# Fabrication of a Knudsen micropump for integration in a Pulsed tube Cryocooler

Phassawat Leelaburanathanakul, Thanasis Basdanis, Thierry Camps, Marcos

Rojas-Cardenas, Christine Barrot-Lattes, Lucien Baldas, Jürgen Brandner,

Stéphane Colin

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Phassawat Leelaburanathanakul, Thanasis Basdanis, Thierry Camps, Marcos Rojas-Cardenas, Christine Barrot-Lattes, et al. Fabrication of a Knudsen micropump for integration in a Pulsed tube Cryocooler. 9th Micro and Nano Flows Conference, University of Edinburgh, Sep 2025, Edinburgh, United Kingdom. hal-05499536

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# Fabrication of a Knudsen micropump for integration in a Pulsed tube Cryocooler

Phassawat LEELABURANATHANAKUL¹,*, Thanasis BASDANIS¹, Thierry CAMPS², Marcos ROJAS CARDENAS¹, Christine BARROT¹, Lucien BALDAS¹, Jürgen J. BRANDNER³, Stéphane COLIN¹

¹Institut Clément Ader (ICA), Université de Toulouse, CNRS, INSA Toulouse, ISAE-SUPAERO, IMT Mines Albi, Toulouse, France

²CNRS, LAAS, 7 Avenue du Colonel Roche, Toulouse, F-31400, France

³Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany

## Abstract

Cryogenic temperatures below 150 K are essential for advanced applications such as superconducting systems and infrared sensors. Pulsed tube cryocoolers (PTCC) offer a compact, cryogen-free solution for achieving these temperatures, but their reliance on pressure oscillations poses challenges for miniaturization. To address this, we propose the integration of a Knudsen pump as a vibration-free compressor for a miniaturized PTCC. The Knudsen pump operates using thermal transpiration within nanochannels, eliminating the need for moving parts. However, high-pressure operation for PTCCs requires sub-micrometer channels and dense parallel arrays, posing fabrication and thermal management challenges. In this work, high-aspect-ratio nanochannels are fabricated in borosilicate glass using Bessel beam laser processing, achieving around 300,000 channels on a 1 cm² area. Metal heaters and silicon-based heat sinks are utilized to enhance the thermal gradient. Two prototype samples are fabricated and characterized via microscopy and SEM, with flow performance characterization planned.

**Keywords:** Knudsen pumps, thermal control, nanochannels, thermal transpiration, laser micromachining

## 1. Introduction

Knudsen pumps are a promising solution for generation of vibration-free pressure difference required to drive a miniaturized pulsed tube cryocooler (PTCC). As conventional compressors introduce vibrations that are problematic at small scales, Knudsen pumps become suitable for macroscopic gas flow generation due to their ability to operate without any moving parts. Integrating a Knudsen pump into a PTCC system involves addressing specific operational requirements. Effective thermal transpiration at pressure near atmospheric occurs only in sub-micrometer-sized channels. Achieving sufficient mass flow at this scale demands many parallel channels. The high-pressure oscillations needed by the PTCC also require excellent

thermal management and a multi-stage pump to reach the necessary compression ratios. This work describes the process of fabricating and characterizing a Knudsen pump as a vibration-free compressor for a miniaturized PTCC.

## 2. Fabrication of the Knudsen pump

### 2.1 Nanochannels Fabrication

Maximum pressure difference from the thermal transpiration effect occurs at rarefaction parameter $\delta = rP/\mu v_0 = 3.5$ where $v_0 = (2R_gT)^{0.5}$, r, P, $\mu$, $R_g$, T are the most probable molecular speed, channel radius, pressure, dynamic viscosity, specific gas constant, and temperature, respectively. In long circular channels, this corresponds to a radius of ~0.3 µm for operation with air at the atmospheric pressure.

<footnote>* Corresponding author: Tel.: +33 (0) 6 11 55 55 65; Email: leelabur@insa-toulouse.fr</footnote>
Thermal transpiration is driven by temperature gradients achieved in long channels with low thermal conductivity. As a result, microfabrication techniques like deep reactive-ion etching (DRIE), which are limited to aspect ratios around 70, are no longer suitable. On the other hand, Bessel beam laser processing offers a promising alternative by enabling the fabrication of very high-aspect-ratio channels—exceeding 10,000—in glass substrates [1]. With writing speeds of up to 1 kHz, rapid fabrication of dense channel arrays suitable for scalable nanochannels production is possible.

## 2.2 Integrated Heater and Heat Sink

Electrical Joule heaters made of three metal layers are used to precisely increase the temperature near the nanochannels on one side of the glass substrate. On the opposite side, silicon pillars are used as an integrated heatsink. After fabricating the silicon pillars and gas openings using reactive-ion etching (RIE) and DRIE processes on the silicon substrate, this substrate is anodically bonded to the glass substrate to allow precise heat diffusion close to the nanochannels.

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Single-stage Knudsen pump: a) electrical connections and channels area (black), b) closer view of a section of the 1×1 cm² area showing four DRIE openings in the silicon, c) magnified view of the Knudsen pump array with channels as black dots, gold deposition in yellow, and titanium deposition in purple, d) bottom view of silicon pillars around the channels.</figcaption></figure>

Layers of titanium, titanium-tungsten (TiW), and gold are deposited onto the glass substrate. The 20 nm-thick Ti layer acts as an adhesion layer between the glass and the subsequent metal layers while functioning as a heater

without covering the nanochannel openings. A sacrificial layer of TiW (~200 nm-thick) is used as an intermediate layer between the Ti and the Au (~200 nm-thick) layers to keep the photoresist from entering the nanochannels during the photolithography process. Fig. 1 shows the patterns of the heater electrical connections.

## 3. Results

Two proof-of-concept prototypes of the Knudsen pump are fabricated using a 0.5 mm-thick and 2×2 cm² borosilicate glass substrate. The difference between the two prototypes is the spacing between the channels, i.e., 10 and 20 µm, resulting in samples with 1,200,000 and 300,000 channels, respectively. Microscope and SEM characterizations show consistent pattern of nanochannel openings on both sides of the glass substrate. The diameter of the channels at the opening are observed to be around 331.5 and 254.5 nm for the 10 and 20 µm-spacing prototypes, respectively. Metallization tests are also conducted to determine the correct thicknesses necessary for future photolithography processes.

## 4. Channels Characterization

The fabricated prototypes are planned to be characterized on a test bench with pressure-driven flow experiments. Using the constant-volume technique, the mass flow of the parallel channels can be computed using pressure measurements. The experimental results are compared with the Knudsen pump characteristics curve computed using gas flow kinetic modeling.

## Acknowledgement

This work was funded by the French National Research Agency (ANR) and the German Research Agency (DFG) under the project "ANR-2022-CE92-0017-01".

## References

[1] R. Meyer, et al., "Extremely high-aspect-ratio ultrafast Bessel beam generation and stealth dicing of multi-millimeter thick glass," *Appl. Phys. Letters*, vol. 114, no. 20, p. 201105, 2019.