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Development of an Automated Semiconductor Energy Band Gap Measurement Experiment with Fuzzy-PID Temperature Stabilization

This study presents an automated laboratory platform for semiconductor energy band gap measurement that utilizes a Fuzzy-PID controller to achieve superior temperature stabilization, thereby significantly improving measurement accuracy and repeatability for undergraduate physics education and research.

Original authors: Ahmad Radhy, Rifky Firmansyah, Dimas Dwi Firmansyah, Herry Sufyan Hadi, Zulkaida Akbar, M Jauhar Kholili

Published 2026-08-13

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CC BY 4.0

Original authors: Ahmad Radhy, Rifky Firmansyah, Dimas Dwi Firmansyah, Herry Sufyan Hadi, Zulkaida Akbar, M Jauhar Kholili

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

Imagine electricity as a bustling city where electrons are the commuters. In most materials, these commuters can zip around freely, but in semiconductors—the tiny chips that power our phones and computers—they live in a strict gated community. To get from their home (the valence band) to the busy downtown (the conduction band), they need a specific amount of energy to jump the fence. This "jump fee" is called the energy band gap. It's the magic number that decides if a material acts like a conductor, an insulator, or a semiconductor. Scientists need to measure this fee with extreme precision because it dictates how fast and efficient our electronic devices can be. However, measuring it is tricky. Just like a runner's time changes if the weather is hot or cold, a semiconductor's behavior shifts wildly with temperature. If the lab bench isn't perfectly stable, the measurements get messy, leaving students and researchers scratching their heads over why their data looks like a squiggly line instead of a straight one.

This paper is about building a smarter, more automated way to measure that energy band gap, specifically for Silicon and Germanium diodes. The researchers, working at the Institut Teknologi Sepuluh Nopember and the National Research and Innovation Agency in Indonesia, realized that old-school lab experiments often struggle to keep the temperature steady. They decided to upgrade the setup by replacing a standard "thermostat" with a brainier system called Fuzzy-PID control. Think of a standard PID controller as a driver who only knows how to press the gas or brake based on how far they are from the destination. A Fuzzy-PID controller is like a seasoned driver who also checks the speed, the road conditions, and how quickly they are approaching the stop, adjusting their foot pressure with a bit of intuition. By combining this smart temperature control with an automated system that reads voltage and current, the team created a "one-stop-shop" machine that does the whole experiment without constant human babysitting.

The team built a compact, 3D-printed box to hold the semiconductor samples, keeping them in a climate-controlled chamber. Inside, a special cooling and heating module (a Peltier device) acts like a reversible air conditioner, while sensors constantly whisper the temperature to the computer. The computer uses the Fuzzy-PID logic to decide exactly how much to heat or cool to hit the target temperature, whether that's 20°C, 50°C, or 80°C. They tested this new system against the old, standard PID method. The results showed that the new "smart" controller was a clear winner at higher temperatures. At a 50°C target, the old system made a mistake of about 1.67%, while the new Fuzzy-PID system only missed by 0.65%. At 80°C, the improvement was even more dramatic, dropping the error from 1.56% down to 0.89%. The only hiccup was at a chilly 20°C, where the smart system actually struggled a bit more than the old one, suggesting it might need a little more tuning for cold weather.

Once the temperature was locked in, the machine measured the energy band gap using two different tricks. The first was the "forward bias" method, where they pushed electricity through the diode and watched how the voltage changed as the temperature rose. For Silicon, they found values between 1.0601 eV and 1.0833 eV, which is very close to the textbook value of 1.1 eV. For Germanium, they got values around 0.6170 eV to 0.7706 eV, hovering near the expected 0.67 eV. The second method, "reverse bias," involved looking at tiny, sneaky currents that leak through when the diode is turned the other way. Here, the Germanium results were spot-on, averaging 0.666 eV, almost perfectly matching the theory. The Silicon results were a bit higher than expected (around 1.278 eV), but the measurements were incredibly consistent and precise, showing the system could detect tiny changes reliably.

Ultimately, the paper suggests that this automated, fuzzy-logic-controlled platform is a reliable and cost-effective tool for teaching students and helping researchers. It proves that by making the temperature control "smarter," you can get cleaner, more repeatable data without needing a PhD in thermodynamics to run the experiment. While the system isn't perfect for every single temperature scenario yet, it successfully demonstrates that automated, intelligent control can make the complex world of semiconductor physics much more accessible and accurate for the next generation of scientists.

Technical Summary: Development of an Automated Semiconductor Energy Band Gap Measurement Experiment with Fuzzy-PID Temperature Stabilization

Problem Statement
Accurate determination of the semiconductor energy band gap is a fundamental requirement for understanding electrical properties in solid-state physics and electronic materials. While current–voltage (I–V) characterization is a standard experimental approach, conventional laboratory methods suffer from significant limitations. These include unstable temperature conditions, limited measurement sensitivity, and fragmented experimental procedures. Inadequate temperature regulation introduces uncertainty into the I–V characteristics, reducing the reliability and repeatability of calculated band gap values. Furthermore, existing educational measurement systems often lack an integrated platform that combines stable temperature regulation, automated data acquisition, and structured data management, particularly failing to address the nonlinear thermal dynamics that degrade the performance of conventional PID controllers.

Methodology
The study presents the development of a compact, automated laboratory platform designed to measure the energy band gaps of silicon and germanium diodes. The system architecture integrates three core components:

Hardware and Thermal Control: A custom 3D-printed measurement chamber lined with thermal insulation houses the semiconductor sample. Temperature regulation is achieved using a thermoelectric (TEC-12707) module driven by a BTS7960 H-bridge, allowing for bidirectional heating and cooling. An SHT-30 sensor provides real-time feedback.
Control Strategy: To address the nonlinear thermal dynamics of the chamber, the authors implemented a Fuzzy-PID controller. This system adaptively tunes the proportional ( $K_p$ ), integral ( $K_i$ ), and derivative ( $K_d$ ) gains based on the control error and its rate of change. Initial PID parameters were derived from open-loop step tests using a First-Order Plus Dead Time (FOPDT) model and Ziegler–Nichols tuning. The fuzzy inference engine utilizes seven linguistic labels for inputs and outputs to manage the adaptive tuning.
Data Acquisition and Analysis: An STM32F401CCU6 microcontroller coordinates the system. Voltage and current are measured using an INA219 sensor and a custom MCP6002-based transimpedance amplifier (TIA) for nanoampere-level reverse saturation currents, respectively. A ZK-4KX buck–boost converter serves as a constant-current source for forward-bias measurements.
Measurement Techniques: The system supports two methods for band gap extraction:
- Forward-Bias Method: Analyzing the linear relationship between forward voltage and temperature at constant current.
- Reverse-Bias Method: Analyzing the linear relationship between the natural logarithm of reverse saturation current ( $\ln I_r$ ) and the reciprocal of absolute temperature ( $1/T$ ).
- A graphical user interface (GUI) facilitates real-time visualization, linear regression analysis, and uncertainty estimation.

Key Results

Sensor Calibration: The system achieved high measurement accuracy post-calibration, with the voltage sensor reaching 99.94% accuracy and the nanoampere current sensor reaching 98.63% accuracy relative to reference instruments.
Temperature Control Performance: The Fuzzy-PID controller demonstrated superior performance over conventional PID at medium and high temperatures. At a 50°C setpoint, the steady-state error was reduced from 1.67% (PID) to 0.65% (Fuzzy-PID). At 80°C, the error decreased from 1.56% to 0.89%. However, the Fuzzy-PID controller struggled at a 20°C setpoint, failing to reach the target due to the adaptive reduction of the integral gain, whereas the conventional PID successfully maintained the setpoint.
Band Gap Measurements:
- Silicon (Forward-Bias): Measured values ranged from $1.0601 \pm 0.0072$ eV to $1.0833 \pm 0.0075$ eV across different currents, closely aligning with the theoretical value of 1.1 eV.
- Germanium (Forward-Bias): Measured values ranged from $0.6170 \pm 0.0755$ eV to $0.8166 \pm 0.0839$ eV.
- Germanium (Reverse-Bias): The average measured band gap was 0.666 eV, showing excellent agreement with the theoretical 0.67 eV.
- Silicon (Reverse-Bias): Measured values were consistently higher than the theoretical 1.11 eV (e.g., 1.278 eV), though the system demonstrated high repeatability with low uncertainty ( $\pm 0.00534$ eV).

Key Contributions
The primary contribution of this work is the integration of adaptive Fuzzy-PID temperature stabilization into a unified, automated semiconductor characterization platform. Unlike previous educational kits that often neglect thermal stability or separate data acquisition from control, this system provides:

A single-platform solution for temperature control, I–V acquisition, and data analysis.
An adaptive control strategy that significantly reduces steady-state error and overshoot in nonlinear thermal environments compared to fixed-gain PID controllers.
A validated methodology for extracting energy band gaps with quantified uncertainty using both forward and reverse bias techniques.

Significance and Claims
The authors claim that the developed system provides a reliable, cost-effective, and educationally effective platform for undergraduate laboratory instruction. By ensuring stable thermal conditions through adaptive control, the system enhances the accuracy and repeatability of energy band gap measurements, thereby supporting a clearer understanding of the relationship between semiconductor theory and experimental observation. The study concludes that while the Fuzzy-PID controller requires further refinement for low-temperature cooling applications, it successfully enables precise semiconductor characterization at standard operating temperatures, bridging the gap between theoretical concepts and practical laboratory implementation.

Technical Summary: Development of an Automated Semiconductor Energy Band Gap Measurement Experiment with Fuzzy-PID Temperature Stabilization

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