Humidity measurement with capacitive humidity sensors between − 70 ◦ C and 25 ◦ C in low vacuum

Abstract. At the German Aerospace Center (DLR), capacitive humidity sensors are used to measure relative humidity in experiments under extreme atmospheric conditions such as on Mars or in the coldest regions on Earth. This raises the question whether such experiments can be performed using low-cost humidity sensors with a tolerable measurement uncertainty. As part of the standardizing project SMADLUSEA (project no. SF11021A), nine capacitive humidity sensors (Sensirion SHT75) were investigated for pressure ranging from 10 to 1000 hPa (low vacuum) and temperatures from −70 to 25 °C. It has been shown that these sensors worked reliably and with reproducibly measured values over the entire investigated pressure and temperature range. There was no aging of the sensors observable. In addition to the known strong temperature dependency, the SHT75 also shows a pressure dependency below −10 °C. A characteristic curve for the SHT75 was calculated with an expanded uncertainty of 7% of the measured values. In conclusion, low-cost capacitive humidity sensors offer the option to obtain reliably measured values even under extreme conditions with comparatively little effort.


Introduction
What are the most useful sensor principles and their potential measurement ranges under Martian conditions?This was a fundamental question for the development of the in situ trace humidity measuring system called MiniHUM, designed for the ExoMars lander to measure the humidity of the nearsurface Martian atmosphere (Koncz, 2012).The coulometric and capacitive sensor principles were chosen to develop a lightweight and low-energy device.The coulometric sensors (Lorek et al., 2010), which we will not further described in this paper, measure the absolute humidity and have the potential to detect trace humidity below frost points of −100 • C.However, our own measurements have shown low chemical activity at temperatures less than −50 • C which leads to a limited functionality for this type of sensor.
At standard environmental conditions (25 • C and 1013 hPa), the capacitive sensors measure reliably in the range from 10 to 90 % relative humidity (U w,i ).However, there are only insufficient data, even for coulometric sensors, about the behavior in low vacuum (1 to 1000 hPa) and temperatures between −70 and 25 • C. Evidence for the ability of the capacitive sensor principle is the Phoenix Mars mission (Zent et al., 2010).Capacitive humidity sensors are also used successfully in meteorology, for example, on radiosondes in weather balloons.While some of them have been investigated for temperatures down to −70 • C (Miloshevich et al., 2001;Hudson et al., 2004), there are not sufficient data on their behavior in a low vacuum especially down to 10 Pa.
Our measurements of nine capacitive humidity sensors type SHT75 from Sensirion AG (2011) provide a database which demonstrates function and measurement uncertainty of off-the-shelf sensors in the already mentioned pressure and temperature range.The experiments were performed at the Martian Simulation Facility (MSF) at DLR (Lorek and Koncz, 2013).

Theoretical background
The SHT75-sensors measure the relative humidity U w,i (Eq.1), defined as the ratio in per cent of the water vapor partial pressure (1) In this paper conditions of pure phase e were assumed and used for calculations and not the water vapor partial pressure in a real gas e , because the difference between both pressures is < 0.5 % and negligible for this investigation (VDI/VDE 3514 Part 1, 2007;Bögel, 1977;WMO, 2012).
The following Eqs.( 2) for e w [hPa] and ( 3) for e i [hPa] are recommended by WMO (2012).Equation ( 2) is related within the temperature range from −50 to 100 and Eq. ( 3) from −100 to 0 • C with T 1 = 273.16K (triple point temperature of water): The WMO (2012) recommends calculating the relative humidity relative to U w .One reason is that for temperatures below 0 • C, the relative humidity in clouds is often supersaturated with respect to ice (U i > 100 %).A further reason is a better comparability of the most meteorological measurements witch are often displayed in U w .However, the measurements discussed in this paper were partially performed down to −70 • C.This is out of the range of Eq. (2).A super-saturation of the sample gas seems to be unlikely because there are enough inner surfaces in pipes and measurement cells for the condensation of surplus water vapor.Therefore, in this paper, the relative humidity below 0 • C is obtained in relation to ice (U i ) according to the technical definition for the relative humidity (VDI/VDE 3514 Part 1, 2007).

Sensors and measured value acquisition
The investigated SHT75 is a polymer based capacitive humidity sensor manufactured in CMOS technology.In addition it has a band-gap temperature sensor and electronic units for signal processing (Sensirion AG, 2011).The humidity sensor measures the permittivity of the hydrophilic polymer depending of the adsorbed water content which is affected by the partial water vapor pressure of the surrounding atmosphere.An integrated A/D converter generates a serial output from the analog measurement signal at the digital interface.The dimensions without electrical connectors are (6.4 × 3.7 × 3.1) mm (length × width × height).
A nine-channel measuring device for SHT sensors from dr. wernecke Feuchtemesstechnik GmbH was used to process the serial data and output an integer rough humidity value (SO RH ) and temperature value.From these, the device calculates the relative humidity value U w(SHT75) , based on Eq. ( 4).
The measuring range for U w specified by the manufacturer is from 0 to 100 % and for the temperature from −40 to 123.8 • C.
Equation ( 4) is the manufacturer formula (Sensirion AG, 2011) for the calculation of the temperature compensated relative humidity: The expanded uncertainties (U 99 ) for U w(SHT75) is U 99 = 1.8 % within U w 10 to 90 % at 25 • C and increase to the measuring range limits of U 99 = 4 %.The expanded uncertainty for the temperature increases from U 99 = 0.3 K at 25 • C to a maximum of 1.5 K at −40 • C (Sensirion AG, 2011).
The expanded uncertainties U 99 , given in this paper, result from a multiplication of the standard uncertainty u (type A or B) with factor of 3 (k = 3) and include 99 % of the measured values (GUM, 2008).
Using SHT75 has an historical background.To measure in situ the near-surface atmospheric humidity on Mars in 2003 our laboratory was looking for a humidity sensor.Information from the Open University about this sensor working under extreme conditions and its special features (e.g., digital output, low hysteresis, inexpensive, low power consumption, off-the-shelf product and certified) led to the choice of the SHT75.Since then, the laboratory has been using this sensor.
The investigated temperatures range down to −70 • C which is lower than the threshold of −40 • C for the SHT75 measuring range.Therefore and as a reference, 15 Pt100 temperature sensors were used.Twelve of them were Pt100 thin-film resistors 6W 538 from IST AG (2012) with the dimensions 5 × 3.8 × 0.65 mm (length × width × height) and three were Pt100-wire-wound resistors from Service für Messtechnik Geraberg GmbH, all with classification A. The wire-wound resistors were cased in a copper block to prevent damage by the mounting on the exterior measuring cell housing.The block dimensions are 10 × 3 × 3 mm (length × width × height).The Pt100 sensors were calibrated for temperatures between −75 and 50 • C (Deep-Well-Bad 7831, Fluke Europe B.V) with a resulting expanded uncertainty for all Pt100 of U 99 = 0.1 K.
The pressure measurement was done using an Active Capacitive Transmitter CMR 361 (Pfeiffer Vacuum GmbH).It has an effective range from 0.1 to 1100 hPa and an U 99 = 0.01 % (full scale) in the range from 1 to 40 000 Pa and an U 99 = 0.1 % for p > 40 000 Pa.
A Keithley-digital multimeter DMM 3706 with integrated Dual 1 × 20 Multiplexer-card (Model 3721 with 3721-ST screw terminal) was used for data acquisition from CMR 361 and all Pt100.
A dew point mirror hygrometer S8000RS (Michell Instruments GmbH) was the reference for the humidity of the sample gas.It has a measuring range from ca. −100 • C frost point temperature (t f ) to 20 • C dew point temperature (t p ) with an expanded uncertainty of U 99 = 0.3 K at 20 • C to 0.51 K at −60 • C.

Experimental setup
The experimental setup, basically described by Lorek and Koncz (2013), consists of a gas mixing system, a temperature test chamber which contains the measuring cells, a membrane vacuum pump (Fig. 1) and the measurement equipment mentioned in Sect.3.1.1.The pipes, measuring cells and connection components between gas mixing system and vacuum pump consisted of stainless steel to minimize adsorption at and permeation through the pipe walls.
The sample gas can be nearly continuously humidified in an absolute humidity range from −73 • C (t f ) to 5 • C (t p ).
It was found that for the pipes which transport the sample gas inside the chamber to the measuring cells, a diameter of DN 16 is sufficient to ensure constant pressure and prevent water condensation in pipes and cells inside the chamber (Fig. 2).The dimensions of the measuring cells are 180 × 70 × 70 mm (length × width × height).Each cell has a centered 38 mm diameter hole over the entire length and two blind holes of the same dimensions down to the vertical center with a distance of 80 mm.These blind holes form the measuring chambers holding the sensors and exposing them to the sample gas (Fig. 2a).

Sensor setup
Each of the CF-DN40 flanges sealing the first measuring chamber of each measuring cell (Fig. 2) is equipped with a 2 mm stainless steel pipe for the pressure measurement and a 32-pin male connector.Both were glued into the flange using ECCOBOND 286 (2013).The connectors provide the electrical feedthrough for 4 Pt100 (four-wire configuration) and three SHT75 on each measuring cell.
The SHT75 measurement range for temperature is limited at −40 • C. Therefore, a calibrated Pt100 was glued onto each SHT75 (Sect.3.1.1).The fourth Pt100 was placed in  the center of the three mounted SHT75/Pt100 combinations (Fig. 3).This Pt100 measured the undisturbed gas temperature to reveal temperature differences between the Pt100-SHT75 combinations and the housing temperature.In order to place sensors in the center of the gas flow, they were soldered to the connector with 15 mm enameled copper wires (diameter 150 µm).
A 1.8 m four-wire cable with PFA-coating (usable down to −200 • C) was used to connect each sensor with the measurement device.To minimize heat influences from the outside, cables were routed mainly inside the temperature test chamber.Finally, for every measuring cell, one Pt100 (Sect.3.1.1)was mounted outside every measurement cell to measure the housing temperature.The quantity of nine SHT75 is given by the Pt100 measuring equipment and the selected 32-pin male connector.
In the following each SHT75 and Pt100 will be designated using the nomenclature in Table 1.

Experimental procedure
After a leakage test, a continuous volume flow of VN = 30 L h −1 (at 20 • C and 1013 hPa) sample gas was passed through each cell (Figs. 1 and 2a).At 10 hPa, the flow has to be reduced to VN = 15 L h −1 to ensure not to exceed the performance of the vacuum pump.When at the required temperature thermal equilibrium was reached inside the measuring chamber, the measurements were started at the highest pressure for this temperature (Table 2) and, if possible, the relative humidity steps between U w,i(ref) ca. 5 and 95 % were generated.The achievable relative humidity was limited due to the chamber temperature and the generated humidity of the gas mixing system.The pressure was kept constant over 0.5 to 15 h depending on the expected duration to reach humidity equilibrium at each humidity step of the measuring chambers and sensors.

Temperature
Figure 4 shows the average values of the temperature differences ( T ), calculated from the measurements of the Pt100 glued onto the SHT75 (see Table 1, column 3, and Fig. 3b) and the SHT75 temperature values relative to the Pt100 placed in the center (see Table 1, column 4, and Fig. 3b) at each temperature (see Table 2, column 1).The expanded uncertainty of T is in Fig. 4a U 99 = 0.32 K at 25 • C to U 99 = 1.5 K at −40 • C and in Fig. 4b U 99 = 0.15 K. Figure 4a shows the aberration development for the SHT75 band-gap temperature sensors from 0.5 K at 25 • C to 1.3 K at −40 • C.This increase of aberration to the Pt100 reference is due to the reduction of accuracy at low temperatures (Sensirion AG, 2011).
Figure 4b shows clearly that the temperature measurement with Pt100 compared to the measurement with the SHT75 band-gap temperature sensor (Fig. 4a) leads to a significantly smaller and temperature-independent variability of the measured values.This has a direct influence on the precision and accuracy of the relative humidity measurements.The observable offset of ca.0.2 K in Fig. 4b probably results from the emitted heat of the active SHT75 (see Sensirion AG, 2011) and is, due to the strong scattering of the T values, in Fig. 4a not clearly observable.
A comparison of the temperature measured by the Pt100 mounted outside the cells (see Table 1, column 5) with the Pt100 placed in the center (see Table 1, column 4) shows nearly identical temperature values with deviations within the uncertainty of the measurement (see Sect. 3.1.1).Therefore, it can be assumed that the sample gas temperature was identical to the cell housing temperature and that the active SHT75 sensors indeed generate the temperature increase of 0.2 K.

Relative humidity
In Fig. 5a-d, we show the signal of the SHT75_5 (see Table 2) representative for the other eight SHT75.U w(SHT75) was calculated from Eq. ( 4) based on the temperature and humidity measurements of the SHT75 and U w(ref) from Eqs. ( 2) and ( 5) based on the t p,f values of the dew point hygrometer and the measurements of the Pt100 glued onto the SHT75 (see Table 1, column 3).Note that the U w values for −70 • C in Fig. 5d lie outside the range of validity of Eq. ( 2) but these values are irrelevant for the demonstration of the reliability.The peaks in Fig. 5d result from the automatic calibration function of the dew point hygrometer.Temperature and pressure influence the sorption rate of water molecules at the sensors and at the walls of pipes and measuring cells.This effect changes the equilibration time of the entire experimental system.A comparison of the sensor response time (T 90) of Fig. 5a with b at the same pressure of 1000 hPa shows a significant delay of some minutes at 10 • C and nearly an hour at −40 • C and therefore a strong dependency on temperature.For this reason, we did not perform measurements at −70 • C and 1000 hPa because the response time of the sensors for each humidity step would have required several days with a resulting increase of the scatter of the measured values and a decrease of the sensitivity (see the 500 hPa-fit in Sect.3.4.3).The situation was different at lower pressure.A comparison at 1000 hPa (Fig. 5b) with 10 hPa (Fig. 5c) at −40 • C shows a reduction of the T 90 time to < 10 min.
The nine SHT75 sensors were tested in several test series over 136 days.On 74 days of this time, the sensors were subjected to temperatures < −40 • C, which is outside their specifications (see Sect. 3.1.1).Nevertheless, the sensors were still functioning (Fig. 5d) and showed reproducible results (see Sects. 3.4.3 and 3.4.4)over the entire temperature and pressure range (Table 2).Pt100 onto the SHT75 (see Sect. 3.1.3).A final determination of the reason for the error is not possible because an unaltered SHT75 was not tested.

Aging of the SHT75
Figure 7 illustrates the U w(SHT75) values of all SHT75 at 10 • C and 1000 hPa at the start and end of the 136 day test time.The area marked in grey shows the expanded uncertainty from Sect.3.4.1 but relative to the linear regression fit of the measurements rather than to the diagonal as in Fig. 6.Therefore, the systematic error (see Sect. 3.4.1) is included in the error analysis.
Even though the sensors were exposed to conditions beyond their specifications (see Sect. 3.1.1),for 74 days out of 136 days the U w(SHT75) values in Fig. 7 are mainly within the expected uncertainty.A drift in the measurements was not observed.We do not observe pressure dependence (Table 2) in the temperature range from −10 to 25 • C (see Fig. 8a).In the range from −20 to −50 • C (Fig. 8b to d), an increase of the scatter in the measurements as a function of increasing pressure was detected.At −60 • C (Fig. 8e), the regression fits of 1000 hPa, 500 hPa and 200 hPa are in better mutual agreement again.Only the 10 hPa fit differs clearly from the others.At −70 • C (Fig. 8f), a pressure dependence can no longer be observed.The deviation of the fit at 500 hPa is a result of the strong variation of the measured values which are located below the fit as the humidity is decreased and above the fit as the humidity is increased.This could be an indication of a hysteresis of the sensors caused by sorption behavior of the polymer and not by instability of the polymer under these extreme conditions because there is no drift at the pressure of 10 hPa observable (Fig. 8f) and no aging (see Sect. 3.4.2and Fig. 7).In general, the measurements showed a decrease in the equilibration times of the system with decreasing pressure and simultaneous increase of the sensitivity of the SHT75.

Temperature dependency of the SHT75
The SHT75 showed a strong temperature dependency of the SO RH values which was also observed by the manufacturer (Sensirion AG, 2011).We perform a linear fit (see Fig. 9a, b) for the different temperatures under investigation (Fig. 9c, d).
A polynomial fit performed for the data in Fig. 9c and d gives m = 3.74557 × 10 −8 t 3 + 6.894 × 10 −6 t 2 − 6.42783 × 10 −6 t + 0.03 ( 7) Figure 10 shows the U w,i(SHT75/Pt100) values calculated from Eqs. ( 6)-( 8) based on all SO RH values, measured at the temperatures and pressures listed in Table 2.In the calculation, the temperature values of the Pt100 glued onto the SHT75 (see Table 1, column 3) were used.The expanded uncertainty of U w,i(SHT75/Pt100) and U w,i(ref) is U 99 = 7 % (grey area in Fig. 10).The statistical error analysis is based on Hässelbarth (2004) for a linear calibration of type A (GUM, 2008).The values outside the area marked in grey are mainly caused by the large scatter of the measured humidity values at −70 • C (see Fig. 8e).
For fits with lower uncertainties, we recommend to calibrate the sensors for individual temperatures and/or pressures.

Conclusions
Pt100 and SHT75-sensors work reliably in the operating range given by manufacturer and the SHT75 even outside.The temperature measurement with SHT75 leads to significantly stronger variation of the measured values than with the Pt100 (Sect.3.3).The comparison of the SHT75 humidity values with the reference humidity of the dew point hygrometer shows a difference to the manufacturers fit at relative humidities below 20 % (see Sect. 3.4.1).The reason for this deviation remains unclear.The SHT75 shows a strong temperature dependency (Sect. 3.4.4)and also a pressure dependency below −10 • C (Sect.3.4.3).No aging effects were observed (Sect. 3.4.2).A characteristic curve for the Pt100-SHT75 combination (Sect.3.1.3)was calculated with an U 99 of 7 % of the measured values (Sect. 3.4.4).
The experiment has demonstrated that it is possible to perform reliable humidity measurements at low vacuum and temperatures down to −70 • C using off-the-shelf sensors.The use of additional Pt100 instead of the SHT75 internal band-gap sensor is recommended for the reduction of measurement uncertainties.Moreover, characteristic curves should be recorded for each pressure, especially at temperatures < −20 • C (Sects.3.4.3and 3.4.4).
Further measurements of cross-sensitivity to other gases (e.g., CO 2 ), cf.Koncz et al. (2010), are necessary in order to validate these sensors for humidity measurements under extreme conditions such as a simulated Martian atmosphere.
e [Pa] to saturation vapor pressure under Published by Copernicus Publications on behalf of the AMA Association for Sensor Technology.saturation conditions above a planar water e w [Pa] or ice surface e i [Pa] at the same total pressure p [Pa] and temperature T [K] (derived from WMO, 2012): U w,i = e e w,i p,T 100 %.

Figure 2 .
Figure 2. (a) Illustration of measuring cells and pipe routing inside the temperature test chamber; (b) temperature test chamber with measuring cells.

Figure 4 .
Figure 4. T of the measured values relative to the Pt100 in the middle of each measuring chamber.In (a) temperature is measured by the Pt100 glued onto SHT75, while in (b) temperature is measured by the SHT75 itself.

Figure 6
Figure 6 shows the U w(SHT75) values from Eq. (4) at temperatures between −40 and 10 • C and a pressure of 1000 hPa based only on SHT75 measurements.The calculation of U w(ref) has been described in Sect.3.4.The area marked in grey illustrates the expanded uncertainty U 99 calculated using the standard uncertainty (type B GUM, 2008) with the

Figure 5 .
Figure 5. Signal of SHT75_5 (representative for all SHT75 sensors) at different temperatures and pressures.

Figure 7 .
Figure 7. U w(SHT75) values at 10 • C and 1000 hPa of all SHT75 at the start and end of the 136 days test time; expanded uncertainty area marked in grey.
3.4.3Pressure dependency of the SHT75 In this section, the relation of the SO RH values (see Sect. 3.1.1)and U i(ref) values (see Sect. 3.4) is evaluated as a function of pressure.

Figure 9 .
Figure 9.All SO RH values of the nine SHT75 at (a) 0 • C and (b) −40 • C; (c) slope m and (d) offset n of the linear regression fit for all temperatures.

Table 1 .
Nomenclature for the Pt100 and SHT75 used.

Table 2 .
Range of the relative humidity under investigation for the different temperature and pressure conditions.Relative humidity is calculated with respect to water U w or ice U i (marked by brackets).