1.

INTRODUCTION

Vibration-free miniature cryogenic coolers are relevant to a wide variety of applications, including cooling of detectors in space missions, low-noise amplifiers and superconducting electronics. In these applications, the operating temperature of electronic devices is lowered to reduce thermal noise and/or increase speed. In order to fully exploit low-temperature electronic devices, the cryogenic system (cooler plus interface) should be ‘invisible’ to the user. It should be small, low-cost, low-interference, and above all very reliable (long-life). Although different groups around the world have tried to build small cryogenic refrigerators, such small microcoolers are not yet available.

Within the Cooling and Instrumentation group at the University of Twente a MEMS-based cold stage was designed and prototypes were realized and tested (MEMS: Micro-Electro-Mechanical Systems). These coolers operate on basis of the Joule-Thomson effect and have cooling powers of typically 10 to 20 mW at about 100 K. The next section describes the design of these microcooler tips, whereas the fabrication is considered in section 3. The measurement setup in which the coolers are characterized as well as the experimental results are presented in section 4. The paper is closed with a discussion in section 5.

2.

COLD-STAGE OPERATION

In the microcooler, cooling is obtained by using the socalled Joule-Thomson effect [1]. Nitrogen is expanded from a high pressure of 80 bar to a low pressure of 6 bar over a flow restriction that is only 300 nm high, see Fig. 1. Through this restriction, the gas undergoes isenthalpic expansion and changes its phase to a liquid. At the low pressure of 6 bar, the boiling temperature of nitrogen is 96 K which determines the temperature of the cold tip. The evaporated working fluid returns to the low-pressure side of the system via a counter-flow heat exchanger (CFHX). In passing this heat exchanger, it takes up heat from the incoming high-pressure gas that thus is precooled on its way to the restriction [2].

Fig. 1

Left: 3D schematic of a cold stage; Right top: schematic cross section of a cold stage; Right bottom: photograph of a cold stage.

The cooling power at the cold tip equals the mass-flow rate (ṁ) times the specific heat of evaporation. Since the Joule-Thomson expansion is an isenthalpic process and furthermore, the enthalpy is maintained in the CFHX, the cooling power can also be expressed as

Here, dh is the difference in specific enthalpy of the gas between the high and low pressures at the warm end of the CFHX [2]. At a flow of 1 mg/s, the gross cooling power is about 15 mW.

In contrast to earlier micro cold stages [3-5], this cold tip is optimized for maximum performance in combination with minimal size. The dimensions are optimized by minimizing the entropy that is generated. In this optimization, all heat- and pressure-drop losses in the cooler are written as a production of entropy. By minimizing the total entropy production, it is possible to find an optimal cold-stage configuration, which has minimum losses and thus maximum performance [6]. A photograph of the prototypes can be found in Fig. 2.

Fig. 2

Photograph of five prototype microcoolers.

3.

FABRICATION

The microcoolers are fabricated in glass wafers using HF etching and abrasive etching (a.k.a. powder blasting). The production process has seven lithography steps and roughly 100 process steps. The cold stage consists of a stack of three glass wafers. In the top wafer, the high-pressure line is etched as a rectangular channel. This line ends in a flow restriction and an evaporator volume that crosses the center wafer into the bottom wafer. This bottom wafer contains the low-pressure line, again etched as a rectangular channel, thus forming a CFHX, see Fig. 1. The high- and low-pressure gas channels are fabricated by HF etching. The channels are 50 µm deep and 2 mm wide. To create a mass flow of 1 mg/s with the pressure difference of 74 bar, the height of the restriction has to be only 0.3 µm. Since the absolute pressure inside the high-pressure channel is relatively high (80 bar) and the thickness of the wafer is only 150 µm, the channel is supported by micro pillars as is shown in Fig. 3. The cold-stage fabrication process is described in more detail in [7].

Fig. 3

Zoom of the cold tip; Right: SEM picture of a grid of 50 µm wide pillars to support the high-pressure channel construction.

4.

CHARACTERIZATION EXPERIMENTS

4.2

Results

Fig. 4 shows a typical cool-down curve of cold stage 3. Two graphs give the temperature of the cold tip and the mass flow through the system both versus time. The variation of the flow with temperature is caused by the temperature dependence of the gas density and viscosity. The micro cold stage cools down from 300 K to 107 K in about 800 seconds. At t ≈ 800 s, the mass-flow curve starts to fluctuate which is an indication that liquid nitrogen is being formed inside the evaporator. It can be seen that the temperature as measured does not reach the predicted 96 K. This is caused by the heat resistance of the thin layer of glass and the heat flow through the thermocouple from the environment to the cold stage. This can easily give a temperature difference of about 15 K. After 1000 s, the cold stage stabilizes at constant tip temperature and mass flow.

Fig. 4

Cool-down registration of microcooler prototype 3.

Table 1 summarizes the results for all prototypes depicted in Fig. 2. The net cooling powers as measured [9] and as calculated [12] are given in which parasitics, as discussed above, are taken into account. The characterization experiments are more extensively discussed in [9].

Table 1

Measured and calculated cooling powers of the microcooler prototypes

Prototype number	1	2	3	4	5
CFHX channel width (mm)	2.0	2.0	2.0	2.0	4.0
CFHX channel length (mm)	25	15	25	35	25
mass flow (mg/s)	1.0 ± 0.06	1.0 ± 0.06	2.0 ± 0.06	2.0 ± 0.06	2.0 ± 0.06
net cooling power calculated (mW)	12.5	10.8	22.0	25.0	25.4
net cooling power measured (mW)	11 ± 2.1	9 ± 2.1	19 ± 2.6	24 ± 2.1	26.5 ± 2.6

5.

DISCUSSION

Micro Joule-Thomson cryocoolers, of which the production process is fully based on MEMS technology, have been developed and tested. The design of the cold stage has been optimized for maximum performance in combination with minimal dimensions. The dimensions of a cold stage are typically 30 × 2.2 × 0.5 mm with a net cooling power of 10 to 20 mW. Five different microcooler designs, varying in cold stage dimensions and mass flow, were fabricated and tested. In one of two new research projects at the University of Twente, the microcoolers will be combined with sorption compressors in order to realize a closed-cycle system [10, 11]. In the second project, integration of optical detectors with microcooler tips is investigated for space applications [12]. The microcoolers are made available through a new university spin-off company [13].