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. 2023 Dec 20;18(1):1041–1053. doi: 10.1021/acsnano.3c10308

Heteronanostructured Field-Effect Transistors for Enhancing Entropy and Parameter Space in Electrical Unclonable Primitives

Jaeseo Park †,‡, Jung Woo Leem §, Minji Park †, Jun Oh Kim †, Zahyun Ku ∥, Won Chegal †, Sang-Woo Kang †,‡,*, Young L Kim §,⊥,*
PMCID: PMC10786166  PMID: 38117976

Abstract

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Hardware security is not a new problem but is ever-growing in consumer and medical domains owing to hyperconnectivity. A physical unclonable function (PUF) offers a promising hardware security solution for cryptographic key generation, identification, and authentication. However, electrical PUFs using nanomaterials or two-dimensional (2D) transition metal dichalcogenides (TMDCs) often have limited entropy and parameter space sources, both of which increase the vulnerability to attacks and act as bottlenecks for practical applications. We report an electrical PUF with enhanced entropy as well as parameter space by incorporating 2D TMDC heteronanostructures into field-effect transistors (FETs). Lateral heteronanostructures of 2D molybdenum disulfide and tungsten disulfide serve as a potent entropy source. The variable feature of FETs is further leveraged to enhance the parameter space that provides multiple challenge–response pairs, which are essential for PUFs. This combination results in stably repeatable yet highly variable FET characteristics as alternative electrical PUFs. Comprehensive PUF performance analyses validate the bit uniformity, reproducibility, uniqueness, randomness, false rates, and encoding capacity. The 2D material heteronanostructure-driven electrical PUFs with strong FET-to-FET variability can potentially be augmented as an immediately deployable and scalable security solution for various hardware devices.

Keywords: heteronanostructure, 2D transition metal dichalcogenides, field-effect transistor, physical unclonable function, entropy, parameter space

Introduction

Internet of Things devices, including consumer and healthcare wearables, have become highly vulnerable to potential attacks, partly because of the rapid growth in communication technologies, including fifth-generation mobile networks.1,2 Recent advances in quantum computing also imply an imperative need for high-level security in the cyberspace and physical space domains.3−5 Advanced cryptographic primitives with high-level security have received considerable attention as a solution for mediating security protocols and hardware security operations.6−10 Such hardware security technologies often do not rely on conventional nonvolatile memory.6−10 Specifically, a physical unclonable function (PUF) is considered as an immediately available hardware security solution for key generation, authentication, and identification.6,11−15

PUFs exploit inherently unpredictable nano- and microstructural variations (i.e., physical disorders) embedded in individual devices during manufacturing processes.7,11−15 Physical disorder is unique to each device, serving as an entropy source for unclonability. Another important aspect of PUFs is the parameter space.13−17 The parameter space determines possible challenge–response pairs that can be generated by a PUF on a single device, which makes it difficult for an attacker to train a mathematical model that can predict the responses. Upon a given stimulus (e.g., light or voltage) as an input challenge, a PUF generates a physically defined “digital fingerprint” unique output (i.e., response) that is derived from the embedded disordered structure. Thus, a high-dimensional parameter space, which enables multiple pairs of input challenges and output responses, is mandatory for ensuring a high level of security in identification and authentication by overcoming the limitations of conventional PUFs against external attacks. In addition, there is no need to store a security key in nonvolatile memory, because a key can be extracted from a physical disorder formed during the manufacturing process. Overall, both high entropy and enhanced parameter space differentiate PUFs from other unique objects and security tags used for hardware security purposes, making them extremely difficult for counterfeiters or attackers to clone or model.

Historically, the term PUF was coined with the concept of physical one-way functions using optical stimuli.18 Optical PUFs leverage linear speckle patterns or fluorescent properties, which often limit their practical implementation because of the requirement of bulky light sources and detectors (e.g., light-emitting diodes, laser diodes, lamps, cameras, and spectrometers).19−25 As a result, silicon-based electrical PUFs have exploited the advantage of intrinsic manufacturing-induced variations in integrated circuits and demonstrated potential for realistic PUF implementation due to miniature and compact form factors.14,26−28 However, these conventional electrical PUF approaches have several manufacturing and operational limitations, including high power consumption, area inefficiency, and high manufacturing cost.29,30 Low entropy and large bit-error ratios often require pre- and postprocessing steps for error correction and augmented security, which can compromise security due to vulnerability to external attacks.11,31−34

To overcome these limitations, electrical PUFs using non-silicon nanomaterials and nanostructures have recently been proposed. In particular, two-dimensional transition metal dichalcogenides (2D TMDCs) have shown electrical PUF applications.35−37 2D TMDCs are excellent channel materials for high-performance, low-power-consumption transistors, owing to the distinctive characteristics including high charge carrier mobility, high on/off current ratio, appreciable bandgap, low interface scattering, and low gate leakage current by a dangling-bond-free surface and band-to-band tunneling, comparable to silicon.38−45 Moreover, wafer-scale growth and ambient stability make them ideal for practical applications.44−46 While the recent studies35−37 have successfully leveraged the excellent properties exhibited by 2D TMDCs, the full potential for electrical PUFs with high-security levels has not yet been realized.

Unfortunately, electrical PUFs using such single-structured 2D TMDC-based transistors are typically subject to two major limitations: insufficient randomness and limited parameter space. Insufficient randomness with low entropy is often associated with output responses that follow a Gaussian distribution in a predictable manner. A single challenge–response pair in the existing transistor-based electrical PUFs using 2D TMDCs increases vulnerability to external attacks; field effect transistor (FET)-based PUFs using bare MoS2 or WS2 are intrinsically disadvantaged to enhance the parameter space, due to the limited measurements of gate voltage and drain current.35,36,47−49 It should be noted that an enhanced parameter space is of paramount importance in deployable and scalable PUFs.13−17 Unfortunately, other electrical PUFs using nanomaterials and nanostructures47−64 have a limited parameter space (see Table S1 of Supporting Information for comprehensive comparisons).

In this work, we report an electrical PUF with an enhanced parameter space as well as a strong entropy source derived from 2D TMDC heteronanostructure-embedded FETs. The FET platform offers a means to realize multiple challenge–response pairs, and the lateral heteronanostructure of molybdenum disulfide (MoS2) and tungsten disulfide (WS2) offers a source of high entropy (i.e., FET-to-FET variability) as well as good electrical stability (the proposed parameter space and entropy-enhanced electrical PUF is hereafter referred to as PePUF). MoS2/WS2 heteronanostructures are formed by using a metal–organic chemical vapor deposition (MOCVD) system, which is scalable for mass production. The growth of laterally heteronanostructured MoS2/WS2 results in a spatially random distribution of nanoislands. The unpredictable electrical properties guarantee high FET-to-FET variability, which in turn enhances the entropy and parameter space. After digitized keys are generated using a bit extraction process, comprehensive PUF performance analyses, including bit uniformity, randomness, reproducibility, uniqueness, false rates, and stability, support the feasibility of PePUF for an immediately exploitable hardware security cryptosystem.

Results

Figure 1a illustrates the concept of parameter space enhancement derived from a combination of FETs and heteronanostructured MoS2/WS2 for a PePUF. The three variables of a FET (gate voltage (VG), drain current (ID), and drain voltage (VD)) offer a platform to increase the electrical PUF parameter space to implement multiple challenge–response pairs, while the previous FET-based PUFs are not utilized for increasing the PUF parameter space.35,36,47−49 In our case, one PePUF is composed of 64 FETs and each FET has a channel of laterally heteronanostructured MoS2/WS2 (Figure S1, Experimental Section). A FET enables variable configurations to enhance the parameter space of the electrical PUFs. We analyze the ID–VG transfer characteristics of 64 FETs in a PePUF to configure the proposed PUF and ensure the generation of reliable multiple challenge–response pairs. VD is used as an input challenge (Cn), while ID is employed as an output response (Rn) with a fixed VG value of +20 V. Importantly, laterally heteronanostructured MoS2/WS2 intrinsically possesses a random distribution and density of nanoislands, erratic electrode connections between the source and drain, interface defects in heterostructures, and MoS2/WS2 mono- or bilayers. The FET-to-FET variability (i.e., various drain current levels) of FETs derived from the inherent randomness of heteronanostructured MoS2/WS2 can serve as a physical entropy source for unclonability. Consequently, the swing behavior of ID of each FET at different VD values leads to drastic changes in the ID distributions in FETs. Finally, the digitized key (Kn) of a binary bitstream is generated by using a binary-bit extractor.

Figure 1.

Figure 1

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Parameter space and entropy-enhanced electrical PUF using FETs and 2D heteronanostructures. (a) Schematic illustration of parameter space enhancement derived from MoS2/WS2 heteronanostructure-based FETs for parameter space and entropy-enhanced electrical PUFs (PePUFs). A PePUF is composed of 64 various FETs with a channel of laterally heteronanostructured MoS2/WS2. As an input challenge (Cn), drain voltage (VD) is utilized in the FETs. As an output response (Rn), drain current (ID) is acquired at a gate voltage (VG) of +20 V. Through the extraction process of binary bits, a digitized key (Kn) is generated. (b) Microscopic images of a PePUF consisting of 64 FETs (8 × 8 arrays). The top-view scanning electron microscopy (SEM) image shows a FET with a channel of laterally heteronanostructured MoS2/WS2. (c) SEM images of bare WS2, bare MoS2, and laterally heteronanostructured MoS2/WS2. (d–f) ID–VG transfer characteristics of 64 FETs for different channels of (d) bare WS2, (e) bare MoS2, and (f) laterally heteronanostructured MoS2/WS2 at VD = +1 V. (g) Histograms of ID at VG = +20 V from panels d–f. Laterally heteronanostructured MoS2/WS2 has a distinct bimodal distribution leading to reliable key generation. (h, i) Raman spectra (h) and normalized photoluminescence spectra (i) of bare WS2 (black line), bare MoS2 (red line), and laterally heteronanostructured MoS2/WS2 (blue line).

One PePUF consists of 64 FETs for three different channels: WS2, MoS2, and MoS2/WS2 (Figure 1b). Specifically, laterally heteronanostructured MoS2/WS2 is fabricated by a two-step sequential method using MOCVD (Figure S2, Experimental Section). First, WS2 is synthesized by flowing tungsten hexacarbonyl (W(CO)6) (precursor) into the chamber along with an injection of hydrogen (H2) and hydrogen sulfide (H2S) gases. After synthesis, the flow of the W(CO)6 precursor is terminated, while the inflow of H2 and H2S gases is maintained. Second, a molybdenum hexacarbonyl (Mo(CO)6) precursor is injected into the chamber to synthesize heteronanostructured MoS2/WS2. Importantly, the MoS2 layer is grown laterally at the unpassivated edges of WS2 owing to H2 ambient gas and excess H2S reactant gas relative to Mo(CO)6 and W(CO)6 precursors.65−67 WS2, MoS2, and laterally heteronanostructured MoS2/WS2 have triangular-shaped nanoislands (Figure 1c) as follows: WS2 has a larger size range of 178 ± 100 nm (mean ± standard deviation) with a low nucleation site density, whereas MoS2 has a smaller size range of 144 ± 10 nm with a high nucleation site density. These various sizes are attributed to the driving force for nucleation, determined by the different vapor pressure levels of W(CO)6 precursor used to synthesize WS2 or MoS2.67−69 Laterally heteronanostructured MoS2/WS2 has a size range of 346 ± 160 nm. Notably, MoS2/WS2 exhibits a high degree of disorder with small monolayer or large bilayer nanoislands, forming a bright triangular center for WS2 and a dark outer edge for MoS2 (Figure S3).

For a FET-based PUF, we characterize the electrical properties of 64 FETs with different channel materials of bare WS2, bare MoS2, and heteronanostructured MoS2/WS2, focusing on the entropy (i.e., FET-to-FET variability) and electrical stability. Figure 1d–f shows the ID–VG transfer curves of 64 FETs in a logarithmic scale by plotting ID as a function of VG at VD = +1 V. From the ID–VG transfer curves of the FETs, we also analyze the ID distributions and ID ratio of the maximum to minimum values (on/off ratio) at VG = +20 V, threshold voltage (VTH), and subthreshold-swing (SS) (Figure 1g, Figure S4, and Table S2). The distinct bimodal distribution of laterally heteronanostructured MoS2/WS2 is different from the monotonous distributions of WS2 and MoS2 (Figure 1g). To capture the FET-to-FET variability (i.e., ID distributions at VG = +20 V), we use the Shannon entropy (Es):48

graphic file with name nn3c10308_m001.jpg 1

where P(x) is the probability of the occurrence of an event x and n denotes the number of specific ranges of ID, which is set at 8 (Table S3). In Figure 1d, FETs with a channel of bare WS2 have a high Es value of 1.1449 for ID distributions at a VG of +20 V, but the electrical performance is poor. ID on/off ratios at VG of +20 V are quite low, showing a mean value of 8.76 × 101. This is attributable to the low-density distribution of 8% in the area coverage (per μm2) of WS2, the irregular size of nanoislands, Coulomb impurities, charge traps, and WS2 defects.70−73 In Figure 1e, FETs with a channel of bare MoS2 show relatively stable transfer characteristics with high ID on/off ratios (mean = 3.43 × 105) due to the uniform size and relatively larger density of 34% in the area coverage of MoS2. Unfortunately, Es is not as high as 0.2730 for ID distributions at VG = +20 V. Importantly, laterally heteronanostructured MoS2/WS2 shows both reliable electrical performance and a high Es of 1.9553 for ID distributions at VG = +20 V in FETs (Figure 1f), supporting the selection of 2D heteronanostructured TMDCs for the proposed PUF with high entropy and increased parameter space.

We validate the heteronanostructure formation of MoS2/WS2 using Raman and photoluminescence analyses. In Figure 1h, bare WS2 and bare MoS2 show two major Raman modes with in-plane (E12g) at 355.79 cm–1 and out-of-plane (A1g) vibrations at 419.40 cm–1 for WS2 and E12g at 385.38 cm–1 and A1g vibrations at 403.54 cm–1 for MoS2, respectively. To evaluate the number of layers, we examine the frequency difference (Δk) between the two vibration modes and the ratio between the two peak intensity values (IE12g/IA1g).74−76 For WS2, Δk of 63.61 cm–1 and IE12g/IA1g of 2.95 indicate bilayered WS2. For MoS2, Δk of 18.16 cm–1 and IE12g/IA1g of 2.38 indicate monolayered MoS2. In contrast, laterally heteronanostructured MoS2/WS2 shows peaks corresponding to E12g and A1g vibrations for both WS2 and MoS2; Δk of 63.61 and 20.43 cm–1 and IE12g/IA1g of 2.73 and 2.39, respectively, correspond to bilayered MoS2/WS2. In addition, the full width at half-maximum values of 7.13 (E12g) and 7.47 (A1g) for WS2 and 6.31 (E12g) and 7.02 (A1g) for MoS2 indicate high crystallinity of both layers.77 In Figure 1i, two different peaks are observed at 618 nm for WS2 and 663 nm for MoS2, resulting from the direct excitonic transition in the 2H-phase WS2 bilayer and MoS2 monolayer.78,79 As expected, laterally heteronanostructured MoS2/WS2 has both peaks that correspond to WS2 and MoS2, which are at the same positions as those of WS2 and MoS2, also supporting the possibility of scalable manufacturing using MOCVD.

We generate a cryptographic key from a PePUF composed of 64 FETs with a channel of laterally heteronanostructured MoS2/WS2 (Figure 2a). In a FET, VD serves as Cn. From the ID–VG transfer curves of 64 FETs, 64 ID points at VG of +20 V are acquired as Rn at three different VD levels of +0.01, +0.1, and +1 V, creating three challenge–response pairs (Figure S5 and Experimental Section). Kn is generated from the response using a binary key extraction process (Figure 2b). Specifically, we regroup 64 ID values into octal numbers (i.e., 0–7) with specific ID ranges, resulting in a map of an 8 × 8 matrix array for each response (Figures S6–S8 and Table S4 for binary and quaternary numbers). Each number is then converted into a three-level binary bit configuration (e.g., 000, 001, or 111 bits), resulting in 192 bits from each response. A single PePUF returns a 576-bit stream from all of the responses. Using 11520 bits collected from 20 PePUFs (Figure 3), we further analyze PUF performance metrics, including bit uniformity, randomness, reproducibility, uniqueness, false rates, and encoding capacity.

Figure 2.

Figure 2

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Cryptographic key generation from a PePUF. (a) Schematic illustration of generating a cryptographic key from a PePUF composed of 64 FETs with a channel of laterally heteronanostructured MoS2/WS2. In a FET, VD serves as Cn. Rn includes 64 ID data points acquired at VG = +20 V from 64 FETs. From Rn, Kn is generated by an extractor. (b) Flowchart of Kn extraction process from Rn. ID is regrouped into octal numbers (i.e., 0 to 7) with specific ID ranges. Then, each number is converted into a three-level binary-bit configuration (e.g., 000, 001, ..., or 111 bits), resulting in 192 bits in each Kn. Consequently, a single PePUF generates a 576-bit stream from all the responses.

Figure 3.

Figure 3

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Representative binary bitmap of digitized keys of 20 different PePUFs. A PUF generates a digitized key of a 576-bit stream from three responses (3 × 192). Digitized keys from 20 different PUFs are stacked side by side for visualization, resulting in a total of 11520 bits (3 × 192 × 20). This bitstream is used to test the randomness quality of PePUFs in the NIST statistical test suite (Table 1).

First, we examine the bit uniformity (or bit bias) of a particular key across several PUFs (Figure 4a):80

graphic file with name nn3c10308_m002.jpg 2

where Ki is the ith binary bit (0 or 1) of the key with s-key size. The digitized keys from 20 PePUFs return a mean (μ) probability of 0.5187 with a standard deviation (σ) of 0.0194. This value is close to the ideal probability of 0.5 (binary entropy of 1) without pre- and postprocessing, which can result in the maximum number of random combinations. We also calculate binary entropy (Eb).49

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where p is the probability of a random variable with only two values 0 and 1, returning a high binary entropy value of 0.9990.

Figure 4.

Figure 4

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Comprehensive performance of PePUFs. (a) Bit uniformity of keys generated from 20 PePUFs (mean μ of 0.5187 and standard deviation σ of 0.0194). (b) Uniqueness of the responses through comparisons among three keys (i.e., K1, K2, and K3) in each PePUF. Hamming distance (HD) from 20 various PePUFs is plotted (μ = 0.4571 and σ = 0.0287). (c) PUF uniqueness and readout reproducibility for PePUFs. The inter-HD indicates the uniqueness of each PUF among 20 various PePUFs (μ = 0.4393 and σ = 0.0345). The intra-HD of two repeated challenge–response cycles in each PePUF represents the readout reproducibility (i.e., bit error ratio) of a PePUF (μ = 0.0374 and σ = 0.0194). (d) Estimated false-positive and false-negative rates of PePUFs. A cutoff threshold is determined based on the inter-HD and intra-HD probability distributions. The cutoff threshold of 0.1847 returns a low false-positive rate of 1.0133 × 10–13 and a false-negative rate of 3.9449 × 10–13.

Second, we assess the randomness of digitized keys using the NIST statistical test suite.81 Some of the NIST tests need a sequence length of 106 and a minimum of 55 sequences, which means a total of 5.5 × 107 bitstream length. However, the key size of the PePUFs is much shorter than the required bitstream length. Thus, we utilize seven tests that can run with a length of 11520 binary bits summed from 20 PePUFs (Table 1). The specific aspects of randomness and parameters for each test are summarized in Table S5. To acquire statistically meaningful results, we divide a bitstream of 11520 into 60 sequences, each comprising 192 bits. From the NIST test suite, two key statistical results are obtained: the p-value for a chi-squared (χ2) test (confidence of randomness) and proportion (random sequence rate). For all tests, each sequence is considered random only if the p-value is ≥ 0.01. The χ2 distribution compares the goodness-of-fit of the p-value distribution of the sequences from the entire bitstream to the expected distribution. As shown in Table 1, the tested bitstream has a p-value higher than 0.0001 for a χ2 test and a proportion greater than 57 for 60 sequences in each test. This indicates that the bitstream successfully passes all seven tests, supporting the unpredictability of the key generated from PePUFs. Laterally heteronanostructured MoS2/WS2 as a channel of a FET for PUF applications serves as an excellent entropy source.

Table 1. Randomness Assessment of Digitized Keys from PePUFs Using the NIST Statistical Test Suite.

testa p-valueb proportion resultc
frequency 0.028181 60/60 pass
block frequency 0.162606 58/60 pass
cumulative sums 0.148094, 0.110952 60/60, 60/60 pass
runs 0.407091 59/60 pass
longest run of ones 0.000737 59/60 pass
approximate entropy 0.299251 58/60 pass
serial 0.275709, 0.122325 59/60, 59/60 pass
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a

Seven NIST statistical tests are performed using a stream of 11520 bits acquired from 20 PePUFs. The bitstream is divided into 60 sequences of 192 bits each. Each test returns two statistical results: p-value for a chi-squared (χ2) test (confidence of randomness) and proportion (random sequence rate). In all tests, the sequence is considered to be random only if the p-value is ≥0.01. The χ2 distribution is used to compare the goodness-of-fit of the p-value distribution of the sequences from the entire bitstream to the expected distribution.

b

The p-value is calculated from the χ2 test. If the p-value is ≥ 0.0001, then the 60 sequences are considered to be uniformly distributed.

c

If the proportion for each test is greater than 57 (57/60), the test result is regarded as a pass.

Subsequently, we examine the degree of correlation between the digitized keys extracted from the three responses in a single PePUF (Figure 4b). For three digitized keys (K1, K2, and K3) of a 192-bit stream, the hamming distance (HD) is calculated. If the keys are ideally uncorrelated, the HD is 0.5, implying that half of the keys are completely different from each other. For 20 PePUFs, when the HDs acquired from three comparisons for three responses of each PUF are averaged, the mean HD of μ = 0.4571 (σ = 0.0287) is obtained, which supports the uniqueness of each response.

Next, we evaluate the readout reproducibility and PUF uniqueness by calculating the intra-HD and inter-HD from 20 PePUFs, respectively (Figure 4c). In particular, intra-HD represents the bit error ratio (ideal value of 0) that may occur over time when generating the same PUF response multiple times. We calculate the intra-HD by repeating measurements of the ID–VG characteristics in each PUF:80

graphic file with name nn3c10308_m004.jpg 4

where m is the number of repeated readings, Ki is the s-bit reference key, and Ki,t is an s-bit key extracted from the same PUF at different time t. A mean intra-HD of 0.0374 (bit error ratio of 3.74%) shows reliability over temporal variations without postprocessing or error correction. To measure the PUF uniqueness, the degree of correlation between keys from two different PUFs is evaluated by calculating the inter-HD. If two PUFs have s-bit keys Ki and Kj (ith PUF, jth PUF, and i ≠ j), the inter-HD among n different PUFs is defined:80

graphic file with name nn3c10308_m005.jpg 5

where HD(Ki, Kj) denotes the HD between Ki and Kj. In Figure 4c, when 190 comparisons (i.e., 20C2) from 20 different PePUFs are performed, the inter-HD histogram shows a Gaussian distribution with μ = 0.4393 (σ = 0.0345). We also analyze theoretical false-positive and false-negative rates from the intra-HD and inter-HD distributions (Figure 4d). The HD cutoff threshold of 0.1847 returns false positive rate of 1.0133 × 10–13 and false negative rate of 3.9449 × 10–13, respectively. Such low rates guarantee high-security authentication applications.82,83

Finally, we estimate the encoding capacity of a key generated from a single PUF. As the number of possible combinations, the encoding capacity of a key with a binary bitstream is 2s, where 2 is the bit level (i.e., 0 and 1) and s is the key size. A PePUF has a nominal encoding capacity of 2576. As the PUF keys are not completely independent, the actual encoding capacity is less than the nominal encoding capacity. To determine the exact number of independent variables, we calculate the degree of freedom, μ(1 – μ)/σ2, where μ and σ are the mean and standard deviation of the inter-HD. The key size of mutually independent bits is 206, still generating a large encoding capacity of 2206 (≈1.0284 × 1062). Importantly, the number of challenge–response pairs and the encoding capacity for PePUFs can further be scaled by adjusting the level of the characteristic variables (i.e., VG, ID, and VD) of FETs.

For one-on-one comparisons, we also analyze the comprehensive PUF performance for FET channels of bare WS2, bare MoS2, and heteronanostructured MoS2/WS2 (Supporting Information and Tables S6 and S7). PUFs with a bare WS2 or MoS2 FET channel have suboptimal performance as follows: WS2 FET-based PUFs show poor bit uniformity, PUF uniqueness, and response uniqueness due to the low quality of their electrical performance. For MoS2 FET-based PUFs, the bit uniformity and PUF uniqueness are close to the ideal value (i.e., 0.5), while they show poor readout reproducibility and response uniqueness because of the low FET-to-FET variability. In contrast, PePUFs with a laterally heteronanostructured MoS2/WS2 channel exhibit relatively superior PUF performance, including bit uniformity, readout reproducibility, PUF uniqueness, and response uniqueness, as well as scalability in key size, when compared to PUFs with a FET channel of only WS2 or MoS2. This is attributable to the high entropy and good electrical stability of FETs, resulting from the laterally heteronanostructured MoS2/WS2.

Finally, we test long-term and thermal stability. For long-term stability, we evaluate PePUFs with and without encapsulation by an aluminum oxide layer, which are stored in a laboratory environment of 22 ± 2 °C and 40–50% relative humidity. Specifically, 192 ID values at VG = +20 V are collected from 64 FETs in PePUFs under three VD levels of +0.01, +0.1, and +1 V, and the extracted keys are compared. For the PePUF without an encapsulation layer, the correlation coefficient r for 192 ID values is as high as 0.9845 after 60 d (Figures 5a and S9). The encapsulated PePUF also shows high readout reproducibility with a low mean HD of 0.0330 (i.e., bit error ratio of 3.30%) even after 365 d (Figures S10 and S11). These results support the reliability of the PePUF over time without requiring postprocessing or error correction steps. For thermal stability, we test PePUFs at various temperature settings from −25 to 100 °C (Figures 5b and S12). The correlation coefficient r gradually decreases with increased variations in temperature, attributable to the intrinsic characteristics of FETs based on 2D semiconducting materials.84−87 However, when the temperature change is reasonable at around 25 °C (room temperature), MoS2/WS2-based FETs maintain their electrical performance without significant degradation.

Figure 5.

Figure 5

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Reliability evaluation of PePUFs without an encapsulation layer. (a) Scatter plot of 192 ID values collected at VG = +20 V from 64 FETs under three VD levels of +0.01, +0.1, and +1 V acquired 60 days apart to evaluate the long-term stability; r is the correlation coefficient. (b) Color map of correlation coefficients in pairwise comparisons for 192 ID values collected at VG = +20 V of 64 FETs under three VD levels of +0.01, +0.1, and +1 V to test the thermal stability at various temperatures from −25 to 100 °C.

Discussion

The primary focus of our hardware security solution is to enhance the parameter space of electrical PUFs, which is crucial for ensuring that the performance of PUF is accepted as an alternative hardware security primitive. Specifically, the parameter space of a PUF is directly related to the number of challenge–response pairs that can be generated by the physical system on a single device.13−17 A high-dimensional parameter space is essential for the security of PUFs, as it makes them difficult to model or clone. In other words, the larger and more complex the parameter space, the harder it is for an attacker or counterfeiter to observe enough challenge–response pairs to build a model with the same behavior as the PUF exhibits. In a simplistic manner, the number of challenge–response pairs on a single device determines the strength of the PUF (strong vs. weak).11,14,15,31,33 In addition, a large parameter space enables a PUF to provide a large encoding capacity that can be highly beneficial for cryptographic keys or identifiers.24,33,60

Obviously, conventional silicon-based electrical PUFs have demonstrated relatively large parameter spaces by leveraging intrinsic manufacturing-induced variations in integrated circuits.14,16,26,28,88,89 Typically, integrated circuit (silicon) PUFs are characterized by generating hundreds to thousands of challenge–response pairs.27,31,33,90 However, such strong silicon PUFs are often vulnerable even to standard machine learning attacks;11,31−34 the low entropy and high bit-error ratios necessitate pre- and postprocessing steps for error correction and enhanced security, posing vulnerabilities to external attacks, particularly machine learning attacks.11,31−34 In addition, conventional silicon-based electrical PUFs have limitations, such as high-power usage, low area efficiency, and high manufacturing cost.29

Optimizing and expanding the parameter space is one of the paramount aspects of non-silicon PUF research and design. Specifically, the enhancement of the parameter space in optical PUFs has been demonstrated in various studies, including linear scattering speckle patterns or fluorescent properties.18−25 Importantly, such optical PUFs have shown the possibility of increasing the strength of the PUF in a manner similar to that of integrated circuit PUFs without compromising the security level. However, these optical PUFs face fundamental limitations in practical implementation due to the need for bulky light sources and detectors such as light-emitting diodes, laser diodes, lamps, cameras, and spectrometers.

In this respect, electrical PUFs using non-silicon nanomaterials have been actively studied.47−64 A variety of nanomaterials as entropy sources have been employed in different types of electronic devices, including transistors, FETs, resistors, and memristors (Table S1). Notable constituent nanomaterials include poly[(2,5-bis(2-octyldodecyl)-3,6-bis(thien-2-yl)-pyrrolo[3,4-c]pyrrole-1,4-diyl)-co-(2,2′-(2,1,3-benzothiadiazole)]-5,5′-diyl)] (PODTPPD-BT),50 2,8-difluoro-5,11-bis(triethylsilylethynyl) anthradithiophene (diF-TESADT),51 indium oxide,52 indium tin oxide (ITO),53 silicon nanowires,54 propyl pyridinium lead iodide (PrPyr[PbI3]),55 hafnium(IV) oxide,56,57 Ta/CoFeB/MgO,58 germanium–antimony–tellurium (GaSbTe),59 poly(styrene-b-methyl methacrylate) and hydroxyl-terminated P(S-r-MMA) random copolymer,60 a mixture of octadecyltrichlorosilane and 1H,1H,2H,2H-perfluorodecyltriethoxysilane (ODTS/PFOTES),61 carbon nanotubes (CNTs),47,48,62,63 and graphene.49,64 However, these electrical PUFs based on nanomaterials possess a restricted parameter space, often limited to a single challenge–response pair.

The reported electrical PUFs expand the parameter space by utilizing the physical variables of FETs (i.e., VG, ID, and VD), resulting from 2D heteronanostructured TMDCs. Specifically, a FET channel with laterally heteronanostructured 2D TMDCs (i.e., MoS2/WS2) effectively enhances the parameter space, which differentiates PePUFs from the previously reported electrical PUFs using nanomaterials and single-structured 2D TMDCs. MoS2/WS2 heteronanostructures further guarantee high entropy (i.e., FET-to-FET variability) and good electrical stability in FETs. Overall, MoS2/WS2 heteronanostructures enable us not only to realize the distinctive and unclonable features of the proposed PUF but also to ensure PUF performance for high-level security electrical PUF development.

Conclusion

We have demonstrated that a combination of FET and laterally heteronanostructured MoS2/WS2 can enhance the entropy and parameter space as the main building blocks of high-security electrical PUFs. The reported configuration guarantees high entropy (i.e., FET-to-FET variability) and electrical stability. The previously developed electrical PUFs with only a single challenge–response pair are intrinsically vulnerable to attacks and may not completely align with the PUF concept. In the reported PUFs, the physical variables (VG, ID, and VD) of FETs are leveraged to effectively increase the parameter space. The unclonable characteristics of the proposed PUFs are governed by the inherent randomness of MoS2/WS2 heteronanostructures, which can be easily synthesized using MOCVD. After the generation of cryptographic keys from multiple challenge–response pairs by an extraction process, the experimental PUF analyses validate the bit uniformity, reproducibility, uniqueness, randomness, false rates, and encoding capacity to support the feasibility of hardware security applications. The proposed electrical PUFs can potentially provide an immediately exploitable cryptographic system for authentication and identification of a variety of consumer and healthcare devices.

Experimental Section

Materials and Chemicals

Silicon wafers (p-type) coated with 300 nm thick silicon dioxide (SiO2/Si, < 0.005 Ω·cm) were purchased from iTASCO Co. (Republic of Korea). Molybdenum hexacarbonyl (Mo(CO)6, ≥99.9%) and tungsten hexacarbonyl (W(CO) 6, ≥99.99%) were purchased from Sigma-Aldrich Co. (USA). Argon (Ar, 99.999%) and hydrogen (H2, 99.999%) gases were purchased from Samogas Co. (Republic of Korea). Hydrogen sulfide (H2S, 99.9% purity) gas was purchased from Noble Gas Co.(Republic of Korea). Poly(methyl methacrylate) (PMMA) 950 C4 was purchased from MicroChem Co. (USA). Methyl isobutyl ketone (MIBK) was purchased from Kayaku Co. (Japan). Isopropyl alcohol (IPA) and acetone solvents were purchased from Duksan Pure Chemicals Co. (Republic of Korea).

Growth of Laterally Heteronanostructured MoS2/WS2

2D TMDCs of MoS2, WS2, and MoS2/WS2 heteronanostructures were grown on SiO2/Si substrates with a square size of 10 × 10 mm2 using a MOCVD system. First, the substrate was loaded on a silicon carbide-coated graphite susceptor in a chamber equipped with a showerhead-type reactor under a temperature of 400 °C. H2S (600 sccm) and H2 (600 sccm) gases flowed into the chamber, and the working pressure was maintained at 40 Torr. The presence of excess H2S reactant gas relative to the Mo(CO)6 and W(CO)6 precursors facilitated the lateral growth of the 2D TMDC thin films.65,66,91−94 H2 ambient gas suppresses the multilayer growth of 2D TMDCs such that clean surfaces and interfaces are formed. It also promotes the decomposition of the precursors, leading to a high growth rate.91,95,96 After stabilizing gas flow and substrate temperature for 10 min, the flow rate of Mo(CO)6 and W(CO)6 precursors was controlled by a circulation chiller (2 °C) connected to precursor canisters with Ar carrier gas (0.3 sccm). MoS2 and WS2 were grown under a pressure of 40 Torr and at a temperature of 400 °C for 2 and 8 h, respectively. The samples were cooled to room temperature. Meanwhile, the growth of laterally heteronanostructured MoS2/WS2 was performed by using a two-step MOCVD process in a simple sequential manner. After WS2 was grown on a SiO2/Si substrate, the flow of the W(CO)6 precursor was stopped by injecting H2S and H2 gases into the working chamber at 40 Torr. This stabilization process was performed for 1 h by purging the precursors and byproducts. A second Mo(CO)6 precursor was injected to grow MoS2. MoS2 grew laterally at the edges of WS2 because of unpassivated edges, resulting in laterally heteronanostructured MoS2/WS2.

Fabrication of Field-Effect Transistors (FETs) for PePUFs

MoS2, WS2, and MoS2/WS2 were utilized as the FET channels. Back-gated FETs with 8 × 8 (64) arrays were fabricated by the following steps (Figure S1). The PMMA e-beam resist (ER) was spin-coated on a TMDC/SiO2/Si substrate at 500 rpm for 5 s and 5000 rpm for 40 s, followed by baking at 180 °C for 90 s. The 64 FETs with an area of 400 × 400 μm2 each were formed on the ER layer with an area dose of 300 μC cm–2 at 30 keV exposure through a field-emission scanning electron microscopy (FE-SEM; FEI Sirion 400, Czech) system. The 64 FETs consisted of 5 source and 32 drain electrodes, with a line width of 2 μm, spacing of 250 nm, and contact pads of 35 × 35 μm2. The exposed sample was then developed by using a mixed solution of MIBK/IPA (1:3 volume concentration ratio) for 30 s. For an electrode, titanium (Ti) and gold (Au) films (i.e., 100/10 nm Au/Ti) were deposited at a pressure of 10–8 Torr and a deposition rate of ∼0.2 Å s–1 using an e-beam evaporator system (IVT Co., Ltd., Republic of Korea). The lift-off of the metal films deposited on the ER layer was performed by using an acetone solvent at room temperature for 24 h. The samples were then rinsed with acetone and IPA to remove the ER layer and dried with nitrogen gas. Thus, a total of 20 PePUFs consisting of 64 FETs with a channel of laterally heteronanostructured MoS2/WS2 were prepared.

Characterization

The structural and morphological properties of the samples were characterized using optical microscopy (Olympus BX51, Japan), FE-SEM at accelerating voltages of 10 kV (Hitachi S-4800, Japan) and 1 kV (Zeiss Sigma 300 VP, Germany), and atomic force microscopy (AFM; Park Systems XE-150, Republic of Korea) using a silicon- and aluminum-coated cantilever (PPP-NCHR 10M; Park Systems, Republic of Korea). Raman and PL measurements were conducted using a confocal Raman spectroscopy (Renishaw inVia, UK) system with a 488 nm laser at a power of 100 μW. The electrical properties of the FETs, including VG, ID, and VD were characterized using a measurement system consisting of a semiconductor parameter analyzer (Keysight 4156A, USA) and two probe stations (Cascade Microtech Alessi REL-5500 and Lakeshore CPX-VF, USA).

Extraction of Cryptographic Keys

To extract digitized keys from the PePUFs, the electrical properties of 64 FETs in a PUF were used. Three VD levels (+0.01, +0.1, and +1 V) were applied as Cn. From the 64 FETs, 64 ID points at VG of +20 V as Rn were acquired. The 64 ID points were classified into octal numbers (0 to 7) using a specific ID range. The classified numbers were converted into the corresponding three-level binary bit configuration. Thus, a 192-bit stream was extracted from each response in the PePUF. Consequently, all of the responses in a single PePUF returned a 576-bit stream.

Acknowledgments

This research was supported by the development of core technologies for advanced measuring instruments funded from the Korea Research Institute of Standards and Science (KRISS-2023-GP2023-0012), the Korea Research Institute of Standards and Science Virtual Lab Program, the Ministry of Trade, Industry and Energy (RS-2023-00235844), the United States Air Force Office of Scientific Research (FA2386-17-1-4072), the Technology Accelerator Challenge Prize from the NIH National Institute of Biomedical Imaging and Bioengineering, and the Ralph W. and Grace M. Showalter Trust.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.3c10308.

  • Illustrations of the fabrication of a PePUF and the process of the growth for laterally heteronanostructured MoS2/WS2; SEM and AFM images of WS2 and laterally heterostructured MoS2/WS2; electrical characteristics of FETs with different channels of WS2, MoS2, and MoS2/WS2; ID–VG characteristics at different VD levels for PePUF; key generation from 20 PePUFs at a group of binary and quaternary numbers; comparison of the PePUF performance with different number of groups; long-term stability of PePUFs; thermal stability of PePUFs; comparisons for nanomaterial-based electrical PUFs; brief characteristic descriptions of the NIST statistical tests; comparison of PUF performance among bare WS2, bare MoS2, and heteronanostructured MoS2/WS2 FET-based PUFs (PDF)

Author Contributions

∇ J.P. and J.W.L. contributed equally to this work

The authors declare no competing financial interest.

Supplementary Material

nn3c10308_si_001.pdf (3.5MB, pdf)

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