Physically Unclonable Function Using GSHE Driven SOT Assisted p-MTJ for Next Generation Hardware Security Applications

The increasing threat of security attacks on hardware security applications has driven research towards exploring beyond CMOS devices as an alternative. Spintronic devices offer advantages like low power, non-volatility, inherent spatial and temporal randomness, simplicity of integration with a silicon substrate, etc., making them a potential candidate for next-generation hardware security systems. In this work, we explore the Giant Spin Hall effect driven spin-orbit torque magnetic tunnel junction implementing physically unclonable function. The effect of process variation is considered in key MTJ parameters like TMR ratio, free and oxide layer thickness following Gaussian distribution, and Monte-Carlo simulations to determine the effect of the process variations. A unique challenge-response pair is obtained utilizing the inherent variations in magnetization dynamics of the free layer due to process variations.

The PUF should be capable of generating repeated responses 87 FIGURE 1. p-MTJ structure and switching between the two states.
for the same challenge with respect to aging and varying envi-88 ronmental conditions (electromagnetic interference, voltage 89 noise, temperature). This attribute of the PUF is called intra-90 hamming distance, which should be near zero. Moreover, 91 different PUFs generate different responses when subjected 92 to the same challenge. This property is measured as inter-93 hamming distance, which should be near 50% [9]. In recent 94 years, several PUF architectures have been proposed in the 95 literature. The simplest PUF is a ring oscillator that generates 96 a unique frequency for each IC it is fabricated on [27]. Delay-97 based arbiter is another example of a PUF that generates a 98 fingerprint based on the propagation delay of the circuit [28]. 99 Error Correction Codes (ECCs) have been widely employed 100 as an effective means of smoothing noise response to improve 101 PUF reliability but die area or design complexity is sac-102 rificed [29]. PUFs based on non-volatile memory (NVM) 103 devices such as spin torque effect, phase change memory 104 (PCM), etc. are attracting considerable research interest due 105 to their high scalability and low power consumption [3].  Fig. 1 shows a typical p-MTJ structure comprised of two 108 relatively thick ferromagnetic layers (a fixed layer and a free 109 layer) separated by a relatively thin tunnel barrier layer [30]. 110 When the fixed layer and the free layer have the same mag-111 netic direction (parallel, denoted by P), the MTJ shows a 112 lower resistance (R P ). On the contrary, when the magnetic 113 directions of both layers are opposite (Anti-parallel, denoted 114 by AP), the MTJ shows a higher resistance (R AP ). In GSHE-115 driven MTJ, a spin current is generated perpendicularly by 116 passing a SHE write current through the heavy metal. This 117 spin current exerts torque on the free layer, causing the 118 switching of the MTJ state. The spin current is due to the 119 directional and coherent motion of electron spin and is a 120 rank-two pseudo-tensor quantity with multiple components. 121 The TMR ratio characterizes the resistance difference and is 122 defined by the following equation: If the difference between the resistances in parallel and 125 anti-parallel is larger, it shows higher TMR and readability. 126 Here, m and m r are the unit vector along with magneti-   Kelvin), the data retention time is around ten years and has 197 deterministic switching characteristics which are utilized for 198 non-volatile memory applications [31]. The simulation is 199 performed with 5% process variation in TMR, free layer 200 thickness, and oxide layer thickness. The parametric analysis 201 in the spectre simulator is then performed for other parame-202 ters like temperature, heavy metal thickness, and anisotropy 203 field value to demonstrate that other parameter variations can 204 create a unique free layer magnetization response and thus a 205 variable resistance behavior at the output side which can be 206 utilized for generating unique C-R. As two identical device 207 fabrication in such a multilayer structure is not possible, this 208 leads to distinct input/output characteristics, and the ability 209  to utilize such behavior in MRAM structure for hardware 210 security is being explored in recent research [9].  Table 2. Table 3  of temperature, as shown below: where, E b is the energy barrier height

246
In SOT-assisted MTJ switching, an extra heavy metal is 247 required through which charge current is passed, generating 248 a spin current in the perpendicular direction through the stack. 249 The SOT mechanism assists in the switching. Any variation 250 in heavy metal dimension would change the requirement of 251 critical current density required for switching and thus will 252 create a unique switching response as shown in Fig. 4(a) 253 for the case of variation in heavy metal thickness. As it is 254 not possible to fabricate an identical multilayered stack with 255 some variation in dimensions is to be expected which can 256 be utilized for generating unique C-R pair. Other physical 257 parameters also result in variation in free layer magnetization 258 dynamics along with variation in supply currents; thus, SOT-259 assisted MTJ offers a complex and rich source of entropy 260 and non-linearity, making them an ideal candidate for PUFs. 261 where H kp is the perpendicular anisotropy field along the z-  Table 4 to obtain the required thermal stability 282 factor based on:      (8)

368
The key requirement for PUF is high process variation and 369 non-linearity to ensure enough randomness and uniqueness 370 in the structure. An extra heavy metal for generating the 371 spin-orbit torque creates more chaotic magnetization dynam-372 ics for the free layer than another non-volatile device-based 373 PUF. The requirement of two sets of current sources will 374 make it more difficult to reverse engineer systems based on 375 such PUF. 376 Fig. 8(a) represents the schematic for generating the C-R 377 pair. Fig. 8(b) represents the C-R implementation waveform 378 based on the above PUF, in which we include process varia-379 tion of 10% (TMR ratio = 1.2, free layer thickness = 1.4nm, 380 and oxide layer thickness = 1.2 nm) in p-MTJ with high 381 barrier height. We performed 200 times Monte Carlo simu-382 lations to generate C-R pair in TSMC 65nm technology node 383 with CMOS W/L ratio = 10/3 and Vdd = 1.2 V. No process 384 variation for the CMOS device was considered during the 385 simulation, and other simulation parameters are the same as 386 mentioned in Table 2 with simulation steps of 1 ps, asy = 387 1.1 and fac_fl = 2.5. In Fig. 8(b)-(c), due to process variation 388 and the random sampling method used during simulation 389 unique magnetization orientation of the free layer would lead 390 to a unique response for a given challenge. Fig. 8(c) shows 391 the applied current density to the PUF structure. In Fig. 8(d), 392 MTJ resistance, a critical parameter, is obtained using Monte 393 Carlo simulation for 200 points, and variation in resistance 394 due to process variations is demonstrated. The energy per bit 395 can be calculated according to the following equation: where t sw is the switching delay, V dd is the supply voltage, 398 and i dd (t) is the total current from the power supply. The write 399 current is set at a value larger than the critical current density 400 required for obtaining a switching probability of 100%. 401 Table 5 contains the effect of different amounts of process 402 variations in MTJ average resistance value. As the process 403 variations that follow the Gaussian distribution increase, the 404 variation in the range of minimum and maximum value of 405 resistance increases, and the standard deviation increases. 406 Thus, the higher the process variations, the more the differ-407 ence in the expected value of MTJ resistance is exploited to 408 obtain a unique device signature, which is one of the criti-409 cal requirements of PUFs, thus making SOT-assisted MTJ a 410 potential candidate for PUF implementation. Dual PUF circuits are designed to enable unique responses, 413 and a larger number of stages provide more degree of ran-414 domness in signature. The multistage PUF structure can be 415 designed for a specific type of application and considering 416 other design constraints. In Fig. 9 (a), we present a simple 417 VOLUME 10, 2022    Fig. 8(a).
approach where PUF 1 and PUF 2 have different process vari-418 ations (10% and 5%, respectively), and we provide a specific 419 set of challenges 1 and 2. Further, we create another logic 420 stage for generating the unique response signature. In many 421 previous works, the use of delay and toggle path is used to 422 create unique C-R pair. In Fig. 9(b), we perform a similar 423 analysis as done in section III-A for the Monte Carlo analysis 424 of the circuit presented in Fig. 9 (a). 425 Table 6 shows that the standard deviation in the average 426 value of the response is significant compared to the mean 427 value, which is also clear from the Monte Carlo results in 428 Fig. 9 (b)  He has published more than 400 papers in leading peer-reviewed journals 673 and conference publications. His research interests include design of state-674 of-the-art innovative technological solutions that span a broad range of 675 technical areas including smart cities, autonomy, smart health, smart mobil-676 ity, embedded systems, nanophotonics, and spintronics. His research group 677 was responsible for developing the world's first realization of compressive 678 sensing systems for signals, which provided an unprecedented one order of 679 magnitude savings in power consumption and significant reductions in size 680 and cost and has enabled the implementation of self-powered sensors for 681 smart cities and ultra-low-power biomedical implantable devices.