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International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015
DOI : 10.5121/vlsic.2015.6503 37
AREA, DELAY AND POWER ANALYSIS OF BUILT
IN SELF REPAIR USING 2-D REDUNDANCY
Aman Kumar Sabnani1
and Balwinder Singh2
1
Research Scholar, C-DAC, Mohali (P.B.), India
2
Coordinator, ACSD, C-DAC, Mohali (P.B.), India
ABSTRACT
System on Chip comprises of programmable processor, different controller and memory. As chip size is
decreasing memory density is increasing. These high density memories are susceptible to faults. To
increase the yield and make device reliable, testing and self-repair are the important issues. To repair
embedded memories in SOC, Built in self-repair techniques are used by firstly detecting, then locating and
in the end repairing the memory. In this paper six BISR are designed using six different March algorithms
as MBIST then compared altogether. Since power dissipation during testing operation is around twice the
power dissipation during normal operational mode, thus low power BISR design is necessary considering
the power constraints these days. Due to high switching activity chip can get overheated resulting in
malfunction and damage. Power consumption is reduced by reducing the switching activity in the address
line when writing and reading the memory during test.
KEYWORDS
Memory Built In Self-Test (MBIST), Built In Self-Repair (BISR), Low Power Testing, March Algorithm,
Embedded Memories.
1. INTRODUCTION
System-on-Chip being the demand of today‟s world brings hardware and software components
together. SOC provides complete solution by incorporating programmable processor, memory,
different controllers like audio video and graphics on a single chip. If a single component
becomes faulty whole chip needs to be replaced thus affecting the yield. Memory occupies more
than 90% of the total chip area. Such high density memories are susceptible to faults which
reduces the yield of SOC. This leads to the need of self-repair. Built In Self Repair (BISR) uses
Memory Built In Self Test (MBIST) to detect and locate faults in the memory. After locating the
faults in the memory the Built In Redundancy Allocation (BIRA) allocates the redundant memory
against the faulty memory. Also, according to recent researches it is revealed that the power
dissipation is high during testing due to high number of bit transitions. Since in CMOS heat
dissipation is proportional to switching activity thus chip can get damaged due to overheating
resulting in low yield of SOC. Thus reduction in power consumption during testing and repairing
is an important design challenge.
International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015
38
2. MEMORY BUILT IN SELF TEST
Memory Built In Self Test(MBIST) are used to test memories. In MBIST March Algorithms are
used to provide test patterns in a specific sequence of read and write operations which are
discussed below. Architecture of MBIST is shown in figure 1 below:
Figure 1. Block Diagram of BIST
In the figure 1, when Test signal is low normal read and write operations will be performed.
Clock (CLK), address (ADR), data (Din), enable, memory read writes (ReadWR) are the
corresponding inputs given by the user. When test signal is high BIST will take over the control
of memory. BIST will provide the input to be written on the specific memory address and will
read the desired memory address. Thus it will compare and detect the fault. When fault is
detected fault signal will be high and fail signal will give the faulty location. To provide patterns
for testing March algorithms are used in BIST. A March test consists of a finite sequence of
March elements. An operation can consist of writing a 0 into a cell (w0), writing a 1 into a cell
(w1), reading an expected 0 from a cell (r0), and reading an expected 1 from a cell (r1). Some of
the most popular notations for MARCH tests are described as follows:
↑: address ordering transition in ascending order
↓: address ordering transition in descending order
↕: address ordering can alter in either way
r0: read action (reading a 0 from a cell)
International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015
39
r1: read action (reading a 0 from a cell)
w0: write action (writing a 0 to a cell)
w1: write action (writing a 0 to a cell).
Six different march algorithms namely MATS, MATS+, March X, March Y, March LR, March
C- are used in designed BIST. Their corresponding fault coverage is given in the Table 1. March
LR algorithm has the maximum fault coverage and is most efficient of all. MATS, MATS+ are
simple and fast operating algorithm but with low fault coverage. Faults namely SAF (stuck at
fault), TF (transition fault), CF (coupling fault), ADF (address decoder fault), RF (retention
fault), LF (linked fault), can be easily detected using March LR algorithm.
Table 1. Fault Coverage of March Algorithms
3. REDUNDANCY ALLOCATION ALGORITHM
Redundant memory is the spare memory only used to repair faults. Normal memory operation on
specific redundant memory address occurs only when it has replaced the faulty main memory.
Redundancy used in the designed BISR is two dimensional (spare rows and spare columns).
International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015
40
Repair rules:
• The first rule is that if there are multiple faults in a row; repair the faulty row by spare
row. Save the location of the faulty row corresponding to the redundant row used.
• The second rule is that, if there is one bit fault in a memory address then it will be
repaired using the redundant column within that row. Store the faulty bit location and
Spare row will not be used.
4. BUILT IN SELF REPAIR
Built In Self Repair (BISR) comprises Memory Built In Self Test (MBIST) and Built In
Redundancy Allocation (BIRA).Architecture of BISR is discussed in figure 2 below:
Figure 2. Architecture of BISR
In this BISR memory of 1100x8 is designed. Main memory is of 1KB and rest is redundant
memory. In normal mode simple operations like reading and writing memory are carried out.
Inputs like data, address and RD/WR are given. RD/WR input decides whether data is to be
written or read. Data is the 8 bit data which is either to be written or read. Address is the 10 bit
address of memory location where data is to be retrieved or to be stored. When test input is high
MBIST takes over control of the memory. MBIST provides all inputs that are Data, Address and
RD/WR to the memory. MBIST writes the memory either „0‟ or „1‟ in a specific order and reads
back the memory to check the faulty locations. If fault is detected then fault signal goes high and
location of the fault is given to the BIRA. It assigns the redundant memory corresponding to the
faulty memory according to the repair rules. After allocation fault signal is turned low. Six
different BISR are designed using Xilinx tool. Comparative analysis of all the designed
algorithms is also performed in terms of number of slices, delay and power dissipation as shown
in Table 2.
International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015
41
Table 2. Comparative Analysis of all BISR Designs
Algorithm No. of slices used Delay (ns) Static
Power (W)
Dynamic Power
(W)
MATS 14775 4.603 4.400 0.860
MATS+ 18200 5.299 4.400 0.861
MARCH X 18214 5.230 4.407 1.048
MARCH Y 21739 5.289 4.409 1.111
MARCH C- 21341 5.468 4.410 1.140
MARCH LR 19948 5.638 4.409 1.125
5. DYNAMIC POWER REDUCTION
The methodology to reduce power uses the principle that is: reorder the original test such that
signal transitions on address line are minimized without affecting the fault coverage. Switching
activity on each address line depend on the address counting method (order in which addresses
are enumerated while reading and writing the memory). As shown in the Table 3, to reduce the
dynamic power the first two march elements of the all algorithms are modified and merged such
that transition on address line is reduced. In original test counter is used one more time than in
low power test. Thus, this leads to the reduction in dynamic power. Reduction in dynamic power
is shown in Table 4 for all the algorithms.
Table 3. Algorithm for Test
International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015
42
Table 4 Power Reduction
Algorithm Dynamic Power Reduction (W) Reduction (%)
Original
Test
Low Power
Test
MATS 0.860 0.764 0.096 11.16
MATS+ 0.861 0.774 0.087 10.10
March X 1.048 0.933 0.115 11
March Y 1.111 0.981 0.31 11.7
March C- 1.140 0.988 0.152 13.3
March LR 1.125 0.980 0.145 12.9
6. SIMULATION RESULTS
Size of the memory designed is 1KB (1024x8 bits). Size of the redundant memory is 76x8 bit.
Synthesis is performed using Xilinx project navigator 14.6 tools. Technology mapping chosen
was Virtex 6. Simulation is performed on Isim simulator. Faults are injected in the memory
deliberately at positions „2‟, „4‟ and „6‟. At position „2‟ single bit fault is injected and at „4‟
and „6‟ multiple bit faults are injected. After giving input test high faults are detected using
MBIST and fault location are stored. For repair the „4‟ and „6‟ locations are repaired using
redundant location and „2‟ location is repaired using redundant column. Location of the faulty
memory is stored corresponding to the redundant replacement. Simulations of fault injection,
detection and repairing using rows and column are shown in the figure 3 and 4.
Figure 3. Fault Injection and Detection
International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015
43
Figure 4. Using Redundant Rows After Repair
In figure 3 faults injection and detection are shown in the simulation. In figure 4 fault is being
repaired using redundant rows.
7. CONCLUSION
In this paper, BISR architecture is designed to test and repair 1KB memory. BIST module detects
the fault using six March algorithms (MATS, MATS+, March X, March Y, March C- and March
LR). Simulation results show that faults are detected and repaired using redundant memory (spare
column and rows). Single bit fault is repaired with spare column within that row and multiple bit
faults are repaired using redundant row. Analysis of device utilization and delay has been done
using Xilinx synthesis tool for all MBIST. BISR design using all MBIST is compared altogether.
BISR using March LR algorithm has maximum fault coverage. BISR using March C- algorithm
uses more device slices among other BISR designs. BISR using MATS algorithm is easy to
design and implement which also has low dynamic power dissipation. Power is calculated using
Xpower analyser and dynamic power is reduced by reducing the memory address transition in the
algorithm. Dynamic power is reduced around 10%-13% for different BISR designs.
REFERENCES
[1] Jin-Fu Li, Jen-ChiehYeh, Rei-Fu Huang, Cheng-Wen Wu, “A built-in self-repair design for RAMs
with 2-D redundancy,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol.13,
no.6, pp.742-745, June 2005.
[2] Yu-Ying Hsiao, Chao-Hsun Chen, Cheng-Wen Wu, "A built-in self-repair scheme for NOR-type
flash memory,” In: Proceedings of 24th VLSI Test Symposium, April 30 2006-May 4 2006.
[3] Banupriya, C., Chandrakala, S., "A low power Built in Self Repair technique for word oriented
memories," In: Proceedings of International Conference on Electronics and Communication Systems
(ICECS), 13-14 February 2014.
[4] Van de Goor, A.J., Gaydadjiev, G.N., Mikitjuk, V.G., Yarmolik, V.N., "March LR: a test for realistic
linked and unlinked faults," In: Proceedings of 14th VLSI Test Symposium, 28 April-1 May 1996.
[5] Shyue-Kung Lu, Yu-Chen Tsai, Hsu, C.H., Kuo-HuaWang, Cheng-Wen Wu, "Efficient built-in
redundancy analysis for embedded memories with 2-D redundancy," IEEE Transactions on Very
Large Scale Integration (VLSI) Systems, vol.14, no.1, pp.34-42, January 2006.
[6] Seongmoon Wang, "A BIST TPG for Low Power Dissipation and High Fault Coverage," IEEE
Transactions on Very Large Scale Integration (VLSI) Systems, vol.15, no.7, pp.777-789, July 2007.
International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015
44
[7] Lee, M., Li-Ming Denq, Cheng-Wen Wu, "A Memory Built-In Self-Repair Scheme Based on
Configurable Spares," IEEE Transactions on Computer-Aided Design of Integrated Circuits and
Systems, vol.30, no.6, pp.919-929, June 2011.
[8] Tsu-Wei Tseng, Jin-Fu Li, Hsu, Chih-Chiang, "ReBISR: A Reconfigurable Built-In Self-Repair
Scheme for Random Access Memories in SOCs," IEEE Transactions on Very Large Scale Integration
(VLSI) Systems, vol.18, no.6, pp.921-932, June 2010.
[9] Lala, Parag K. “Transient and permanent fault injection in VHDL description of digital circuits.”
IEEE Transactions on Circuits and Systems, vol.3, no.12, pp. 192. April 2012.
[10] Singh, Balwinder, Sukhleen Bindra Narang, and Arun Khosla. “Modeling and Simulation of Efficient
March Algorithm for memory Testing,” In: Proceedings of conference on Contemporary Computing
Springer Berlin Heidelberg, pp. 96-107, June 2010.
[11] Jyotika; Singh, B., "Memory yield and repair rate improvement scheme using built in self repair
techniques," In: proceedings of IEEE conference on Innovative Applications of Computational
Intelligence on Power, Energy and Controls with their impact on Humanity (CIPECH), pp.350-354,
28-29 Nov. 2014.
[12] A. A. Ivaniuk, “Random Access Memory Faults Descriptions and Simulations using VHDL,” In:
Proceedings of 14th International Conference on Microelectronics & Computer Science, pp 29-33,
June 2007.

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AREA, DELAY AND POWER ANALYSIS OF BUILT IN SELF REPAIR USING 2-D REDUNDANCY

  • 1. International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015 DOI : 10.5121/vlsic.2015.6503 37 AREA, DELAY AND POWER ANALYSIS OF BUILT IN SELF REPAIR USING 2-D REDUNDANCY Aman Kumar Sabnani1 and Balwinder Singh2 1 Research Scholar, C-DAC, Mohali (P.B.), India 2 Coordinator, ACSD, C-DAC, Mohali (P.B.), India ABSTRACT System on Chip comprises of programmable processor, different controller and memory. As chip size is decreasing memory density is increasing. These high density memories are susceptible to faults. To increase the yield and make device reliable, testing and self-repair are the important issues. To repair embedded memories in SOC, Built in self-repair techniques are used by firstly detecting, then locating and in the end repairing the memory. In this paper six BISR are designed using six different March algorithms as MBIST then compared altogether. Since power dissipation during testing operation is around twice the power dissipation during normal operational mode, thus low power BISR design is necessary considering the power constraints these days. Due to high switching activity chip can get overheated resulting in malfunction and damage. Power consumption is reduced by reducing the switching activity in the address line when writing and reading the memory during test. KEYWORDS Memory Built In Self-Test (MBIST), Built In Self-Repair (BISR), Low Power Testing, March Algorithm, Embedded Memories. 1. INTRODUCTION System-on-Chip being the demand of today‟s world brings hardware and software components together. SOC provides complete solution by incorporating programmable processor, memory, different controllers like audio video and graphics on a single chip. If a single component becomes faulty whole chip needs to be replaced thus affecting the yield. Memory occupies more than 90% of the total chip area. Such high density memories are susceptible to faults which reduces the yield of SOC. This leads to the need of self-repair. Built In Self Repair (BISR) uses Memory Built In Self Test (MBIST) to detect and locate faults in the memory. After locating the faults in the memory the Built In Redundancy Allocation (BIRA) allocates the redundant memory against the faulty memory. Also, according to recent researches it is revealed that the power dissipation is high during testing due to high number of bit transitions. Since in CMOS heat dissipation is proportional to switching activity thus chip can get damaged due to overheating resulting in low yield of SOC. Thus reduction in power consumption during testing and repairing is an important design challenge.
  • 2. International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015 38 2. MEMORY BUILT IN SELF TEST Memory Built In Self Test(MBIST) are used to test memories. In MBIST March Algorithms are used to provide test patterns in a specific sequence of read and write operations which are discussed below. Architecture of MBIST is shown in figure 1 below: Figure 1. Block Diagram of BIST In the figure 1, when Test signal is low normal read and write operations will be performed. Clock (CLK), address (ADR), data (Din), enable, memory read writes (ReadWR) are the corresponding inputs given by the user. When test signal is high BIST will take over the control of memory. BIST will provide the input to be written on the specific memory address and will read the desired memory address. Thus it will compare and detect the fault. When fault is detected fault signal will be high and fail signal will give the faulty location. To provide patterns for testing March algorithms are used in BIST. A March test consists of a finite sequence of March elements. An operation can consist of writing a 0 into a cell (w0), writing a 1 into a cell (w1), reading an expected 0 from a cell (r0), and reading an expected 1 from a cell (r1). Some of the most popular notations for MARCH tests are described as follows: ↑: address ordering transition in ascending order ↓: address ordering transition in descending order ↕: address ordering can alter in either way r0: read action (reading a 0 from a cell)
  • 3. International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015 39 r1: read action (reading a 0 from a cell) w0: write action (writing a 0 to a cell) w1: write action (writing a 0 to a cell). Six different march algorithms namely MATS, MATS+, March X, March Y, March LR, March C- are used in designed BIST. Their corresponding fault coverage is given in the Table 1. March LR algorithm has the maximum fault coverage and is most efficient of all. MATS, MATS+ are simple and fast operating algorithm but with low fault coverage. Faults namely SAF (stuck at fault), TF (transition fault), CF (coupling fault), ADF (address decoder fault), RF (retention fault), LF (linked fault), can be easily detected using March LR algorithm. Table 1. Fault Coverage of March Algorithms 3. REDUNDANCY ALLOCATION ALGORITHM Redundant memory is the spare memory only used to repair faults. Normal memory operation on specific redundant memory address occurs only when it has replaced the faulty main memory. Redundancy used in the designed BISR is two dimensional (spare rows and spare columns).
  • 4. International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015 40 Repair rules: • The first rule is that if there are multiple faults in a row; repair the faulty row by spare row. Save the location of the faulty row corresponding to the redundant row used. • The second rule is that, if there is one bit fault in a memory address then it will be repaired using the redundant column within that row. Store the faulty bit location and Spare row will not be used. 4. BUILT IN SELF REPAIR Built In Self Repair (BISR) comprises Memory Built In Self Test (MBIST) and Built In Redundancy Allocation (BIRA).Architecture of BISR is discussed in figure 2 below: Figure 2. Architecture of BISR In this BISR memory of 1100x8 is designed. Main memory is of 1KB and rest is redundant memory. In normal mode simple operations like reading and writing memory are carried out. Inputs like data, address and RD/WR are given. RD/WR input decides whether data is to be written or read. Data is the 8 bit data which is either to be written or read. Address is the 10 bit address of memory location where data is to be retrieved or to be stored. When test input is high MBIST takes over control of the memory. MBIST provides all inputs that are Data, Address and RD/WR to the memory. MBIST writes the memory either „0‟ or „1‟ in a specific order and reads back the memory to check the faulty locations. If fault is detected then fault signal goes high and location of the fault is given to the BIRA. It assigns the redundant memory corresponding to the faulty memory according to the repair rules. After allocation fault signal is turned low. Six different BISR are designed using Xilinx tool. Comparative analysis of all the designed algorithms is also performed in terms of number of slices, delay and power dissipation as shown in Table 2.
  • 5. International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015 41 Table 2. Comparative Analysis of all BISR Designs Algorithm No. of slices used Delay (ns) Static Power (W) Dynamic Power (W) MATS 14775 4.603 4.400 0.860 MATS+ 18200 5.299 4.400 0.861 MARCH X 18214 5.230 4.407 1.048 MARCH Y 21739 5.289 4.409 1.111 MARCH C- 21341 5.468 4.410 1.140 MARCH LR 19948 5.638 4.409 1.125 5. DYNAMIC POWER REDUCTION The methodology to reduce power uses the principle that is: reorder the original test such that signal transitions on address line are minimized without affecting the fault coverage. Switching activity on each address line depend on the address counting method (order in which addresses are enumerated while reading and writing the memory). As shown in the Table 3, to reduce the dynamic power the first two march elements of the all algorithms are modified and merged such that transition on address line is reduced. In original test counter is used one more time than in low power test. Thus, this leads to the reduction in dynamic power. Reduction in dynamic power is shown in Table 4 for all the algorithms. Table 3. Algorithm for Test
  • 6. International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015 42 Table 4 Power Reduction Algorithm Dynamic Power Reduction (W) Reduction (%) Original Test Low Power Test MATS 0.860 0.764 0.096 11.16 MATS+ 0.861 0.774 0.087 10.10 March X 1.048 0.933 0.115 11 March Y 1.111 0.981 0.31 11.7 March C- 1.140 0.988 0.152 13.3 March LR 1.125 0.980 0.145 12.9 6. SIMULATION RESULTS Size of the memory designed is 1KB (1024x8 bits). Size of the redundant memory is 76x8 bit. Synthesis is performed using Xilinx project navigator 14.6 tools. Technology mapping chosen was Virtex 6. Simulation is performed on Isim simulator. Faults are injected in the memory deliberately at positions „2‟, „4‟ and „6‟. At position „2‟ single bit fault is injected and at „4‟ and „6‟ multiple bit faults are injected. After giving input test high faults are detected using MBIST and fault location are stored. For repair the „4‟ and „6‟ locations are repaired using redundant location and „2‟ location is repaired using redundant column. Location of the faulty memory is stored corresponding to the redundant replacement. Simulations of fault injection, detection and repairing using rows and column are shown in the figure 3 and 4. Figure 3. Fault Injection and Detection
  • 7. International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015 43 Figure 4. Using Redundant Rows After Repair In figure 3 faults injection and detection are shown in the simulation. In figure 4 fault is being repaired using redundant rows. 7. CONCLUSION In this paper, BISR architecture is designed to test and repair 1KB memory. BIST module detects the fault using six March algorithms (MATS, MATS+, March X, March Y, March C- and March LR). Simulation results show that faults are detected and repaired using redundant memory (spare column and rows). Single bit fault is repaired with spare column within that row and multiple bit faults are repaired using redundant row. Analysis of device utilization and delay has been done using Xilinx synthesis tool for all MBIST. BISR design using all MBIST is compared altogether. BISR using March LR algorithm has maximum fault coverage. BISR using March C- algorithm uses more device slices among other BISR designs. BISR using MATS algorithm is easy to design and implement which also has low dynamic power dissipation. Power is calculated using Xpower analyser and dynamic power is reduced by reducing the memory address transition in the algorithm. Dynamic power is reduced around 10%-13% for different BISR designs. REFERENCES [1] Jin-Fu Li, Jen-ChiehYeh, Rei-Fu Huang, Cheng-Wen Wu, “A built-in self-repair design for RAMs with 2-D redundancy,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol.13, no.6, pp.742-745, June 2005. [2] Yu-Ying Hsiao, Chao-Hsun Chen, Cheng-Wen Wu, "A built-in self-repair scheme for NOR-type flash memory,” In: Proceedings of 24th VLSI Test Symposium, April 30 2006-May 4 2006. [3] Banupriya, C., Chandrakala, S., "A low power Built in Self Repair technique for word oriented memories," In: Proceedings of International Conference on Electronics and Communication Systems (ICECS), 13-14 February 2014. [4] Van de Goor, A.J., Gaydadjiev, G.N., Mikitjuk, V.G., Yarmolik, V.N., "March LR: a test for realistic linked and unlinked faults," In: Proceedings of 14th VLSI Test Symposium, 28 April-1 May 1996. [5] Shyue-Kung Lu, Yu-Chen Tsai, Hsu, C.H., Kuo-HuaWang, Cheng-Wen Wu, "Efficient built-in redundancy analysis for embedded memories with 2-D redundancy," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol.14, no.1, pp.34-42, January 2006. [6] Seongmoon Wang, "A BIST TPG for Low Power Dissipation and High Fault Coverage," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol.15, no.7, pp.777-789, July 2007.
  • 8. International Journal of VLSI design & Communication Systems (VLSICS) Vol.6, No.5, October 2015 44 [7] Lee, M., Li-Ming Denq, Cheng-Wen Wu, "A Memory Built-In Self-Repair Scheme Based on Configurable Spares," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.30, no.6, pp.919-929, June 2011. [8] Tsu-Wei Tseng, Jin-Fu Li, Hsu, Chih-Chiang, "ReBISR: A Reconfigurable Built-In Self-Repair Scheme for Random Access Memories in SOCs," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol.18, no.6, pp.921-932, June 2010. [9] Lala, Parag K. “Transient and permanent fault injection in VHDL description of digital circuits.” IEEE Transactions on Circuits and Systems, vol.3, no.12, pp. 192. April 2012. [10] Singh, Balwinder, Sukhleen Bindra Narang, and Arun Khosla. “Modeling and Simulation of Efficient March Algorithm for memory Testing,” In: Proceedings of conference on Contemporary Computing Springer Berlin Heidelberg, pp. 96-107, June 2010. [11] Jyotika; Singh, B., "Memory yield and repair rate improvement scheme using built in self repair techniques," In: proceedings of IEEE conference on Innovative Applications of Computational Intelligence on Power, Energy and Controls with their impact on Humanity (CIPECH), pp.350-354, 28-29 Nov. 2014. [12] A. A. Ivaniuk, “Random Access Memory Faults Descriptions and Simulations using VHDL,” In: Proceedings of 14th International Conference on Microelectronics & Computer Science, pp 29-33, June 2007.