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Micrometer-scale displacement and thickness sensing using a single terahertz resonant-tunneling diode

This paper presents a 280 GHz radar concept utilizing a single resonant tunneling diode for self-mixing detection, experimentally demonstrating the ability to measure micrometer-scale displacements and resolve thin-film thicknesses at room temperature.

Original authors: Li Yi, Shota Ito, Chao Tang, Yousuke Nishida, Koji Terumoto, Toshihisa Maeda, Yuta Inose, Masayuki Fujita

Published 2026-03-02

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CC BY 4.0

Original authors: Li Yi, Shota Ito, Chao Tang, Yousuke Nishida, Koji Terumoto, Toshihisa Maeda, Yuta Inose, Masayuki Fujita

Original paper licensed under CC BY 4.0 (http://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 you are trying to measure the thickness of a piece of paper or the tiny movement of a wall, but you can't touch it. You need a tool that is incredibly sensitive, small enough to fit in your pocket, and cheap enough to mass-produce.

This paper introduces a solution using a tiny electronic component called a Resonant Tunneling Diode (RTD). Think of this device as a "Swiss Army Knife" for light waves, specifically Terahertz waves (a type of invisible light that sits between microwaves and infrared).

Here is the story of how they turned this tiny chip into a super-sensitive ruler, explained simply.

1. The Problem: The Expensive, Bulky Ruler

Traditionally, to measure things with this level of precision using Terahertz waves, you need a massive setup. It's like trying to measure a hair's width using a construction crane. You need:

A laser to generate the light.
A separate transmitter to shoot the light.
A separate receiver to catch the reflection.
Complex electronics to mix the signals.

It's expensive, heavy, and hard to fit into a smartphone or a small sensor.

2. The Solution: The "Echo-Location" Chip

The researchers realized they could use one single chip to do everything. The RTD is special because it has a "negative resistance" property.

The Oscillator: When you give it a little electricity, it starts vibrating (oscillating) at Terahertz frequencies, acting like a flashlight.
The Mixer: Because of its unique physics, it can also listen to its own echo.

The Analogy: Imagine a bat that doesn't just shout and then listen with its ears. Instead, the bat's mouth is its ear. When the sound bounces off a wall and hits the bat's mouth, it changes the vibration of the bat's voice slightly. The bat can "hear" the wall by listening to how its own voice changed.

This is called Self-Mixing. The chip sends a wave, the wave bounces off an object, comes back, and messes with the chip's own vibration.

3. The Trick: The "Sweeping" Ruler

To measure distance, the researchers didn't just turn the chip on and off. They slowly changed the voltage going into the chip.

The Analogy: Imagine a singer holding a single note. If they slowly slide their voice up and down the scale (a "sweep"), and a wall reflects the sound back, the pitch of the echo will be slightly different from the pitch of the voice at that exact moment.
By sweeping the frequency, the chip creates a "beat" pattern (a wobble in the signal) that tells them exactly how far away the object is.

4. The Superpower: Seeing the Invisible Shifts

The real magic of this paper is measuring microscopic changes.

The Goal: They wanted to measure movements as small as 5 micrometers (that's thinner than a human hair) and film thicknesses of 12.5 micrometers.
The Challenge: Usually, if you move something that tiny, the "beat" pattern is too messy to read because the signal gets distorted.
The Fix: They treated the messy signal like a sliding puzzle. Even though the shape of the wave was weird (distorted), they realized that when the object moved, the entire weird wave just shifted slightly to the left or right.
By using a clever math trick (comparing the "before" and "after" waves), they could calculate exactly how much the wave shifted, and therefore, how much the object moved.

5. The Results: A Pocket-Sized Lab

They built a prototype and tested it:

Displacement: They moved a metal plate back and forth by tiny amounts (5 to 200 micrometers). The chip detected every single step accurately.
Thickness: They stacked layers of plastic film (12.5, 25, and 50 micrometers thick). The chip could "see" through the air and tell them exactly how thick the plastic was, just by measuring how the light slowed down inside it.

Why This Matters

Think of this technology as the difference between a professional film camera and a smartphone camera.

Old Way: Professional, huge, expensive, requires a team to operate.
New Way (This Paper): Tiny, cheap, runs on a battery, and fits on a circuit board.

Because the system only needs simple, low-speed electronics (like those in a standard computer) to read the signal, it opens the door for:

Smart Factories: Sensors that check if a pill coating is the right thickness on a conveyor belt.
Medical Devices: Tiny probes that can measure skin swelling or tissue changes without touching them.
3D Imaging: Creating 3D maps of objects using a sensor the size of a coin.

In a nutshell: They turned a single, tiny electronic component into a super-precise, pocket-sized ruler that can measure things smaller than a human hair by listening to its own echoes.

1. Problem Statement

Terahertz (THz) sensing is crucial for non-destructive evaluation, imaging, and metrology due to its ability to penetrate non-conducting materials and its sub-millimeter wavelength. However, existing technologies face significant trade-offs:

Terahertz Time-Domain Spectroscopy (THz-TDS): Offers high resolution and broadband capabilities but relies on complex, bulky, and expensive femtosecond laser systems.
Continuous-Wave (CW) Radar: More compact but typically requires high-end hardware, including tunable high-frequency sources, dedicated transmit/receive chains, and coherent mixing circuits. Implementing these above 300 GHz is challenging due to output power limitations and front-end losses in standard semiconductor technologies (CMOS/SiGe).

The core problem addressed is the need for a compact, low-cost, and low-power THz sensing system capable of micrometer-scale displacement and thin-film thickness measurement without the complexity of traditional radar architectures or ultrafast optical systems.

2. Methodology

The authors propose a novel radar concept utilizing a single Resonant Tunneling Diode (RTD) operating near 280 GHz. The system leverages the unique properties of RTDs to function as both the oscillator and the mixer.

Single-Device Transceiver: An RTD exhibits negative differential conductance (NDC), allowing it to sustain room-temperature THz oscillation. Due to strong intrinsic nonlinearity, the same device acts as a detector. When a portion of the radiated signal reflects off a target and re-enters the RTD, it creates a self-mixing effect (analogous to optical self-mixing in lasers).
Interferometric Radar Approach: Instead of relying on large bandwidths for range resolution (which is limited in RTDs to ~10% of the center frequency), the system uses interferometric phase sensing.
- The RTD bias voltage is swept linearly to modulate the oscillation frequency over a narrow bandwidth (~2 GHz).
- The reflected signal creates a low-frequency self-mixing voltage waveform.
- Small target displacements ( $\Delta d$ ) cause a phase shift in this waveform.
Signal Processing:
- Modeling: The system is modeled using the Lang–Kobayashi framework for delay-feedback systems. The self-mixing signal is treated as a periodic function of the feedback-modified phase.
- Waveform Shift Estimation: Under the assumption of weak-to-moderate feedback ( $0 < C < 1$ ), small displacements result in a near-constant shift of the entire self-mixing waveform across the frequency sweep.
- Algorithm: A bounded Normalized Cross-Correlation (NCC) algorithm is employed to estimate the time shift between successive sweeps. This method is robust against waveform distortion and baseline drift. Sub-sample accuracy is achieved via parabolic interpolation.
- Displacement Calculation: The estimated sample delay is converted to physical displacement using the relationship $\Delta d \approx \frac{k R \Delta f}{f_c}$ , where $k$ is the delay, $R$ is the target range, and $f_c$ is the center frequency.

3. Key Contributions

Single-Device THz Transceiver: Demonstrated a system where a single RTD acts as a bias-tunable oscillator and a self-oscillating mixer, eliminating the need for separate transmit/receive chains and external local oscillators.
Low-Frequency Control and Readout: The sensing signal is confined to the sub-MHz bandwidth (baseband), enabling the use of low-cost, moderate-speed acquisition electronics (FPGA, standard ADCs) rather than high-speed RF components.
Interferometric Processing for Micrometer Sensing: Introduced a phase-based processing technique specifically tailored to the distorted self-mixing waveforms of RTDs. This allows for micrometer-scale resolution despite the limited frequency tuning bandwidth of the device.
Experimental Validation: Validated the approach for both displacement sensing and thin-film thickness measurement, proving the feasibility of RTD-based interferometric radar.

4. Experimental Results

The system was tested using a packaged ROHM RTD module (0.02 mm² chip area) operating at ~280 GHz with an output power of ~20 µW.

Displacement Sensing:
- Successfully measured commanded translation steps ranging from 5 µm to 200 µm.
- Achieved a minimum detectable displacement of ~5 µm.
- Statistical analysis showed a Root Mean Square Error (RMSE) of approximately 3–4 µm for steps of 12.5 µm and above.
- The system demonstrated high stability, with measurements averaged over 1024 sweeps (acquisition time ~10 ms).
Thin-Film Thickness Sensing:
- Quantitatively resolved polymer film thicknesses of 12.5 µm, 25 µm, and 50 µm.
- The system treated the film insertion as an equivalent air-path displacement based on the refractive index ( $n \approx 1.7$ ).
- An RMSE of approximately 3 µm was achieved across the tested thicknesses.
- Lateral scans successfully distinguished between adjacent film regions with a spatial resolution of ~2 mm.
Range Performance: The system maintained detectable signals up to 70 cm for metallic reflectors, despite the low output power, due to the high sensitivity of the self-mixing mechanism.

5. Significance and Impact

System Miniaturization and Cost Reduction: By integrating the oscillator and mixer into a single chip and operating at baseband frequencies, the proposed architecture drastically reduces system size, power consumption, and cost compared to conventional THz radar or THz-TDS systems.
Scalability: The low-frequency nature of the readout electronics facilitates the creation of monostatic arrays using standard microwave components, paving the way for compact THz imaging systems.
Practical Metrology: The technique offers a practical solution for industrial non-destructive testing (NDT), specifically for monitoring small vibrations, displacement, and thin-film thickness variations in materials where high resolution is required but ultrafast optics are impractical.
Future Potential: The authors note that operating at higher RTD frequencies (e.g., 2 THz) could theoretically push displacement sensitivity toward the nanometer scale, provided phase noise is managed.

In conclusion, this work establishes a new paradigm for compact THz sensing, proving that a single RTD can serve as a highly sensitive, interferometric radar capable of resolving micrometer-scale changes, bridging the gap between high-performance metrology and low-cost, portable sensing.