Memory Testing Algorithm

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    Memory Fault Models and

    Testing Algorithms

    Hardik Doshi

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    Memory Functional Faults

    Stuck at Faults (SAF)

    Transition Faults (TF)

    Coupling Faults (CF) Neighborhood Pattern Sensitive Faults (NPSF)

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    Stuck at Faults (SAF)

    The logic value of a cell or line is stuck at always 0 or 1.

    Stuck at 0 (SA0) If stuck at always is 0 logic value.

    Stuck at 1 (SA1) if stuck at always is 1 logic value.

    From each cell, a 0 and 1 must be read.

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    Stuck at Fault

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    Transition Fault (TF)

    A special case of SAF is Transition Fault (TF).

    A cell or line which fails to undergo a from 0 to 1 when it is

    written is said to contain an up transition fault .

    A cell or line which fails to undergo a from 1 to 0 when it is

    written is said to contain an down transition fault.

    Each cell must undergo a transition and a transition, andbe read after each transition before any further transitions.

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    Transition Fault (TF)

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    transition fault

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    Coupling Faults (CF)

    Write Operation which transits or in one cellchanges the contents of a second cell.

    Ci coupled to Cj means that an transition incell j causes or transition in cell i.

    Inversion Coupling Faults (Cfin)

    Idempotent Coupling Faults (Cfid)

    Bridging and State Coupling Faults

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    State Transition Diagram of Two Good

    Cells, iand j

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    Sij represent the state of cell i and j.

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    Inversion & Idempotent Coupling Faults

    An or transition in one cell inverts thecontents of the second cell is called inversion

    coupling cell (Cfin).

    Ci is coupled to Cj means transition inCj inverts the content of the Ci.

    Ci Cj coupled to Cj means transition inCj inverts the content of the Ci.

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    Inversion Coupling Cfin

    Sij represent the state of cell i and j

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    Coupling Fault (CF)

    A CF is called Asymmetric fault when the coupled cell only undergoes from0 to 1 or a 1 to 0 transition due to fault.

    A CF is called Symmetric fault when the coupled cell undergo both from 0 to1 and from 1 to 0 due to fault.

    The Cfid is asymmetric fault and the Cfin is a symmetric fault.

    A CF is called one way CF if the CF is sensitized only upon one transition ofthe coupling cell.

    A CF is called two way CF if the CF is sensitized upon either transition of thecoupling cell.

    Single Cfid is a one way, asymmetric CF.

    Combination of the Cfids and is a two way asymmetric CF. 11

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    Idempotent Coupling Fault(Cifd)

    An or transition in one cell force thecontents of the second cell to a particular

    value 0 or 1 is called inversion coupling cell

    (Cfid).

    Ci is coupled to cj means transition in cell j would make 0 in cell i.

    Ci Cj , Ci Cj, Ci Cj12

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    Idempotent Coupling Fault Cfid

    Sij represent the state of cell i and j

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    Neighborhood Pattern Sensitive Faults(NPSF)

    The content of a cell is influenced by the contents of all other cells in thememory. The content consists of a pattern of 0s and 1s, or changes inthese contents.

    Its also considered as K-coupling fault.

    Active NPSF

    Passive NPSF

    Static NPSF

    Memory Array

    b : Base cell

    d : Deleted Neighborhood cell

    b+d : Neighborhood

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    d

    d b d

    d

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    Active NPSF

    The base cell changes its contents due to a change in the

    deleted neighborhood pattern.

    This transition is in only one deleted neighbor cell whileother neighbor and bas cell contain a certain pattern.

    Example Ci,j

    where Ci,j is location of base cell.

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    Passive & Static NPSF (PNPSF & SNPSF)

    The content of the base cell cant be changed due tocertain deleted neighborhood pattern.(PNPSF)

    The content of the base cell is forced to certain state dueto certain deleted neighborhood pattern.(SNPSF)

    Ci,j < 0,0,1,1; /x >

    Ci,j < 0,1,0,0; -/0 >

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    Address Decoder Faults (AF)

    Fault 1 Ax

    Fault 2 Cx

    Fault 3 Cx

    Ay Cy

    Fault 4 AxAy Cx

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    Address Decoder Fault Combinations(AF)

    Fault A:- (1+2) Ax Cx

    Fault B:- (1+3) Ax Cx

    Ay Ay Fault C:- (2+4) Ax Cx

    Ay Cy

    Fault D:- (3+4) Ax Cx

    Ay Cy

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    Condition for detection AF

    The in a march element indicates thepresence of read or write operations.

    1. (rx,,wx)

    2. (rx,,wx)

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    Linked and Unlinked Faults

    When the fault may influence the behavior of the other

    faults is called Linked Faults.

    When the fault does not influence the behavior of otherfaults called Unlinked Faults.

    SAF linked with TFs and CFs

    TFs linked with CFs

    Afs linked with SAFs/TFs/CFs

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    Zero-One

    (w0);(r0);(w1);(r1);

    This test algorithm has minimum set to detect

    the fault

    All SAFs are detectable.

    TF is not detectable.

    CFs , and are not detectable.

    Not all Afs are detectable.

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    Checkerboard

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    Cells are divided in two groups cell-1 & cell-2.

    0s and 1s are written alternate pattern and make the

    checkerboard pattern.

    All SAFs are detectable.

    Not all Afs ,TFs and CFs are detectable.

    Mainly used for sleeping sickness in DRAM chip.

    Pattern 1 Pattern 2

    1 0 1 0

    0 1 0 1

    1 0 1 0

    0 1 0 1

    0 1 0 1

    1 0 1 0

    0 1 0 1

    1 0 1 0

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    Walking 1/0

    Memory is filled with 0s(or 1s) except for the base-cell, whichcontains 1(respectively a 0).

    During Test, the base cell walks through the memory.

    All cells read with the base cell last.

    All Afs, SAF, TFs, Coupling faults are detectable.

    0 0 0 0

    0 1 0 0

    0 0 0 0

    0 0 0 0

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    GALPAT

    Memory is filled with 0s(or 1s) except for the base-cell,which contains 1(respectively a 0).

    During Test, the base cell walks through the memory.

    Base cell is read after each cell of memory read.

    0 0 0 0

    0 1 0 0

    0 0 0 0

    0 0 0 0

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    Sliding Diagonal

    Uses diagonal of base cell instead of single base cell because eachcell has a different row and column address so that it checking the

    row and column simultaneously.

    Writes diagonal 1s to background of 0s. All memory cells are read,after which diagonal is shifted until all diagonal are not covered.

    1 0 0 0 0 0 1 0

    0 1 0 0 0 0 0 1

    0 0 1 0 1 0 0 0

    0 0 0 1 0 1 0 0

    First Diagonal Third Diagonal

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    MATS Algorithm MATS requires total 4*n operations.

    (w0); (r0,w1); (r1) ;

    M0 M1 M2

    M0=(w0); M1=(r0,w1); M2=(r1);

    M0:for :=0 to n-1 do

    begin

    A[i]:=0;

    end; Same for M1 and M2;

    Fault coverage is very poor not capable of detection of

    Coupling Faults.

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    Moving 1/0 Algorithm

    (w0); (r0,w1,r1); (r1,w0,r0); (w1); (r1,w0,r0);(r0,w1,r1); Here ji (;) Operation Cj Ci

    M5 on Cj r0 0 0

    M5 on Cj w1 1 1

    M5 on Cj r1 1 1

    M5 on Ci r0 1 1

    j

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    MATS++ Algorithm

    (w0);(r0,w1);(r1,w0,r0);

    SAFs :- (M1) and (M2)

    TFs :- (M1 and M2) and (M2) Afs are detected by given above conditions.

    This algorithm cant detect any coupling faults.

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    March X Algorithm

    (w0);(r0,w1);(r1,w0)(r0);

    All Afs are detected.

    SAF :- (M1 or M3) and (M2)

    TFs :- (M1 followed by M2) and (M2 followed by M3)

    Cfin (ji) :- Ci Cj detected by M1 followed by M2

    Ci Cj detected by M2 Idempotent faults ,(only when j

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    March C- Algorithm

    (w0);(r0,w1);(r1,w0);(r0,w1);(r1,w0);(r0);

    Unlinked Idempotent Coupling Faults(Cfid), SAF, TFS, Cfin, Afs.

    Ci Cj :- M3 followed by M4 and M1 followed by M2

    Ci is coupled to Cj means transition in j cell causes