A Physical Unclonable Function Based on Variations of Write Times in STT-MRAM due to Manufacturing Defects

A physical unclonable function (PUF) utilizes the unclonable random variations in a device’s responses to a set of inputs to produce a unique “biometric” that can be used for authentication. The variations are caused by unpredictable, unclonable and random manufacturing defects. Here, we show that the switching time of a magnetic tunnel junction injected with a spin-polarized current generating spin transfer torque is sensitive to the nature of structural defects introduced during manufacturing and hence can be the basis of a PUF. We use micromagnetic simulations to study the switching times under a constant current excitation for six different (commonly encountered) defect morphologies in spin-transfer-torque magnetic random access memory (STT-MRAM) to establish the viability of a PUF.

💡 Research Summary

The paper proposes a novel physical unclonable function (PUF) that exploits the sensitivity of spin‑transfer‑torque magnetic random‑access memory (STT‑MRAM) switching times to manufacturing defects. Traditional MRAM‑based PUFs rely mainly on resistance variations; this work instead focuses on the stochastic switching time required to achieve a target switching probability under a fixed current pulse. Six representative defect morphologies (C0–C6) observed in real MTJ devices are modeled: a pristine ellipse (C0), a central 5 nm hole (C1), a half‑thick/half‑thin step (C2‑3), a 10 nm rim lift (C4), a 5 nm surface‑rise (C5), and a through‑hole (C6).

Micromagnetic simulations are performed with MuMax3 at 300 K, using a cobalt soft layer shaped as a 100 nm × 90 nm ellipse, 3 nm average thickness, discretized into 32 × 32 × 4 cells (≈2.8 nm × 3.1 nm × 1 nm). A constant 3 mA spin‑polarized current (30 % polarization) is applied perpendicular to the layer, and 100 stochastic trajectories are generated for each defect type. Switching is defined as the normalized y‑component of magnetization exceeding 0.9. The resulting switching probability versus pulse width curves reveal distinct signatures: C1 and C6 reach ~69 % probability at 0.75 ns, while C2‑3 only attains ~20 %.

To construct a PUF, three MTJs are grouped into a “unit”. Each MTJ is assigned a different defect type (e.g., C1, C4, C2‑3). The same 3 mA, 0.75 ns pulse is applied to all three. A binary response is generated by mapping a high switching probability (>50 %) to ‘1’ and a low probability to ‘0’. This yields response strings such as 110, 101, or 011 depending on the defect distribution. By varying the challenge (pulse width or amplitude) a full challenge‑response table can be built, which is unique to the specific defect morphology of the unit.

Security is evaluated using the inter‑Hamming distance (IHD) between response strings of different units. For the six permutations of defect assignments (no repetition), the average IHD is 0.533 for the 0.75 ns challenge, and 0.479 when repetitions are allowed (27 possible units). Both values are close to the ideal 0.5, indicating good randomness. Changing the pulse width to 0.7 ns modifies the response bits, further expanding the challenge space.

The authors also suggest a stronger PUF variant based on the full distribution of switching times rather than a single probability point. By running 1000 trials per defect type, distinct time‑histograms are obtained, which can be used as high‑entropy features for authentication.

Overall, the study demonstrates (1) that defect‑induced variations in STT‑MRAM switching dynamics provide a viable entropy source, (2) a systematic simulation‑driven methodology to quantify these variations, and (3) that the resulting PUF exhibits near‑ideal statistical properties. While experimental validation remains future work, the simulation framework enables rapid exploration of defect scenarios and supports the development of robust, hardware‑level security primitives for emerging non‑volatile memory technologies.