Victor Champac

Andres Gomez

Freddy Forero

Kaushik Roy

Analysis of Bridge Defects in STT-MRAM Cells Under Process Variations and a Robust DFT Technique for their Detection

Keywords: STT-MRAM, Short defect, Test, Design-for-Test, FinFET

Spin-Transfer-Torque Magnetic RAM (STT-MRAM) is a promising non-volatile memory technology due to its ultra-integration density capability, nanosecond speeds for reading and writing operations and CMOS/FinFET fabrication process compatibility. STT-MRAMs may be affected by manufacturing defects, which may be challenging to detect under process variations in deeply scaled semiconductor technologies. Because of this, the importance of test techniques to target defects in this emerging memory technology. In this work, an STT-MRAM bitcell is presented with its states due to the magnetic orientation of the ferromagnetic layers. The read and write operations of an STT-MRAM cell, including the read and write circuits, are revised in the scope of this work. The write time definition for an STT-MRAM cell is also revised. A defect model is used to analyze the STT-MRAM cell under short defects in the presence of process variations. A Design-For-Test (DFT) circuit to detect short defects in the STT-MRAM cells is proposed. The proposed methodology is based on the observation that a short defect modifies the amplitude of the currents entering and leaving the memory cell. Hence, the current difference between the currents entering and leaving the memory cell is used to discriminate between good cells and defective cells. The proposed DFT circuitry is robust to process-induced parameters variations in the memory cell. In such a way, defects detection probabilities are increased, and a high-quality product can be guaranteed.

Introduction

Spin-Transfer-Torque Magnetic RAM (STT-MRAM) is an emerging non-volatile memory technology with high endurance and CMOS/FinFET compatibility [START_REF] Bhattacharya | Implementation of finfet based stt-mram bitcell[END_REF]. STT-MRAM has attractive features such as non-volatility, which means that the stored information remains when the power supply is turned off, and high endurance, which means it is possible to write data for an unlimited number of times. STT-MRAM also provides zero standby leakage. The International Technology Roadmap for Semiconductor (ITRS) highlighted STT-MRAM as a promising candidate for future on-chip memory applications [START_REF]ITRS International Technology Roadmap for Semiconductor[END_REF].

Like in other types of memories, the main operations carried out in STT-MRAM are the writing and reading operations. The correct behavior of an STT-MRAM may be impacted by manufacturing defects, which may affect the access transistor, the MTJ and the interconnections of the STT-MRAM cell. If the access transistor is fabricated with FinFET technology new defects like stuckopen fin or single open gate in multi-fin structures may affect it [START_REF] Liu | On modeling faults in FinFET logic circuits[END_REF] [4] [START_REF] Mesalles | Behavior and test of opengate defects in FinFET based cells[END_REF]. The MTJ device may be affected by different types of defects like a short on the insulator oxide [START_REF] Panagopoulos | Modeling of dielectric breakdowninduced time-dependent STT-MRAM performance degradation[END_REF], an open defect in any terminal and a stuck-at-AP/stuckat-P faults [START_REF] Bishnoi | Design of defect and fault-tolerant nonvolatile spintronic flip-flops[END_REF]. Resistive shorts/opens may affect the interconnections in the STT-MRAM memory [START_REF] Chintaluri | A Model Study of Defects and Faults in Embedded Spin Transfer Torque (STT) MRAM Arrays[END_REF] [START_REF] Chintaluri | Analysis of defects and variations in embedded spin transfer torque (stt) mram arrays[END_REF]. Fault models based on defective memory behavior are usually developed for test purposes [START_REF] Chintaluri | Analysis of defects and variations in embedded spin transfer torque (stt) mram arrays[END_REF]. Fault models may be used for test pattern generation. Memory fault models are usually classified depending on the operation they affect, reading or writing operation, as shown in Fig. 1. In a writing operation, an open resistive defect may reduce the current applied to the cell memory, and the cell may not change state. However, in an STT-RAM memory, the writing process has a probabilistic nature, so write failure also has the same nature, and it can not be known with certainty if the failure occurs always occur [START_REF] Diao | Spin-transfer torque switching in magnetic tunnel junctions and spintransfer torque random access memory[END_REF]. This fault is known as Undefined Write Fault (UWF) [START_REF] Vatajelu | Challenges and Solutions in Emerging Memory Testing[END_REF]. It is said that a Time Fault (TF) [START_REF] Chintaluri | Analysis of defects and variations in embedded spin transfer torque (stt) mram arrays[END_REF] occurs if the open resistive defect allows the current to be large enough to ensure that the desired state is written in the STT-MRAM cell, but it does not allow the memory cell to perform the writing process in a particular time. A short resistive defect may affect the gates of the access transistors in two STT-MRAM cells. The short defect is sensitized when trying to write a cell, and the access transistor is not completely turned on. As a consequence, the writing operation is not correctly performed. This fault is known as Coupling Fault (CF) [START_REF] Chintaluri | Analysis of defects and variations in embedded spin transfer torque (stt) mram arrays[END_REF]. An incorrect Reading Fault (IRF) [START_REF] Vatajelu | Challenges and Solutions in Emerging Memory Testing[END_REF] is said to occur when a resistive defect changes the measured voltage value of the cell in a read operation. A Read Disturbance Fault (RDF) [START_REF] Chintaluri | Analysis of defects and variations in embedded spin transfer torque (stt) mram arrays[END_REF] occurs when a short defect increases the current in a reading operation and change the value stored in STT-MRAM memory. In the Stuck-at Fault (SaF) a resistive short defect connects the internal node of the STT-MRAM cell with the power rails electrically, which causes malfunctions in both writing and reading operations [START_REF] Vatajelu | Challenges and Solutions in Emerging Memory Testing[END_REF]. Recently, a novel generic defect modeling methodology that captures the non-linear behavior of the STT-MRAM has been proposed [START_REF] Wu | Electrical Modeling of STT-MRAM Defects[END_REF] .

Efficient defect test and diagnosis are critical to assure high-quality memory arrays, but this is a challenging task due to process-induced parameters variations, which may mask the impact of a defect on the functionality of the cell. The test approaches for digital integrated circuits can be categorized as fault-oriented or defect-oriented tests. In a fault-oriented test, the obtained logic result at the primary outputs is compared against the expected result. In a defect-oriented test approach, a parameter of the tested circuit (i.e., current consumption) is monitored to detect the presence of a defect. There is not required to observe the faulty logic behavior at main circuit outputs, which is a significant advantage. Thus, a defect-oriented test is more adequate for the detection of both strong and weak defects. In [START_REF] Bishnoi | Read disturb fault detection in STT-MRAM[END_REF], a circuit-level approach to detect read disturbs faults was proposed. The circuit detects the change in the current through a cell when a read disturb fault occurs.

In this work, we propose a modified Design-For-Test (DFT) read circuit to detect resistive-short defects between an internal node of an STT-MRAM and an external node [START_REF] Gomez | Robust Detection of Bridge Defects in STT-MRAM Cells Under Process Variations[END_REF]. The proposed test circuit performs a defect-oriented test, which is adequate for the detection of weak defects that may escape to conventional logic test and degrade the memory block reliability [START_REF] Gomez | Effectiveness of a hardware-based approach to detect resistiveopen defects in sram cells under process variations[END_REF]. The proposed test circuit is based on the observation that a short defect makes different the amplitude of the currents entering and leaving a memory cell. The DFT read circuitry can measure both the currents entering and leaving a memory cell. The proposed test technique provides higher defect detection and diagnosis capabilities. The capability of the proposed test circuit to detect resistive-short defects that can escape conventional logic test is validated under process variations effects, and it is shown that the defect detectability is improved. This chapter extends the analysis of the previous work and performs a comparative analysis between the conventional test techniques and the proposed DFT technique.

The rest of this chapter is organized as follows: Section 2 presents the operating principles of an STT-MRAM cell. Section 3 describes the read and write operation of the STT-MRAM cell with the read and write circuits used. In section 4, the writing time definition of an STT-MRAM cell is analyzed closely. Section 5 presents an analysis of the electrical behavior of the memory cell under the presence of resistive short defects. Section 6 presents the proposed test technique. Section 7 analyzes the cost of the proposed test technique, and a comparison between the proposed test technique and a conventional logic based test is made. Finally, Section 8 presents the conclusions of this work.

Memories Based on STT-MRAM

A single STT-MRAM memory is formed by a Magnetic Tunneling Junction (MTJ), which is a spintronic storage device, and an access transistor as illustrated in Fig. 2(a). The MTJ has two ferromagnetic layers separated by a very thin insulator [START_REF] Hosomi | A novel nonvolatile memory with spin torque transfer magnetization switching: spin-ram[END_REF]. The use of a FinFET transistor as the access device is pre-ferred over a CMOS planar transistor due to its superior gate controllability, larger "ON" current, and lower variability. The magnetic orientation of the bottom layer, called Pinned Layer (PL), is fixed. However, the magnetic orientation of the top layer, called Free Layer (FL), is allowed to switch its magnetic orientation concerning the PL using a spin-polarized current through the MTJ. The electrical resistance of the device depends on the magnetic orientation of the two ferromagnetic layers (See Fig. 2(b)). A larger electrical resistance is observed when the magnetic orientations of the layers point in opposite directions (known as Anti-parallel state) compared to the state when the magnetic orientations of the layers point in the same direction (known as Parallel state) [17] [18]. This phenomenon is known as Giant Magneto Resistance [START_REF] Baibich | Giant magnetoresistance of (001) Fe/(001) Cr magnetic superlattices[END_REF] [START_REF] Yuasa | Giant room-temperature magnetoresistance in single-crystal Fe/MgO/Fe magnetic tunnel junctions[END_REF]. The low and high MTJ resistance states correspond to the logic 0 and 1 states, respectively.

A data can be written into and read from the cell by applying appropriate voltages to bit-line (BL), source-line (SL) and Word-Line (WL) terminals of the cell (See Table 1). A current needs to flow from the BL to the SL terminals for writing a Parallel (P) state, which is accomplished by applying BL=VDD, and SL=0. On the other hand, a current needs to flow from the SL to the BL terminals for writing an Anti-Parallel Parallel (AP) state, which is accomplished by applying BL=0, and SL=VDD. The current that flows through the MTJ has to be large enough to switch the magnetization orientation of the free-layer [START_REF] Fong | Bit-cell level optimization for non-volatile memories using magnetic tunnel junctions and spin-transfer torque switching[END_REF] during a write operation successfully. In this way, the memory can change from anti-parallel state to parallel state (AP → P ) or vice-versa (P → AP ). It is important to mention that this current must be bidirectional to perform the change of state in both cases.

The read operation is performed by sensing the resistance of the MTJ. This is done by applying a small read current to the cell and comparing the voltage drop with a reference voltage. Unlike write operation that requires bi-directional current, the read operation only requires current flowing from BL to SL terminals. In the reading procedure, a lower current than the write current is applied at the cell, and the voltage at the cell is measured to identify its state [START_REF] Hosomi | A novel nonvolatile memory with spin torque transfer magnetization switching: spin-ram[END_REF].

Table 1. Signal conditions for write and read operations.

Node

Write Read AP → P P → AP

WL V DD V DD V DD BL 0 V DD V DD SL V DD 0 0
Table 2 shows some of the main MTJ parameters used in this work. Other parameters were settled as default in [START_REF] Fong | Spice models for magnetic tunnel junctions based on monodomain approximation[END_REF]. Memory cells are accessed by activating a word line (W L i ) and the pass transistors of the desired column. The access to the cells is defined by the word and column decoder circuitries. It should be noted that the number of selected columns depend on the required application. Figure 4 shows a single STT-MRAM cell with the used read and write circuits. The access transistor of the cell, which is driven by the word-line (WL) signal, controls whether current can flow through the MTJ to perform write and read operations.

Read Operation

The read circuit (See Fig. 4) is activated when the Read Enable signal is set at a high logic state (RE=1). A current I REF is generated using a reference cell whose resistance is designed to be the average between the parallel (R P ) and anti-parallel (R AP ) resistances of the STT-MRAM cell (R P + R AP )/2). This current is copied and applied to the memory cell to be read. The current I REF generates a voltage V REF at one end of the terminals of the current mirror, and the current I cell generates a voltage V cell at the other end terminal of the current mirror. The voltages generated at the current mirror terminals (V REF , V cell ) are not the same since the resistances of the STT-MRAM cell, and the reference cell are different. The voltage difference between V REF and V cell is measured using a sense amplifier to determine whether the STT-MRAM cell is in the P or AP state. The clamp voltage (CLP) is used to limit the amount of reading current (I REF ), so that unintentional writes do not occur.

Write Operation

The write circuit is activated when the Write Enable signal is set at a high logic state (WE=1). The direction of the current applied to the memory cell depends on the Data Input (DI) to be written. The AP state is written if DI = 1 while the parallel state is written if DI = 0. A current flows from SL to BL for DI = 1, and thus, an AP state is written in the MTJ. A current flows from BL to SL for DI = 0, and thus, a P state is written in the MTJ. The transistors of the writing circuit were made large enough to provide sufficient current capability for a correct write operation.

Write Time Definition for an STT-MRAM Cell

One of the major issues for proper operation of the STT-MRAM cell is that a sufficiently large current has to flow through the cell for a long enough time to perform a successful write operation. The required large current leads to a high write energy consumption. Energy efficiency is further degraded due to the required current asymmetry in the write operations [START_REF] Zhang | Asymmetry of mtj switching and its implication to stt-ram designs[END_REF]. Energy efficiency of the STT-MRAM has been addressed by carefully size optimization of the access transistor in [START_REF] Zhang | STT-RAM Cell Optimization Considering MTJ and CMOS Variations[END_REF]. The size of the access transistor is iteratively increased until the desired write time performance for the slow process corner is achieved. This Section closely analyzes the write time behavior when writing P and AP states.

In a conventional STT-MRAM cell, the latency time for each writing transition (P → AP or AP → P ) is different. This asymmetry is caused due to the different spin-transfer efficiency of each MTJ layer, which makes the current to switch the MTJ magnetization state different depending on the state to be written. Write time asymmetry also occurs due to source-degeneration of the access transistor during the P → AP write operation, which reduces the effective gate to source voltage of the NFET, and consequently, its current driving capability, resulting in larger write latency. Figure 5 shows the current waveform for the two write operations in an STT-MRAM cell. A FinFET access transistor with 2 Fins and 2 Fingers (W ef f ∼ 224nm) was used. As can be observed, the write latency is determined by the P → AP operation where source degeneration occurs.

For writing a P → AP state (See Fig. 5), the current that initially flows through the cell is 130µA, which makes the MTJ flip its magnetic orientation in 7.28ns. Then, the current reduces to 76µA when the memory switches its state as the AP state has a higher resistance than the P state. For writing an AP → P state (See Fig. 5), the initial current is 142µA. Note that although the MTJ is at the high resistance state (AP), the access transistor does not experience sourcedegeneration for this transition. Therefore, the current that can flow at the beginning of this operation is larger than the current for the P → AP writing. The writing of the AP → P state takes 2.98ns. Then, the current increases when the memory switches its state as the P state has a lower resistance than the AP state. Note that the current keeps flowing through the cell the slower P → AP transition defines the pulse current duration. This unnecessary current contributes to extra power dissipation and degrades the energy efficiency of the memory cell. STT-MRAM suffers from process variations on the access transistor and the MTJ. Process variations lead to variations in the write time of the cell because they affect the current drive capability of the access transistor as well as the magnetic and electric properties of the MTJ (i.e., MTJ resistance and critical switching currents). Due to process variations, the write delay distribution of the STT-MRAM cell has a long tail, which may degrade the memory yield [START_REF] Emre | Enhancing the Reliability of STT-RAM through Circuit and System Level Techniques[END_REF], [START_REF] Motaman | Impact of Process-variations in STTRAM and Adaptive Boosting for Robustness[END_REF]. The size of the access transistor must be selected to compensate for the impact of process variations with an acceptable write failure probability.

Analysis of STT-MRAM Behavior Under Short Defects

Correct STT-MRAM behavior may be affected by manufacturing defects. A comprehensive analysis of all the possible defects in an STT-MRAM was presented in [START_REF] Chintaluri | Analysis of defects and variations in embedded spin transfer torque (stt) mram arrays[END_REF]. It was shown that due to the fundamental differences between classic SRAM and STT-MRAM, some fault models and test techniques used in SRAM are not extendable to STT-MRAM technology. Resistive short defects may alter the correct functionality of the cell. However, when the defects are not strong enough, its detection becomes very difficult, and they may escape the post-manufacturing test, especially under the effect of process variations.

An STT-MRAM cell including the read and write circuits has been simulated. The design characteristics of the single memory and the set-up conditions for Spice simulations used from now on are given. The MTJ has dimensions of 60nm × 40nm × 1.4nm. A stability factor of ∆ = 70 is considered. Other MTJ parameters are set as in [START_REF] Fong | Spice models for magnetic tunnel junctions based on monodomain approximation[END_REF]. A FinFET access transistor with 6 f ins was used to provide enough current capability to perform a successful write operation in 3.5ns. A Predictive 20nm FinFET technology [START_REF]Predictive technology models[END_REF] is used along with the SPICEcompatible MTJ model proposed in [START_REF] Fong | Spice models for magnetic tunnel junctions based on monodomain approximation[END_REF]. Variations in the MTJ were assumed of 15% for the cross-sectional area (A t ) and 5% for the oxide barrier thickness (t ox ). For the access transistor, 30% of threshold voltage (V th ) variation due to the work function variation was assumed. For simplicity purposes, process parameters variations were only considered for the single memory cell.

Defect Model for Short Defects in the STT-MRAM

Figure 6 shows the used general defect model to analyze the behavior of the STT-MRAM under short defects. The resistance R V DD considers those possible resistive-short defects between the internal node of the STT-MRAM cell and the power supply terminal, and the resistance R GN D considers those possible resistive-short defects between the internal node of the STT-MRAM cell and the ground terminal. R V DD and R GN D represent the behavior of realistic short defects that occur between the internal node of the cell and power/ground terminals. However, the proposed methodology is also valid to detect other types of short defects as explained later in section 7.4. BL SL WL Fig. 6. STT-MRAM cell with resistive short defects.

Impact of Short Defects on Write Operation

The nominal current that flows through the MTJ (I M T J ) during the writing process of a P and an AP states is shown in Figs. 7(a) and 7(b), respectively. The writing time (t wr ) to switch the magnetization orientation of the MTJ depends on the amplitude of the current that initially flows through the MTJ. For writing a parallel state (See Fig. 7(a)), the current that initially flows through a "good" cell is close to 145µA. When a resistive defect R V DD exists, the write time increases because this defect reduces the current that can flow through the MTJ since the access transistor has to drive both the MTJ current and the defect current. On the other hand, defect R GN D slightly reduces the write time because more current flows through the MTJ due to an additional conducting path to ground. For writing an anti-parallel state (See Fig. 7(b)), the current that flows through a "good" cell is close to 139µA. A resistive defect R V DD increases the current that flows through the MTJ, which reduces the write time. A resistive defect R GN D reduces the current that flows through the MTJ, which increases the write time.

Impact of Process Variations

The write pulse duration constraint for the designed cell was of 3.5ns. This write time value corresponds to the largest write time that the defect-free cell can take under process variations. 1000 Monte-Carlo simulations were made. Note that this write time value corresponds to the P → AP operation, which is slower than the AP → P operation due to source degeneration of the access transistor [START_REF] Zhang | Asymmetry of mtj switching and its implication to stt-ram designs[END_REF]. If the cell's write time becomes larger than 3.5ns due to a short defect, an incorrect write operation is performed, and the defect presence can be detected using a conventional logic-based test. A resistive defect value 2kΩ has been considered for R V DD and R GN D .

Write time histograms for the AP → P write operation for good and defective cells are shown in Fig. 8(a). R GN D moves the write time distribution to the left, and therefore, it does not cause a logic fault. R V DD moves the write time distribution to the right, but most of the write time values does not cause a logic fault. It can be observed that most of the write time values are within the designed write time margin of the cell (t wr = 3.5ns), and hence, they represent test escapes.

Write time histograms for the P → AP write operation for good, and defective cells are shown in Fig. 8(b). R V DD moves the write time distribution to the left, and consequently, it does not trigger a logic fault. On the other hand, defect R GN D moves the write time distribution to the right. In this case, most of the write time values of the defective cell are larger than the designed write time margin of the cell (t wr = 3.5ns), and hence, they can be detected using a logic-based test. However, some defective cells with write times smaller than the designed write time margin of the cell are not detected using a logic based test.

Figures 8(a) and 8(b) suggest that a conventional logic-base test using the write operation may fail to detect short defects related to R V DD . Moreover, some short defects related to R GN D also may not be detected.

Impact of Short Defects on the Read Operation

Figure 9 shows the voltage V cell generated at the current mirror terminals in the read circuit (See Fig. 4) as a function of the short defect resistance for both R GN D and R V DD defects. The black dashed lines correspond to the case of V cell of a defect-free cell, where V cell is 0.30V and 0.85V for the MTJ at the P and AP state, respectively. The voltage V REF generated by the reference cell is 0.66V .

A read error of the AP state is assumed for the following condition:

V cell < V REF (1)
A read error of the P state is assumed for the following condition: Resistive defect R V DD injects extra current to the internal node of the cell, which has to be driven by the access transistor. Because of this, the resistance seen from the BL node increases, and hence, the generated voltage V cell increases. Figure 9 shows that no logic error appears for reading an AP state for the defect R V DD . However, a logic error occurs in a small range of defect resistance values for reading a P state.

V cell > V REF (2)
Defect R GN D is placed in parallel with the access transistor. When the resistance of the short defect is large, its effect on the overall cell resistance is negligible. When the resistance of the short defect is small, the equivalent resistance reduces until it becomes closer to the pure resistance of the MTJ. The generated voltage V cell reduces as R GN D becomes smaller (See Fig. 9). Resistive defect R GN D defect does not trigger any incorrect read operations. Therefore, this defect can not be detected by a read operation using conventional logic test.

Impact of Process Variations

Figure 10 shows the histograms of the voltage V cell for good and defective cells. A resistive shorts defect of 20kΩ has been considered for R GN D and R V DD . As expected, the defect R GN D does not trigger an incorrect read. Some of the defective cells with R V DD may not cause an incorrect read (logic fault) and may escape the logic test.

Summary Behavior of Write and Read Operation Under Short Defects

Table 3 shows the summary behavior of the read and write operations of a memory cell in the presence of resistive short defects. It can be observed that resistive short defect R GN D cannot be detected with a read operation, but they may be detected with a write operation for P → AP condition. Resistive short defect R V DD presents poor detectability. Defect R V DD is more difficult to be detected than defect R GN D using conventional write and read operations. Even more, the cell performance metrics as the write margin, read margin, and the MTJ resistance between the AP state and P state, called Tunneling Magnetoresistance Ratio (TMR), may be degraded due to the presence of defects. A higher TMR is desirable because it allows better discrimination between the AP state and the P state during the reading procedure [18] [12]. Figure 11 shows the behavior of the high-resistance state (R AP ), the low-resistance state (R P ) and cell TMR (CTMR) as a function of the resistance value of the short defect. It can be observed that the resistive defect modifies the values of R AP and R P , and as a consequence, the cell TMR. Lower TMR values affect sense margin, and they may pose a reliability concern. The proposed test technique is based on the observation that a resistive-short defect between an external node and the internal node of the memory cell modifies the current flowing into (through BL terminal) and out (through SL terminal) of the cell. As shown in Fig. 12(a), a good cell behaves as a single current path, where the current provided by the read circuitry at BL terminal flows through the MTJ and the access transistor to the SL terminal. In the presence of a short defect R V DD (See Fig. 12(b)), current is injected into the cell (I short ), and hence, I SL becomes greater than I BL . Similarly, in the presence of a R GN D short (See Fig. 12(c)), the current is removed from the cell (I short ), and hence, I BL becomes greater than I SL . Figures 13(a) and 13(b) show the currents flowing through BL (I BL ) and SL (I SL ) terminals and also the current flowing through the short defect (I short ). These currents are plotted as a function of the resistance values of R V DD and R GN D for a read operation. It can be observed that the currents in the terminals SL (I SL ) and BL (I BL ) have different behavior. This is due to the existence of an alternative conducting in the presence of the resistive short defect. Another important observation is that the current difference between I SL and I BL is more significant for lower resistance values of the short defect. The current difference between I SL and I BL indicates that monitoring the current difference between I SL and I BL is more effective than monitoring only a single current value. Resistive defect R V DD causes a more significant current difference than the defect R GN D (See Figs. 13(a Figure 14 illustrates the benefits of our proposal under the effect of process variations for resistive defect R GN D , which present lower current values. Figure 14(a) shows the single values of the currents I BL and I SL under process variations. It can be observed that the single current values go up and down from the nominal value, which makes difficult to discriminate good circuits from bad circuits sensing only one of these currents. Figure 14(b) b shows the current difference values between the currents I BL and I SL under process variations. It can be observed that the current difference values increase following a mono-tonic trend as the resistive defect values decreases. This behavior of the current difference allows distinguishing good circuits from bad circuits.

Proposed Test Circuitry

In this Section, a DFT circuit oriented to defect detection without observability capability of the logic faulty behavior at main circuit outputs is proposed. This approach is adequate for the detection of weak defects, which are difficult to detect with a test based on classic logic fault observation. The benefit of the proposed test circuit to detect short defects sizes that can escape conventional logic test is validated under process variations effects. Therefore, the proposed test technique is able to detect those weak short defects that do not cause a faulty behavior, but limiting the quality and lifetime of the entire memory block. Figure 15 shows the proposed modified readout circuit with test capability based on the previous observation that a resistive short defect between an external node and the internal node of the memory cell modifies the current flowing into and out of the cell. The modified read circuit measures the difference between the current flowing into and out of the cell in the column. A significant current difference indicates the presence of a defect. Differential current amplifiers are introduced at both sides of the column (BL and SL). The modified read circuit has three possible operation modes: 1) Normal mode, 2) Test 1, and 3) Test 2 (See Fig. 15 The detection capability of the proposed circuit has been analyzed under the effect of process variations. Figures 16(a) and 16(b) show histograms of the current difference between BL and SL at the output of the proposed test circuit for both operation modes Test 1 and Test 2, respectively. 1000 Montecarlo simulations were run. Figure 16(a) shows that for strong resistive defects (smaller resistance), the test output current difference is more significant making easier the detection of the defect. Defective cells with weak short R V DD as large as 100kΩ can be fully distinguished from good cells as there is no overlap between the distribution of the defective cell and the good one. Defect R GN D is more difficult to detect. For defect R GN D = 100kΩ, there is still a significant overlap between the current distribution of a good cell and the defective cell. However, resistive short defects of 20kΩ can be fully detectable, which is still a significant improvement of the detection capability compared to the logic test.

WL 0 WL 1 BL SL WL n + - R REF RE CLP V REF Reference V cell Normal Test1 Test2 V 1 V 2 M 2c M 2d M 2e M 2f M 1b M 1a I BL I = I -I TEST2 BL SL I SL Normal Test1 Test2 V 2 V 1 M 1c M 1d M 1e M 1f M 2b
The obtained results show that the proposed DFT test circuit is capable of detected the resistive short defects with sizes that are not detectable using a conventional logic test. Moreover, the proposed test circuit could be used to diagnose the severity of a short defect by defining thresholds in the current difference.

7 Cost and Comparison of Our Proposal with Logic Test

Detection Probability Comparison

Figures 17 and18 shows the value of the detection probability (P det ) of short defects as a function of its resistance value for conventional test techniques (write and read operations test) and the proposed current difference test technique. 500 Monte Carlo simulations are done for each resistance value of the short defect. The Detection Probability (P det ) is computed with [START_REF] Liu | On modeling faults in FinFET logic circuits[END_REF], where N f is the number of runs presenting a fault and N M C is the total number of Monte Carlo simulations. The largest write time (P → AP ) including process variations has been considered for a write fault to occur. A write fault occurs when the write time of the defective cell is greater than 3.5ns. A read fault occurs when the V cell is lower (higher) than V ref = 0.66V for P state (AP state). The detection thresholds of the proposed test technique are obtained from the histograms of the defectfree currents. A resistive short defect is assumed detectable when the current difference is higher than the maximum defect-free current from the histogram. The detection threshold current is 4.6µA for I T EST,1 and 4.0µA for I T EST,2 .

P det = N f M M C (3)
For the R V DD defect (See Fig. 17), a conventional write test detects the defect in the range from 0 to 1kΩ. The defect is not detectable using a conventional read operation when the cell has stored an AP state (P det = 0), but when the cell has stored a P state the defect is detectable in the range from 0 to 200kΩ. The proposed test technique increases the detection range of this defect in two orders of magnitude concerning the test based in the read operation when the cell has stored at P state. With the proposed DFT technique the R V DD defects with values up to 1M Ω are fully detectable and partially detectable at the range from 1M Ω to 10M Ω.

On the other hand, the R GN D defect presents a lower detection range than the R V DD defect (See Fig. 18). This defect can not be detected with a test based in the cell read operation, (P det = 0 for both states). However, with a conventional test during the write operation, R GN D defects with values up to 1kΩ are fully detectable and partially detectable in the range from 1kΩ to 10kΩ. The proposed DFT technique fully detect the R GN D defect in a range from 0Ω to 40kΩ and partially detects this defect in a range from 40kΩ and 100kΩ.

Hardware Comparison

A conventional test based in write and read operation does not present area overhead. Our proposal requires to include additional transistors and test control signals. The total area of the channels of all the transistors is used as an estimation on the area overhead of the proposed DFT technique. The area of the access transistor of each memory cell is taken into account. It is assumed that the MTJ does not impact the area as is located above the access transistor. It is important to emphasize that the transistors used to copy currents in the DFT circuit have a longer channel length to ensure a correct copy of the currents. For a column composed of 2kbit, the DFT read circuit adds an approximated area overhead of 5% for the column. It should be noted that modern memories are much bigger, so the area overhead significantly decreases for larger memories. Even more, read circuit in memory arrays may be shared for several columns.

Other Issues

Regarding test time, a logic test requires to perform multiple writes and reads operations. The test time of our proposal depends on the actual method to measure the currents (built-in or external). Our proposal does not add performance degradation because the transistors connected to BL and SL have the same sizes in the DFT read circuit and the original read circuit. Even more, our proposal presents robustness against process variations. The differential current amplifier cancels most of the variations in the memory, as they impact the current flowing into and out of the cell similarly.

Short Defects that Can Be Detected

The analysis above is based on assuming a defect modeling of short defects between supply rails (VDD and GND) and the internal node (nx) of the STT-MRAM cell. The proposed technique is valid to detect all those short defects that create an unbalanced current between BL and SL nodes. Note that resistiveopen defects cannot be detected with the proposed approach, as these defects do not make different the current flowing through BL and SL terminals. Figure 19 shows a memory array, where some short defects that can be detected using the proposed approach are highlighted. The probability of occurrence of the short defects depends on the memory array architecture and how its layout is made. Typically, wider lines placed closer to other lines are more likely to present bridge defects [START_REF] Forero | Detectability challenges of bridge defects in finfet based logic cells[END_REF]. The defects that are shown in Fig. 19 exhibit similar behavior to defects R V DD and the R GN D in the defect model used in this work. Gate short defects between the W L0 and either B L0 , nx0, or S L0 behave as R V DD because WL signal is settled to V DD during a read operation to activate the access to the cell. Similarly, inter-cell shorts could be detected by previously setting the voltages of the adjacent cell at adequate values. For example, R BL0-SL1 behaves as R V DD is S L1 terminal is set to V DD . Therefore, the proposed test technique can cover a wide variety of manufacturing short defects.

Fig. 19. Resistive shorts that can be detected using the proposed approach.

Conclusions

The behavior of an STT-MRAM cell under short defects in the presence of process variations has been analyzed. A DFT circuit for a defect-oriented test of resistive-shorts in an STT-MRAM cell was proposed. The proposed test technique is based on the observation that a short defect modifies the amplitude of the currents entering (I BL ) and leaving (I SL ) the memory cell. Thus, the DFT circuit senses the current difference between the currents I BL and I SL . The proposed approach is robust to process variations and significantly improves the detectability of resistive short defects that otherwise could escape to the conventional logic test. Detection probabilities of the resistive short defects are increased leading to high-quality electronic products.

Fig. 1 .

 1 Fig. 1. STT-MRAM cell fault models

Fig. 2 .

 2 Fig.2. STT-MRAM bit-cell and its states due to the magnetic orientation of the ferromagnetic layers.

Figure 3

 3 Figure3illustrates a memory array architecture using the STT-MRAM cell. Memory cells are accessed by activating a word line (W L i ) and the pass transistors of the desired column. The access to the cells is defined by the word and column decoder circuitries. It should be noted that the number of selected columns depend on the required application. Figure4shows a single STT-MRAM cell with the used read and write circuits. The access transistor of the cell, which is driven by the word-line (WL) signal, controls whether current can flow through the MTJ to perform write and read operations.

Fig. 3 .FinFETFig. 4 .

 34 Fig. 3. Memory array using the STT-MRAM bit-cell.

Fig. 5 .

 5 Fig. 5. Current waveforms for both P → AP and AP → P write operation.

Fig. 7 .

 7 Fig. 7. Current waveforms for both P → AP and AP → P write transitions.

Fig. 8 .

 8 Fig. 8. Write time histograms for the good and defective cells.

Fig. 9 .

 9 Fig.9. Voltage generated by the memory cell (V cell in Fig.4) in a read operation as a function of the short defect resistance.

  41

Fig. 10 .

 10 Fig. 10. Histogram of the voltage generated by the memory cell (V cell in Fig. 4) in a P state read operation.

Fig. 11 .Fig. 12 .

 1112 Fig. 11. Impact of the resistance value of the short defect on the Cell TMR.

Fig. 13 .

 13 Fig. 13. Behavior of BL and SL currents as function of the short defect resistance.

Fig. 14 .

 14 Fig. 14. Comparison between monitoring single and current difference under process variations.

Fig. 15 .

 15 Fig. 15. Modified read circuit with test capability.

  Figure15shows the proposed modified readout circuit with test capability based on the previous observation that a resistive short defect between an external node and the internal node of the memory cell modifies the current flowing into and out of the cell. The modified read circuit measures the difference between the current flowing into and out of the cell in the column. A significant current difference indicates the presence of a defect. Differential current amplifiers are introduced at both sides of the column (BL and SL). The modified read circuit has three possible operation modes: 1) Normal mode, 2) Test 1, and 3) Test 2 (See Fig.15).The mode Normal is activated by setting the signals N ormal = 1 and Test 1=Test 2=0. Under these conditions, the normal functionality of the read circuit is obtained. The mode Test 1 is activated by setting the signals "Test 1=1" and

Fig. 16 .

 16 Fig. 16. Current difference histograms for good and defective cells.

Table 2 .

 2 MTJ parameters

	Parameter	Value
	MTJ Size	30nm × 30nm × 1.5nm
	Saturation Magnetization	850emu/cm 3
	Energy Barrier	56k B T
	M gO thickness	1nm
	3 Read and Write Operations of STT-MRAM Cells

Table 3 .

 3 Summary behavior of write and read operation under short defects

	Defect	Write AP → P P → AP	Read AP	P
	R GN D	NO	YES	NO	NO
	R V DD	Poor	NO	NO	Poor
	6 Proposed Test Technique

6.1 Fundamental of the Proposed Test Technique

  Our proposal requires two additional control signals I T EST,1 and I T EST,2 . Detection Probability for RGND short.

	Detection Proba	0.2 0.4 0.6	Conv. Write Test Conv. Read Test (P) Conv. Read Test (AP) Proposed Test
			0
			10 0	10 1	10 2	10 3		10 4	10 5	10 6	10 7	10 8
						R	VDD ( )
			1
	Detection Probability	0.2 0.4 0.6 0.8	Conv. Write Test Conv. Read Test (P & AP) Proposed Test
			0
			10 0	10 1	10 2	10 3		10 4	10 5	10 6	10 7	10 8
						R	GND ( )
				18.

Acknowledgments. This work was supported by CONACYT (Mexico) through the PhD scholarship number 434673/294398.