG. 34  is a block diagram illustrating a computing system comprising a flash memory device according to an embodiment of the inventive concept. 
         FIG. 35  is a block diagram illustrating a memory controller of the computing system of  FIG. 34  according to an embodiment of the inventive concept. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Embodiments of the inventive concept are described below with reference to the accompanying drawings. These embodiments are presented as teaching examples and should not be construed to limit the scope of the inventive concept. 
     In the description that follows, where a first feature is referred to as being “connected” to a second feature, the first feature can be either “directly connected” to the second feature, or “electrically connected” to the second feature via an intervening feature. Terms in singular form encompass plural forms unless the context indicates otherwise. The terms “include,” “comprise,” “including,” or “comprising,” specify the presence of a feature, but do not exclude other features. 
       FIG. 1  is a block diagram illustrating a flash memory device according to an embodiment of the inventive concept. For explanation purposes, it will be assumed that the flash memory device of  FIG. 1  is a NAND flash memory device. However, embodiments of the inventive concept are not limited to NAND flash memory devices. 
     Referring to  FIG. 1 , the flash memory device comprises a memory cell array  100  comprising memory cells arranged in rows connected to wordlines WL and columns connected to bitlines BL. Each memory cell stores 1-bit data or M-bit data, where M is an integer greater than one. Each memory cell can store information using a charge storage layer such as a floating gate or a charge trapping layer, a variable resistor, or another type of memory element. 
     Memory cell array  100  can be implemented with a single-layer array structure (called a two-dimensional array structure) or a multi-layer array structure (called a three-dimensional array structure). Examples of a three-dimensional array structure are disclosed in U.S. Patent Publication No. 2008/0023747 entitled “SEMICONDUCTOR MEMORY DEVICE WITH MEMORY CELLS ON MULTIPLE LAYERS” and U.S. Patent Publication No. 2008/0084729 entitled “SEMICONDUCTOR DEVICE WITH THREE-DIMENSIONAL ARRAY STRUCTURE”, the respective disclosures of which are hereby incorporated by reference. 
     A row decoder  200  performs selection and driving operations for the rows of memory cell array  100 . A voltage generator  300  is controlled by a control logic  400  and generates voltages (for example, a program voltage, a pass voltage, an erase voltage, and a read voltage) for program, erase, and read operations. A read/write circuit  500  is controlled by control logic  400  and operates as a sense amplifier or a write driver according to various operation modes of the flash memory device. For example, in a read operation, read/write circuit  500  operates as a sense amplifier for sensing data from selected memory cells of a selected row. An input/output circuit  600  receives read data from read/write circuit  500  and transmits the read data to an external destination. In a programming operation, read/write circuit  500  operates as a write driver to drive selected memory cells of a selected row according to program data. Read/write circuit  500  comprises page buffers that correspond to respective bitlines or bitline pairs. Where the selected memory cells store multi-bit/multi-level data, each page buffer of read/write circuit  500  may include two or more latches. Input/output circuit  600  typically interfaces with an external device, such as a memory controller or a host. 
     Control logic  400  controls the overall operation of the flash memory device and comprises a pass bit detector  410 , a pass/fail determiner  420 , and a register  430 . 
     Pass bit detector  410  receives data that has been read by read/write circuit  500  in a verification operation. Pass bit detector  410  then determines whether a threshold voltage of at least one of the selected memory cells is greater than or equal to a verification level of a first program state (i.e., whether the at least one selected memory cell is “program passed” with respect to the first program state), based on the data read by read/write circuit  500 . Where at least one of the selected memory cells is determined to be program passed with respect to the first program state, control logic  400  determines verification start points for performing verification operations with respect to further program states. 
     A verification start point is a point of a program operation, such as a specific program loop, where a verification operation is first performed for a particular program state. For instance, a verification start point for a program state P 2  of selected memory cells can be a first program loop in which a verification operation is performed to determine whether the selected memory cells are successfully programmed to state P 2 . In program loops that precede the verification start point for program state P 2 , verification operations for program state P 2  are omitted. 
     In certain embodiments, the verification start point for a program state P 2  is determined according to a saved value of a program voltage at which a first selected memory cell is detected to be successfully programmed to program state P 1 . For instance, in some embodiments, the verification start point is a program loop where the value of the program voltage equals a sum of the saved value and a predetermined value. 
     Register  430  stores pass bit information from control logic  400  to indicate a program-passed loop. The program-passed loop is a program loop where at least one selected memory cell is program passed with respect to a particular program state. The pass bit information determines the start points of verification operations for subsequent program states, as will be described below. The pass bit information can also be provided to an external device, such as a memory controller. Pass/fail determiner  420  determines whether all the selected memory cells are successfully programmed on the basis of read data provided from read/write circuit  500  during the verification operation. 
     In other words, pass/fail determination determines whether all of the selected memory cells to be programmed to a particular program state have reached that state. Meanwhile, pass bit detection detects whether at least one of the selected memory cell to be programmed to the particular program state have reached that state. The order of pass/fail determination and pass bit detection can be changed in various alternative embodiments. For example, in some embodiments, pass bit detection is performed before pass/fail determination, and in other embodiments, pass bit detection is performed after pass/fail determination. 
       FIG. 2  is a diagram illustrating a flash memory device comprising a memory cell array with memory blocks having an all bitline architecture or an odd-even bitline architecture. In the example of  FIG. 2 , a NAND flash memory device comprises memory cell array  100  having 1024 memory blocks. In memory cell array  100 , data stored in the same memory block is erased simultaneously. In each memory block, memory cells are arranged in columns connected to the same bitline (e.g., 1 KB bitlines). 
     In the all bitline architecture, all bitlines of a memory block are simultaneously selected during read and programming operations. Accordingly, memory cells connected to a common wordline and connected to all the bitlines are simultaneously programmed. In the example of  FIG. 2 , memory cells in the same column are serially connected to form NAND string  111 . One end of NAND string  111  is connected to a corresponding bitline through a selection transistor controlled by a string selection line SSL, and another end is connected to a common source line CSL through a selection transistor controlled by a ground selection line GSL. 
     In the odd-even architecture, bitlines are divided into even bitlines BLe and odd bitlines BLo. Memory cells connected to a common wordline and connected to odd bitlines are programmed together, while memory cells connected to the common wordline and connected to even bitlines are programmed together. Data can be programmed in different memory blocks and read from different memory blocks. These operations can be performed at the same time. 
       FIGS. 3A through 3C  are diagrams illustrating threshold voltage distributions for memory cells storing different numbers of bits. In particular,  FIG. 3A  shows threshold voltage distributions for memory cells storing 2-bit data,  FIG. 3B  shows threshold voltage distributions for memory cells storing 3-bit data, and  FIG. 3C  shows threshold voltage distributions for memory cells storing 4-bit data. The threshold voltage distributions of  FIGS. 3A through 3C  correspond to program states of memory cells. Accordingly, the threshold voltage distributions will at times be referred to as program states in the description that follows. 
     Where 2-bit data (4-level data or 2-page data) is stored in a group of memory cells, as shown in  FIG. 3A , each of the memory cells has a threshold voltage within one of four threshold voltage distributions  10  through  13 . Threshold voltage distribution  10  encompasses threshold voltages of erased memory cells, and threshold voltage distributions  11  through  13  encompass threshold voltages of programmed memory cells. Voltages VP 1  through VP 3  are verification voltages for determining whether memory cells are programmed into respective threshold voltage distributions  11  through  13 . 
     Where 3-bit data (8-level data or 3-page data) is stored in a group of memory cells, as shown in  FIG. 3B , each of the memory cells has a threshold voltage within one of eight threshold voltage distributions  20  through  27 . Threshold voltage distribution  20  comprises threshold voltages of erased memory cells, and threshold voltage distributions  21  through  27  comprise threshold voltages of programmed memory cells. Voltages VP 1  through VP 7  are verification voltages for determining whether memory cells are respectively programmed into threshold voltage distributions  21  through  27 . 
     Where 4-bit data (16-level data or 4-page data) is stored in a group of memory cells, as shown in  FIG. 3C , each of the memory cells has a threshold voltage within one of sixteen threshold voltage distributions  30  through  45 . Threshold voltage distribution  30  comprises threshold voltages of erased memory cells, and threshold voltage distributions  31  through  45  comprise threshold voltages of programmed memory cells. Voltages VP 1  through VP 15  are verification voltages for determining whether selected memory cells are programmed into threshold voltage distributions  31  through  45 . 
       FIG. 4  is a diagram illustrating a series of programming pulses used to program selected memory cells connected to a selected wordline. The example of  FIG. 4  uses a general ISPP scheme. Certain embodiments of the inventive concept use a programming scheme that is modified relative to the general ISPP scheme of  FIG. 4 . 
     In the general ISPP scheme, a program voltage Vpgm is applied to control gates of selected memory cells as a series of programming pulses. The level of the programming pulses increases in successive iterations. 
     In periods between programming pulses, verification operations (or verification read operations) are performed. The verification operations determine whether the threshold voltages of selected memory cells have reached a verification level. 
     In an array of multi-level flash memory cells such as those described with respect to  FIG. 3 , a verification operation is performed to determine whether a selected memory cell has reached a threshold voltage distribution corresponding to a desired logic state. For instance, as illustrated in  FIG. 4 , in a 4-level MLC, verification operations are performed using verification voltages VP 1  through VP 3  to determine whether a selected memory cell has been successfully programmed to a logic state corresponding to one of threshold voltage distributions  11  through  13 . Similarly, in an 8-level MLC, verification operations are performed using verification voltages VP 1  through VP 7 , and in a 16-level MLC, verification operations are performed using fifteen verification voltages VP 1  through VP 15 . 
     The time required to perform programming operations using the general programming scheme of  FIG. 4  tends to increase in proportion to the number of program states of the selected memory cells. Moreover, in these programming operations, verification operations tend to occupy a large portion of the total programming time. Accordingly, a flash memory device according to certain embodiments of the inventive concept applies an adaptive verification scheme that reduces the verification time even where the number of program states of the selected memory cells is relatively large. 
       FIGS. 5A through 5C  are diagrams illustrating a method of programming a flash memory device according to an embodiment of the inventive concept. In the embodiment of  FIGS. 5A through 5C , it is assumed that a flash memory device stores 4-bit data in each cell and performs a programming operation according to a 3-step programming scheme. 
     In the method of  FIGS. 5A through 5C , first and second page data is simultaneously programmed in selected memory cells connected to a selected wordline. As illustrated in  FIG. 5A , selected memory cells having threshold voltage distributions corresponding to an erased state E are programmed to threshold voltage distributions corresponding to program states Q 1  through Q 3  according to data to be programmed. 
     Next, third and fourth page data is simultaneously stored in the selected memory cells. As illustrated in  FIG. 5B , selected memory cells in erased state E are programmed to threshold voltage distributions corresponding to program states P 1 ′ through P 3 ′ according to data to be programmed. Selected memory cells in program state Q 1  of  FIG. 5A  are programmed to threshold voltage distributions corresponding to program states P 4 ′ through P 7 ′ according to data to be programmed. Selected memory cells in program state Q 2  of  FIG. 5A  are programmed to threshold voltage distributions corresponding to program states P 8 ′ through P 11 ′ according to data to be programmed. Selected memory cells in program state Q 3  of  FIG. 5A  are programmed to threshold voltage distributions corresponding to program states P 12 ′ through P 15 ′ according to data to be programmed. 
     Verification voltages VP 1 ′ through VP 15 ′, which are used to determine program states P 1 ′ through P 15 ′, are lower than verification voltages VP 1  through VP 15 , which are used to determine final program states P 1  through P 15  (see  FIG. 5C ). For example, a verification voltage VP 1 ′, which is used to determine a program state P 1 ′, is lower than a verification voltage VP 1 , which is used to determine a corresponding final threshold voltage distribution P 1  (see  FIG. 5C ). An operation that programs selected memory cells to the threshold voltage distributions of  FIG. 5B , is referred to as a coarse programming operation. 
     Selected memory cells in program states P 1 ′ through P 15 ′ are programmed to have final program states P 1  through P 15  in a fine programming operation (or a reprogramming operation). 
     The programming operations of  FIGS. 5A through 5C  can be successively or non-successively performed. These programming operations can have verification operations for determining whether selected memory cells are programmed to target threshold voltage distributions. 
       FIGS. 6 and 7  are diagrams illustrating a method of verifying the programming operation of  FIG. 5A . 
     Referring to  FIG. 6 , after a program voltage Vpgm is applied to selected memory cells connected to a selected wordline, a verification voltage for verifying a program state Q 1  is applied to the selected wordline. At this point, as illustrated in  FIG. 6 , verification operations for other program states Q 2  and Q 3  are not performed. A verification voltage is then applied to the selected wordline, and read/write circuit  500  reads data from the memory cells. Subsequently, pass bit detector  410  of control logic  400  detects whether a threshold voltage of at least one selected memory cell is greater than or equal to a verification voltage VQ 1  of program state Q 1  on the basis of read data. Where no selected memory cell has a threshold voltage greater than or equal to verification voltage VQ 1 , program voltage Vpgm increases by a predetermined amount and the programming operation proceeds to a next program loop. Otherwise, the flash memory device determines verification start points for program states Q 2  and Q 3 . 
     Referring to  FIG. 7 , where at least one selected memory cell is detected to have a threshold voltage greater than or equal to verification voltage VQ 1 , control logic  400  sets a verification start point of program state Q 2  according to a present value of program voltage Vpgm. In particular, control logic  400  sets the verification start point as a program loop having a value of program voltage Vpgm equal to a sum of the present value of program voltage Vpgm and a voltage difference ΔV between verification voltages VQ 1  and VQ 2 . In addition, assuming that a voltage difference between verification voltages VQ 2  and VQ 3  is also ΔV, control logic  400  sets a verification start point of program state Q 3  as a program loop having a value of program voltage Vpgm equal to the sum of the present value of program voltage Vpgm and  2 ΔV. As illustrated in  FIG. 6 , verification operations of program states Q 2  and Q 3  are not performed until the determined verification start point. 
     In some embodiments, a program loop where a pass bit is detected (or a program voltage applied to selected memory cell(s) determined as a pass bit) is stored in register  430  of control logic  400 . Alternatively, the program loop (or program voltage) is provided to an external device, such as a memory controller, under the control of control logic  400 . 
     As indicated above, pass/fail determination can be performed by pass/fail determiner  420  before or after pass bit detection is performed. Where a selected memory cell is successfully programmed to its target state, a program-inhibition voltage is applied to the selected memory cell in subsequent program loops. 
       FIGS. 8 and 9  are diagrams illustrating a method of verifying a programming operation of  FIG. 5B . 
     Referring to  FIG. 8 , after program voltage Vpgm is applied to selected memory cells connected to a selected wordline, a verification voltage for verifying program state P 1 ′ is applied to the selected wordline. At this point, as illustrated in  FIG. 8 , verification operations for other program states P 2 ′ through P 15 ′ are not performed. A verification voltage is then applied to the selected wordline, and read/write circuit  500  reads data from the selected memory cells. Subsequently, pass bit detector  410  of control logic  400  detects whether a threshold voltage of at least one selected memory cell is greater than or equal to verification voltage VP 1 ′ of program state P 1 ′ on the basis of the read data. Where no selected memory cell has a threshold voltage greater than or equal to verification voltage VP 1 ′ of program state P 1 ′, program voltage Vpgm is increased by a predetermined amount, and the programming operation proceeds to a next program loop. Otherwise, the flash memory device determines verification start points for program states P 2 ′ through P 15 ′. 
     Referring to  FIG. 9 , where at least one selected memory cell is detected to have a threshold voltage greater than or equal to verification voltage VP 1 ′, control logic  400  sets a verification start point of program state P 2 ′ according to a present value of program voltage Vpgm. In particular, control logic  400  sets the verification start point as a program loop having a value of program voltage Vpgm equal to a sum of the present value of program voltage Vpgm and a voltage difference ΔV 1  between verification voltages VP 1 ′ and VP 2 ′. In addition, assuming that a voltage difference between verification voltages VP 2 ′ and VP 3 ′ is also ΔV 1 , control logic  400  sets a verification start point of program state P 3 ′ as a program loop having a value of program voltage Vpgm equal to the sum of the present value of program voltage Vpgm and  2 ΔV 1 . As illustrated in  FIG. 8 , verification operations of program states P 2 ′ through P 15 ′ are not performed until corresponding verification start points. 
     In some embodiments, register  430  of control logic  400  stores pass bit information, such as a program loop where a pass bit is detected, or a program voltage of the loop, during a coarse programming operation. The pass bit information stored in register  430  can then be used to determine verification start points of final program states P 1  through P 15  for a fine programming operation. 
     In some embodiments, pass bit information is output to an external device, such as a memory controller. The pass bit information can be used to perform a fine programming operation for selected memory cells. 
       FIGS. 10 and 11  are diagrams illustrating a method of verifying the programming operation of  FIG. 5C . 
     Referring to  FIG. 10 , control logic  400  determines verification start points of program states P 1  through P 15  based on pass bit information detected in a previous programming operation. The pass bit information can be accessed, for instance, from register  430 . Referring to  FIG. 11 , control logic  400  determines the verification start point of program state P 1  on the basis of pass bit information indicating a pass bit detected in a previous page programming operation of a selected wordline. Control logic  400  determines the verification start point of program state P 2  as a program loop where program voltage Vpgm equals a sum of a voltage difference ΔV 2  between verification voltages VP 1  and VP 2 , and a program voltage Vpgm corresponding to the pass bit information detected in the previous programming operation. In addition, assuming that a voltage difference between verification voltages VP 2  and VP 3  is also ΔV 2 , control logic  400  sets a verification start point of program state Q 3  as a program loop having a value of program voltage Vpgm equal to the sum of the present value of program voltage Vpgm and  2 ΔV 2 . As illustrated in  FIG. 10 , verification operations of program states P 2  through P 15  are not performed until the corresponding verification start points. 
     In the programming method described above with reference to  FIG. 5 , the verification operations for program states P 1  through P 15  are not performed until corresponding verification start points. For example, verification voltages for verifying program states P 1  through P 15  are applied to selected wordlines only after a current loop reaches a verification start point for the corresponding program state. 
       FIG. 12A  is a voltage diagram showing program voltages and verification voltages for the method of  FIG. 5A .  FIG. 12B  is a voltage diagram showing program voltages and verification voltages for the method of  FIG. 5B .  FIG. 12C  is a voltage diagram showing program voltages and verification voltages for the method of  FIG. 5C . 
     As illustrated in  FIG. 12A , a pass bit is detected during a verification operation of program state Q 1 . Once the pass bit is detected, verification start points of other program states Q 2  and Q 3  are determined by control logic  400 . As illustrated in  FIG. 12B , a pass bit is detected during a verification operation of program state P 1 ′. Once the pass bit is detected, verification start points of other program states P 2 ′ and P 15 ′ are determined by control logic  400 . At this point, pass bit information is stored in register  430  of control logic  400  to determine verification start points of subsequent page programming operations, such as fine programming stages. Finally, as illustrated in  FIG. 12C , verification start points of final program states P 1  through P 15  are determined on the basis of information stored in register  430 . 
     In the programming operations described with reference to  FIGS. 5 through 12 , programming speed is increased by eliminating certain verification operations. 
       FIG. 13  is a diagram illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. In the method of  FIG. 13 , memory cells are programmed using different techniques according to different cases shown on the left side of  FIG. 13 . 
     In the two different cases of  FIG. 13 , verification start points of program states are variably set according to previous states and target states of selected memory cells. In a first case, the previous state and the target state do not overlap because the threshold voltage distribution of the previous state does not exceed the verification voltage of the target state. In a second case, the previous state and the target state overlap because the threshold voltage distribution of the previous state exceeds the verification voltage of the target state. 
     Where a target state to be verified corresponds to the first case, the verification start point of the target state uses a verification voltage illustrated by a dashed line to the right of a solid line in  FIG. 13 . On the other hand, where a target state to be verified corresponds to the second case, the verification start point of the target state uses a verification voltage illustrated as a dotted line to the left of the solid line in  FIG. 13 . In the example of  FIG. 13 , the verification start point corresponding to the solid line is determined according to the method of  FIG. 6  or  FIG. 8 . 
     Applying the method of  FIG. 13  to the example of  FIG. 5A , the first case can be realized by previous state E and target states Q 1  through Q 3 . In the example of  FIG. 5A , the second case does not arise because memory cells are not programmed between threshold voltage distributions that overlap each other. Applying the method of  FIG. 13  to the example of  FIG. 5B , the first case can be realized by previous state E and target states P 1 ′ through P 3 ′, a previous state Q 1  and target states P 5 ′ through P 7 ′, a previous state Q 2  and target states P 9 ′ through P 11 ′, and a previous state Q 3  and target states P 13 ′ through P 15 ′. The second case can be realized by a previous state Q 1  and a target state P 4 ′, a previous state Q 2  and a target state P 8 , and a previous state Q 3  and a target state P 12 . Applying the method of  FIG. 13  to the example of  FIG. 5C , the second case can be realized by previous states P 1 ′ through P 15 ′ and target states P 1  through P 15 . 
       FIG. 14  is a diagram illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
     The method of  FIG. 14  is substantially the same as the method of  FIG. 13 , except that the determination of verification start points is performed on the basis of pass bit information from a previous page programming operation of the same wordline instead of pass bit detection for first programming state P 1 . 
     As indicated in the above descriptions of  FIGS. 13 and 14 , the verification start point of each program state is determined on the basis of a detected pass bit, a stored pass bit, or a relationship between the detected pass bit or the stored pass bit and a previous state and a target state. 
       FIG. 15  is a diagram illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
     In the method of  FIG. 15 , selected memory cells are programmed according to a shadow programming scheme. Even when performing a programming operation using the shadow programming scheme, the above described methods can be used to determine verification start points. For example, the verification start point of each program state can be determined on the basis of a detected pass bit, a stored pass bit, or a relationship between the detected pass bit or the stored pass bit and a previous state and a target state. 
       FIG. 16  is a flowchart illustrating a method of programming a flash memory device according to another embodiment of the inventive concept.  FIG. 17  is a diagram showing the threshold voltage distributions of multi-bit data programmed by the method of  FIG. 16 . 
     In the method of  FIG. 16 , the flash memory device is programmed using a programming operation comprising a programming execution section and a verification section. The programming execution section changes threshold voltages of selected memory cells of a selected wordline, and the verification section determines whether the threshold voltages of the selected memory cells, which have changed during the programming execution section, have reached corresponding target voltages. A program voltage is applied to the selected wordline during the programming execution section, and a series of verification voltages are sequentially applied to the selected wordline during the verification section. The series of verification voltages correspond to threshold voltage distributions representing multi-bit data in the selected memory cells. Data to be programmed is loaded to the flash memory device before the programming execution section. Previously programmed data can be read before loading of data to be programmed. 
     Referring to  FIG. 16 , variables FLAG and Pi_FLAG are set to ‘0’ in operation S 100 . The variable FLAG is used to indicate whether the lowest program state (for example, state P 1  of  FIG. 2 ) is passed, and the variable Pi_FLAG is used to indicate whether other program states are passed. A “passed” status of a program state indicates that all threshold voltages of selected memory cells corresponding to the program state are greater than or equal to a verification voltage of the program state. A passed status of a program state differs from the program pass of a programming operation. 
     A programming operation is performed in operation S 110 . Operation S 110  corresponds to the programming execution section. Then, operation S 120  determines whether the variable FLAG is set to ‘1’. Where the variable FLAG is not set to ‘j’ (S 120 =No), the method proceeds to operation S 130 . In operation S 130 , a verification operation is performed for program state P 1 . Then, in operation S 140 , the method determines whether all of the selected memory cells corresponding to program state P 1  have threshold voltages that are greater than or equal to the verification voltages. In other words, operation S 140  determines whether program state P 1  is passed. 
     Where program state P 1  is determined to be passed (S 140 =Yes), the method proceeds to operation S 150 , where the variable FLAG is set to ‘1’. Thereafter, a verification operation for program state P 1  is omitted during the verification section of further program loops. The last point, such as a last program loop, where verification is performed for program state P 1  is referred to as a verification end point, or verification end loop. Next, operation S 160  predicts verification end points of remaining program states. The verification end points of the remaining program states are predicted as follows. 
     Where program state P 1  is detected as being passed, the method determines or predicts a pass point for each of the remaining program states, where a pass point indicates a program loop or program voltage where a program state is passed. The pass points can then be used to determine verification end points for the remaining program states. 
     The pass points of the remaining program states are determined by an equation “Vpgm(i)=Vpgm(pass)+Vdiff”, where Vdiff indicates a difference voltage “N*ΔV” (where N≧1) between verification voltage VP 1  of program state P 1  and the verification voltage of another program state, Vpgm(i) (i≧2) indicates the programmed voltage of the pass point of each of remaining program states (for example, program states P 2  through P 7 ) other than program state P 1 , and Vpgm(pass) indicates the program voltage of a point where program state P 1  is passed. 
     Assuming that 3-bit data is stored in each memory cell, as illustrated in  FIG. 2 , each memory cell has any one of eight threshold voltage distributions corresponding to states E and P 1  through P 7 . Program states P 1  through P 7  are determined by corresponding verification voltages Vvfy 1  through Vvfy 7 . The state distribution diagram of  FIG. 2  is illustrated under a condition where a difference voltage “ΔV” is identical between verification voltages (for example, Vvfy 1  and Vvfy 2 ) corresponding to adjacent program states (for example, P 1  and P 2 ). However, the voltage differences between verification voltages can vary in other embodiments. 
     The pass points of remaining program states other than program state P 1  are determined as illustrated above. Verification end points of the remaining program states are determined on the basis of the determined pass points. The verification end points are determined through an equation “Vpgm(i)_VE=Vpgm(i)−Voffset(i)”, where Vpgm(i)_VE indicates a program voltage corresponding to the verification end point of each of the remaining program states, and Voffset(i) indicates the offset voltage of each of the remaining program states. The offset voltages of the remaining program states can be set to the same value or different values in various embodiments. 
     In some embodiments, a flash memory device determines whether a verification end point has been reached for a particular program state by comparing a program voltage of a current program loop with a program voltage associated with the verification end point. Alternatively, the flash memory device can determine whether the verification end point has been reached for the particular program state by comparing an index or other identifier of a current program loop with a program loop identifier of the verification end point. 
     In some embodiments, the verification end point for a program state may occur before all of the relevant memory cells are programmed to that state. This can occur because the verification end point may be determined according to a prediction as described above. Where this occurs, the memory cells that have not been successfully programmed include fail bits. The fail bits can be corrected by an error correction code (ECC) unit of a memory controller during read bits. The fail bits are typically associated with memory cells having a slow programming speed and are called slow bits. 
     Once the verification end points are determined for the remaining program states P 2  through P 7 , the method proceeds to operation S 170 . In operation S 170 , verification operations are performed for the remaining program states P 2  through P 7 , as will be described below. The method also proceeds to operation S 170  where operation S 120  determines that the variable FLAG is set as ‘j’ (S 120 =Yes), or where operation S 140  determines that program state P 1  is not passed (S 140 =No). 
     The verification operations of the remaining program states, which are performed in operation S 170 , are automatically ended based on the verification end points determined in operation S 160 . As an example, a verification operation is performed for a next program state (e.g., state P 2 ) in operation S 171 . Operation S 172  determines whether the threshold voltages of memory cells corresponding to program state P 2  are greater than or equal to verification voltage Vvfy 2 . That is, operation S 172  determines whether all memory cells corresponding to program state P 2  are program passed. Where all of the memory cells corresponding to program state P 2  are determined as being program passed (S 172 =Yes), the method proceeds to operation S 173 . Otherwise (S 172 =No), the method proceeds to operation S 174 . 
     In operation S 174 , the method determines whether the current program loop has reached a verification end point for program state P 2 . If so (S 174 =Yes), the method proceeds to operation S 173 . Otherwise (S 174 =No), the method proceeds to operation S 175 . 
     In operation S 173 , the variable Pi_FLAG is set to a passed state to indicate that a verification operation for program state P 2  is to be omitted in a next program loop. 
     In operation S 175 , the method determines whether all verification operations for remaining program states P 2  through P 7  have been performed. Where not all of the verification operations for program states P 2  through P 7  have been performed (S 175 =No), the method proceeds to operation S 176 . Otherwise (S 175 =Yes), the method proceeds to operation S 180 . In operation S 176 , the variable T is increased by 1 and the method returns to operation S 171 . 
     In operation S 180 , the method determines whether all program states (e.g., P 1  through P 7 ) are passed. Where one or more of the program states is determined as not being passed (S 180 =No), the method operation proceeds to operation S 190 . Otherwise (S 180 =Yes), the method ends. 
     In operation S 190 , a variable LOOP indicating a program loop is increased by 1 and the method returns to operation S 110 . Subsequent program loops are performed until all the program states are determined as being passed. 
       FIG. 18  is a diagram illustrating a verification scheme used in the method of  FIG. 16  according to an embodiment of the inventive concept. 
     Referring to  FIG. 18 , where program state P 1  is passed, verification end points for remaining program states P 2  to P 7  are predicted. Where a current program loop (or program voltage) corresponds to a predicted verification end point of program state, the program state is passed, and verification operations of the program state are ended. As illustrated in  FIG. 18 , verification operations are omitted for each program state after it reaches a corresponding predicted verification end point. 
       FIG. 19  is a diagram illustrating a verification scheme used in the method of  FIG. 16  according to another embodiment of the inventive concept. 
     In the method of  FIG. 19 , the verification end points of the remaining program states are determined with respect to the pass points of at least two program states among a plurality of program states. For example, program states are divided into “n” groups G 1  through Gn. The verification end points of remaining program states belonging to each group are determined with respect to the pass point of a lowest program state belonging to the group. The verification end points can be determined as described above. As an example, in a first group G 1 , the verification end points of remaining program states P 2  through P 4  are determined with respect to a pass point of program state P 1 . In a second group G 2 , the verification end points of remaining program states P 6  through P 8  are determined with respect to a pass point of program state P 5 . 
     In other embodiments, the number of program states belonging to each group can be varied. Moreover, offset voltages applied to different groups can be set identically or differently, and the offset voltages of the program states belonging to the same group can be set identically or differently. 
       FIG. 20  is a flowchart illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
     In the method of  FIG. 20 , variables FBCPS, VPS, and Pi_FLAG are set to ‘j’ in operation S 200 . The variable FBCPS indicates a program state where a fail bit count is performed, and the variable VPS indicates a program state where a verification operation is performed. The variable Pi_FLAG is used to indicate the passed status of a program state where a verification operation has been performed. 
     A programming operation is performed in operation S 210 . Operation S 210  corresponds to a programming execution section. Next, operation S 220  determines whether the value of the variable FBCPS is equal to the value of the variable VPS. Assuming that a current program loop is a first program loop, the value of the variable FBCPS is equal to the value of the variable VPS (S 220 =Yes). Consequently, the method proceeds to operation S 230 . In operation S 230 , a verification operation is performed for program state P 1 , and the method proceeds to operation S 240 . 
     Operation S 240  counts the number of fail bits among data bits that are read in a verification operation of program state P 1 . The counting of fail bits can be implemented in various ways. For example, the number of fail bits can be counted based on the amount of a current that flows in selected memory cells during a verification operation. Alternatively, the number of fail bits can be counted using a counter. 
     Next, in operation S 250 , the method determines whether the counted number of fail bits is less than a predetermined reference value. Where the counted number of fail bits is less than the predetermined reference value (S 250 =Yes), the method proceeds to operation S 260 . Otherwise (S 250 =No), the method proceeds to operation S 270 . In operation S 250 , the reference value is determined according to the error correction capability of an ECC unit of the memory controller. In operation S 260 , the value of the variable FBCPS is increased by 1 and the variable Pi_FLAG is set to indicate a passed status. In other words, first program state P 1  is determined to have a passed status, and consequently, a verification operation for program state P 1  is omitted in successive program loops. Following operation, the method proceeds to operation S 270 . 
     As indicated by the above description, where the number of fail bits among data bits corresponding to a program state is less than the predetermined reference value, a program state is determined to have a passed status. Consequently, verification operations of the program state can be omitted even where the data bits corresponding to the program state include the fail bits. The fail bits are slow bits. In other words, where the number of fail bits among the data bits corresponding to the program state is less than the predetermined reference value, a verification operation for a slow bit is omitted. 
     Returning to operation S 220 , where the value of the variable FBCPS is not equal to that of the variable VPS (S 220 =No), the method proceeds to operation S 280 . Where the counted number of fail bits for program state P 1  is greater than the reference value, the value of the variable FBCPS is not changed. In this case, assuming that a present verification operation is associated with a verification operation for second program state P 2  or another higher program state, the value of the variable FBCPS, which indicates a program state where the number of fail bits has been counted, is not equal to the value of the variable VPS, which indicates a program state where the verification operation is performed. 
     In operation S 280 , a verification operation is performed for a current program state corresponding to the value of the variable VPS, and the method proceeds to operation S 290 . In operation S 290 , the method determines whether all read data bits are passed data bits. Where all of the read data bits are passed data bits (S 290 =Yes), the variable Pi_FLAG is set to indicate a passed status for the current program state, and the method proceeds to operation S 300 . Otherwise (S 290 =No), the method proceeds to operation S 270 . In operation S 270 , the method determines whether all verification operations for the program states have been performed. If not (S 270 =No), the method proceeds to operation S 310 . Otherwise (S 270 =Yes), the method proceeds to operation S 320 . 
     In operation S 310 , the value of the variable VPS, which indicates a program loop where a verification operation is to be performed, is increased by 1, and the method returns to operation S 220 . In operation S 320 , the method determines whether all program states are passed. Where at least one of the program states is not passed (S 320 =No), operation S 330  increases the value of a program loop by 1, and sets the variable VPS to ‘N’. In operation S 330 , “N” has a value indicating a lowest program state among the program states that are not passed. Following operation S 330 , the method returns to operation S 210 . Where all the program states are determined as being passed (S 320 =Yes), the method ends. 
     In certain embodiments, the method of  FIG. 20  can be modified so that it determines, between operations S 230  and S 240 , whether a program state is passed. 
       FIG. 21  is a diagram illustrating a verification scheme used in the method of  FIG. 20  according to an embodiment of the inventive concept. 
     Referring to  FIG. 21 , a bit count operation for first program state P 1  is performed until the number of fail bits becomes less than a predetermined reference value. At this point, a fail bit count operation for remaining program states is not performed. Once the number of fail bits of first program state P 1  becomes less than the predetermined reference value, a verification operation for first program state P 1  is ended, and a fail bit count operation for second program state P 2  is started. At this point, a fail bit count operation is not performed for remaining program states (i.e., the upper program states of the second program state). Where the number of fail bits of second program state P 2  becomes less than the predetermined reference value, a verification operation for second program state P 2  is ended, and a fail bit count operation for third program state P 3  is started. A fail bit count operation for remaining program states is determined through the substantially same scheme as shown in  FIG. 21 . 
       FIG. 22  is a block diagram illustrating a flash memory device capable of performing the method of  FIG. 20 . 
     The device of  FIG. 22  is substantially the same the device of  FIG. 1 , except that that the device of  FIG. 22  further comprises a circuit  440  within control logic  400  for counting the number of fail bits using current sensing. The counting of the number of fail bits is not limited to current sensing, and can be implemented using other techniques, such as a counter. 
       FIGS. 23A and 23B  are flowcharts illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
     In the example of  FIGS. 23A and 23B , it is assumed that 3-bit data is stored in each memory cell using one erased state E and seven program states P 1  through P 7 . In addition, the method of  FIG. 23  can incorporate the scheme for determining the verification start point as described above with reference to  FIG. 6  or  FIG. 8  and the scheme for determining the verification end point as described above with reference to  FIG. 16 . Verification operations for fast bits can be skipped using verification start point determination, and verification operations for slow bits can be skipped through the verification end point determining scheme. 
     Referring to  FIG. 23A , in operation S 300 , upon initiation of a programming operation, a variable i_PGM_Loop is set as ‘1’, and variables P(j)_Verify_Start and P(j)_Verify_End are respectively set as maximum program loop times Max_PGM_Loop. The variable i_PGM_Loop indicates a current program loop, the variable P(j)_Verify_Start indicates a verification start point for a j-th program state, and the variable P(j)_Verify_End indicates a verification end point for a j-th program state. Next, in operation S 310 , a programming operation is executed under the control of control logic  400 . 
     Thereafter, in operation S 320 , upon completion of the programming operation, the method determines whether program state P 1  is passed. Where the verification operation determines that program state P 1  is not passed (S 320 =No), the method proceeds to operation S 330 . 
     In operation S 330 , a verification operation is performed for program state P 1  to determine whether at least one selected memory cell has been successfully programmed to program state P 1 . In other words, operation S 330  determines whether the selected memory cells include a pass bit. 
     Where a pass bit is detected during the verification operation of program state P 1  (S 340 =Yes), the method proceeds to operation S 350 . Otherwise (S 340 =No), the method proceeds to operation S 360 . 
     Operation S 350  implements a method such as those described with reference to  FIG. 6  and  FIG. 8  to predict verification start points P(j)_Verify_Start of remaining program states P 2  through P 7  on the basis of a detected pass bit. In particular, operation S 350  comprises setting a variable ‘j’ to 2 in operation S 351 ; predicting a verification start point P(j)_Verify_Start of a j-th program state in operation S 352 ; determining whether T has reached 7 indicating a most significant bit (MSB) program state P 7  in operation S 353 ; and increasing ‘j’ by 1 where ‘j’ has not reached 7 (S 353 =No) in operation S 354 . 
     Verification start points can also be predicted according to the scheme that has been described above with reference to  FIGS. 13 and 14 . After the verification start points P(j)_Verify_Start of the remaining program states P 2  through P 7  are predicted in operation S 350 , the method proceeds to operation S 360 . 
     In operation S 360 , the method determines whether program state P 1  is passed. Upon determining that program state P 1  is passed (S 360 =Yes), the method proceeds to operation S 370 . Otherwise (S 360 =No), the method proceeds to operation S 380 . 
     Operation S 370  uses a method similar to that described with reference to  FIG. 16  to predict verification end points P(j)_Verify_End of the remaining program states P 2  through P 7 . In particular, operation S 370  comprises setting T to indicate program state P 2  in operation S 371 ; predicting a verification end point P(j)_Verify_End of the j-th program state in operation S 372 ; determining whether ‘j’ has reached 7 in operation S 373 ; and increasing ‘j’ by 1 where ‘j’ has not reached 7 (S 373 =No) in operation S 374 . After the verification end points P(j)_Verify_End of the remaining program states P 2  through P 7  are predicted in operation S 370 , the method proceeds to operation S 380 . 
     In operation S 380 , the method sets ‘j’ to 2 to indicate program state P 2 . Next, in operation S 390 , the method determines whether a current program loop i_PGM_Loop is between the verification start point P(j)_Verify_Start and the verification end point P(j)_Verify_End of program state P(j). If so, the verification operation of program state P(j) is performed. Otherwise, the verification operation is omitted. 
     Where operation S 390  determines that the current program loop i_PGM_Loop is greater than or equal to the verification end point P(j)_Verify_End of program state P(j) or is less than or equal to the verification end point P(j)_Verify_End of program state P(j) (S 390 =Yes), the method proceeds to operation S 400 . Otherwise (S 390 =No), the method proceeds to operation S 410 . 
     In operation S 400 , the method performs the verification operation of program state P(j) and proceeds to operation S 410 . In operation S 410 , the method determines whether ‘j’ has reached 7 indicating program state P 7 . Where T has not reached 7 (S 410 =No), ‘j’ is increased by 1 in operation S 420  and the method returns to operation S 390 . Otherwise (S 410 =Yes), the method proceeds to operation S 430 . In operation S 430 , the method determines whether all program states are passed. If not (S 430 =No), operation S 440  is performed to increase variable i_PGM_Loop by 1. Otherwise (S 430 =Yes), the method ends. After operation S 440 , the method returns to operation S 310 . 
       FIGS. 24A and 24B  are flowcharts illustrating a method of programming a flash memory device according to another embodiment of the inventive concept. 
     In the method of  FIGS. 24A and 24B , it is assumed that 3-bit data is stored in each memory cell using one erased state E and seven program states P 1  through P 7 . In addition, the method of  FIG. 24  can include the scheme for predicting verification start points as described above with reference to  FIG. 6  or  FIG. 8  and the scheme of predicting verification end points as described above with reference to  FIG. 20 . In the method of  FIGS. 24A and 24B , verification operations for fast bits are skipped according to the verification start point predicting scheme, and verification operations for slow bits are skipped according to the verification end point predicting scheme. 
     Referring to  FIG. 24A , operation S 500  is performed upon initiation of a programming operation to set a variable i_PGM_Loop is to ‘1’, and to set variables P(j)_Verify_Start and P(j)_Verify_End as maximum program loop times Max_PGM_Loop. The variable i_PGM_Loop indicates a current program loop, and the variable P(j)_Verify_Start indicates a verification start point for a j-th program state. Next, in operation S 510 , a programming operation is executed under the control of control logic  400 . 
     After the programming operation, operation S 520  determines whether program state P 1  is passed. Where program state P 1  is not passed (S 520 =No), the method proceeds to operation S 530 . Otherwise (S 520 =Yes), the method proceeds to operation S 560 . In operation S 530 , the method performs a verification operation for program state P 1  and determines the number of fail bits for program state P 1 . As described above with reference to  FIG. 20 , where the number of fail bits for program state P 1  is less than or equal to a reference value, program state P 1  is set as being passed. 
     Next, in operation S 540 , the method determines whether at least one pass bit (i.e., a fast bit) is detected during the verification operation of program state P 1 . Where a pass bit is detected (S 540 =Yes), the method proceeds to operation S 550 . Otherwise (S 540 =No), the method proceeds to operation S 560 . Operation S 560  comprises operations similar to those described above with reference to  FIG. 6  or  FIG. 8 , in which the verification start points P(j)_Verify_Start of remaining program states P 2  through P 7  are predicted on the basis of a detected pass bit. Accordingly, operation S 550  comprises setting a variable ‘j’ to 2 in operation S 551 ; predicting a verification start point P(j)_Verify_Start of a j-th program state in operation S 552 ; determining whether ‘j’ has reached 7 in operation S 553 ; and increasing ‘j’ by 1 where ‘j’ has not reached 7 (S 553 =No) in operation S 554 . Verification start points can be predicted according to the scheme that has been described above with reference to  FIGS. 13 and 14 . After the verification start points P(j)_Verify_Start of the remaining program states P 2  through P 7  are predicted in operation S 550 , the method proceeds to operation S 560 . 
     In operation S 560 , the method sets ‘j’ to 2 to indicate program state P 2 . Then, in operation S 570 , the method determines whether program state P(j) is passed. Where program state P(j) is not passed (S 570 =No), the method proceeds to operation S 580 . Otherwise (S 570 =Yes), the method proceeds to operation S 600 . In operation S 580 , the method determines whether the predicted verification start point of program state P(j) is less than or equal to a current program loop i_PGM_Loop. Where the current program loop i_PGM_Loop is less than the verification start point P(j)_Verify_Start of program state P(j), the verification operation of program state P(j) is omitted. Where the current program loop i_PGM_Loop is greater than the verification start point P(j)_Verify_Start of program state P(j), the verification operation of program state P(j) is performed. 
     Where the current program loop i_PGM_Loop is greater than or equal to the verification start point P(j)_Verify_Start of program state P(j), the method proceeds to operation S 590 . In operation S 590 , a verification operation is performed for program state P(j) and the number of fail bits for program state P(j) is counted. As described above with reference to  FIG. 20 , where the number of fail bits for program state P(j) is less than or equal to a reference value, program state P(j) is set as being passed. In other embodiments, as described above with reference to  FIG. 20 , a fail bit detecting operation for program state P(j) is performed after program state P 1  is passed. Following operation S 590 , the method proceeds to operation S 600 . 
     In operation S 600 , the method determines whether ‘j’ has reached 7 indicating program state P 7 . Where ‘j’ has not reached 7 (S 600 =No), ‘j’ is increased by 1 in operation S 610 . Otherwise (S 600 =Yes), the method proceeds to operation S 620 . 
     In operation S 620 , the method determines whether all of program states P 1  through P 7  are passed. If so (S 620 =Yes), the method ends. Otherwise (S 620 =No), operation S 630  is performed to increase the variable i_PGM_Loop by 1, and the method returns to operation S 510 . 
       FIGS. 25A and 25B  are flowcharts illustrating a method of programming a flash memory device according to still another embodiment of the inventive concept. 
     In the method of  FIGS. 25A and 25B , it is assumed that 3-bit data is stored in each memory cell using one erased state E and seven program states P 1  through P 7 . In addition, the method of  FIGS. 25A and 25B  use the scheme for predicting the verification start point as described above with reference to  FIG. 10  and the scheme for predicting the verification end point as described above with reference to  FIG. 16 . A verification operation for fast bits can be skipped according to the verification start point predicting scheme, and a verification operation for slow bits can be skipped according to the verification end point predicting scheme. 
     Referring to  FIG. 25A , upon initiation of a programming operation, operation S 700  is performed to set a variable i_PGM_Loop to ‘1’, and to set variables P(j)_Verify_Start and P(j)_Verify_End as maximum program loop times Max_PGM_Loop. The variable i_PGM_Loop is used to indicate a current program loop, and the variable P(j)_Verify_End is used to indicate a verification end point for a j-th program state. Next, in operation S 710 , the verification start points of program states P 1  through P 7  are predicted on the basis of pass bit information (e.g., a program voltage or a program loop) from a previous page or previous step programming operation. In particular, operation S 710  comprises setting a variable ‘j’ to 1 in operation S 711 ; predicting a verification start point of program state P(j) in operation S 712 ; determining whether ‘j’ has reached 7 indicating program state P 7  in operation S 713 ; increasing ‘j’ by 1 where ‘j’ has not reached 7 (S 713 =No) in operation S 714 . Where T has reached 7 (S 713 =Yes), the method proceeds to operation S 720 . In operation S 720 , a programming operation is performed under the control of control logic  400 . 
     After the programming operation, operation S 730  determines whether program state P 1  is passed. Where program state P 1  is not passed (S 730 =No), a verification operation is performed for program state P 1  in operation S 740 . Otherwise (S 730 =Yes), the method proceeds to operation S 770 . 
     In operation S 750 , the method determines whether program state P 1  is passed. Where program state P 1  is passed (S 750 =Yes), the method proceeds to operation S 760 . Otherwise (S 750 =No), the method proceeds to operation S 770 . 
     Operation S 760  is performed similar to the method of  FIG. 16 , in which the verification end points P(j)_Verify_End of remaining program states P 2  through P 7  are predicted. In particular, operation S 760  comprises setting ‘j’ to 2 in operation S 761 ; predicting a verification end point P(j)_Verify_End of a j-th program state in operation S 762 ; determining whether ‘j’ has reached 7 in operation S 763 ; and increasing ‘j’ by 1 in operation S 764  if ‘j’ has not reached 7 (S 763 =No). After the verification end points P(j)_Verify_End of the remaining program states P 2  through P 7  are predicted in operation S 760 , the method proceeds to operation S 770 . 
     In operation S 770 , ‘j’ is set to 2 to indicate program state P 2 . Then, in operation S 780 , the method determines whether a current program loop i_PGM_Loop is between the verification start point P(j)_Verify_Start of program state P(j) and the verification end point P(j)_Verify_End of program state P(j). If so, the verification operation of program state P(j) is performed in the current program loop. Otherwise, it is omitted. Where operation S 780  determines that the current program loop i_PGM_Loop is greater than or equal to the verification start point P(j)_Verify_Start of program state P 2  and less than or equal to the verification end point P(j)_Verify_End of program state P 2  (S 780 =Yes), the method proceeds to operation S 790 . Otherwise, the method proceeds to operation S 800 . In operation S 790 , the verification operation of program state P 2  is performed, and the method proceeds to operation S 800 . 
     Operation S 800  determines whether ‘j’ has reached 7 indicating program state P 7 . Where T has not reached 7 (S 800 =No), ‘j’ is increased by 1 in operation S 810 , and the method returns to operation S 780 . Otherwise (S 800 =Yes), the method proceeds to operation S 820 . Operation S 820  determines whether the all program states are passed. Where not all program states are passed (S 820 =No), operation S 830  is performed to increase the variable i_PGM_Loop by 1, and the method then returns to operation S 720 . Otherwise (S 820 =Yes), the method ends. 
       FIGS. 26A and 26B  are flowcharts illustrating a method of programming a flash memory device according to yet another embodiment of the inventive concept. 
     In the method of  FIGS. 26A and 26B , it is assumed that 3-bit data is stored in each memory cell using one erased state E and seven program states P 1  through P 7 . In addition, the method of  FIGS. 26A and 26B  can use the scheme for predicting the verification start point as described above with reference to  FIG. 10  and the scheme for predicting the verification end point as described above with reference to  FIG. 20 . A verification operation for fast bits is skipped according to the verification start point predicting scheme, and a verification operation for slow bits is skipped according to the verification end point predicting scheme. 
     Referring to  FIG. 26A , operation S 900  is performed upon initiation of a programming operation. Operation S 900  sets a variable i_PGM_Loop to ‘1’, and sets variables P(j)_Verify_Start and P(j)_Verify_End as maximum program loop times Max_PGM_Loop. The variable i_PGM_Loop indicates a current program loop, and the variable P(j)_Verify_End indicates a verification end point for a j-th program state. Next, in operation S 910 , the verification start points of the program states (e.g., P 1  through P 7 ) are predicted on the basis of pass bit information (e.g., a program voltage or a program loop) that is detected in a previous page or step programming operation. More specifically, operation S 910  comprises setting a variable ‘j’ as 1 in operation S 911 ; predicting a verification start point of program state P 2  in operation S 912 ; determining whether ‘j’ has reached 7 indicating program state P 7  in operation S 913 ; and increasing ‘j’ by 1 where ‘j’ has not reached 7 (S 913 =No) in operation S 914 . Where ‘j’ has reached 7 (S 913 =Yes), the method proceeds to operation S 920 . 
     In operation S 920 , a programming operation is performed on selected memory cells. Then, in operation S 930 , ‘j’ is set to 1. Next, in operation S 940 , the method determines whether the predicted verification start point of program state P 1  is less than or equal to a current program loop i_PGM_Loop. Where the current program loop i_PGM_Loop is less than the verification start point P(j)_Verify_Start of program state P 1 , the verification operation of program state P 1  is omitted. Where the current program loop i_PGM_Loop is greater than or equal to the verification start point P(j)_Verify_Start of program state P 1 , the verification operation of program state P 2  is performed. 
     Where the current program loop i_PGM_Loop is greater than or equal to the verification start point P(j)_Verify_Start of program state P 1  (S 940 =Yes), the method proceeds to operation S 950 . Otherwise (S 940 =No), the method proceeds to operation S 960 . 
     In operation S 950 , a verification operation is performed for program state P 1  and the number of fail bits for program state P 1  is counted. Like the method of  FIG. 20 , where the number of fail bits for program state P 1  is less than or equal to a reference value, program state P 1  is deemed to be passed. Following operation S 950 , the method proceeds to operation S 960 . 
     In operation S 960 , the method determines whether ‘j’ has reached a value of 7 indicating program state P 7 . Where ‘j’ has not reached 7 (S 960 =No), operation S 970  is performed to increase ‘j’ by 1, and the method returns to operation S 940 . Otherwise, (S 960 =Yes), the method proceeds to operation S 980 . In operation S 980 , the method determines whether all of program states P 1  through P 7  are passed. Where not all of program states are passed (S 980 =No), the variable i_PGM_Loop is increased by 1 in operation S 990  and the method returns to operation S 920 . Otherwise (S 980 =Yes), the method ends. 
       FIG. 27  is a flowchart illustrating a method of programming a flash memory device according to yet another embodiment of the inventive concept. 
     First of all, in operation S 1000 , variables FBCPS and Pi_FLAG are set to ‘1’. The variable FBCPS indicates a program state where a fail bit count operation is performed, and the variable Pi_FLAG is used to indicate the passed status of a program state where a verification operation has been performed. 
     A programming operation is performed in operation S 1100 . Further, in operation S 1100 , fail bit counting on a program state corresponding to a value of the variable FBCPS may be made. Assuming that a current program loop is a first program loop, the fail bit counting may be made with respect to a first program state P 1 . Since a current program is a first program loop, the fail bit counting may be made based on program data bits stored in a read/write circuit  500  (refer to  FIG. 1 ). If a current program loop is a second program loop, the fail bit counting may be made based on data bits read at a verification operation of a previous program loop. 
     In operation S 1200 , there is checked whether the counted fail bit number is less than a predetermined reference value. If the counted fail bit number is less than the predetermined reference value, the method proceeds to operation S 1300 . In operation S 1300 , fail bits corresponding to the program state P 1  are set to a program-inhibit value (for example, ‘1’). This means that memory cells corresponding to the program state P 1  are program inhibited at a next program loop although a program voltage is applied to the memory cells of fail bits corresponding to the program state P 1 . Further, in operation S 1300 , the variable Pi_FLAG is set to indicate a pass status, and the variable FBCPS is increased by 1. As the variable FBCPS is increased, fail bit counting may be made with respect to a next program state P 2 , instead of the program state P 1 . Where the variable Pi_FLAG is set to indicate a pass status, a verification operation is omitted with respect to a program state (for example, P 1 ) corresponding to a value of the variable Pi_FLAG. Afterwards, the method proceeds to operation S 1400 . 
     Returning to operation S 1200 , if the counted fail bit number is not less than the predetermined reference value, the method proceeds to operation S 1400 . In operation S 1400 , a verification operation is performed with respect to program states other than a program state being passed, respectively. For example, in the event that P 1 _FLAG is set to a pass status, a verification operation is performed with respect to remaining program states other than a program state P 1  corresponding to the P 1 _FLAG, respectively. Where no program state being passed exists, a verification operation is performed with respect to all program states in operation S 1400 , respectively. 
     Operation S 1500  determines whether all program states are passed. If at least one program state is not passed, the method proceeds to operation S 1600 , in which a program loop number is increased by 1. Afterwards, the method proceeds to operation S 1100 . Where all program states are passed, the method ends. 
     With the above-described method, a fail bit count operation is performed using a verification result of a previous program loop while a programming operation is being performed at a current program loop (or, while a program voltage is being applied to a selected word line). For this reason, although a counted fail bit number is determined to be less than a predetermined reference value, a program voltage is applied once more to memory cells corresponding to fail bits at the current program loop. As a result, that the number of fail bits corresponding to a program state to be omitted (or, skipped) is decreased. 
     In an exemplary embodiment, the same reference value is utilized with respect to all program states in order to judge whether each program state is passed. But, it is possible to apply different reference values to program states (or, pages in each row) in order to judge whether corresponding program states are passed. 
       FIG. 28  is a diagram illustrating a verification scheme used in the method of  FIG. 27  according to an embodiment of the inventive concept. 
     As described above, a bit count operation on a first program state P 1  is performed until the number of fail bits (or, called slow bits) becomes less than a predetermined reference value. At this point, a fail bit count operation on remaining program states is not performed. A bit counting operation on a program state corresponding to a variable FBCPS is performed during a programming operation in which a program voltage is applied to selected memory cells. 
     For example, as illustrated in  FIG. 28 , a verification operation is performed with respect to program states P 1 , P 2 , and P 3  at an Nth program loop. A fail bit count operation on the program state P 1  is performed during a programming operation of a (N+1)th program loop, based on data bits corresponding to the program state P 1  read at a verification operation of the Nth program loop. If a counted fail bit number FBC is more than a predetermined reference value, a fail bit count operation on the program state P 1  is again performed during a programming operation of a (N+2)th program loop. If the counted fail bit number FBC is determined to be less than the predetermined reference value at the (N+2)th program loop, fail bits among data bits corresponding to the program state P 1  are set to a program-inhibit value, and a verification operation on the program state P 1  is omitted after the following program loops including a current program loop (for example, the (N+2)th program loop). When the program state P 1  is passed, as illustrated in  FIG. 28 , a fail bit count operation is performed with respect to a next program state P 2 . 
     As understood from the above description, a program voltage is applied to memory cells corresponding to fail bits once more after a counted fail bit number is determined to be less than a predetermined reference value. This means that the number of fail bits corresponding to a program state to be omitted (or, skipped) is decreased. 
     In an exemplary embodiment, in case of the highest program state, if a counted fail bit number is determined to be less than a predetermined reference value, it is possible to prevent a further program voltage from being applied to memory cells corresponding to fail bits. 
       FIG. 29  is a flowchart illustrating a method of programming a flash memory device according to yet another embodiment of the inventive concept. 
     A program method in  FIG. 29  is substantially identical to that illustrated in  FIG. 27  except that step S 1700  of judging whether all program states are passed can be made before step S 1800  of performing verification operation on program states other than a program state being passed. Description for a program method in  FIG. 29  is thus omitted. 
       FIG. 30  is a flowchart illustrating a method of programming a flash memory device according to yet another embodiment of the inventive concept. 
     First of all, in operation S 2000 , variables FBCPS and Pi_FLAG are set to ‘1’. The variable FBCPS indicates a program state where a fail bit count operation is performed, and the variable Pi_FLAG is used to indicate the passed status of a program state where a verification operation has been performed. 
     A programming operation is performed in operation S 2100 . In operation S 2200 , there is checked whether a counted fail bit number is less than a predetermined reference value. As will be described later, the counted fail bit number is maintained by control logic  400  in  FIG. 1 . As a fail bit number of a previous program loop, for example, the counted fail bit number may be set to a default value more than a predetermined reference value. If the counted fail bit number is less than the predetermined reference value, the method proceeds to operation S 2300 . In operation S 2300 , fail bits corresponding to the program state P 1  are set to a program-inhibit value (for example, ‘1’). This means that memory cells corresponding to the program state P 1  are program inhibited at a next program loop although a program voltage is applied to the memory cells of fail bits corresponding to the program state P 1 . Further, in operation S 2300 , the variable Pi_FLAG is set to indicate a pass status, and the variable FBCPS is increased by 1. As the variable FBCPS is increased, a fail bit counting may be made with respect to a next program state P 2 , instead of the program state P 1 . Where the variable Pi_FLAG is set to indicate a pass status, a verification operation is omitted with respect to a program state (for example, P 1 ) corresponding to a value of the variable Pi_FLAG. Afterwards, the method proceeds to operation S 2400 . 
     Returning to operation S 2200 , if the counted fail bit number is not less than the predetermined reference value, the method proceeds to operation S 2400 . In operation S 2400 , a verification operation is performed with respect to program states other than a program state being passed, respectively. For example, in the event that P 1 _FLAG is set to a pass status, a verification operation is performed with respect to remaining program states other than a program state P 1  corresponding to the P 1 _FLAG, respectively. Where no program state being passed exists, a verification operation is performed with respect to all program states in operation S 2400 , respectively. Further, in operation  2400 , a fail bit count operation is performed on a program state corresponding to the variable FBCPS. The counted fail bit number is stored in the control logic  400 . The counted fail bit number is used as a fail bit number of a previous program loop in operation S 2200 . 
     Operation S 2500  determines whether all program states are passed. If at least one program state is not passed, the method proceeds to operation S 2600 , in which a program loop number is increased by 1. Afterwards, the method proceeds to operation S 1100 . Where all program states are passed, the method ends. 
     With the above-described method, a verification operation on a program state is omitted using a verification result of a previous program loop after a programming operation is performed at a current program loop. For this reason, although a counted fail bit number is determined to be less than a predetermined reference value, a program voltage is further applied to memory cells corresponding to fail bits at the current program loop. As a result, that the number of fail bits corresponding to a program state to be omitted (or, skipped) is decreased. 
     In an exemplary embodiment, the same reference value is utilized with respect to all program states in order to judge whether each program state is passed. But, it is possible to apply different reference values to program states (or, pages in each row) in order to judge whether corresponding program states are passed. 
       FIG. 31  is a diagram illustrating a verification scheme used in the method of  FIG. 29  according to an embodiment of the inventive concept. 
     As described above, a bit count operation on a first program state P 1  is performed until the number of fail bits (or, called slow bits) becomes less than a predetermined reference value. At this point, a fail bit count operation on remaining program states is not performed. A bit counting operation on a program state corresponding to a variable FBCPS is performed during a programming operation in which a program voltage is applied to selected memory cells. 
     For example, first of all, a program voltage is applied to selected memory cells. And then, as illustrated in  FIG. 31 , whether a fail bit number is less than a predetermined reference value is checked before a verification operation is performed. If the fail bit number is not less than the predetermined reference value, a verification operation is performed with respect to program states P 1 , P 2 , and P 3  at an Nth program loop. A fail bit count operation on the program state P 1  is performed during the Nth program loop, based on data bits corresponding to the program state P 1  read at a verification operation of the Nth program loop. The counted fail bit number may be retained by control logic  400  in  FIG. 1 . 
     If a (N+1)th program loop is performed, a program voltage is applied to selected memory cells. And then, whether a fail bit number is less than a predetermined reference value is checked before a verification operation of the (N+1)th program loop is performed. The counted fail bit number may be retained by the control logic  400  in  FIG. 1 . 
     If the counted fail bit number FBC is determined to be less than the predetermined reference value at the (N+2)th program loop, fail bits among data bits corresponding to the program state P 1  are set to a program-inhibit value, and a verification operation on the program state P 1  is omitted after the following program loops including a current program loop (for example, the (N+2)th program loop). As the program state P 1  is passed, as illustrated in  FIG. 31 , a fail bit count operation is performed with respect to a next program state P 2 . 
     As understood from the above description, a program voltage is applied to memory cells corresponding to fail bits once more after a counted fail bit number is determined to be less than a predetermined reference value. This means that the number of fail bits corresponding to a program state to be omitted (or, skipped) is decreased. 
     In an exemplary embodiment, in case of the highest program state, if a counted fail bit number is determined to be less than a predetermined reference value, it is possible to prevent a further program voltage from being applied to memory cells corresponding to fail bits. 
       FIG. 32  is a flowchart illustrating a method of programming a flash memory device according to yet another embodiment of the inventive concept. 
     A program method in  FIG. 32  is substantially identical to that illustrated in  FIG. 30  except that operation S 2700  of judging whether all program states are passed can be made before operation S 2800  of performing verification operation on program states other than a program state being passed. Description for a program method in  FIG. 32  is thus omitted. 
     As described in  FIGS. 16 to 21 and 27 to 30 , there is omitted (or, skipped) a verification operation for a program state determined to be passed. This means that although a program voltage is applied to a word line, memory cells corresponding to the program state(s) determined to be passed are program inhibited. In other words, program Inhibiting of memory cells corresponding to a slow bit (or a fail bit) may be made in two manners: the first program inhibiting manner being described in  FIGS. 16 to 21  and the second program inhibiting manner being described in  FIGS. 27 to 30 . 
       FIG. 33  is a block diagram illustrating an integrated circuit card comprising a flash memory device according to an embodiment of the inventive concept. 
     Referring to  FIG. 33 , an integrated circuit, such as a smart card, comprises a nonvolatile memory device  1000  and a controller  2000 . Nonvolatile memory device  1000  is the substantially same as that illustrated in  FIG. 1 , and so a detailed description thereof will be omitted in order to avoid redundancy. Controller  2000  controls nonvolatile memory device  1000  and comprises a central processing unit (CPU)  2100 , a read only memory (ROM)  2200 , a random access memory (RAM)  2300 , and an input/output (I/O) interface  2400 . CPU  2100  controls the overall operation of the integrated circuit card according to various programs stored in ROM  2200 , and input/output interface  2400  interfaces with external devices. Controller  2000  stores information indicating a pass bit that is detected during the programming operation of nonvolatile memory device  1000  and provides the information indicating the detected pass bit to nonvolatile memory device  1000 . The information can be used to determine verification start points in one or more of the above-described methods. 
       FIG. 34  is a diagram illustrating a computing system comprising a flash memory device according to an embodiment of the inventive concept. The computing system can take a variety of forms, such as a cellular phone, personal digital assistant, digital camera, portable game console, MP3 player, high definition television, digital video disk, router, global positioning system (GPS), and many others. 
     Referring to  FIG. 34 , the computing system comprises a processing unit  3100 , a user interface  3200 , a modem  3300  such as a baseband chipset, a memory controller  3400 , and a flash memory device  3500 , which are electrically connected to each other via a bus  3001 . Flash memory device  3500  is substantially the same as the flash memory device of  FIG. 1  and performs a programming operation using an adaptive verification scheme, such as those described above. Accordingly, a further description of flash memory device  3500  will be omitted to avoid redundancy. N-bit data (N≧1), which has been processed or is to be processed by processing unit  3100 , is stored in flash memory device  3500  through memory controller  3400 . Where the computing system is a mobile device, it may further comprise a battery  3600  for supplying the operation voltage of the computing system. Although not shown, the computing system can further comprise an application chipset, a camera image processor (CIS), or a mobile dynamic random access memory (DRAM). The memory controller and the flash memory device can form a solid state drive (SSD) that uses a nonvolatile memory for storing data. 
       FIG. 35  is a block diagram illustrating memory controller  3400  of  FIG. 32  according to an embodiment of the inventive concept. 
     Referring to  FIG. 35 , memory controller  3400  stores data in a storage medium and reads data from the storage medium. The controller comprises a host interface  4100 , a memory interface  4200 , a processing unit  4300 , a buffer memory  4400 , and an error correction code unit  4500 . Host interface  4100  interfaces with external devices, such as a host, and memory interface  4200  interfaces with the storage medium. Processing unit  4300  controls the overall operation of memory controller  3400 . Buffer memory  4400  temporarily stores data to be stored in the storage medium or data that is read from the storage medium. Buffer memory  4400  can also be used as the working memory of processing unit  4300 . Buffer memory  4400  can be used to store pass bit information that is output from a flash memory device. Error correction code unit  4500  detects and corrects errors in data that is read from the storage medium. Memory controller  3400  further comprises a ROM  4600  for storing code data. 
     In some embodiments, memory cells are configured with variable resistance memory cells. Examples of variable resistance memory cells and memory devices including variable resistance memory cells are disclosed in U.S. Pat. No. 7,529,124, which is hereby incorporated by reference. 
     In some embodiments, memory cells are implemented using one of various cell structures having a charge storage layer. A cell structure having a charge storage layer can include, for instance, a charge trapping flash structure using a charge trapping layer, a stack flash structure comprising arrays stacked in multi layers, a flash structure having no source-drain, and a pin-type flash structure. Examples of memory devices having a charge trapping flash structure as a charge storage layer are disclosed in U.S. Pat. No. 6,858,906, U.S. Patent Publication No. 2004-0169238, and U.S. Patent Publication No. 2006-0180851, which are hereby incorporated by reference. An example of a flash structure having no source-drain is disclosed in Korea Patent No. 673,020, which is hereby incorporated by reference. 
     Devices according to various embodiments of the inventive concept can be mounted in any of several types of packages. For example, the above-described flash memory devices and/or memory controllers can be mounted in package types such as package on package (PoP), ball grid arrays (BGAs), chip scale package (CSP), plastic leaded chip carrier (PLCC), plastic dual in-line package (PDIP), die in waffle pack (DIWP), die in wafer form (DIWF), chip on board (COB), ceramic dual in-line package (CERDIP), plastic metric quad flat pack (MQFP), small outline package (SOP), shrink small outline package (SSOP), thin small outline package (TSOP), thin quad flat pack (TQFP), system in package (SIP), multi-chip package (MCP), wafer-level stack package (WLSP), die in wafer form (DIWF), die on waffle package (DOWP), wafer-level fabricated package (WFP) and wafer-level processed stack package (WSP). 
     As indicated by the foregoing, in various embodiments of the inventive concept, by omitting verification operations before verification start points corresponding to programming states, programming performance can be improved. Moreover, by omitting verification operations after verification end points of programming states, programming performance can be improved. 
     The foregoing is illustrative of embodiments and is not to be construed as limiting thereof. Although a few embodiments have been described, those skilled in the art will readily appreciate that many modifications are possible in the embodiments without materially departing from the novel teachings and advantages of the inventive concept. Accordingly, all such modifications are intended to be included within the scope of the inventive concept as defined in the claims.