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Monotonic increase of conductivity with non-monotonic defect content: ZnO thin films at precursor molar concentrations of 0.3–0.5 M

This study of ultrasonic spray pyrolysis-grown ZnO thin films reveals that a widely used diagnostic for hopping conduction is an artifact of fixed-frequency analysis, while demonstrating that charge-transport parameters vary monotonically with precursor concentration despite non-monotonic changes in defect content and surface morphology.

Original authors: Andrey Nebesniy, Azamat Arslanov, Pavel Parchinskiy, Abdumanap Nasirov, Shavkat Yuldashev

Published 2026-09-17

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CC BY 4.0

Original authors: Andrey Nebesniy, Azamat Arslanov, Pavel Parchinskiy, Abdumanap Nasirov, Shavkat Yuldashev

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Zinc oxide is a material that sits quietly at the intersection of light and electricity. It is a wide-band-gap semiconductor, meaning it normally resists the flow of electric current, but it can be coaxed into conducting if its internal structure is slightly imperfect. These imperfections, known as defects, are not flaws in the traditional sense; they are missing atoms or misplaced ones that create tiny pockets of energy within the material. In the world of electronics, these pockets act as stepping stones, allowing electrons to hop from one place to another. This hopping mechanism is crucial for making zinc oxide useful in everything from transparent screens to gas sensors. Scientists have long believed that the quality of a zinc oxide film is a simple story: if you make the film with more of the starting chemical mixture, the film becomes better, smoother, and more conductive. It is a linear expectation, where more input equals a better output.

A team of researchers at the National University of Uzbekistan decided to test this simple story by growing zinc oxide films using a method called ultrasonic spray pyrolysis. Imagine a fine mist of a chemical solution being sprayed onto a hot surface, where the heat instantly turns the liquid into a solid film. The researchers created three films using slightly different concentrations of the starting chemical: 0.3 molar, 0.4 molar, and 0.5 molar. They then subjected these films to a rigorous examination, looking at their surface texture, their internal crystal structure, how they glowed under ultraviolet light, and how electricity moved through them at temperatures ranging from the cold of liquid nitrogen to the warmth of a summer day. What they found was a picture far more complex than the standard story of "more is better."

The most striking discovery was that the film with the best electrical performance was not the one with the fewest defects, nor was it the one with the most defects. Instead, the electrical properties improved steadily as the concentration increased. The film made with the highest concentration, 0.5 molar, conducted electricity far better than the others, with its resistance dropping significantly. However, when the researchers looked at the defects themselves using light, the story changed. The amount of defects did not rise or fall in a straight line. The film made with the middle concentration, 0.4 molar, actually had the fewest defects and the most uniform surface, appearing the "cleanest" by optical standards. Yet, this same film did not conduct electricity as well as the 0.5 molar film. This means that the factors controlling how well the material conducts electricity are completely separate from the factors that determine how many defects are visible in the crystal structure or how smooth the surface looks.

This separation of properties challenges a common assumption in materials science: that a single measure of "quality" can describe a material. In this case, no single film was the best at everything. The 0.5 molar film was the champion of conductivity, while the 0.4 molar film was the champion of optical purity and surface smoothness. The researchers also uncovered a subtle but important issue with how scientists often measure these materials. A standard method for determining how electricity moves through a material involves looking at how the current changes with frequency. The researchers found that this method can be misleading. They showed that a common calculation used to identify the mechanism of electron hopping can swing wildly with temperature, even when the actual behavior of the electrons hasn't changed at all. This swing is an illusion created by the way the measurement window is set, not a real change in the physics. By using a more direct approach to track the movement of charge, they confirmed that the electrical improvements in the 0.5 molar film were real and not an artifact of measurement.

The study also revealed that the improvements in conductivity were not caused by changes in the fundamental energy levels of the material. The energy gap that electrons must cross to move through the material remained the same for all three films. Instead, the difference lay in the states trapped within that gap, the very defects that were visible in the light measurements. The researchers concluded that the path to a better zinc oxide film depends entirely on what property you need. If you need a material that conducts electricity efficiently, a higher concentration of the starting chemical is the way to go. If you need a material that is optically pure and structurally uniform, a middle concentration is superior. The idea that quality improves in a straight line with concentration is incomplete; in reality, the different characteristics of the material evolve independently, each following its own path.

Technical Summary: Monotonic Increase of Conductivity with Non-Monotonic Defect Content in ZnO Thin Films

Problem Statement
The functional properties of zinc oxide (ZnO) thin films are governed by native defects and charge transport mechanisms. While the influence of precursor molar concentration on the structural and optical properties of ZnO films grown by ultrasonic spray pyrolysis has been studied, a systematic comparison linking concentration to charge-transport mechanisms—specifically under AC excitation where frequency dispersion is sensitive to hopping transport—remains lacking. Furthermore, a widely used diagnostic for identifying changes in hopping-conduction mechanisms, the exponent of the Jonscher power law evaluated within a fixed frequency window, is suspected to yield misleading results due to temperature-dependent shifts in the conductivity spectrum relative to the measurement window. This study addresses these gaps by analyzing three ZnO films (0.3, 0.4, and 0.5 M precursor concentrations) to determine if a single "film quality" parameter exists and to validate the reliability of standard transport diagnostics.

Methodology
ZnO films were deposited on Si(100) substrates via ultrasonic spray pyrolysis using zinc acetate dihydrate solutions at 0.3, 0.4, and 0.5 M. The films were annealed at 550 °C. Thickness was determined via two independent methods: specular reflectance interference patterns and capacitance measurements.

Characterization included:

Structural/Morphological: Atomic Force Microscopy (AFM) for surface relief and grain size; X-ray Diffraction (XRD) for phase purity and crystallite size.
Optical: Reflectance spectroscopy and temperature-dependent Photoluminescence (PL) (78–400 K) to analyze near-band-edge (NBE) emission, defect-related green emission, and thermal quenching.
Electrical: DC resistance measurements (96–370 K) and AC impedance spectroscopy (20 Hz–200 kHz, 95–370 K).
Data Analysis: The study employed time–temperature superposition (TTS) to test for master curve collapse. A critical methodological step involved reconstructing spectra from a temperature-independent master curve to isolate artifacts in the Jonscher exponent ( $s$ ) caused by fixed frequency windows. DC transport was analyzed using Mott variable-range hopping (VRH) models, while AC data were fitted to equivalent circuits and analyzed for dielectric relaxation frequencies.

Key Results

Methodological Finding on Transport Diagnostics:
The study demonstrates that the Jonscher power law exponent ( $s$ ), when evaluated in a fixed frequency window, varies with temperature even when the underlying conductivity spectra do not change shape. By collapsing the spectra of all samples onto a single temperature-independent master curve (scatter 0.004–0.028 decades) and reconstructing the data, the authors found that 45–49% of the observed temperature swing in $s$ is an artifact of the window's position on the curve. Consequently, $s(T)$ alone cannot reliably indicate a change in the hopping mechanism; the position of the dielectric relaxation is a more robust indicator.
Divergence of Transport and Optical Properties:
- Transport (Monotonic): Charge-transport parameters improve monotonically with increasing precursor concentration. The Mott parameter $T_0$ decreases from $4.3 \times 10^5$ K (0.3 M) to $3.3 \times 10^4$ K (0.5 M). The high-temperature activation energy decreases from 233 meV to 95 meV, and sheet resistance drops from $3.1 \times 10^5$ to $4.0 \times 10^4$ $\Omega$ /sq. The 0.5 M sample exhibits the highest conductivity.
- Optical/Morphological (Non-Monotonic): Defect content and surface morphology peak at 0.4 M. The ratio of defect emission to NBE emission ( $I_{def}/I_{NBE}$ ) is minimal at 0.4 M (<0.037) but significantly higher at 0.3 M (3.15) and 0.5 M (0.49). Similarly, the near-band-edge linewidth is narrowest at 0.4 M (63.2 meV), and surface roughness ( $S_q$ ) and large-scale agglomerates are maximal at 0.4 M.
- Band Structure: No significant difference in the band-edge position ( $E_0$ ) was detected between samples (spread ~6 meV), indicating that transport differences arise from in-gap states rather than band-structure modifications.
AC and DC Correlation:
For the 0.4 M and 0.5 M samples, the activation energy derived from dielectric relaxation (159 ± 6 meV and 106 ± 5 meV, respectively) closely matches the DC activation energy (164 meV and 95 meV). For the 0.5 M sample, a break in the Arrhenius dependence of the relaxation frequency coincides with the crossover from hopping to activated transport observed in DC measurements.

Significance and Claims
The paper claims two primary contributions:

Correction of a Diagnostic Artifact: It establishes that the temperature dependence of the Jonscher exponent in a fixed window is largely an artifact of spectral shifting and cannot be used as a standalone indicator of a change in hopping transport mechanisms. The authors propose using the dielectric relaxation position as a more reliable metric.
Decoupling of Quality Metrics: The study concludes that "film quality" in ZnO cannot be defined by a single parameter. While charge transport improves monotonically with precursor concentration (best at 0.5 M), optical quality and defect minimization are non-monotonic, with an optimum at 0.4 M. The transport properties are governed by in-gap states rather than the band structure or grain size (which remains constant).

The authors note that this is, to their knowledge, the first impedance-spectroscopy study of undoped ultrasonic-spray-pyrolysis ZnO films over the 95–370 K range. They emphasize that while no single concentration is optimal by all measures, the transport differences are robust and linked to defect-related in-gap states, as evidenced by the correlation between defect emission intensity and the splitting of the near-band-edge doublet.

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