Improved Robustness against Magnetic Field in Spin–Orbit‐Torque‐Based Physical Unclonable Functions through Write‐Back Operation

Physical unclonable functions (PUFs), which exploit uncontrollable and unpredictable randomness of materials or devices, have been investigated as a hardware‐based security primitive owing to their robustness against adversarial attacks. Spin–orbit torque (SOT) switching is one of the promising techniques for PUF applications because it can provide randomness by the stochastic switching distribution of perpendicular magnetization. In this study, the improvement in the reliability of SOT‐based PUFs against external magnetic fields with write‐back operation (WBO) is demonstrated. A PUF consisting of 8 × 4 array Hall‐bar devices with a Ta/CoFeB/MgO structure is fabricated, where the random distribution of the SOT switching current serves as an entropy source. However, the information stored in the PUF is easily modified by the application of an external magnetic field. To improve the robustness against magnetic fields, a WBO is introduced that applies an additional current to saturate the magnetization in either the upward or downward direction depending on the magnetic state. As a result, the SOT‐based PUF maintains an entropy value close to unity under a magnetic field of up to the coercive field of the CoFeB layer. Furthermore, the WBO provides a digitalized output, which potentially reduces peripheral circuitry such as analog‐to‐digital converters.


Introduction
The rapid development of information technology, such as the internet of things (IoT), big data, and cloud computing, has led to an increase in data processed through edge computing devices. [1] In this data-centric era, the importance of information security is continuously increasing. However, conventional software-based security solutions are susceptible to adversary attacks. [2] To overcome this security threat, hardware-based security technology has attracted a great deal of attention as a promising alternative. [3] One example is the physical unclonable function (PUF), which generates uncontrollable and unpredictable cryptographic keys from stochastic variations of the physical properties of materials or devices. [3][4][5][6] Therefore, PUFs can be used as security keys for hardware authentication as each device creates a unique output response to an identical input challenge.
Among the various systems for PUF applications, Si-based PUFs, such as arbiter, [7] ring-oscillator, [8] and static random-access memory [9] PUFs, have been widely investigated due to their compatibility with existing semiconductor technology. [10] These Si-based PUFs utilize process-induced random variations in integrated circuits (ICs) such as delay time or frequency differences between two identical ICs. However, they show reduced reliability in environments with temperature or bias fluctuations. [11][12][13][14] Additional power consumption and area overhead for bit error correction codes are therefore essential for reliable operations. [15,16] Furthermore, the challenge-response pairs (CRPs) of Si-based PUFs can be predicted by side-channel analysis or machine learning attacks. [17][18][19][20] To tackle those challenges, emerging materials such as graphene [21] and halide perovskite [22] recently have been investigated as PUF materials. The chaotic nature of the response of these materials to external stimuli, such as a random impurity distribution in graphene and stochastic switching behavior in halide perovskite memristor, which can serve as entropy sources, is robust against environmental changes and difficult to predict. [23][24] Physical unclonable functions (PUFs), which exploit uncontrollable and unpredictable randomness of materials or devices, have been investigated as a hardware-based security primitive owing to their robustness against adversarial attacks. Spin-orbit torque (SOT) switching is one of the promising techniques for PUF applications because it can provide randomness by the stochastic switching distribution of perpendicular magnetization. In this study, the improvement in the reliability of SOT-based PUFs against external magnetic fields with write-back operation (WBO) is demonstrated. A PUF consisting of 8 × 4 array Hall-bar devices with a Ta/CoFeB/MgO structure is fabricated, where the random distribution of the SOT switching current serves as an entropy source. However, the information stored in the PUF is easily modified by the application of an external magnetic field. To improve the robustness against magnetic fields, a WBO is introduced that applies an additional current to saturate the magnetization in either the upward or downward direction depending on the magnetic state. As a result, the SOTbased PUF maintains an entropy value close to unity under a magnetic field of up to the coercive field of the CoFeB layer. Furthermore, the WBO provides a digitalized output, which potentially reduces peripheral circuitry such as analog-to-digital converters.
Recent studies have demonstrated spintronic PUFs, which also generate unique CRPs by utilizing stochastic variations in magnetic properties such as magnetic anisotropy [25] and magnetization switching characteristics. [26][27][28] One example is to exploit spin-orbit torque (SOT), [29][30][31] which has a nondeterministic switching characteristic of perpendicular magnetization unless an intentional symmetry break is introduced into the sample. It was demonstrated that SOT-based PUFs can be realized by utilizing either stochastic SOT switching [26] or random pinning of domain wall motion [27] as an entropy source. For the latter case, SOT-induced domain wall motion in Ta/CoFeB/MgO structures created multiple intermediate magnetic states that convert the digital bit stream through analog-to-digital converters, generating cryptographic keys. [27] Note that information stored in such spintronic PUFs can be lost by an external magnetic field. However, the reliability of those PUFs under an external magnetic field has yet to be addressed.
In this study, we demonstrate improved reliability of SOTbased spintronic PUFs against external magnetic fields by introducing a write-back operation (WBO). Note that WBO was initially proposed to improve reliability against aging and environmental variations by reducing the bit-error-rate of nonvolatile memory-based PUFs [32,33] and later experimentally demonstrated in resistive memory-based PUFs. [22,34] Here, we show that the SOT switching behavior in Ta/CoFeB/MgO structures depends on the writing conditions, and multistate switching occurs with a reduced writing current pulse width and in-plane magnetic field. This causes a distribution of SOT switching currents between the devices, allowing an 8 × 4 array SOT-based PUF to be built. However, the information stored in the PUF is easily modified by an external magnetic field. To improve the robustness against magnetic fields, we apply an additional writing current to saturate the magnetization in either the upward or downward direction depending on the magnetic state: this is referred to as a WBO. As a consequence, the SOTbased PUF maintains an entropy value close to unity under a magnetic field of up to the coercive field of the CoFeB layer. Furthermore, the SOT-based PUF with WBO provides digital outputs, potentially reducing peripheral circuitry such as the analog-to-digital converters. Our results, combined with the advantages of current state-of-the-art magnetic random-access memory (MRAM) technology, facilitate reliable and energy-efficient spintronic PUFs.

Stochastic Distribution of the SOT Switching Current
To construct a SOT-based PUF, we employ Hall-bar devices with a Ta (4 nm)/CoFeB (1 nm)/MgO (3.2 nm) structure, as shown in Figure 1a. Figure 1b shows the anomalous Hall resistance (R H ) of the device as a function of the out-of-plane magnetic field (B z ), indicating that the CoFeB layer has perpendicular magnetic anisotropy. The magnetization direction of the CoFeB layer can be switched by SOT, where an in-plane current (I x )-induced spin current through the spin Hall effect in Ta exerts a torque and manipulates the magnetization with the help of an in-plane magnetic field (B x ). We first investigated the SOT switching behavior according to the pulse width of I x and the magnitude of B x . Figure 1c shows the SOT switching curves under conditions with two different I x width and B x combinations; the red (black) curve is the result obtained when the I x width is 80 µs (10 µs) and B x is 50 mT (10 mT). As seen in Figure 1c, with sufficiently large I x width and B x , abrupt switching is obtained. In contrast, multistate switching, where magnetization switching is completed through several intermediate states, is observed with reduced I x width and B x . The multistate switching is believed to be due to domain wall pinning, [27] which differs from device to device. Therefore, we exploit this as an entropy source for SOT-based PUFs, as discussed below.
Next, we fabricated a SOT-based PUF composed of an 8 × 4 Hall-bar device array, as shown in Figure 1d, where each device is numbered from 1 to 32. To investigate the switching current (I C ) distribution within the SOT-based PUF, SOT switching experiments were performed for each Hall-bar device with an I x of 10 µs and a B x of 10 mT. Figure 1e shows the results presenting the normalized R H versus I x curves of all devices. It is shown that the I C 's of the Hall-bar devices, which were identically fabricated and measured under the same conditions, have a distribution as indicated by the magenta-shaded area in Figure 1e. This is attributed to differences in domain wall pinning sites between devices, resulting from uncontrollable defects introduced during device fabrication. [35,36] We further examined the I C distribution of a single Hall-bar device by repeating the switching experiments 32 times. Figure 1f shows the SOT switching curves of a representative device, demonstrating the I C distribution due to the repeated operation (≈0.24 mA) being much narrower than that between the devices (≈1.50 mA). This demonstrates that the I C distribution shown in Figure 1e can be used as an entropy source of our SOT-based PUF. Figure 1g presents the I C 's of the 32 Hall-bar devices, where we define the median I C value as the challenge current I challenge to construct the PUF. For our sample, I challenge is −8.8 mA. It is expected that applying I challenge to the Hallbar devices will make half of the devices have a positive R H and the other half have a negative R H . Note that the multistate switching behavior is maintained at temperatures ranging from 25 to 100 °C (Supporting Information S1). This indicates that SOT-based PUFs can be constructed with the same procedure even at high temperatures.

SOT-Based PUF with Write-Back Operation
We now discuss how to construct a reliable spintronic PUF with a write-back operation (WBO). Using the same sample as shown in Figure 1d, we first initialized the magnetization direction of the CoFeB to the up-state and then applied an I challenge of -8.8 mA. Note that the pulse width of I challenge and the magnitude of B x are 10 µs and 10 mT, respectively.

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R H and the remaining devices have a negative R H , which can be used as binary bits of "0" and "1" in our SOT-based PUF. Furthermore, the binary digital bits are evenly distributed in space, as demonstrated in Figure 2b, where colors indicate the magnitude and sign of R H values. Although not demonstrated here, it can be expected that different CRPs can be generated by modulating the SOT switching conditions, such as the strength of external magnetic fields and/or the width of pulsed currents. Note that the analog values of R H can be converted into the digital bit stream through analog-to-digital converters. [27] However, the intermediate magnetization states can be easily modified by an external magnetic field, even when the external magnetic field is smaller than the coercivity of CoFeB. To address this problem, we introduce a write-back operation (WBO). As shown in Figure 2c, WBO is a process of saturating the magnetization state according to the sign of R H by applying a write-back current (I WB ) that is sufficiently larger than I C .  Figure 2d,e shows the normalized R H and its spatial distribution for the same PUF device as those shown in Figure 2a,b after the WBO. This demonstrates that the magnetizations are fully saturated in either the upward or downward direction, which can represent two digitalized bits each. It is found that the WBO can be successfully performed at high temperatures with reduced I WB (Section S1, Supporting Information). We now discuss advantages of the SOT-based PUFs with WBO. In this study, to demonstrate the working principle of the SOT-based PUF, Hall-bar devices were used to detect the magnetization directions. However, for practical applications, we can implement magnetic tunnel junctions with large magnetoresistance, which provides digitalized outputs with increased sensing margin. This can simplify peripheral circuitry by potentially eliminating the need for analog-to-digital converters, which lead to a reduction of energy consumption and area overhead (Section S2, Supporting Information). Furthermore, WBO enhances robustness against an external magnetic field, which will be discussed later.

Enhanced Robustness against External Magnetic Field
To investigate the effect of the WBO on robustness against an external magnetic field, we performed magnetic tampering. To this end, we constructed the R H distribution patterns using the same procedure with and without the WBO, as described in Figure 2. We then exposed the sample to an out-of-plane magnetic field (B z ) for 2 s and monitored the changes in the www.advelectronicmat.de patterns with each magnetic field. Figure 3a shows the results, where the upper (lower) panel represents the sample without (with) WBO. For the sample without the WBO, the color starts to change at a B z of 1.0 mT and is significantly modified by a B z of 1.5 mT. Note that the coercivity of the CoFeB layer is about 7.5 mT (Figure 1b). This indicates that the information stored in our SOT-based PUF will be lost by magnetic tampering with a magnetic field smaller than the coercivity of the CoFeB layer. This is likely due to the fact that the domain wall can move even with a relatively small magnetic field in the unsaturated magnetic state. On the other hand, the sample with the WBO maintains the patterns unchanged at a larger B z . The lower panel of Figure 3a shows the results of the sample with the WBO, where the color starts to change at a B z of +7.5 mT. This demonstrates that the robustness against external magnetic fields has been improved by saturating the magnetic state through the WBO.
To characterize the robustness of the SOT-based PUF against a magnetic field, we calculated entropy E as a function of the tampering field B z . Note that E is a PUF metric used to evaluate the distribution of bits "1" and "0," which is expressed by where p is the probability of finding "1" ("0"). In our PUF device, "1" ("0") is defined as the upward and downward magnetization states of the top CoFeB layer, respectively. The E value of the ideal PUF with a uniform distribution of "1" and "0" (p = 0.5) would be 1. Figure 3b shows that the entropy value of both samples is initially 1 and decreases with increasing B z . However, the B z dependence of entropy is very different between the samples. The sample without WBO shows the strong dependence of E on B z , E becomes zero when B z = +2.0 mT. In contrast, the E of the sample with WBO maintains a value close to 1 until B z = +7.5 mT and starts to decrease at B z larger than 10 mT. These results demonstrate that the output response of the SOT-based PUF is maintained even when an external magnetic field up to the coercivity is applied, confirming the enhanced robustness against magnetic tampering.

PUF Metrics of Spintronic PUFs
To evaluate the device characteristics of the spintronic PUF, we fabricated 12 different PUFs with the same procedure described above. Figure 4a shows the PUF patterns of the 12 spintronic PUFs, where the red (blue) color represents the magnetization aligned in the upward (downward) direction. Note that the SOT switching curves of each PUF are given in Section S3, Supporting Information. To quantitively estimate the uniqueness of our device, we calculate the inter-Hamming distance (inter-HD), which represents the difference between the CRPs of the two PUFs. The HD is the difference between two-bit streams, and inter-HD is evaluated by calculating the HDs of all combinations of two PUFs. Figure 4b shows the probability mass function (PMF) as a function of the inter-HD. From the Gaussian fit shown in the red curve, we extract a mean normalized inter-HD of 0.505 and a standard deviation of 0.098. This demonstrates the uniqueness of our SOT-based PUFs, which can be used as security keys for hardware authentication. Furthermore, we also calculate the entropy of the 12 PUFs, all of which are close to the ideal value of 1 (Figure 4c). This again confirms that our SOTbased PUFs have a uniform distribution of binary bits.

Conclusion
We have demonstrated that the reliability of the SOT-based PUFs against external magnetic fields can be enhanced by introducing a write-back operation (WBO). Using the stochastic multistate SOT switching behavior in Ta/CoFeB/MgO structures, we construct a SOT-based PUF consisting of an 8 × 4 array Hall-bar device. However, the PUF responses of the SOT-based PUF are easily modified by an external magnetic field. To improve the robustness against magnetic fields, we introduce a WBO that saturates the magnetization in either the upward or downward direction depending on the magnetic state by applying an additional writing current. This improves the robustness to magnetic fields in the SOT-based PUF, where the entropy value remains close to unity even when a magnetic www.advelectronicmat.de field corresponding to the coercive field of the CoFeB layer is applied. Moreover, the WBO provides digitalized outputs corresponding to the magnetization directions of the top CoFeB layer, which can potentially reduce peripheral circuitry such as analog-to-digital converters. Our results, combined with magnetic tunnel junctions with larger output signals, facilitate reliable, and energy-efficient spintronic PUFs.

Experimental Section
Device Fabrication: The sample structure was composed of Ta (4 nm)/ CoFeB (1 nm)/MgO (3.2 nm)/Ta (2 nm). Each layer was deposited by magnetron sputtering on a SiO x substrate at room temperature with a base pressure below 3.0 × 10 −8 Torr. The metal layers (Ta, CoFeB) were deposited by DC sputtering with a power of 30 W and a working pressure of 3.0 × 10 −3 Torr and the MgO layer was deposited by RF sputtering with a power of 150 W and a working pressure of 1.0 × 10 −2 Torr. The annealing process was conducted at 200 °C for 40 min in a vacuum condition to enhance perpendicular magnetic anisotropy of the CoFeB layer. To fabricate a 32-bit spintronic PUF, 8 × 4 array Hall-bars were patterned using photolithography and Ar ion beam etching. The width and length of the Hall-bar were 5 and 25 µm, respectively. For the electrical measurement, Cr (7 nm)/Au (150 nm) electrodes were fabricated by a lift-off process after deposition on the patterned sample.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.