Excess noise and thermoelectric effect in magnetron-sputtered VO₂ thin films

Vanadium dioxide (VO₂) is a popular phase-change material for its near room temperature (∼340 K) insulator-to-metal (or semiconductor-to-metal) phase transition (IMT). One way of triggering the phase transition in VO₂ is by heating. During the IMT, electrical resistance (R) and optical transmittance (T˜) of the material undergo a dramatic change. In VO₂ thin films, R may change by 3–5 orders of magnitude depending on the material quality (e.g., stoichiometry and crystal orientation).^1–3 Vanadium dioxide films have versatile and desirable electrical and optical properties that can be controlled through this phase change. The reversible switching properties of VO₂ can be utilized in various applications such as optical modulators,⁴ switches,⁵ sensors,⁶ smart windows,⁷ optical memory devices,⁸ resistive random-access memories (RRAMs),⁹ and neuromorphic devices.¹⁰ VO₂ may be used in different forms such as thin films,^11–13 microrods,^14,15 nanobelts,^16,17 and nanosheets.^18,19 The unresolved nature of the phase transition of VO₂ has been topical research.^20–22 Both structural (Peierls) and electronic (Mott–Hubbard) transitions have been supported by experimental evidence thus far.^23–28 On the contrary, there have been discussions and works focused on a hybrid phenomenon (Peierls/Mott–Hubbard), in which these transitions are somehow interrelated.^29–31 The phase transition properties strongly depend on the fabrication process of VO₂ films and the choice of substrate.^2,32–35 These choices may be used to tailor the type of defects and crystalline growth of as-prepared VO₂ films. It has also been supported in many experimental and analytical studies that the overall IMT in VO₂ is a result of the appearance and growth of local percolation of the metallic (M) phase within the insulating domain.^36–39 

Excess noise is an undesirable component of conductance fluctuations above shot and thermal noise. This type of noise is likely to cause distortions in signal transfer leading to false output signals in electronic devices and systems. One particular form of excess noise is 1/f (or flicker) noise. Noise characterization is essential in developing models to eliminate noise and produce high signal-to-noise ratio (SNR) systems. It is important to mention that noise characterization can also be used as a tool in obtaining information on the quality of materials and performance of devices (e.g., MOSFETs), with the general understanding that defects lead to higher excess noise as reviewed in the literature (e.g., Refs. 40–42). The electronic noise phenomenon depends on the density of charge carriers present in the material, which varies with respect to the volume of the material. So far, there have only been a limited number of investigations on the excess noise properties of VO₂. The 1/f noise originating in the bulk of magnetron-sputtered VO₂ thin films has not yet been widely studied and appears to be a significant gap in the literature. Another topical research for such a phase-change material is characterizing temperature-dependent electrical (charge transport) properties. Such charge carrier properties of VO₂ films in the semiconducting (SC) phase and through the IMT may be examined using the Hall effect^43–46 as well as the thermoelectric (Seebeck) effect.^47–49 As a phenomenon, the thermoelectric effect may be referred to as identifying the dominant carrier type within the SC-phase. Consecutively, the characterization of such a property can also provide insight into the synergetic relation between the electrical and structural phase transitions in VO₂ thin films.

The present paper investigates the excess 1/f noise and thermoelectric effect in VO₂ films grown on r-cut sapphire substrates by the reactive DC magnetron sputtering technique. We analyze the excess noise characteristics at the SC-phase, IMT region, and M-phase of VO₂. We also examine the Seebeck coefficient (S) of VO₂ across both heating (through IMT) and cooling (through metal-to-insulator transition, MIT) schedules. We interpret the behavior of S by taking into account the percolative nature of the SC- and M- phases during IMT and MIT. Additionally, we extract Hooge's parameter (α_H) of VO₂ films and attempt to deliver a reasonable explanation with regard to our findings.

Vanadium dioxide thin films were grown on r-cut sapphire substrates using the reactive DC magnetron sputtering technique. A high-purity (99.95%) vanadium (V) target (Plasmionique, Inc.) was used during the deposition process. The deposition was conducted at 650 °C with an applied DC power of 100 W at a stable chamber pressure of 1.33 Pa and stable oxygen (O₂, 1.3 SCCM) and argon (Ar, 100 SCCM) flow rates. These optimized parameters have been investigated and determined to deliver highly stoichiometric near-epitaxial (the majority of grain growth is along the crystal direction of the substrate) VO₂ films.^35,50 The structural characterization of the as-prepared VO₂ films was carried out using Raman spectroscopy. The Raman spectrum was obtained using a Renishaw InVia Reflex Raman microscope equipped with a 514 nm-Ar⁺ laser (Modulaser StellarPro-50). A scanning electron microscope (Hitachi HT-7700 SEM) was used to examine the surface morphology of the as-prepared films. The samples used in both excess noise and thermoelectric measurements were from the same deposition batch as those reported in our previous papers^14,36 and are the highest quality VO₂ films obtained by depositing the film on an r-cut sapphire substrate due to a relatively small mismatch in the lattice constant.^35,51

The excess noise measurements were carried out by depositing two coplanar 1.5 × 1.5 mm² gold contacts on the VO₂ thin film separated by a distance of d = 4.55 mm. The sample volume is 1.21 × 10⁶ μm³. This volume was chosen so that the sample is polycrystalline but, at the same time, it is not too large to prevent noise measurements. These contacts were deposited by an RF magnetron sputtering system with their thickness measured by a crystal monitor to be ∼87 nm. The noise power spectrum of conductance fluctuations in the sample was measured as a function of current (I_s) and temperature (T) in the low-frequency region (below 12.8 kHz). Examination of the excess noise was performed using a purpose-built setup presented in Fig. 1(a), the description of which has been given in Refs. 52 and 53. Due to the large change of sample resistance (R_S) values of VO₂ through the IMT, two different signal amplification stages were used to measure the excess noise at high and low film resistivities, corresponding to the SC- and M-phases, respectively. Essentially, to measure the conductance fluctuations, a current I_s was passed through the sample. For high R_S measurements, current fluctuations at the midpoint of a voltage divider consisting of a sample and a divider resistor (R_div), matched to the R_S, were capacitively coupled to a current amplifier (Ithaco 654). The noise signal was further amplified through a low-noise voltage amplifier (EG&G 5113). The amplified signal was fed into a spectrum analyzer (Stanford Research Systems, SR785), where the voltage–time series of the signal was Fourier-transformed into a frequency spectrum of noise power density. For low R_S (300–500 Ω), excess noise was measured by means of voltage fluctuations across the sample by replacing the Ithaco 564 with a voltage amplifier (Ithaco 565) which was used with the DC coupling mode (R_in = 100 kΩ, R_out = 10 kΩ, and Gain = 40 dB). The measurements in the SC-phase of VO₂ were taken in a frequency range between 1 Hz and 10 kHz. In the M-phase, the frequency span of the measurements was limited to the range between 1 and 100 Hz. Noise measurements were also taken at the insulator-to-metal transition (IMT) necks which were around 335 and 344 K.

The temperature gradient is controlled while the corresponding potential gradient is measured and plotted. The positive and negative signs indicate p-type and n-type behavior, respectively. For the heating and cooling schedules, the maximum ΔT applied between the hot and cold sides was 5 K for the SC-phase and 9 K for the M-phase because the M-phase has a smaller magnitude of S. In the transition region of VO₂ (between 327 and 337 K), the maximum ΔT was ≈6.5 K.

Figure 2(a) presents the Raman spectrum of VO₂ samples used in the present work. The characteristic VO₂ peaks at 139, 195, 223, 263, 310, 341, 396, 441, 497, 618, and 824 cm⁻¹ were obtained for both samples. Figure 2(b) gives the surface image of a VO₂ sample taken by SEM. The average grain size was estimated to be 159 ± 12 nm, with 146 ± 9 nm in the x-direction, 154 ± 3 nm in the y-direction, and 176 ± 8 nm in diagonal (x, y and x, −y) directions. Figure 2(c) shows the cross-sectional image of the sample shown in Fig. 2(b) yielding an estimated film thickness of 175 ± 5 nm. Also, a zoomed image of the film region is presented to facilitate the observation of the grains. Additional structural characterizations such as XRD and XPS measurements on similar films have been reported³⁵ and confirm that the film is stoichiometric VO₂ and is polycrystalline.

Figure 3(a) shows the temperature dependence of resistance R of an as-prepared VO₂ film grown on an r-cut sapphire substrate. The resistance of the SC-phase decreases with the temperature in the range of 300–330 K, which is observed typically on VO₂ films grown on r-cut sapphire substrates.³⁶ The resistance drops by five orders of magnitude during the IMT. The hysteresis of IMT and MIT is observed to be approximately 10 K, which is due to the grain size, boundaries, and defects^57,58 throughout the volume of the as-prepared VO₂ films. Figure 3(b) shows the I–V characteristic of the film. The curves obtained at different temperatures in the SC-phase indicate Ohmic contact between the Au electrodes and the VO₂ film.

Figure 5 presents the NSPD of the VO₂ sample obtained at five different temperatures falling in the SC-phase of VO₂, which are T = 298, 305, 312, 319, and 325 K. The spectra are plotted for I_S = 0.5, 1.0, and 2.0 μA. As expected, the NSPD spectrum appears clearer at a higher I_S. The average noise slope (γ) is obtained to be 1.13 in the SC-phase of the sample and is comparable with the slopes obtained for VO₂ single crystals⁶⁰ and polycrystalline microbridge structures.⁶¹ 

Figures 6(a) and 6(b) show the NSPD of films obtained at IMT transition necks at 335 and 344 K, respectively. The excess noise was measured by means of voltage fluctuations due to low R_S. Here, the noise was obtained for three different voltages (V_S) across the sample. Around T ≈ 335 K, the R_S is unstable and varies by dropping from 5 to about 2 kΩ. In this near IMT region, the NSPD spectra observed at different V_S do not overlap, i.e., NSPD spectra do not obey Eq. (2). The excess noise is only observed up to 100 Hz and flattens out at higher frequencies due to the system’s background noise. This difference between the noise levels at different voltages may be attributed to the increasing chaotic structure within the material due to the growth of the conductive sites near the percolation threshold (X_C ≈ 0.57) which has also been referred to by Ref. 62. Also, as pointed out in Ref. 60, the latter behavior in normalized noise may be attributed to the hetero-phase fluctuation near the first-order IMT-phase transition, in which the large noise on the transition neck (∼335 K in this work) originates from the deviations in phase uniformity across the volume of the film. So, the difference in the scaling of noise can be related to the increased heterogeneity in the structure due to co-existence of the SC- and M-phases in the transition region. On the other hand, the normalized noise spectra obtained, T ≈ 344 K, right after the IMT also do not overlap, again indicating that Eq. (2) is not satisfied. For frequencies below 100 Hz, the slope γ is 1.4–2.0. At this temperature, R_S is around 300 Ω and the material has already passed the IMT temperature, and the M-phase dominates the structure.

Figure 7(a) gives the SPD and (b) shows the NSPD spectra of the VO₂ film at 359 K, well into the M-phase. The noise was measured at three different voltages, which were 4, 8, and 16 mV, and was obtained from voltage fluctuations in the 1–100 Hz frequency range. As mentioned earlier, we were unable to measure the excess noise at higher frequencies because the noise signal dropped below the background noise of the system. Notice that there is some partial overlap in the NSPD spectra in the 10–100 Hz range.

Figure 8 presents the normalized noise spectra of VO₂ obtained at four different temperatures in the metallic phase of VO₂. The noise spectra are obtained for three different applied V_S. For the low voltage measurements at V_S= 4.0 and 8.0 mV, the spectra display no clear overlap. However, the data captured at a higher bias at V_S = 16.0 mV appear to be quite similar and display an overlap. The average γ value in the M-phase is 2.0.

Figure 9 shows the Seebeck coefficient (S) of VO₂ films on r-cut sapphire measured under heating and cooling schedules. The S values obtained in the SC-phase during the heating schedule (S_SC−H) vary between −600 and −200 μV/K with an average value of S_SC−H= −272 ± 34 μV/K. These are in the range of values that have been reported in Refs. 28, 38, and 39. The negative sign indicates that the majority carriers are electrons in the as-prepared VO₂ films. In the M-phase, the average value during the heating schedule is S_M-H = 37 ± 9 μV/K, whose sign is positive. For the cooling schedule, the average Seebeck coefficient is S_SC-C = – 409 ± 65 μV/K in the SC-phase and S_M-C= 48 ± 8 μV/K in the M-phase. It can be seen that the sign of S changes from negative to positive as VO₂ transitions from the SC-phase to the M-phase. A similar observation has been found for VO₂ films grown on c-cut sapphire substrates by RF magnetron sputtering.⁴⁷ The S values obtained in the M-phase in the cooling schedule are scattered and do not show a specific trend nor consistency in the sign of S (e.g., S at 340 K, cooling from the M-phase has a value of −31 μV/K). There are several factors that can lead to the Seebeck coefficient being positive.⁶³ First and the most well-known is the energy dependence of the mean free path at the Fermi surface, which is the nature of the scattering of carriers around the Fermi surface. The second factor is the shape of the Fermi surface and its dependence on impurities. The third factor is the relative magnitude of effective masses of electrons and holes. Furthermore, sputtered VO₂ thin films host oxygen vacancies that complicate the Fermi energy level.^64,65 The short dashed lines in Fig. 9 indicate the relationship between conductivity (σ) and the partial metallic content (X_m) in a VO₂ film grown on r-cut sapphire³⁶ which is explained by the relations introduced by the Efros–Shklovskii (ES) percolation model⁶⁶ as applied to the present sample. These relations for IM and MI transitions can be found in Table I.

The term $X c ¯$ in Table I is the percolation threshold undergoing a phase transition which describes the critical metallic content reached across the entire film (both heating and cooling). The term $X m ¯$ represents the overall partial metallic content in the film. The conductivity of VO₂ is denoted by σ and depends on $X m ¯$⁠. This relation is illustrated as solid lines in Fig. 9 for both heating and cooling schedules. The term σ_sc describes the lowest conductivity in the SC-phase and σ_m is the highest conductivity in the M-phase of VO₂. The indices t and q are critical indices assigned above and below $X c ¯$⁠, respectively. The IMT in the as-prepared films occurs at ∼337 K which corresponds to X_c = 0.57 as shown in our previous work.³⁶ The latter is achieved for S measured at ∼333 K, which is indicative of an early phase transition in the overall sample. This can be related to the temperature difference (ΔT) applied between the hot and cold sides of the film, where T_hot is higher than T_cold by a maximum temperature of 5 K, which is not negligible. For example, for a temperature of 334 K, there is an average value of 336 K (hot) and 332 K (cold), where the hot side is within the IMT region, and the highly conductive channels of the M-phase are already formed in the sample. Hence, this results in an early IMT specified by the black arrow in Fig. 9. As the material undergoes IMT and becomes metallic, the magnitude of S drops to a very small value, near zero. The T dependence of S in the cooling schedule shows a different behavior from that of the heating schedule. In particular, this can be observed in the trend of S values measured in the SC-phase. The S values in the cooling schedule appear to be large and more scattered, especially in the temperatures right after MIT. The Seebeck coefficient eventually recovers to the original value at room temperature (∼308 K), within the range of S_SC-H. The metal-to-insulator transition in a VO₂ film grown on r-cut sapphire has already been shown to occur at a lower percolation threshold (X_c ≈ 0.06) corresponding to a temperature of ∼327 K in Ref. 36. Consequently, during cooling, until this temperature is attained, the structure is a mixture of the two phases in which the SC-phase grows as spherical inclusions within a metallic volume, analogous to air pores in Swiss cheese. During the cooling schedule, the film experienced a temperature difference (ΔT) of 5–6.5 K, which affected the partial metallic content, creating a non-uniform X_m from the “hot” side to the “cold” side of the examined film. Suppose that the hot side has T_hot = 325 K and the cold side has T_cold = 321 K. The two ends act against each other in the vicinity of the transition temperatures because the hot end encourages IMT while the cold end favors MIT. This results in a delay in the overall metallic content $( X m ¯)$ to reach the threshold $X c ¯$ which occurs at lower temperatures. It is expected that the trend of S complies with the relation described in Ref. 66 for MIT. The delay in the “overall” MIT is indicated by the black solid arrow in Fig. 9. In this regard, the scatter in the data and the decrease in S with decreasing T can be related to the chaotic structure as $X c ¯$ is approached. A detailed analytical study of the effect caused by ΔT in both heating and cooling schedules is beyond the scope of this work.

Figure 10(a) displays the temperature dependence of the excess noise slope parameter γ in both SC- and M-phases of VO₂. In the SC-phase, the γ values are around 1.13. This result is comparable to those reported in early works (γ = 1.05 in Ref. 60, and 1.1 in Ref. 61). The large variance in γ near the IMT temperature (T ≈ 335 K and 2 kΩ ≤ R_S ≤ 5 kΩ), we believe, is due to the stochastic processes in the chaotic structure of the coexisting SC- and M-phases near the percolation threshold (X_c = 0.57).³⁶ This is also reflected in the variance of the NSPD noise level S_n near the IMT in Fig. 10(b). The stochastic processes can be generated from locally transitioning sites, where they become highly conductive, and from grain boundaries (GBs) that act as trapping sites for free electrons. It has been suggested in the literature that the variance in γ and S_n is caused by this chaotic structure and the presence of generation-recombination (GR) noise in the film near IMT.⁶⁷ As the material undergoes IMT, the M-phase dominates in the film. At 344 K and above, a larger but highly variant γ is obtained as 1.6 ± 0.3. We suggest that this represents a possible contact noise that can exhibit such γ-values.

We have also examined NSPD obtained at 10 Hz as a function of the sample resistance as presented in Fig. 11. For comparison, the data obtained for a polycrystalline VO₂ microbridge⁶¹ with a volume of 1.0 × 10² μm³ is included in the graph. For materials that consist of percolating phases, the relation between S_n and R_S is established by a scaling exponent x $( S n ( f ) ∝ R S x )$⁠. In Ref. 61, these exponents are obtained as x = −2.6 for the SC-phase and x = + 2.6 for the M-phase of VO₂. However, in the present work, we find x ≈ 0; in other words, a temperature-independent S_n. This signifies that the noise is unlikely to be due to electron number fluctuations. We suggest that the excess noise in our samples originates from mobility fluctuations due to the presence of GBs and defects (i.e., oxygen vacancies). The large volume of the film hosts grains of an average size of 159 nm and nearly 42 GB crossing per μm². This corresponds to 2.87 × 10⁸ GB crossings along the current path through the film. These GBs can act as scattering sites for free electrons. As the material becomes fully metallic (R_S < 300 Ω), no clear exponent can be observed (x → ∞) and contact noise prevails.

The small α_H calculated for the microbridge sample with a very small volume, where the effect of GBs is negligible, would make the first term dominant in Eq. (4). On the contrary, the larger value (α_H = 4) obtained for a single crystal cannot be explained easily. In our case, a blind application of the Hooge expression to the NSPD yields an average α_H of about 580 as given in Table II. The difference between the two terms in Eq. (4) is that while N in the first term depends on temperature through n, N_GB in the second term (including α_GB)—most likely—is temperature independent. Consequently, our results can be interpreted as the second term dominating the first (Hooge) term, given S_n is independent of temperature. Furthermore, considering the nearly constant noise level across the SC-phase, the second term implies that mobility fluctuations are the main factor of noise in the sample. The effect of such fluctuations due to GBs leading to high noise levels has been reported for polycrystalline graphene.⁶⁹ Hence, for an average number of GB crossings of 2.87 × 10⁸ in the examined VO₂ film with a volume of 1.21 × 10⁶ μm³ and an average S_n (10 Hz) of 3.3 × 10⁻¹² Hz⁻¹ in the SC-phase, the constant α_GB is found to be 9.2 × 10⁻³.

This work has examined the excess electronic noise and the Seebeck coefficient in VO₂ films grown on r-cut sapphire using reactive DC magnetron sputtering. The excess noise shows flicker-type characteristics with a power spectrum that follows 1/f^γ throughout the semiconducting (SC) phase with an average slope parameter (γ) of 1.13. The normalized spectral power density S_n spectra overlapped for different current values and scaled with the reciprocal volume V, i.e., S_n ∝ 1/f^γ. The S_n spectra in the SC-phase showed no temperature dependence, and an interpretation based on electron number fluctuations N alone in the Hooge model S_n = α_H/f^γN leads to an unrealistically high Hooge parameter α_H (∼10³) and had to be ruled out.

We propose that the fluctuations are related to mobility fluctuations arising primarily from grain-boundary (GB) scattering, which gives a fair explanation for the observed characteristics. Specifically, we suggest that the noise arises from fluctuations in the number of GB scattering events, i.e., GBs act as “fluctuators.” We can use the Hooge equation in this case with N replaced by N_GB, that is, S_n = α_GB/f^γN_GB, where N_GB is the number of grain-boundary crossings and α_GB is an equivalent Hooge parameter in the GB model. With N_GB determined from the number of grain-boundary crossings (using the SEM image), this model gives α_GB ≈ 9 × 10⁻³, which is a reasonable Hooge parameter in supporting fluctuations in N_GB rather than N.

Near IMT, S_n exhibited an unusual increase, which is likely to be due to additional fluctuations being introduced upon the formation of mixed phases and the associated fluctuations in their volume fraction. The normalized noise spectra in the metallic (M) phase displayed an average slope of 2.0 and the spectra at different applied bias voltages did not overlap entirely except in certain frequency regions. The excess noise in the M-phase is most likely due to contact or surface noise.

The thermoelectric measurements confirm that the as-prepared VO₂ film on the r-cut sapphire substrate is n-type in the SC-phase. In the M-phase, on the other hand, the Seebeck coefficient is small and positive during the heating schedule. Moreover, the trend of the Seebeck coefficients obtained in the heating and cooling schedules correlated well with the difference in the topology of the percolating phases within the dominant phase: two-dimensional growth of the metallic phase (infinite conductive clusters) in the SC-phase and three-dimensional growth of semiconducting pores in the M-phase, as reported previously.³⁶ 

The authors thank the Royal Society (London) for an International Exchanges Grant (No. IE160035), the Engineering and Physical Sciences Research Council (UK) (Grant Nos. EP/N020057/1 and EP/V001914/1), the Natural Sciences and Engineering Research Council of Canada (NSERC), and Cisco Systems, Inc. for sponsoring a Silicon Valley Community Foundation Grant [No. 2020-225324 (3696)] to support this work.

The authors have no conflicts to disclose.

Ozan Gunes: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Onyebuchi I. Onumonu: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Writing – review & editing (equal). A. Baset Gholizadeh: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Chunzi Zhang: Data curation (equal); Investigation (equal); Writing – review & editing (equal). Qiaoqin Yang: Funding acquisition (equal); Resources (equal); Writing – review & editing (equal). Shi-Jie Wen: Conceptualization (equal); Funding acquisition (equal); Writing – review & editing (equal). Richard J. Curry: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Robert E. Johanson: Conceptualization (equal); Project administration (equal); Resources (equal); Visualization (equal); Writing – review & editing (equal). Safa O. Kasap: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.