1. 14. Memory testing Motivation for testing memories (4)
Modeling memory chips (6)
Reduced functional fault models (17)
Traditional tests (7)
March tests (7)
Pseudorandom memory tests (10)

2. 1.1 Importance of memories
Memories dominate chip area (94% of chip area in 2014)
Memories are most defect sensitive parts
Because they are fabricated with minimal feature widths
Memories have a large impact on total chip DPM level
Therefore high quality tests required
(Self) Repair becoming standard for larger memories (> 1 Mbit)
% of chip area
year

3. 1.2 Memory chip cost over time
Price of high-volume parts is constant in time; except for inflation
Note: Slope of line matches inflation!
Dollars per DRAM chip

4. 1.3 Table with test times
Note: A memory is tested with several algorithms, which together may go through the total address space over 100 times
 Effective test time for 16 Mb DRAM, using O(n) tests, is about 168 s
Test time reduced using on-chip parallelism (DFT and BIST)

5. 1.4 Problems with testing memories
Number of bits/chip increases exponentially (4*in <3 years)
Price/bit decreases exponentially
Test cost has to decrease exponentially as well
Older traditional tests were of O(n2)
Current tests have to be of O(n) or less
DFT and BIST used to reduce test time to about O(n)
Area/cell decreases exponentially
Line widths decrease (more: opens, resistance)
Line distances decrease (more: shorts, couplings)
Cell leakage increases with reduced threshold voltages
Consequence
More complex fault behavior
More global fault behavior (ground bounce, coupling effects)
 Result: Number of bits to be tested increases exponentially, fault
behavior becomes more complex, while test cost has to be same

6. 2.1 Functional SRAM memory model
Fig. 4.2 pag. 35

7. 2.2 Electrical SRAM cell model
Structure of a CMOS SRAM cell (left cell below)
Q1--Q3 and Q2--Q4 form inverters (Q3 and Q4 are the load devices)
Inverters are cross coupled to form a latch
Q5 and Q6 are pass transistors
Addressing of a cell uses
a row address (using the word line WL)
a column address (using the bit lines BL and BL*)
Operations
Write: precharge BLs; drive BL, BL* and WL
Read: precharge BLs; drive WL; feed BLs to sense amplifiers BL WL
CMOS
SRAM
Cell
VDD
VSS Q3 Q4 Q5 Q6 Q1 Q2 BL
VDD
VSS WL Q5 Q6 Q1 Q2
L1 L2
SRAM
Cell with
Polysilicon
Load Devices
L1 and L2

8. 2.3 Electrical DRAM cell model
DRAM cell stores information as a charge in a capacitor
Cell capacitance  40 fF = 40* F; BL capacitance  300 fF!
(SRAM cell stores information in terms of the state of a latch)
This charge leaks away over time
DRAMs require refresh circuitry (Refresh rate:  64 ms)
DRAM cells require 1/4th the area of SRAM cells
DRAM cells dissipate less power (thicker gate oxide)
DRAMs are less sensitive to Soft Errors
DRAMs are slower
Operations
Read: precharge BL; drive WL;
feed BL to sense amplifier
Write: drive BL; drive WL
Vcc BL WL
Cell capacitor

9. Example of a simple k-input decoder
2.4 Decoders
Decoders address a specific cell in the Memory Cell Array ‘MCA’
If the MCA would be a vector, then 1 Mbit MCA requires 1M WLs
By arranging the cells in the MCA in a two-dimensional structure,
a 1 Mbit MCA requires 1K WLs and 1 K BLs
This is a significant reduction in the decoder area!
Hence, the MCA is two dimensional and consists of rows and columns
The Column decoder selects a particular Column
The Row decoder selects a particular Row
Decoders may be simple logic gate structures
Example of a simple k-input decoder

10. 2.5 Read/write drivers The write driver can be rather simple
The data-to-be-written is presented on BL
The inverse data-to-be-written is presented on BL*
The sense amplifier can be
a simple inverter; e.g. for small arrays, which have strong signals
a differential amplifier; for larger arrays, which have weak signals

11. 2.6 The reduced functional model
For test purposes Functional model
reduced (simplified) to three blocks
The functional faults also reduced:
single-cell faults (SAFs, TFs, etc.)
two-cell faults (Coupling faults)
k-cell faults (NPSFs)
The functional fault models have
a hierarchy:
1. Stuck-at fault (SAF)
2. Transition fault (TF)
3a. Coupling fault (CF)
3b. Neighborhood pattern
sensitive fault (NPSF)
Address
Address decoder
Memory cell array
Read/write logic
Data

12. 3.1 Notation for describing faults
<…> describes a fault
<S/F> describes a single-cell fault
S describes the state/operation sensitizing the fault
A fault is sensitized when the fault effect is made present
F describes the fault effect in the victim cell (v-cell)
<S;F> describes a two-cell fault (a Coupling Fault)
S describes the state/operation of the aggressor cell (a-cell) sensitizing the fault
F describes the fault effect in the v-cell
Examples
</0>: a SA0 fault </1>: a SA1 fault
</0>: an  TF </1>: a  TF
<;0>: a CFid <;1>: a CFid
<;0>: a CFid <;1>: a CFid
1-cell fault <S/F> /
2-cell fault <S;F> ;

13. 3.2 Stuck-At Fault (SAF) S1 S0 S0 S1 w1 w0 Good cell w0 w1 SA0 fault
The logic value of a Stuck-At cell or line is always:
0: a SA0 fault
1: a SA1 fault
Only one fault (a SA0 or a SA1) can be present at a time
SAF fault type has two subtypes S1 w1 w0 S0
Good cell S0 w0 w1
SA0 fault S1 w0 w1
SA1 fault

14. 3.3 Stuck-Open Fault (SOpF)
SOpF: A cell cannot be accessed; e.g., due to an open in its WL
When a read operation is applied to a cell, the differential sense amplifier has to sense a voltage difference between BL and BL*
In case of an SOpF BL and BL* have the same (high) level
Output Sense Amplifier:
fixed value (SOpF behaves as a SAF)
previous value of sense amplifier
Detected when in a march element
a ‘0’ and ‘1’ is read. Required form of
the march element: (…,rx,…,rx*)
3. random (fault detected probabilistically)
Every read operation detects the SOpF with a probability of 50%
SOpF BL
VDD
VSS WL Q5 Q6 Q1 Q2
L1 L2

15. 3.4 Transition fault (TF) S0 S1 w1 S Q Cell with </0> TF Cell R
A cell fails to undergo the following transition(s):
Fails up-transition: a </0> TF
Fails down-transition: a </1> TF
Fault type has two subtypes: the </0> and the </1> TF
A single cell may contain both faults
The Set input may not work (e.g., SA0)
The Reset input may not work
Test: Every cell should make  and  transition and be read
Conceptual TF representation
Defect S1 w0 S0 w1
Cell with
</0> TF
Cell S R Q Q*

16. 3.5 Data retention fault (DRF)
DRF: A cell cannot retain its logic value
Typically caused by a broken pull-up device which causes the leakage current of the node with a logic 1 not to be replenished
After a time delay ‘Del’ (Typically: 100 ms  Del  500 ms) the cell will flip
The DRF fault type has two subtypes, which may be present simultaneously in the same cell: <1T/0> and <0T/1>
<1T/0> means that a logic 1 will become a logic 0 after a delay time T
DRF BL
VDD
VSS WL Q5 Q6 Q1 Q2
L1 L2

17. 3.6 Faults involving 2 cells: Coupling Faults ‘CFs’
CF: The state of, or an operation applied to, the a-cell (aggressor cell) forces or changes the state of the v-cell (victim cell)
Fault type Idempotent CF: CFid
A transition write operation (=0 1 & =10 change) applied to the a-cell forces the contents of the v-cell
CFid has 4 subtypes: <;0>, <;1>, <;0> and <;1>
The or  write operations to a-cell sensitize the fault
The ‘0’ or ‘1’ are the fault effect in the v-cell
In addition, each subtype has two positions:
A. address of a-cell < address of v-cell
B. address of a-cell > address of v-cell
a-cell
v-cell
<;0> A
v-cell
a-cell
<;0> B

18. 3.7 Coupling faults (CFst, CFin)
State CF (CFst): A CF whereby the state of the
a-cell forces a fixed value in the v-cell
Four fault subtypes : <1;0>, <1;1>, <0;0> and <0;1>
Each subtype has 2 positions:
addr. a-cell < addr. v-cell
addr. a-cell > addr. v-cell
Inversion CF (CFin): A transition write operation to the a-cell toggles the contents of the v-cell (Note:  denotes toggling)
Two fault subtypes exist: <;> and <;>
addr. a-cell < addr. v-cell
Note: CFin not a realistic fault
An SRAM cell is a latch, rather then a flip-flop
 Cannot toggle!

19. 3.8 Pattern sensitive fault (k-CF, PSF)
A k-Coupling Fault (k-CF), also called a Pattern Sensitive Fault (PSF), involves k cells which form a neighbourhood
The v-cell is also called the base cell
The k-1 non-v-cells are the deleted neighbourhood cells
The k cells can be anywhere in memory
Example: Active PSF
A CFid with k-2 enabling values
a = a-cell, v = v-cell, e = enabling cell
Neighbourhood PSFs (NPSFs) more realistic
The cells have to be physical neighbours
Example: Active NPSF (ANPSF)
a-cell sensitises fault in v-cell
iff e-cells have enabling state a e v
PSF a e v
NPSF

20. 3.9 Pattern sensitive fault (NPSFs)
A Neighbourhood PSF (NPSF) is a restricted k-CF
The deleted neighbourhood cells have to
be physically adjacent to the base cell
Active NPSF (ANPSF): A conditional CFid
A CFid requiring the k-2 e-cells to have
to have an enabling state
Passive NPSF (PNPSF): A conditional TF
A TF requiring the k-1 e-cells have
Static NPSF (SNPSF): A conditional CFst
A CFst whereby the k-2 e-cells have to
have an enabling state a e v
CFid e v TF a e v
CFst

21. 3.10 Validation of the fault models
R-defect
Probability
Performed by (Dekker, ITC’88) for SRAMs
8 K*8 = 64 Kbits, 4 Transistor (4T) cells
technology: 4 m (Note: R-defect is defect resistivity)
Distribution for R-defect values assumed to be uniform
i.e., no FAB statistics taken into account
Table shows likelihood of functional faults, as a function of the spot defect size
Results:
Two new fault models established: SOpF and DRF
SAFs  50%
CFs due to large spot defects
CFin not present!

22. 3.11 March tests: Concept and notation
A march test consists of a sequence of march elements
A march element consists of a sequence of operations applied to every cell, in either one of two address orders:
1. Increasing () address order; from cell 0 to cell n-1
2. Decreasing () address order; from cell n-1 to cell 0
Note: The  address order may be any sequence of addresses (e.g., 5,2,0,1,3,4,6,7), provided that the  address order is the exact reverse sequence (i.e, 7,6,4,3,1,0,2,5)
Example: MATS+ {(w0);(r0,w1);(r1,w0)}
Test consists of 3 march elements: M0, M1 and M2
The address order of M0 is irrelevant (Denoted by symbol )
M0: (w0) means ‘for i = 0 to n-1 do A[i]:=0’
M1: (r0,w1) means ‘for i = 0 to n-1 do {read A[i]; A[i]:=1}’
M2: (r1,w0) means ‘for i = n-1 to 0 do {read A[i]; A[i]:=0}’

23. 3.12 Combinations of memory cell faults
A memory may contain:
A single fault
Multiple faults (6 cases of CFs shown; ai is a-cell, vj is v-cell)) can be:
Unlinked: Faults do not interact (Cases a, b, c, e)
Linked: Faults do interact (Cases d, f)
Linked faults have a common victim a1 v1 v2 a2
Case a:
Case b:
Case c: v
Case d: a
Case e:
Case f:

24. 3.13 Linked coupling faults
Case a: Two unlinked CFids; detected by the march test
{(w0); (r0,w1);(w0,w1);(r1)}
M M M M3
<;1> CFid sensitized by w1 operation of M1
detected by r0 of M1
<;0> CFid sensitized by w1 of M2, detected by r1 of M3
Case b: Linked CFids
Cannot be detected by test of Case a (for unlinked CFids) because of masking
Linked faults require special, more complex, tests
March elements
Case b:
<;1>
Case a:
<;1>
<;0>
<;0> a1 v1 a2 v2 a1 a2
v1=v2

25. 3.14 Address decoder faults (AFs)
Functional faults in the address decoders:
A. With a certain address, no cell will be accessed
B. A certain address accesses multiple cells
C. A certain cell is accesses with multiple addresses
D. Certain cells are accessed with their own and other addresses
Difficult fault: Read operations may produce a random result
Fault A Ax Cx
Fault D Ay Cy
Fault C
Fault B
Reading from address Ay Ax
Cx=1 Ax
Cx=0 Ay
Cy=1 Ay
Cy=1

26. 3.15 Mapping read/write logic faults
The reduced functional model consists of three blocks
the address decoder
the memory cell array (MCA)
the read/write logic
Read/write logic faults can be mapped
onto MCA faults
SAFs, TFs and CFs will de
detected by tests for the MCA
Address
Address decoder
Memory cell array
Read/write logic
Data w2 x2 b2 z2 y2 x1 b1 z1

27. 3.16 Mapping address decoder faults
March tests for MCAFs detect AFs if they satisfy Cond. AF
Cond. AF: The march test has to contain the following march elements
1. (rx,…,wx*) This means either (r0,…,w1) or (r1,…,w0)
2. (rx*,…,wx) Note: ‘…’ means any # of r or w operations
Proof
Easy for Faults A, B and C
For Fault D the result of a read operation can be:
A deterministic function (Logical AND or OR) of read values
A random result (when the read cells contain different values)
Fault A Ax Cx
Fault D Ay Cy
Fault C
Fault B

28. 3.17 Mapping address decoder faults (cont.)
Fault D: read result random if cells contain different values
Cond. AF-1: (rx,…,wx*) detects Faults D1 & D2
When Ax written with x*, cells Cy...Cz are also written with x*
Fault detected when Cy is read: reads x* while expecting x
Cond. AF-2: (rx*,…,wx) detects Faults D1 & D3
When Ax written with x, cells Cv...Cw are also written with x
Fault detected when Cw is read: reads x while expecting x* . Av Cv Az Cz Ax Cx Aw Cw Ay Cy Az Cz Ax Cx Ay Cy Ax Ay Cx Cy
Fault D2 Av Cv Ax Cx Aw Cw
Original Fault D
Fault D3
Fault D1

29. 4.1 Functional RAM chip testing
Purpose
1. Cover traditional tests (5)
Zero-One (MSCAN)
Checkerboard
GALPAT and Walking 1/0
2. Cover tests for stuck-at, transition and coupling faults (6)
MATS and MATS+
March C-
March A and March B
3. Comparison of march tests (1)

30. 4.2 Fault coverage of tests
When a test detects faults of a particular fault type, it detects:
all subtypes of that type; e.g., if it detects TFs is has to detect all </0> and </1> TFs
all positions of each subtype (addr. a-cell < or > v-cell)
A complete test detects all faults it is designed for
It may, additionally, and unintentionally, detect also other faults
But not all subtypes and not all positions of each of these faults
Example: MATS+ : {(w0);(r0,w1);(r1,w0)}
Detects all AFs
Detects all SAFs
Detects all </0> TFs
Does not detect all </1> TFs
 MATS+ does not detect TFs
Fault coverage
of MATS+
</0> TFs
AFs, SAFs

31. 4.3 Traditional tests Traditional tests are older tests
Usually developed without explicitly using fault models
Usually they also have a relatively long test time
Some have special properties in terms of:
detecting dynamic faults
locating (rather than only detecting) faults
Many traditional tests exist:
1. Zero-One (Usually referred to as Scan Test or MSCAN)
2. Checkerboard
3. GALPAT and Walking 1/0
4. Sliding Diagonal
5. Butterfly
6. Many, many others

32. 4.4 Zero-One test (Scan test, (M)SCAN)
Minimal test, consisting of writing & reading 0s and 1s
Step 1: write 0 in all cells
Step 2: read all cells
Step 3: write 1 in all cells
Step 4: read all cells
March notation for Scan test: {(w0);(r0);(w1);(r1)}
Test length: 4*n operations; which is O(n)
Fault detection capability: AFs not detected
Condition AF not satisfied: 1. (rx,…,wx*) 2. (rx*,…,wx)
If address decoder maps all addresses to a single cell, then it can only be guaranteed that one cell is fault free
Special property: Stresses read/write & precharge circuits when Fast X addressing is used and sequence of write/read data in a column!
Fast X
addressing
Row
stripe
000000
111111
Checker
board
010101
101010
Columns
Rows

33. 4.5 Checkerboard
Is SCAN test, using checkerboard data background pattern
Step 1: w1 in all cells-W
w0 in all cells-B
Step 2: read all cells
Step 3: w0 in all cells-W
w1 in all cells-B
Step 4: read all cells
Test length: 4*2N operations; which is O(n)
Fault detection capability:
Condition AF not satisfied : 1. (rx,…,wx*); 2. (rx*,…,wx)
If address decoder maps all cells-W to one cell, and all cells-B to another cell, then only 2 cells guaranteed fault free
Special property: Maximizes leakage between physically adjacent cells. Used for DRAM retention test!! B W 1
Step1 pattern
Checkerboard
data background

34. 4.6 GALPAT and Walking 1/0
GALPAT and Walking 1/0 are similar algorithms
They walk a base-cell through the memory
After each step of the base-cell, the contents of all other cells is verified, followed by verification of the base-cell
Difference between GALPAT and Walking 1/0 is when, and how often, the base-cell is read
Walking 1/0
GALPAT
Base cell
Base cell

35. 4.7 GALPAT and Walking 1/0: Properties
Tests can locate faults
GALPAT detects write recovery faults (Cause: slow addr. decoders)
Test length: O(n2): Not acceptable for practical purposes
Most coupling faults in a memory are due to sharing
a WL and the column decoder: cells in the same row
BLs and row decoder: cells in the same column
Subsets of GALPAT and Walking I/O used (BC= Base-Cell)
GALROW and WalkROW: Read Action on cells in row of BC
GALCOL and WalkCOL: Read Action on cells in column of BC
Test length (assuming n1/2 rows and n1/2 columns): O(n3/2)
Note: Test time for 4Mb 150 ns memory
For O(n2) test = O(20 days), and for O(n3/2 ) test = O(14 sec.)
GALROW

36. 5.1 March tests
The simplest, and most efficient tests for detecting AFs, SAFs, TFs and CFs are march tests
The following march tests are covered:
MATS+
Detects AFs and SAFs
March C-
Detects AFs, SAFs, TFs, and unlinked CFins, CFsts, CFids
March A
Detects AFs, SAFs, TFs, CFins, CFsts, CFids, linked CFids (but not linked with TFs)
March B
Detects AFs, SAFs, TFs, CFins, CFsts, CFids, linked CFids

37. 5.2 MATS+ MATS+ algorithm: {(w0);(r0,w1);(r1,w0)} Fault coverage
AFs detected because MATS+ satisfies Cond. AF
(When reads, accessing multiple cells, return a random value)
Cond. AF: 1. (rx,…,wx*) and 2. (rx*,…,wx)
(1) satisfied by: (r0,w1) and (2) by: (r1,w0)
SAFs are detected: from each cell the value 0 and 1 is read
Test length: 5*n
Note: If fault model is symmetric with respect to 0/1, /,
and with respect to address a-cell < v-cell and address a-cell > v-cell,
then each march tests has 3 equivalent tests
0s  1s: {(w0);(r0,w1);(r1,w0)} {(w1);(r1,w0);(r0,w1)}
s  s: {(w0);(r0,w1);(r1,w0)} {(w0);(r0,w1);(r1,w0)}
0s1s,ss: {(w1);(r1,w0);(r0,w1)}{(w1);(r1,w0);(r0,w1)}

38. 5.3 March C- March C (Marinescu,1982): an 11*n algorithm
{(w0);(r0,w1);(r1,w0);(r0);(r0,w1);(r1,w0);(r0)}
It can be shown that middle ‘(r0)’ march element is redundant
March C- (van de Goor,1991): a 10*n algorithm
{(w0);(r0,w1);(r1,w0);(r0,w1);(r1,w0);(r0)}
M M M M M M5
Fault coverage of March C-
AFs: Cond. AF satisfied by M1 and M4, or by M2 and M3
SAFs: Detected by M1 (SA1 faults) and M2 (SA0 faults)
TFs: </0> TFs sensitized by M1, detected by M2 (and M3+M4)
</1> TFs sensitized by M2, detected by M3 (and M4+M5)
CFins detected
CFsts detected
CFids detected (see proof)

39. 5.4 March C- detects CFids
March C-: {(w0);(r0,w1);(r1,w0); (r0,w1);(r1,w0);(r0)}
M M M M M M5
Proof for detecting CFs are all similar. Analyze all cases:
Relative positions of a-cell and v-cell
1. address of a-cell < v-cell;
2. address of a-cell > v-cell
Fault subtype
a. CFid <;0>; b. CFid <;1>; c. CFid <;0>; d. CFid<;1>
Consider Case 1a: a-cell < v-cell and CFid <;0>
Fault sensitized by M3 and detected by M4
If the CFid <;0>a1 (a-cell is a1) is linked to CFid <;1>a2, and address of a2 < a1 then linked fault will not be detected
Reason: M3 will sensitize both faults, such that masking occurs
Linked fault
<;0>
<;1>
a2 a v
<;0> CFid
a v
Case 1a

40. 5.5 March A & March B March A algorithm (Suk,1981) M0 M1 M2 M3 M4
{(w0);(r0,w1,w0,w1);(r1,w0,w1);(r1,w0,w1,w0);(r0,w1,w0)}
M M M M M4
March A (Test length: 15*n) detects
AFs, SAFs, TFs, CFins, CFsts, CFids
Linked CFids, but not linked with TFs
March A is complete: detects all intended faults
March A is irredundant: no operation can be removed
March B algorithm (Test length: 17*n)
{(w0);(r0,w1,r1,w0,r0,w1);(r1,w0,w1);(r1,w0,w1,w0);(r0,w1,w0)}
M M M M M4
Detects all faults of March A
Detects CFids linked with TFs, because M1 detects all TFs

41. 5.6 Test requirements for detecting SOpFs
An SOpF is caused by an open WL which makes the cell inaccessible
To detect SOpFs, assuming a non-transparent sense amplifier, a march test has to verify that a 0 and a 1 has to be read from every cell
This will be the case when the march test contains the March Element ‘ME’ of the form: (…, rx, …, rx*, …), for x = 0 and x = 1.
This ME may be broken down into two MEs of the form: (…,rx,…) & (…, rx*,…), for for x = 0 and x = 1.
Example: The ME “(r0,w1,r1,w0,r0,w1)” satisfies the above requirement
Note: Any test can be changed to detect SOpFs by
making sure that the above requirement is
satisfied by possibly adding a rx and/or a rx*
operation to a ME
Example: MATS+ {(w0);(r0,w1);(r1,w0)}
becomes {(w0);(r0,w1,r1); (r1,w0,r0)}
SOpF BL
VDD
VSS WL Q5 Q6 Q1 Q2
L1 L2

42. 5.7 Test requirements for detecting DRFs
Any march test can be extended to detect DRFs
Every cell has to be brought into one state
A time period (Del) has to be waited for the fault to develop
Note: The time for Del is typically between 100 and 500 ms
The cell contents has to be verified (should not be changed)
Above three steps to be done for both states of the every cell
Example: MATS+ {(w0);(r0,w1);(r1,w0)}
becomes {(w0);Del;(r0,w1);Del;(r1,w0)}
DRF BL
VDD
VSS WL Q5 Q6 Q1 Q2
L1 L2

43. 6.1 Pseudo-Random ‘PR’ memory tests
Purpose
Explain concept of pseudo-random (PR) testing (1)
Compute test length of PR tests for SAFs and k-CFs (5)
Evaluation of PR tests (3)
PR pattern generators and test response evaluators (2)
Sources of material
Mazumder, P. and Patel, J.H. (1992). An Efficient Design of Embedded Memories and their Testability Analysis using Markov Chains. JETTA, Vol. 3, No. 3; pp
Krasniewski, A. and Krzysztof, G. (1993). Is There Any Future for Deterministic Self-Test of Embedded RAMs? In Proc. ETC’93; pp
van de Goor, A.J. (1998). Testing Semiconductor Memories, Theory and Practice. ComTex Publishing, Gouda, The Netherlands
van de Goor, A.J. and de Neef, J. (1999). Industrial Evaluation of DRAM Tests. In Proc. Design and Test in Europe (DATe’99), March 8-13, Munich; pp
van de Goor, A.J. and Lin, Mike (1997). The Implementation of Pseudo-Random Tests on Commercial Memory Testers. In Proc. IEEE Int. Test Conf., Washington DC, 1997, pp

44. 6.2 Concepts of PR memory testing
Deterministic tests
Control & Reference data for the RAM under test have predetermined values
The Response data of the RAM under test is compared with the expected data, in order to make Pass/Fail decision
Pseudo-random tests
Control data on some or all inputs established pseudo-randomly
Reference data can be obtained from a Reference RAM or, as shown, from as compressor
Reference data
generator
Control data
RAM
under test
Compara
tor
Response data
Pass/Fail
RAM
under test
Compres
sor
Control data
Response data
Reference data
generator
Reference
Compara
tor
Reference signature
Pass/Fail
Response signature

45. 6.3 Concepts of PR memory testing
Memory tests use
control values for:
Address lines (N)
R/W line (1)
write data values (B)
Deterministic test method
Uses deterministic control and write data values
In a test the following can be Deterministic (D) or PR (R)
The Address (A): DA or RA
The Write (W) operation: DW or RW
The Data (D) to be written: DD or RD
 MATS+ is a DADWDD (Det. Addr, Det. Write, Det. Data) test
In a PR test at least ONE component has to be PR
This can be: A (Addr.) &/or W (Write oper.) &/or D (Dat)
PR tests are preferred above random tests: PR tests are repeatable
Address
lines
RAM
under
test
Data
R/W line N 1 B

46. 6.4 Pseudo-random tests for SAFs
Some probabilities for computing the test length (TL)
The TL is a function of the escape probability ‘e’
p: probability that a line has the value 1
pa: probability that an address line has the value 1
pd: probability that a data line has the value 1
pw: probability that the write line has the value 1
pA: probability of selecting address A (with z 0s and N-z 1s)
pA = (1- pa)z * pa(N-z)
p1: probability of writing 1 to address A; p1 = pd * pw * pA
p0: prob. of writing 0 to address A; p0 =(1- pd )* pw * pA
pr: probability of reading address A; pr = (1- pw )* pA

47. 6.5 Test length of PR test for SAFs
Markov chain for detecting a SA0 fault (SA1 fault is similar)
S0 : state in which a 0 is stored in the cell
S1 : state in which a 1 should be in the cell
SD0 : state in which SA0 fault is detected (absorbing state)
pS0(t) : probability of being in state S0 at time t
Initial conditions: pS0(0) =1-pI1, pS1(0) = pI1 , pSD0(0) =0
pS0(t) = (1- p1)*pS0(t-1) + p0* pS1(t-1)
pS1(t) = p1*pS0(t-1) + (1- p0 -pr)* pS1(t-1)
pSD0(t) = pr*pS1(t-1) + pSD0(t-1)
1-(p0+pr) 1
1-p1 p0 p1 pr S0 S1
SD0

48. 6.6 Test length of PR test for SAFs
With deterministic testing fault detected with certainty
With PR testing fault detected with an escape probability ‘e’
SA0 fault is detected when: pSD0(t)  1-e; T0(e) is TL for SA0 faults
T(e): The test length for SAFs is: T(e) = max(T0(e),T1(e))
Test length coefficient: Independent of n & proportional with ln(e)
Test length coefficient

49. 6.7 Test length of PR tests for k-CFs
PR tests for k-CFids; the k cells may be located anywhere
For k =2 the test will be for CFids; for k >2 the for PSFs
To sensitize the CFid the k-2 cells require enabling value G
For k = 5, there are k-2 = 3 enabling cells
Assume G = 110 = g1g2g3 then pG = pd2*(1-pd)
Several PR tests for k-CFs exist (2 shown below)
DADWRD (Det. Addr., Det. Write, PR Data)
Step 1: (w?); Initialize memory with PR values
Step 2: repeat t times: (r?,w?); Read and write new PR value
Step 3: (r?); Perform a final read
RARWRD (PR Addr, PR Write, PR Data)
Step 1: (w1); Initialize memory
Step 2: repeat t times {Generate PR Addr.,
perform read with pr=1-pw or a write with pw}
CFid a e v

50. 6.8 Test length of PR tests for k-CFs
Test length coefficients Fault coverage of RARWRD tests
Note: k= Neigborhood Size
Observations
Number of operations roughly doubles if k increases by 1
The DADARD test is more time efficient
The RARWRD test will detect more unanticipated faults
(Faults of unexpected or unknown fault models)

51. 6.9 Test lengths: Deterministic -- PR tests
Observations
Note: ANPSFs have k-2 cells in only one position
For simple fault models deterministic tests more efficient
- Detect all faults of some fault models with e = 0
For complex fault models PR tests do exist
- PR tests detect all faults of all fault models, however with e > 0

52. 6.10 Strengths/weaknesses of PR tests
Deterministic tests based on a-priory fault models
Models usually restricted to the memory cell array
5% of real defects not explained (Krasniewski, ETC’93)
Tests detect 100% of targeted faults only
Pseudo-random tests
Not targeted towards a particular fault model
PR tests detect faults of all fault models; however, with some e > 0
Long test time: Test length (TL) proportional to ln(e) and 2k-2
For CFids: 445*n (e = 10-5) versus 10*n (for March C-)
Less of a problem for SRAMs (e.g.,1 Mwrd, 1ns, 1000n test takes1s)
Random pattern resistant faults
with a large data state (e.g., bit line imbalance)
requiring a large address/operation state (e.g., Hammer tests)
Cannot locate faults easily (For laser/dynamic repair)
Well suited for BIST
Very useful for verification purposes
Used for production SRAM testing (together with deterministic tests)
Unknown fault models, short time to volume, high speed SRAM