WO2011062491A1 - Thermogravimetric device - Google Patents

Abstract

Thermogravimetric device (1), comprising a resonator element (10) suspended from a frame (20), at least one actuator (30) for bringing the resonator element (10) in a resonating state and a resonance sensing element (40) for sensing a resonance frequency of the resonator element (10). The resonator element (10) comprises a sample platform (11) to receive a sample and the thermogravimetric device (1) further comprises a heating element (50) for heating the sample when positioned on the sample platform (11). The thermogravimetric device (1) comprises a temperature- sensing element (60) sensing the temperature of the sample platform (11). The thermogravimetric device comprises compensation means to compensate for an increase of the temperature generated by the heating element (50) such that a temperature coefficient of resonance frequency (TCRFsampie platform) of the resonator element (10) for heating of the sample platform (11) without a sample is less than 20 ppm/κ.

Description

Thermogravimetric device

TECHNICAL FIELD

The present invention relates to a thermogravimetric device as defined in the preamble of claim 1. BACKGROUND

Thermo Gravimetric Analysis (TGA) is a thermal analysis technique used to determine changes in weight of a sample-under-test in relation to changes in temperature. The operational range for commercial TGA instruments ( e.g. TGA 4000, PerkinElmer) is 1 μg up to 1500 mg for the mass. MEMS (Micro Electro Mechanical System) devices give an opportunity to shift the operational range towards lower masses.

A commercially available piezo resistive cantilever [1] has been employed for TGA by using the integrated piezo resistor as both heater, temperature sensor and strain gauge. The temperature dependence of the piezo resistive coefficient of the silicon makes the combined temperature and strain sensor problematic. Moreover, using a sensing element for more than one sensing operation creates electronic read-out difficulties and usually reduces performance.

In [2] thermogravimetry has been performed with a cantilever and an external heater and read out. This device needs several external elements for heating and read/out. Using external heating makes the thermal characteristics of this device less well-defined.

A cantilever hot-plate with independent mass sensing, but that still makes use of an external piezoelectric actuator, has been presented in [3]. This device also needs an external element, in this case the piezoelectric actuator. The piezo-electric actuator is driven at the resonance frequency and creates a lot of cross-talk, making the read-out of the device's resonance frequency difficult.

SUMMARY

It is an object to provide a thermogravimetric MEMS device, that is more accurate and easy to perform thermogravimetric measurements with. Therefore, according to an aspect there is provided a thermogravimetric device, as claimed in claim 1.

According to such a thermogravimetric device, which may be a MEMS-device or a NEMS-device, the sample-under-test can be heated by the heating element, without resulting in a significant increase of the temperature of those areas of the resonator element close to the frame. These areas experience the largest stress and strain during resonance. As a result, the resonance frequency of the resonator element will be substantially constant as a function of the temperature of the sample (i.e. during a temperature scan) and the sample platform. This will be explained in more detail below.

This is accomplished by providing a thermogravimetric device that separates the thermal energy generated by the heating element from the part of the resonator element comprising the mechanical resonance energy (base area). The separation of these two energy regimes reduces the temperature coefficient of resonance frequency (TCRFsampie platform) of the resonator element 10 for heating of the sample platform (11) without a sample to less than 20 ppm/K. The design of the thermogravimetric device

incorporates design elements that create a decoupling between the thermal energy within the resonance element generated by the heating element 50 and the mechanical resonance energy within the resonance element 10 generated by the actuator(s) 30. This decoupling is achieved by spatially decoupling the thermal and mechanical energy and/or by decoupling the thermal and mechanical parameters ruling the functioning of the thermogravimetric device and is sufficient to reduce the temperature coefficient of resonance frequency (TCRFsampie platform) of the resonator element (10) for heating of the sample platform (11) without a sample to less than 20 ppm/K.

The compensation means provided to achieve this result may be formed by at least one of :

- thermal isolation between the heater and the frame with a factor GRL² of at least 20 (further explained below),

- parts of the resonator element in between the sample platform and the frame being made of materials having a thermal conductivity of less than 5 W/Km,

- the sample platform being suspended from the frame by one or more beams having a length between 10 and 2000 μιη, a width between 3 and 500 μιη and a thickness between 0.1 and 10 um, - the resonator element comprising a membrane connecting the sample platform to the frame, the membrane having a length spanning the distance between the sample platform and the frame between 50 and 5000μιη, and having outer lateral dimensions between 100 and 10 ΟΟΟμιη and a thickness between 0.01 and ΙΟμιη,

- heat sink elements provided at a distance between 3 - 300 μιη from the resonator element,

- the thermogravimetric device comprising a housing or being incorporated in an enclosure that is arranged to be filled with a gas mixture having a heat conductivity above 26 mW/Km, or at least above 30 mW/Km, or at least above 40 mW/Km, at room temperature,

- the gas mixture comprising additional gas components, formed by at least one of the group of neon and helium, the gas mixture comprises at least 10 volume% of the additional gas components,

- the resonator element comprising a hinge part near the frame,

- the resonator element comprising a first zone near the frame and a second zone in between the sample platform and the first zone, the first zone having a first thermal conductance and the second zone having a second thermal conductance, the first thermal conductance being higher than the second thermal conductance,

- at least one of the resonance sensing element and the temperature-sensing element being an optical element,

- the resonator element comprising a first zone near the frame and a second zone in between the sample platform and the first zone, wherein the first zone has a first flexural rigidity and the second zone having a second flexural rigidity, the first flexural rigidity being smaller than the second flexural rigidity, or

- the resonator element comprising a first zone near the frame and a second zone in between the sample platform and the first zone, wherein the compensation means are formed by providing a first zone that is made of a stack of layers, the stack of layers at least comprising a first layer with a negative Temperature Coefficient of the Young's Modulus and a second layer with a positive Temperature Coefficient of the Young's Modulus.

So, when during the heating of the sample a change in the resonance frequency is determined by the resonance sensing element, this change is mainly due to a change in the mass of the sample, for instance as a result of oxidation or evaporation. This allows for an easy and straightforward way of performing thermogravimetric measurements in which a relation between the mass of the sample and the temperature of the sample can be determined.

The suspension may be formed by one or more beams. The beams may have a width that is substantially smaller than an edge of the sample platform to which they are connected, the limit for the smallest beam width being that the beam does not become so fragile as to be impractical. According to an a variant, the beam and the sample platform may be of the same width, i.e., the width of the beam may be similar to the edge of the sample platform to which it is attached.

Different compensation means may be provided, examples of which will be presented. The compensation means may comprise thermal isolation, thermal guarding and/or providing a resonator element which at least partially comprises a stack of layers.

According to an embodiment the resonator element comprises a base area being attached to the frame, wherein the compensation means are provided by providing thermal isolation to thermally isolate the sample platform and heater from the base area of the resonator element.

The base area is the part of the resonator element that experiences the largest stress and strain during resonance. It is this part of the resonator element that mainly determines the resonance frequency of the resonator element. In case the resonator element is formed by one or more beams, the base area is a first end of the beam being connected to the frame, while a second end of the beam (opposite of the first end of the beam) comprises the sample platform.

According to an embodiment the sample platform is suspended from the frame by a single beam. This may also be referred to as a cantilever design providing an easy to manufacture resonator element which can resonate without excessive deformation and/or tensile stress in the longitudinal body axis of the beams. Because of this, the bending stresses and strains are concentrated near the position where the beam is attached to the frame, and the requirements for a low Temperature Coefficient of Resonance Frequency with respect to the sample platform temperature (TCRF_sampi_e platform) can be met more easily.

According to an embodiment the sample platform is suspended from the frame by two or more beams. Providing two or more beams allows for a design in which at least one actuator and resonance sensing element are positioned remotely with respect to each other. This results in more accurate measurement results.

According to an embodiment the sample platform is suspended from the frame by two or more beams connecting a first edge of the sample platform with the frame.

By providing the two or more beams all on the same edge of the sample platform, the sample platform can resonate without generating excessive deformation and/or tensile stress in the longitudinal body axis of the beams. The same advantages of temperature increase separation from stresses and strains apply as for a single beam device.

A particular advantage of this embodiment is that it allows a U-shaped design, wherein the effective length for resonance is shorter, than the effective length for the heat to travel. Thus a good thermal isolation can be achieved while still keeping the overall length of the resonator within practical limits and the resonance frequency high.

According to an embodiment the sample platform is suspended from the frame by a first beam and a second beam, the first beam connecting a first edge of the platform with the frame and the second beam connecting a second edge of the platform with the frame.

Such a design may also be referred to as a floating membrane device. Providing the two or more beams with respect to different edges of the sample platform, allows for an even further spatial separation between the at least one actuator and the resonance sensing element resulting in even more accurate measurement results.

According to an embodiment wherein one or more thermal actuators interact with a first subset of beams and one or more resonance sensing elements interact with a second subset of beams, the beams of the second subset not being part of the first subset.

Such a thermogravimetric device has the advantage that a separation is achieved between the actuator and the resonance sensing element, reducing thermal interaction between the actuator and the resonance sensing element and reducing crosstalk between the actuator and the resonance sensing element.

According to an embodiment sample platform is formed by a membrane that is suspended from the frame substantially along its entire perimeter. This embodiment may also be referred to as a closed membrane, as the resonator element now forms a membrane that is suspended from the frame, with a sample platform in the middle.

In this closed membrane, the temperature of the sample platform, normally positioned in the centre of the membrane, will fall rapidly to ambient level away from the centre, as the thermal resistance of the membrane, in contrast to a beam of constant cross-section, decreases proportional to the distance from the centre, while the thermal conductance via the surrounding gases increases with the distance from the centre. Thus, a closed membrane is superbly capable of thermally isolating the sample platform in its centre from the areas near the frame where the largest stresses and strains occur. To prevent any stresses and strains near the centre to have an influence, the central region of a membrane can be made stiffer to shift the stresses and strains to the edges. Moreover, the fabrication of the closed membrane is more easy, since no structures need to be etched out of a membrane. This structure is also more robust than beams, beams with paddles, and floating membranes. The structure of a closed membrane is described in more detail in [4], and also in [5], although this article does not relate to thermogravimetric devices.

This structure is more robust and easier to make compared to structures with beams and/or paddles. Such a membrane has the advantage that a relatively high thermal isolation is obtained as a result of the structure of such a device. Based on Minakov, using a closed membrane with similar layers as the other embodiments described, results in a temperature drop of 95% within approximately 200μιη from the heating element 50.

According to an embodiment the thermal isolation between the heater and the frame is given by a factor GRL² of at least 20, wherein

- L is a distance between the sample platform and the frame,

- G is the thermal conductance of gas around the resonator element in W/K per meter of distance L,

- R is the average thermal resistance of the resonator element expressed in K/W per meter of distance L.

The higher this factor, the less thermal interaction there is between the sample platform/heating element and the suspension of the resonator element from the frame. In further embodiments, the factor GRL² may be at least 30, or even above 50. The required value for the factor GRL2 may be different for different embodiments.

According to an embodiment the factor GRL² is at least 50 or at least 100.

According to an embodiment the parts of the resonator element in between the sample platform and the frame are substantially made of materials having a thermal conductivity of less than 5 W/Km. This results in a high value for the average thermal resistance R of the resonator element. The parts in between the resonator element and the frame may for instance be formed by beams.

According to an embodiment the sample platform is suspended from the frame by one or more beams having a length between 10 and 2000 μιη, a width between 3 and 500 μιη and a thickness between 0.1 and 10 μιη.

According to an embodiment the resonator element comprises a membrane connecting the sample platform to the frame, the membrane having a length spanning the distance between the sample platform and the frame between 50 and 5000μιη, and having outer lateral dimensions between 100 and 10 ΟΟΟμιη and a thickness between 0.01 and ΙΟμπι.

According to an embodiment heat sink elements are provided at a distance between 3 - 300 μιη from the resonator element. This is closer than according to prior art devices, having heat sink elements at a distance of for instance 300 - 3000 μιη. These heat sink elements are provided above or below the resonator element.

According to an embodiment the thermogravimetric device further comprises a housing or is incorporated in an enclosure that is arranged to be filled with a gas mixture having a heat conductivity above 26 mW/Km, or at least above 30 mW/Km, or at least above 40 mW/Km, at room temperature.

According to an embodiment the gas mixture comprises additional gas components, formed by at least one of the group of neon and helium, the gas mixture comprises at least 10 volume% of the additional gas components.

According to an embodiment the resonator element comprises a hinge part near the frame.

This is done to further concentrate stress and strain away from the heating element and the sample platform, thereby further reducing the temperature coefficient of resonance frequency (TCRF_sampi_e platform). A hinge provides a local change in moment of inertia, which is a geometrical parameter. According to an embodiment the resonator element comprises a first zone near the frame and a second zone in between the sample platform and the first zone, the first zone having a first thermal conductance and the second zone having a second thermal conductance, the first thermal conductance being higher than the second thermal conductance. The first thermal conductance may be a factor 2 or more higher than the second thermal conductance. This is done to reduce the temperature coefficient of resonance frequency (TCRF_sampi_e platform).

According to an embodiment the resonator element comprises a first zone near the frame and a second zone in between the sample platform and the first zone, wherein the first zone has a first moment of inertia and the second zone having a second moment of inertia, the first moment of inertia being smaller than the second moment of inertia. This causes the stresses and strains to concentrate in the first zone, i.e. to enhance the spatial separation between the areas of largest stresses and strain and the areas of temperature increase. This is done to reduce the temperature coefficient of resonance frequency (TCRF_sampi_e platform). The second moment of inertia may be a factor 2 or more higher than the first moment of inertia.

It is possible to use materials of different Young's moduli. The product of Moment of Inertia I, and Young's modulus E: EI, is called the flexural rigidity. This can be another way to describe how one can concentrate the stress in a limited zone, i.e. the first zone, by having two zones of different flexural rigidity. This difference in product EI can of course be obtained by either changing E, or I, or both.

According to an embodiment the resonator element comprises a first zone near the frame and a second zone in between the sample platform and the first zone, wherein the compensation means are formed by providing a first zone that is made of a stack of layers, the stack of layers at least comprising a first layer with a negative Temperature Coefficient of the Young's Modulus and a second layer with a positive Temperature Coefficient of the Young's Modulus.

This provides an alternative way of realizing a temperature coefficient of resonance frequency (TCRF_sampi_e platform) of the resonator element for heating of the sample platform (11) without a sample less than 20 ppm/K. Of course, this solution can be used in addition to providing thermal isolation.

By providing a stack with different materials, an effective Temperature

Coefficient of the Young's Modulus can be obtained which is substantially low, i.e. near zero. Of course, more than two layers can be provided with different materials, such that the effective Temperature Coefficient of the Young's Modulus of the entire stack is close to zero.

According to an embodiment compensation means are provided by providing a base temperature control element in the vicinity of the first zone to establish a base temperature.

By maintaining the base temperature during the thermogravimetric

measurements, the effect of heat from the sample platform being conducted towards the first zone can be compensated for.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which:

Figs, la - c schematically depict a thermogravimetric device according to an embodiment,

Figs. 2 - 5b schematically depict thermogravimetric devices according to different embodiments,

Fig. 6 schematically shows a resonance frequency of the resonator element as a function of temperature change without a sample,

Figs. 7a - 7b schematically depicts an output of the Wheatstone bridge, normalized to its value at the resonance frequency, versus excitation frequency and a resonance frequency with and without a sample respectively,

Figs. 8a - c schematically show graphs describing a beam,

Figs. 9 - 11 schematically depict further embodiments.

DETAILED DESCRIPTION

Different embodiments will now be provided with reference to the Figures.

The embodiments presented here provide a Micro-Electro-Mechanical System (MEMS) device for Thermo Gravimetric Analysis (TGA) and optionally simultaneous Fast Scanning Calorimetry (FSC), exhibiting a low temperature dependence of the mass measurement. The embodiments described may be formed as MEMS or NEMS devices. The term MEMS is used to refer to a Micro Electro Mechanical System or

micromechanical device. This term will readily be understood by a skilled person and relates to the technology of small devices, i.e. devices with typical dimensions in the range of 1 - 1000 micrometre. It will be understood that smaller dimensions are also conceivable. Such smaller devices may also be referred to as NEMS (Nano Electro Mechanical System), with typical dimensions in the range of 10 - 1000 nanometre.

The embodiments described here provide a thermogravimetric device, i.e. a mass- sensing resonator capable of simultaneously measuring the mass of a sample, and heating the sample according to a predefined temperature program in time, comprising a resonator element 10, comprising a sample platform 11 which can be heated (hot spot). Examples thereof are shown in the Figures, which will be described in more detail below.

In general there is provided a thermogravimetric device 1 , comprising a resonator element 10 suspended from a frame 20, at least one actuator 30 for bringing the resonator element 10 in a resonating state and a resonance sensing element 40 for sensing a resonance frequency of the resonator element 10, wherein the resonator element 10 comprises a sample platform 11 arranged to receive a sample and the thermogravimetric device 1 further comprises a heating element 50 for heating the sample when positioned on the sample platform 11 , wherein the thermogravimetric device 1 comprises a temperature-sensing element 60 sensing the temperature of the sample platform 11 , wherein the thermogravimetric device comprises compensation means to compensate for an increase of the temperature generated by the heating element 50 such that a temperature coefficient of resonance frequency TCRF_sampi_e platform of the resonator element 10 for heating of the sample platform 11 without a sample is less than 20 ppm/K.

This can be accomplished in different ways, such as by using thermal isolation, using a resonator element that comprises a stack of carefully chosen materials, by guarding the temperature and/or by forming the resonator element with a hinge.

In general, the resonator element (one or more beams/membrane)can be made in two zones, a first zone with one set of properties for the zone near the sample platform (the thermal isolation zone), and another set of properties for the second zone near the suspension frame (the stress zone), to further promote the characteristic of the thermogravimetric device, that the interaction between the sample-platform heating and the area of largest stresses and strains is minimized during heating. This characteristic can be promoted in at different ways of differentiating between the two zones.

Firstly, the first zone or stress-zone can be designed to have a high thermal conductance, compared to the thermal isolation zone. This forces the temperature drop from sample-platform temperature to ambient temperature over the thermal- isolation zone, and forces the stress zone to adopt ambient temperature, as this zone is directly connected to the ambient temperature of the frame. Thus, the thermal isolation is emphasized.

Secondly, the first zone or stress zone may be designed to be less stiff then the thermal isolation zone, forcing the stresses and strains to concentrate in the stress zone and to not extend in the thermal isolation zone, emphasizing the spatial separation between temperature increase and stresses and strains. This design can be achieved both by the use of different layers with lower Young's Modulus for the first zone, and also by the use of local thinning and/or narrowing of the effective beam dimensions in the first zone, diminishing the moment of inertia.

Thirdly, the stress zone may be designed to comprise a specific stack of layers so as to minimize the temperature coefficient of the resonance frequency, in particular by constructing the beam of various layers, comprising layers with a positive temperature coefficient of the Young's Modulus and layers with a negative temperature coefficient of the Young's Modulus..

These embodiments, which may all be employed separately and in combination with each other, will be described below. Thermal isolation

The sample platform 11 is thermally isolated with respect to the frame 20 from which the resonator element 10 with the sample platform 11 is suspended. The resonator element 10 may for instance be formed by one or more beams 12, 13, 14 which are designed as a thermal isolation structure. The thermal isolation may be achieved in many ways, as will be discussed in more detail below, such as by choosing a specific material for the resonator element 10 or beam 12, 13, 14 by choosing specific dimensions for the resonator element 10 or beam 12, 13, 14 (length, width, height), by providing the sample platform 11 with certain heat exchanging elements or structures 110, by surrounding the resonator element 10 or beam 12, 13, 14 with a specific gas mixture.

All or a selection of these measures may be taken to create a thermal isolation between the sample platform 11 and the suspension between the resonator element 10 and the frame 20 from which it is suspended.

The resonator element 10 may comprise a first zone which is near the frame 20 and a second zone, which is in between the first zone and the sample platform 11. The first zone is the part of the resonator element 10 in which most stress and strain is generated during resonance. The first zone may also be referred to as the base 19 of the resonator element 10, i.e. the part of the resonator element 10 that is attached to the frame. The second zone may also be referred to as a thermal isolation zone, as it forms an isolation zone between the sample platform 11 (which is heated during use) and the first zone of base 19 of the resonator element 10. The first zone 19 may cover approximately half of the length of the resonator element, for instance half of the length of the beam 12. The second zone 24 may cover approximately the part of the resonator element 10 in between the heating element 50 and the first zone 19.

The sample platform 11 may incorporate an integrated heating element 50 and integrated temperature-sensing element 60 (which may be the same as heating element 50, or separate), making it possible to heat up the sample with respect to the ambient in an arbitrary temperature-time program. The heating element 50 and/or the temperature- sensing element 60 may also be provided as separate from the resonator element 10.

In this way a sample under test on the sample platform 11 can be subjected to this arbitrary temperature-time program, and optionally Fast Scanning Calorimetry can be performed, by measuring the heat needed to achieve the temperature-time program in the presence of the sample, compared to the heat needed in the absence of a sample. The resonator element 10 is a mechanical structure capable of being brought into resonance at a resonance frequency which is dependent upon mass loading by the sample on the sample platform 11.

The thermogravimetric device 1 incorporates a silicon (support) frame 20 in which the resonator element 10 is mechanically suspended and which also acts as heat sink. Together with a housing in which the thermogravimetric device 1 may be mounted, the frame 20 provides a stable ambient (base) temperature. As mentioned above, the design of the thermogravimetric device 1 is such, that a good thermal isolation exists between the sample platform 11, which is heated by the heating element 50, and the first zone or base 19 of the resonator element 10, which is close to the frame 20, in which the largest stresses and strains are concentrated. The resonance-sensing element 40 may customarily be positioned in this first zone, as this resonance-sensing element may consists of a piezo -resistive element that is strain sensitive. The resonance sensing element 40 may comprise a piezo -resistive element located in the first zone (i.e. areas of the resonator element 10 where it is attached to the frame 20), that experience the largest stress and strain, with optionally an identical element (41) on the frame 20 experiencing no strain, but that compensates for ambient temperature fluctuations.

The term "suspension between the resonator element 10 and the frame 20" is used here to denote the position where the resonator element 10 is attached to the frame 20 . The part of the resonator element 10 that is attached to the frame 20 may also be referred to as the base 19 of the resonator element 10. The term "suspension between the resonator element and the frame" may also be referred to as a "suspension location", "mounting position of the resonator element and the frame". The first zone or base 19 may also be referred to as the "stress zone" as mentioned above.

The thermal isolation is provided so that when heating the sample platform 11, the first zone of the resonator element 10, thus near the frame 20, remains at substantially the same temperature, i.e. a base temperature, which is substantially equal to an ambient temperature.

In this way, the parts of the resonator element 10 determining the spring constant of the structure: the first zone of the resonator element 11, remain at or near the base temperature, rendering the resonance frequency nearly independent of the temperature of the sample platform 11.

In addition to or in place of the above, the resonator element 10 may also be manufactured from such (a stack of) materials as to make the spring constant of the resonator element 10 (nearly) independent of temperature, rendering the resonance frequency (nearly) independent of the temperature of the sample platform 11.

Since the first zone of the resonator element 10, i.e. the resonance- frequency determining first zone , remains near ambient temperature even if the thermal isolation between sample platform 11 and beam base 19 is not very high, it is sufficient if the base area 19 is made of (a stack of) materials having a (near)-zero Temperature Coefficient of the Young's Modulus (TCYM, the factor dominant in determining the temperature dependence of the spring constant) around ambient temperature. Since, for example, silicon exhibits a negative TCYM, while both LPCVD-deposited silicon- oxide and silicon-nitride exhibit positive TCYM, such a stack is in practice not difficult to realize. This is also true, since the thermal isolation is required between areas 11 and 19, but area 19 itself does not need to have such very good thermal- isolation properties.

The thermogravimetric device 1 comprises a resonance sensing element 40 arranged to sense the resonance frequency of the resonator element 10. The resonance sensing element 40 may comprise a piezo -resistive element at the first zone (the (cold) side) of the resonator element 10, i.e. near the suspension between the resonator element 10 and the frame 20 or where the resonator element 10 is suspended from the frame 20, area 19. Resonance sensing element 40 may be positioned in the area of largest strain, i.e. at least in the first zone.

The thermogravimetric device 1 may further comprise one or more compensating piezo-resistive elements 41 on the frame 20. These compensating piezo -resistive elements may be designed with an identical lay-out and process as the piezo-resistive element 40 on the resonator element 10, but now located beyond the resonator element 10 on the frame 20, e.g. on the solid silicon support frame, so that they do not experience any strain, but will experience the same ambient temperature fluctuations as element 40 on the resonator and will compensate for that when resonance sensing element 40 and compensating resonance sensing element 41 are used in a bridge configuration. They are also of approximately the same resistance value, so that readout of the resonance-sensing element 40 using a bridge of Wheatstone is facilitated.

The resonance sensing element 40 is arranged to detect the resonance (frequency) of the resonator element 10. From the determined resonance frequency, or at least the resonance frequency as a function of the temperature of the sample, information can be derived about the mass of the sample provided on the sample platform 11. Because of the relatively low temperature scanning rates used even in micro-TGA (below 10 K/s), it can safely be assumed that the temperature of the sample platform and the sample are substantially the same. The thermal lag in such small samples at such low scanning rates will be negligible, as known from the thermal lag experienced in Fast Scanning Calorimetry with chips, where scanning rates can be many orders of magnitude higher. The thermogravimetric device 1 may further comprise a temperature-sensing element, i.e. a temperature-dependent element, to provide an indication of the temperature of the sample. The temperature-sensing element may for instance be used to measure the temperature of the heating element 50, the sample platform 11 or the sample. Such a temperature-sensing element may for instance be formed by the heating element 50, by a separate resistive element, or by a thermopile measuring the temperature increase of the sample platform 11 or sample with respect to the ambient. The temperature-sensing element may comprise a temperature-dependent resistive element on or near the sample platform 11 , made of a metallic or semiconductor material, said element 60 (see Fig. 5b) being different from the heater 50, or being one and the same element.

The temperature-sensing element 60 may comprise a thermocouple made of one strip of 0.3 μιη thick low-stress LPCVD (low-pressure chemical vapour deposition) poly-silicon, boron-doped to a sheet resistance of 75 Ohm/square, and one strip of the same poly-silicon, phosphorous-doped to a sheet resistance of 50 Ohm/square, giving a overall resistance of 8 kOhm.

A thermopile may be formed of one or more thermocouples, laid out between the sample platform 11 and the frame 20, made of semiconductive layers of p-type and/or n-type doped silicon, silicon-germanium, bismuth-antimony or other types or combinations of layers of typically 0.1-1 μιη thickness to serve as resistive heaters or in combinations as thermocouples, and/or conductive layers such as aluminium, gold, platinum, chromium-nickel to serve as heaters or thermocouples, also in combination with semiconductor layers. These layers may be deposited onto or in between the structural layers of the resonator element 10. The thermocouple or thermopile may have hot junction(s) on or near the sample platform 11 , and cold junction(s) on the frame 20, made of semiconductor and/or metallic leads.

The structural layers form the main structural body of the resonator element 10, and can be made of materials with a low thermal conductance, such as low-stress LPCVD SiN and/or LPCVD Si0₂, to obtain a structure of high thermal resistance. The thermocouples, and the connections to the heater and possible other resistive elements run from the frame 20 to the sample platform 11.

The materials of which thermocouples and connection leads to the heating element 50 and other possible resistive elements are made usually have a much higher thermal conductivity than that of the structural materials of the resonator element 10, and therefore the thermocouples and connection leads may be kept as thin and narrow as is practical (considering such considerations as electrical resistance, current-carrying capability, and manufacturability), to minimize the decrease of the thermal isolation between the sample platform 11 and the first zone 19 of the resonator element 10.

Especially in the second zone, i.e. the thermal isolation zone, the leads and thermocouples may even be laid out in a zigzag shape, to increase their length and thus their thermal resistance, while in the first zone of the resonator element 10 (i.e. the base area 19), they may even be widened to attain good thermal conductance throughout this region and toward the frame at ambient (base) temperature.

Fig. la schematically depicts a thermogravimetric device 1 according to an embodiment, comprising a resonator element 10 suspended from a frame 20, for instance a silicon frame 20. Fig. lb shows a perspective view of part of the

thermogravimetric device 1, and Fig. lc shows a top view of a thermogravimetric device 1, now further comprising a temperature sensing element 60.

The embodiment shown in Fig. la may be a thermogravimetric device being formed by a 284 μιη long Silicon nitride (Si ) resonator element 10, formed as a cantilever beam, which is the sensing cantilever.

The resonator element 10 as shown in Figs, la - c comprises a beam 12, fixed at one end, with total length of approximately 284 μιη, a width of 60 μιη and a thickness of about 1 μιη, and widened at the free end into a paddle to form the sample platform 11, of width 300 μιη over a length of 70 μιη, consisting of low-stress LPCVD SiN.

The resonator element 10 may comprise a sample platform 11 arranged to receive a sample. The sample platform 11 may be provided on the resonator element, remote from the suspension of the resonator element 10 from the frame.

In Figs, la - c, the first zone or base 19 of the resonator element 10 and the second zone 24, in between the first zone 19 and the sample platform 11 are indicated.

As stated above the first zone may be approximately cover the first half of the resonator element 10, in this case approximately the first half of the beam 12. As will be explained in more detail below, this dimension is deduced from an elastic energy distribution analysis. However, in case the first zone is defined based on a stress analysis, the first zone 19 may be approximately 3/4 of the beam 12. The resonator element 10, i.e. the sample platform 11, may further comprise a heating element 50 for heating the sample when positioned on the sample platform 11. The heating element 50 may comprise a 7 kOhm resistance , made of 0.3 μιη thick low- stress LPCVD poly-silicon, boron-doped to a sheet resistance of 75 Ohm/square, covering the free end of the cantilever beam over an area of 128x38 μιη.

The thermogravimetric device 10 further comprises at least one actuator 30 for bringing the resonator element 10 in a resonating state.

The actuator 30 may be formed as a thermal actuator, which generates a bending motion by amplification of differences in thermal expansion of two layers, in this embodiment the SiN layer and a metal layer on top of it. In general two layers from the available processes will be chosen that have a significant different coefficient of thermal expansion and significant thicknesses to achieve bending with enough amplitude and force to be able to actuate an object. This principle is used to actuate the resonator element 10. The increase in temperature to generate thermal expansion may be achieved internally by using electrical resistive heating or by using a separate heat source.

The embodiment shown in Figs, la - c may comprise two actuators 30, which are thermal actuators, formed as two membranes arranged symmetrically on both sides of the resonator element 10. The two membranes forming the thermal actuators may be linked to the resonator element 10 by SiN bridges.

The two thermal actuators 30 may consist of a SiN-Platinum (Pt) stack, a SiN- Aluminum (Al) stack, a SiN-Gold (Au) stack, or another stack.

The thermogravimetric device 1 may further comprise a resonance sensing element 40 for sensing a resonance frequency of the resonator element 10. The resonance element 40 may comprise two piezo resistors provided in a Wheatstone bridge configuration to detect the bending of the resonator element 10, by detecting the bending of the resonator element 10.

The resonance sensing element 40 may be integrated in the resonator element 10, close to the frame 20. The resonance sensing element 40 may comprise a piezo- resistive element being of 1.25 kOhm resistance, made of 0.3 μιη thick low-stress LPCVD poly-silicon, boron-doped to a sheet resistance of 75 Ohm/square, having a length of about 96 μιη and a width of 6 μιη, with a U-shaped form, and located near the fixed end of the cantilever. The sample platform 11 may be thermally isolated from a suspension between the resonator element 10 and the frame 20. In other words, a temperature increase caused by the heating element 50 leads to a change in resonance frequency in the absence of a sample smaller than or comparable to the reproducibility in the frequency

measurement. The design may be such that it results in a decrease of the temperature coefficient of resonance frequency (TCRF_sampi_e platform) from of the order of 200 ppm/K (ppm = parts per million) for changes in ambient temperature to less than 20 ppm/K, or at least less than 10 or 5 ppm K, or preferably less than 2 ppm/K for heating of the sample platform 11. So, in case the temperature coefficient of resonance frequency (TCRFsampie platform) is less than 10 ppm/K, this means that when the sample platform 11 is heated, while the resonance frequency of the resonator element 10 is about 10.000 Hz, the resonance frequency of the resonator element 10 changes with less than 0,1 Hz per Kelvin, in the absence of mass changes.

The design is thus such that the temperature dependence of the resonance frequency is virtually determined by the first zone 19 of the resonator element 10 which is closest to the fixed end (on basis of the distribution of stress and strain which determine elastic energy distribution), while restricting the temperature increase generated by the heat element 50 substantially to the sample platform 11. Thermal isolation between the first zone and the sample platform 11 may be provided by the second zone 24, i.e. the last part of the resonator element 10, i.e. in case of a cantilever design (Figs, la - c) near the free end, so that storage of thermal energy and of mechanical elastic energy are spatially separated, so that heating of the sample platform

11 does not substantially influence the resonance frequency. This is graphically shown in Figs. 8a and 8b.

This spatial separation between the heating element 50 and the first zone or base

19 of the resonator element 10 can be achieved in many ways as will be described in more detail below. It may for instance be achieved by constructing the parts of the resonator element 10 in between the sample platform 11 and the first zone or frame 20 of high thermal-resistance material, thus achieving a second zone with a low heat conduction compared to the heat conduction by air. This is shown in Fig. 8b, which gives the interaction between the elastic potential energy and the temperature in beam

12 as a function of the transmission- line loss factor GRL², where G is the thermal conductance of the surrounding gases per meter of beam length, R is the thermal resistance of the beam per unit of beam length, and L is the beam length.

In Fig. 8a the elastic potential energy distribution in a homogeneous cantilever beam (as shown in Fig. la) is given as a function of position on the beam (for a beam of unit length). A distribution proportional to (1-x)⁴ is taken, the product of stress and strain in a homogeneous beam. For the temperature distribution in the homogeneous cantilever beam it is assumed that this is proportional to

sinh{x*(GR)°^'5}/sinh{L*(GR)^0'5} [see prior art ref 6], and in Figs. 8a and 8b the length L is normalized to 1.

Also is given the temperature distribution for GRL² = 64, showing the sharp decrease of temperature from the heater onwards. Finally the product of these two curves is given in Fig.8a. The total interaction is then the integral of this interaction curve over the entire beam. Fig.8b gives this total interaction as a function of the factor GRL². This curve shows that the interaction is decreased from around 20% to less than 1% for the factor GRL²=50. This model clearly shows the idea of thermal isolation, and how it decreases the interaction between elastic potential energy and temperature increase. However, in the very small structures involved here, simple one-dimensional or two-dimensional models for the heat conduction by the gas (determining the factor G) may no longer be valid, and a true 3-D thermal analysis may be required, as heat flows in all 3 dimensions from the sample platform in comparable quantities. This is emphasized by Fig.8a, where it is observed that the temperature in the beam basically drops to nearly ambient temperature in about 30% of the beam's length, which is about 90 μιη. This is comparable to the width of the beam, and even less than the distance to the heat sink at 300 μιη, With this 3-D heat flow, the value for G will in reality even be larger than estimated by 1-D or 2-D models, and the real interaction is then smaller than indicated in the Fig.8b.

So, GRL² is preferably above 25, more preferably above 50 and even more preferably above 100.

The thermogravimetric device 1 as shown in Figs, la - c has a sample platform 11 that is suspended from the frame 20 by a single beam 11. The resonator element 10 is thus formed by a single beam 11 having a sample platform at its free end. This configuration may also be referred to as a cantilever design. The beam 11 has at its fixed end a piezo resistor of about 1 kQ used as strain sensor forming the resonance sensing element 40, and at its free end near the sample platform 11 a heater resistor of about 7 kQ forming the heater element 50. The polysilicon heater on the sample platform covers the sample area of 128x38 μιη².

A compensation resistor may be located outside the sample platform 11 and may be designed to be identical to the strain sensor. The temperature of the heater resistor and sample is measured by a p-type vs. n-type poly-silicon thermocouple with an estimated sensitivity at room temperature of about 0.4 mV/K [see prior art 7].

In Table 1 the major characteristics of a possible thermogravimetric device 1 according to Figs, la - c are listed.

Table 1 Summary of important characteristics of the TGA device.

Manufacturing Thermogravimetric device 1 as described above with reference to the Figures, may be made using a thin-film bulk-micro -machining process. The example provided here is to be regarded as a non-limiting example, alternatives may be employed as well.

The starting material may be a 300-μιη thick silicon wafer of 100 mm diameter with crystal orientation <100> , on which 600 nm low-pressure chemical vapor deposition (LPCVD) Si and 300 nm LPCVD low-stress polysilicon (poly) are deposited.

After implantation of the poly to make low-resistive n-type and p-type regions (50Q/sq and 75 Ω/sq, respectively) the poly is patterned and covered by another 300 nm SiN. The contact openings to the poly are made and an anti-diffusion barrier (40 nm Titanium (Ti) and 80 nm Titanium Nitride (TiN)) is deposited. The Ti/TiN layer is then patterned and RTA is performed to get Titanium Silicide (TiSi2). After the silicidation step 10 nm Tantalum (Ta) and 0.2 μιη Pt are deposited and patterned. Then SiN membranes are etched by anisotropic KOH-etching from the back side. Plasma etching from the front side is used to release the final structures. After sawing the chips or dies are ready for assembly.

Alternatively, below the 600 nm SiN layer, first a sacrificial layer of 200 nm SiN and 100 nm Si0₂ can be deposited. Then, before freeing membranes by KOH-etching, the trenches in the membranes are etched which delineate the cantilever beams, sample platform 11 (e.g. including paddles) and thermal actuators 30, by plasma etching the stack of layers, but stopping on the 100 nm Si0₂ sacrificial layer. After this, KOH etching is performed, where the front side of the wafer is still separated from the KOH- etch solution by the sacrificial layers of SiN and Si0₂. After this, the sacrificial layers of 200 nm SiN and 100 nmSi0₂ are removed at the backside of the beam 12 and actuators 30 by plasma etching and/or wet etching, and the wafer is ready for sawing. This removes the need to process the wafer when fragile membranes are present, and when metals such as gold or platinum are present that may not be desired in a process line.

Alternatively, the wet etching may also be performed from the front side using TMAOH etching solution that etches similarly to KOH etching solutions but is less aggressive towards oxides and metals. Then, the trenches in the SiN layers to delineate the beams and other structures in the membrane are used as openings for the TMAOH to access the silicon to be etched. The membranes are then formed by removing the silicon from underneath the beams and other structures by underetching.

Fig. 2 schematically depicts a thermogravimetric device 1 according to an alternative embodiment. According to this embodiment, the sample platform 11 is suspended from the frame 20 by two or more beams 12, 13, wherein the two or more beams 12, 13 provide a connection between a first edge 15 of the sample platform 11. Of course, more than two beams may be provided for connecting the first edge 15 of the sample platform 11 to the frame 20.

By providing the beams 12, 13 all on the same edge 15 of the sample platform 11, a resonator element 10 is formed that can resonate in a direction substantially perpendicular with respect to a plane defined by the longitudinal body axes of the beams 12, 13, without inducing tensional stress in the beams 12, 13.

According to this embodiment, the at least one actuator 30 may be provided to the first beam 12, i.e. being mechanically coupled to the first beam 12 to actuate the first beam 12, while the resonance sensing element 40 may be provided to sense a resonance frequency of the second beam 13. This provides more accurate

measurements, as electrical crosstalk and thermal interaction between the actuator 30 and the resonance sensing element 40 is minimized.

Electrical crosstalk may for instance cause problems in case the resonance sensing element 40 comprises electrical components, such as piezo elements provided in a Wheatstone bridge configuration.

Unwanted thermal interaction between the actuator 30 and the resonance sensing element 40 may be specifically relevant in case the actuator is a thermal actuator 30 as described above.

Figures 3 and 4 schematically depict a thermogravimetric device 1 , wherein the sample platform 11 is suspended from the frame 20 by a first beam 12 and a second beam 14, the first beam 12 connecting a first edge of the platform 1 with the frame 20 and the second beam 14 connecting a second edge 16 of the sample platform 11 with the frame 20. Such a design may also be referred to as a floating membrane device or a bridge design. Fig. 3 shows an embodiment wherein the first and second edge 15, 16 are parallel, forming opposite edges of the sample platform 11. Fig. 4 shows an

embodiment wherein the first and second edge 15, 16 are adjacent edges, being at an angle with respect to each other. As can be seen in Fig. 4, the thermogravimetric device 1 may comprise further beams 12', 14' connecting further edges of the sample platform 11, i.e. edges 17, 18 with the frame 20.

The embodiments described with reference to Figs. 3 and 4 allow for an even further separation between the actuators 30 and the resonance sensing element(s) 40, allowing an even more accurate determination of the mass of the sample by further reducing unwanted interaction and crosstalk. Fig. 3 schematically depicts an alternative location for the actuator, such as an actuator 30' on the resonator element 10 (i.e. on the beam).

According to a further embodiment, a closed membrane device is provided, i.e. a thermogravimetric device, wherein the sample platform is formed by a membrane 22 that is suspended from the frame 20 substantially along its entire perimeter.

Fig. 5 a schematically depicts a perspective view of a thermogravimetric device according to this embodiment. Instead of providing one or more beams to suspend the sample platform 11 from the frame 20, a membrane 22 is provided that is suspended along its perimeter like a drumhead or a drum skin. Such a membrane 22 can function as a resonator element 10. In the centre of the membrane 22 a sample platform 11 may be provided. Fig. 5b shows a top view of this embodiment.

As can be seen in the Figs. 5a and 5b, the first zone 19 and the second zone 24 are indicated and now have an annular shape. Again, a heating element 50 is provided at or near the sample platform, one or more actuators 30 are provided to actuate the membrane 22 and one or more resonance sensing element 40 may be provided to sense the resonance frequency.

The actuator 30 may be a thermal actuator, which is positioned on the membrane 22 near the frame 20. The thermal actuator 30 may comprise three main layers.

A first layer is formed by the structural layer of the membrane 22 (e.g. SiN- layer).

A second layer, which is a heating layer, may be provided directly on the first layer which can be heated, for instance by AC-Joule heating. A third layer may be provided on top of the second layer, may be a metal layer with a distinct different coefficient of thermal expansion compared to the first layer.

Also, a temperature-sensing element 60 may be provided as a separate element, as is only shown in Fig. 5b by way of example.

Next, an explanation will be provided explaining the above embodiments in more detail. As discussed above, the thermogravimetric device 1 is designed in such a way that the resonance frequency of the resonator element 1 does not change significantly as a result of the heating of the sample platform 11. This is done by providing thermal isolation between the sample platform and the base 19 of the resonator element 10 or the location where the resonator element 11 is suspended from the frame 20. The physics behind this concept will now be explained with respect to a resonator element 10 as described above with reference to Figs, la - c, although the following explanation will also apply to the different embodiments provided above.

The resonance frequency of a resonator element 10 comprising a single beam 1 1

(cantilever design) can be calculated using the formula (1) applied to a single cantilever (2):

where k and rrieff are the stiffness and the effective mass of the resonator element 10 respectively. When a sample with mass m_s, which does not contribute to the stiffness of the resonator element 10, is attached to the free end of the beam 11, i.e. on the sample platform 11, the resonance frequency can be given by:

Where the effective mass is given to be 24% of the cantilever mass

meff ⁼ 0-24 x m_c

Neglecting the temperature dependence of the geometrical dimensions, the heating applied to the sample could affect not only the mass of the sample but also the spring constant of the resonator element 10. For this reason the resonance frequency of the resonator element 10 without sample as function of the temperature has been measured. The results are shown in Fig. 6 and 7b.

From Fig. 7b it can be seen that the resonance frequency of the resonator element 10 (without sample) is substantially temperature independent in the range from ambient temperature (approx. 20 °C) up to at least 650 °C. The temperature increase of the sample platform 11 leads to a change in the resonance frequency in the absence of a sample smaller than or comparable to the reproducibility of the resonance frequency measurement, for instance performed by the resonance sensing element 40. So, it can be assumed that a shift in the resonance frequency of the resonance element 10, loaded with a sample, as function of the temperature is a direct measure of the mass change of the sample.

With a frequency measurement resolution of 1000 ppm, this gives a temperature coefficient TCRF_sampi_e platform of less than 1.6 ppm/K. So in general, the thermal isolation between the sample platform 50 and the suspension of the resonator element 10 from the frame 20 may be such that a temperature coefficient TCRF_sampi_e platform is achieved that is below 20 ppm/K, or even below 10 or 5 ppm/K, preferably less than 2 ppm/K, for instance 1.6 ppm/k.

According to prior art thermogravimetric devices 1, the resonance frequency of the resonator element 1 depends on the temperature of the sample platform 11. This is a result of the set-up of the thermogravimetric device 1, such as the materials forming the beam 12, which have a relatively high temperature dependence of the Young's modulus

E (Pa).

In order to reduce this temperature dependency of the resonance frequency of the resonator element 10 thermal isolation is provided such that the temperature of the parts of the resonator element 10 that mainly determine the resonance frequency, i.e. the first zone or parts close to the frame 20, is not effected by an increasing temperature of the sample platform 11. It has been realized that the resonance frequency of the resonator element 10 is highly determined by the part close to the frame 20, i.e. the first zone or base 19 of the resonator element, e.g. beam 12. So, thermal isolation is provided such that heating of the sample is substantially confined to the sample platform 11. This results in an effective spatial separation between these two areas, and the heating of the sample platform 11 therefore does not induce a resonance frequency change. A resonating homogeneous beam 12 (see Figs, la - c) of length L (m) fixed at one end experiences a periodical stress σ (Pa) in the beam proportional to (L - x)² where x is the distance from the fixed end, i.e. the frame 20. The elastic potential energy density contained in the beam to sustain the oscillating motion is given by ½σ²/Ε (J/m³), and is therefore proportional to (L - x)⁴. Thus, 97% of this energy is contained in a first half of the beam 12 (i.e. the first zone 19) which is closest to the frame 20 and only 3% of the energy is contained in a second half (second zone 24) of the beam 12 which is closest to and comprises the sample platform 11.

If it is assumed that the temperature increase of the first part of the beam 12 is negligible, than it is clear that the first part of the beam 12 most involved in the spring action (storing and releasing of elastic potential energy) is not influenced by the heating of the sample platform 11, and neither is the resonance frequency.

This analysis has been based on the assumption, that temperature changes in the areas of the storage of elastic potential energy (and the associated TCYM) is the determining factor for the temperature coefficient of the resonance frequency

TCRFsampie platform- However, if the analysis is made be based on the stress-distribution, rather than the energy- storage distribution, (L - x)² is to be used instead of (L - x)⁴. This curve does not fall off as quickly, and consequently, to get spatial separation between the spring action and the increased temperature of the heating, first zone 19 is to be enlarged, at the expense of the second zone 24. If the zone 24 is shortened, this requires that the factor GRL² is larger, in order to get a negligible value of the temperature increase at the intersection of first zone 19 and the second zone 24. In Fig. 8c the interaction between stress and temperature increase is shown, for a value of L of 8 (GRL² = 64). Comparing with Fig.8a this shows clearly, that a much better thermal isolation (i.e., higher value of GRL²) would be required to have a quicker drop in temperature. The basic principle of thermal isolation has been shown in practice.

The thermal isolation can achieved in many ways, as described below in more detail.

The above observation that in a thermogravimetric device 1 according to the embodiments the increase of temperature of the sample platform 11 does not extend far beyond the sample platform 11 is supported by the fact, that experiments have shown that in vacuum of less than 1 mPa, the temperature increase of the sample platform 11 is about 8 times the temperature increase when air at atmospheric pressure is present. This is a strong indication that because of the cooling by the air in three dimensions, the temperature very quickly decreases away from the sample platform 1 1. This is caused by the low thermal conductance of the resonator element 10 (e.g. beam 12 or membrane 22) compared to the thermal conductance of the surrounding air, the decrease in sample platform temperature by a factor of 8 indicates that the thermal conduction from the sample platform 1 1 to the ambient through the air is about 7 times as high as through the resonator element 10 itself (e.g. beam 12 or membrane 22). Although described with reference to the embodiment shown and described with reference to Figs, la - c, the same effect will occur for the other embodiments described above, shown and described with reference to Fig.'s 2 - 5.

However, especially in bridges (Fig. 's 3 and 4) the stress distribution may be so different that the spatial separation between the area of major stress and the area of heating may no longer be sufficient to minimize the TCRF_sampi_e platform- Then, special measures can be taken to redistribute the stress to colder areas at the stress zone 19, by locally stiffening the bridge at the location of or near the sample platform 1 1 and the thermal isolation zone 24. Similar measures can be taken for the other embodiments.

A factor that may be used to indicate the temperature isolation between the sample platform 1 1 and the first zone (base or stress zone) 19 is the so-called transmission-line loss factor GRL², wherein, where G is the thermal conductance of the surrounding gases per meter of beam length, R is the thermal resistance of the beam per unit of beam length, and L is the beam length.

This transmission-line loss factor G follows from a theoretical computed thermal distribution of a single beam 12, which is computed as T(x) = smh(yx)/(yL*(cosh(yL)), wherein T(x) is the temperature increase at location x on the beam 12 with respect to ambient, y² = GR, and L is the total length of the beam. For instance, for a value of yL = 8, the temperature distribution in a simple cantilever beam has been calculated and shown in Fig. 8a, for unit length and temperature increase at the tip. This distribution shows that the temperature decreases rapidly with the distance from heating element 50 at the sample platform 1 1. The higher yL, the swifter this decrease, and thus the better the thermal isolation is. Using the formula above, these temperature profiles can be calculated for all values of yL. Because this effect of transmission line losses is needed, the above reasoning applies to all structures where cantilever beams are used, alone or to suspend paddles or floating membranes.

These formulae do not apply to closed membranes with circular heat flow, rather than linear. However, because of the circular heat flow, the parallel conduction by gases increases linearly with the distance from the membranes centre, and grows quickly to an appreciable size. In addition, the temperature gradient due to heat flows in the stress zone becomes very small, because far away from the centre the thermal resistance of the membrane (inversely proportional to the distance to the centre) becomes so low as to create only a negligible temperature gradient, even in the absence of gases. But with gases, the temperature in the membrane usually drops to near ambient temperature within a few hundred micrometer from the heater 50, for air and Si membranes of Ιμιη thickness, and even quicker for helium or neon-helium mixtures. Thus, in closed membranes the thermal isolation between sample platform and stress zone can be attained more easily than with beam structures.

The rapid temperature drop through the membrane 22 is disclosed in [5]

"Temperature distribution in a thin-film chip utilized for advanced nanocalorimetry" by A. Minakov^a'^b , J. Morikawa^c, T. Hashimoto^c, H. Huth^a and C. Schick^a*, although this article does not relate to thermogravimetric devices.

The embodiments described have a sample platform 11 which is thermally isolated from the first zone (base/stress zone) 19 through the second (thermal isolation) zone 24. This thermal isolation may be achieved in different ways as will be discussed here.

Firstly, the second zone 24 may be made from materials with a low thermal conductance compared to the thermal conductance of the stress zone 19. This will cause that any heat flow going through both the first and second zone will create a relatively large temperature drop in the second zone 24, and a much smaller drop in the first zone 19, which is directly connected to the frame 20 which is a good heat sink.

Secondly, heat flow towards the first zone 19 may be reduced by surrounding the resonator element 10 with gas. This will create a heat flow from the resonator element 10 to the surroundings which leads to a non- linear temperature profile in the second (thermal isolation) zone 24. And by offering parallel conduction paths to the ambient through the gas, the heat flow in the resonator element 10 will reduce significantly near the first zone 19 , and there the temperature gradient (heat flow times thermal sheet resistance ) will become practically zero, and thus the temperature increase of the stress zone also.

Furthermore, by adding heat exchanging extensions, such as paddles, to the second zone 24, the effect of heat conduction to the ambient will be enhanced, favourably reducing the heat transfer towards the first zone 19 and altering the temperature profile in a positive way.

The heat transfer towards the first zone 19 can be further reduced in various ways. By increasing the thermal conductivity of the gas (increasing the factor G), by decreasing the distance between the second zone 24 and the heat sink for the gas (also increases the factor G), by decreasing the width of the beam to a value comparable to the distance from the second zone 24 to the heat sink for the gas, which creates a 2-D or even 3-D heat flow pattern (also increases the factor G), by using beam materials with lower thermal conductivity (increases R), by narrowing the beam or by making holes in the beam (increases R), and finally by making the beam longer (increasing L).

Material of the resonator element/beam

Thermal isolation may be achieved by making the second (thermal isolation) zone 24 of materials with a low thermal conductance, i.e. having a thermal conductivity of less than 5 W/Km, for instance in the range of 1-5 W/Km.

The second (thermal isolation) zone 24 may be made of dielectric layers of low thermal conductivity such as SiN, SiC and Si02 and combinations thereof, e.g.

deposited by LPCVD and/or PECVD (Plasma-enhanced chemical vapour deposition) fabrication methods onto a silicon wafer substrate, with total layers thicknesses of typically 0.5-2 μιη. LPCVD is preferred for its better high-temperature resistance and mechanical properties.

Dimensions of the resonator element/beam

The beams 12, 13, 14 may be given relatively small dimensions, such that less heat can be conducted from the sample platform 1 1 through the beams 12, 13, 14 to provide thermal isolation. The beams 12, 13, 14 may have a length L, a width Wand a height H. The length L is measured along a central body axis of the beams 12, 13, 14 and is a measure for the distance covered by the beams 12, 13, 14. The central body axis may be a straight line, or may also comprise one or more bents (see for instance Fig. 4). The width Wis measured in a direction substantially parallel to the sample platform 11 , substantially perpendicular to the body axis along with the length L is measured. The height H is measured in a direction substantially perpendicular to the directions of the length L and the width W.

Typically, practical values for L range between 100 and 1000 μιη. Longer beams will present difficulties with bending due to fabrication stress mismatches, shorter will present difficulties to achieve a good second thermal isolation zone 24 with sufficient yL, and also the beam weight will become too low, severely restricting the mass range for the sample. This is because the upper range of the mass measurement is of the order of the weight of the resonator element 10.

Values for W will range between 10 μιη and 200 μιη, more narrow will make it difficult to accommodate all the wiring for the element in the sample area (heater 50 and sensor 60), and wider will reduce the 2-D heat flow by gases to a more 1-D heat flow, thus reducing the value of yL to a value too low to be effective. Finally, the thickness H will range from values of 200 nm to 5 μιη, thinner will make the device too fragile and also reduce the resonance frequency too much, thicker will lead to high thermal conductance. These values are valid for the present state-of-the art of MEMS.

Gas

The thermogravimetric device 1 according to the embodiments provided above may be positioned in a certain gas environment that provides an increased heat transfer from the resonator element 10, such as the sample platform 11 and the second zone 24 of the resonator element 10 to the surrounding gas.

The thermogravimetric device 1 may be positioned in a housing (not shown) which may be filled with gas mixture which has a heat conductivity coefficient of well above that of oxygen and nitrogen (which have a heat conductivity in the order of 25- 26 mW/Km at room temperature), that are ordinarily used as oxidizing and protecting gases. The heat conductivity of the gas mixture may be above 26 mW/Km, or at least above 40 mW/Km, or at least above 50 mW/Km, at room temperature. The gas mixture may comprise additional gas components, formed by at least one of the group of neon and helium, the gas mixture comprises at least 10 volume% of the additional gas components. As a result, the thermal conductivity is increased and the cooling effect of the second zone 24 is improved. The remainder of the gas mixture may for instance comprise oxygen or nitrogen.

Experimental results

Experiments have been performed with a thermogravimetric device 1 in accordance with the embodiment shown in Figs, la - c and defined in more detail in table 1.

For the measurements the strain sensor (resonance sensing element 40) and the compensation resistor are connected with two external resistors and a potentiometer for fine tuning in a Wheatstone bridge circuit. The output of the Wheatstone bridge is read by a lock-in amplifier (SR830) used also to drive the thermal actuators 30. Before performing a thermogravimetric measurement the thermogravimetric device 1 is positioned into a vacuum chamber. The pressure is set at 1000 mbar and the N2 and 02 are used as purge gasses.

An AC voltage of 1.5 V is applied over the poly-silicon resistors, present on both thermal actuator membranes of the thermal actuators 30. This causes a sinusoidal temperature rise of 80 K in the membranes, bending them due to the bimorph effect. The SiN bridges force the beam 12 (cantilever) to bend as well. The bending of the beam is detected by the resonance sensing element 40 (strain sensor mounted in the Wheatstone bridge configuration).

A sample of CuS0₄-5H₂0 was chosen for the experiments.

To obtain a spectrum the excitation frequency was swept in the frequency range of interest. The measured resonance frequency of the resonator element 10 without a sample on it was 10.390 kHz. For an estimated mass of the resonator element 10 of about 98 ng the minimum and maximum detectable mass is calculated to be about 20 pg and the mass of the resonator element 10 at 1 Hz resolution respectively.

Fig. 7a schematically depicts an output of the Wheatstone bridge, normalized to its value at the resonance frequency, versus excitation frequency. Fig. 7b schematically depicts a resonance frequency with and without CuS0₄-5H₂0 while the heater resistor is Joule heated with a DC voltage. The resonance frequency shifted to 7.840 KHz after loading the CuS0₄-5H₂0 sample, see Fig.7a. Fig. 7b shows the thermogravimetric curves of CuS(V5Fi₂C) samples with estimated mass of 20 ng and 1 ng.

So, the experiments show that the thermogravimetric devices according to the embodiments can successfully used to perform thermogravimetric measurements of a CuS04-5H20 sample. By providing sufficient thermal isolation of the sample platform 11 with respect to the base 19 of the beam 12 or the suspension of the resonator element 10 to the frame 20, the resonance frequency of the empty thermogravimetric device 1 has found to be substantial temperature independent. The mass sensitivity and resolution of the thermogravimetric device 1 are about 200 Hz for 1 ng and 40 pg respectively, within a measurement range of 100 ng - 40 pg.

Stack of materials

According to a further embodiment, a temperature coefficient of resonance frequency (TCRF_sampi_e platform) of the resonator element 10 for heating of the sample platform 11 without a sample is less than 20 ppm/K can be accomplished by forming the first zone 19 being made of a stack of layers, the stack of layers at least comprising a first layer 81 with a negative Temperature Coefficient of the Young's Modulus and a second layer 82 with a positive Temperature Coefficient of the Young's Modulus.

Fig. 9 shows a cross sectional view of part of such a resonator beam 10 in the first zone 19. Of course, more layers may be provided.

For instance, a layer of silicon, with a TCYM of -60 ppm/K may be combined with a layer of Si0₂ with a TCYM of +200 ppm/K. Taking into account the value of the Young's modules, the thickness of the layers and the position of the layers within the stack are chosen to achieve a reduced TCRF_sampi_e platform of less than 20 ppm/K, or preferably lower.

Thermal guarding

According to a further embodiment, a temperature coefficient of resonance frequency (TCRF_sampi_e platform) of the resonator element 10 for heating of the sample platform 11 without a sample is less than 20 ppm/K can be accomplished by a thermogravimetric device 1 , wherein a base temperature control element 51 is provided in the vicinity of the first zone 19 to establish a base temperature.

An example of this is schematically shown in Fig. 10, showing a

thermogravimetric device according to one of the above described examples now comprising a base control element 51.

This base temperature control element 51 may be a base heating element or a base cooling element to impose a base temperature to the first zone 19 and maintain this temperature. The base heating element or heat cooling element may be provided near the border between the zone first 19 and the second zone 24.

The base temperature may be substantially above the ambient temperature, such that heat from the sample platform 11 does not substantially influence the temperature of the first zone 19.

Alternatively, the base temperature control element 51 may be provided with a temperature-sensing element (e.g. thermocouple) and a feedback loop (not shown) to monitor the base temperature and compare the base temperature with a predetermined reference value. The feedback loop may be arranged to control the base temperature by means of the base temperature control element, e.g. by increasing or reducing the amount of supplied heat. The base temperature control element may for instance comprise a heater and/or a cooler.

This way, the temperature of the resonator element within the first zone 19 may be kept at a substantially constant value, for instance an elevated temperature compared to room temperature. No matter what the temperature of the sample platform 11 becomes, the base temperature can always be maintained at the substantially same level, i.e. by compensating for changes of the base temperature due to heat originating from the sample platform 11 and/or changing ambient temperature fluctuations.

Then, the first zone 19 will experience the same temperature profile, and is thus independent of the sample platform temperature. The resonance frequency will be virtually independent of temperature.

Hinge

According to a further embodiment, which may be used independently or in combination with the other embodiments, the resonator element 10 is provided with varying thickness to create a hinge part 91 near the frame 20, i.e. in the first zone 19 This can be accomplished by creating a thin part 91 near the frame and/or by providing thickened parts near the sample platform. The thin part may be at least 20% thinner than the remainder of the resonator element 10 (beam 12).

The hinge can be created by, instead of or in addition to making a thin hinge part 91, a hinge part comprised of materials with a substantially lower value of Young's modulus. The Young's modulus may be at least 50% lower than that of the remainder of the resonator element 10.

Fig. 11 shows an example of such a thermogravimetric device showing such an embodiment, wherein the resonator element 10 is provided with a hinge part 91. Fig. 11 only shows such a thermogravimetric device 1 schematically.

This is done to further concentrate stress and strain remote from the heating element and the sample platform, thereby further reducing the temperature coefficient of resonance frequency (TCRF_sampi_e platform).

Further remarks

By using two or more identical devices, either on separate chips or both integrated in a single chip, and by using one of the devices as a reference without sample, two additional functionalities are created. First of all it is possible to compare the resonance frequency of the reference device with the sample device, and measure only the differential frequency. In this way, any dependence of the resonance frequency on hot spot temperature, ambient temperature or other causes can be compensated for.

Alternatively or in addition, it is possible to use another device and add to the sample position of this device a patch of metal with a well-known mass, and use this device for mass calibration purposes. The addition of the metal mass can be done in the design stage, which will achieve a good accuracy (3%).

Secondly, it is possible to perform FSC by comparing either the temperature if both devices receive the same power to the heating element, or by comparing the compensation power when the power to the sample device is controlled to give the same temperature-time program as the reference device.

One or more of the two or more identical devices may be loaded by patches of, for instance, gold or platinum (if that is the metal used for interconnection), with each a certain, different, weight, that can be used to calibrate the mass sensitivity of the device, even as a function of sample platform temperature. This is an attractive feature in practical applications, and also is a means of reducing the adverse effects of the residual temperature coefficient of the resonance frequency for sample platform temperature, or indeed ambient temperature, as analyses are not always started from the same environmental temperature.

According to further embodiments, at least one of the resonance sensing element

40 and the temperature-sensing element 60 may be an optical element as will be explained in more detail below.

The temperature-sensing element 60 may comprise an optical element. The optical element may generate an optical beam (e.g. laser beam) and may be positioned on or next to the frame 20. The temperature-sensing element 60 may comprise an optical guide structure from the optical element towards the sample platform 11 to guide the optical beam towards the optical platform. At the end of the optical beam a reflective surface is provided, the reflective surface being temperature dependent, i.e. the phase, intensity or frequency of the reflected optical beam may dependent on the temperature of the reflective surface.

The optical beam is reflected by the reflective surface towards a receiver of the optical element, back through the optical guide structure. The optical guide may be formed by layers or tracks suitable for optical guidance back to the optical element.

The receiver may for instance use an interferometer to determine a change in path length, intensity or frequency.

The resonance sensing element 40 may comprise an optical element arranged to generate an optical beam (e.g. laser beam) and may be positioned on or next to the frame 20. An optical guide structure may be provided to guide the optical beam, the optical guide structure traversing the first zone 19 of the resonator element 10, i.e. where it is attached to the frame 20, that experience the largest stress and strain. The optical guide structure may terminate at a receiver of the optical element on or next to the frame for read-out. The optical guide made of layers suitable for light transmission. Bending of the resonator element will influence the path of the optical beam through the optical guide structure, which may be detected by the receiver. The receiver may for instance use an interferometer to determine a change in path length.

An advantage of integrated optics is that it is not needed to use metal conductors with relatively large heat conductance, but dielectric layers (glasses etc), with very low conductance. The descriptions above are intended to be illustrative, not limiting. It will be apparent to the person skilled in the art that alternative and equivalent embodiments of the invention can be conceived and reduced to practice, without departing from the scope of the claims set out below.

List of references

[1] R. Berger et al, Chem. Phys. Lett., 294 (1998), pp. 363-369

[2] T. Ono and M. Esashi, Meas. Sci. Technol, 15 (2004), pp. 1977-1981

[3] J. Lee and W.P. King, Rev. Sci. Instr., 79 (2008), pp. 1-6

[4] G.C.M. Meijer and A.W. van Herwaarden, editors., Thermal Sensors, Adam Hilger,

Bristol (1994) 304 pgs, ISBN 0-7503-0220-8, pp. 45-70

[5] A. Minakov, J. Morikawa, T. Hashimoto, H. Huth and C. Schick, "Temperature distribution in a thin-film chip utilized for advanced nanocalorimetry" ^', Meas. Sci.

Techn. 17 (2006) pp. 199-207

[6] A.W. van Herwaarden and P.M. Sarro, Double Beam Integrated Thermal Vacuum

Sensor, J. Vac. Sci. Techn. A, 5 (1987) pp. 2454-2457

[7]E. Iervolino, A.W. van Herwaarden, P.M. Sarro, Proc. EUROSENSORS 2008, pp.

Claims

1 . Thermogravimetric device ( 1 ), comprising a resonator element ( 10) suspended from a frame (20), at least one actuator (30) for bringing the resonator element ( 10) in a resonating state and a resonance sensing element (40) for sensing a resonance frequency of the resonator element ( 10), wherein the resonator element ( 10) comprises a sample platform ( 1 1 ) arranged to receive a sample and the thermogravimetric device

(I) further comprises a heating element (50) for heating the sample when positioned on the sample platform ( 1 1 ),

wherein the thermogravimetric device ( 1 ) comprises a temperature-sensing element (60) sensing the temperature of the sample platform (1 1 )

characterized in that the thermogravimetric device comprises compensation means to compensate for an increase of the temperature generated by the heating element (50) such that a temperature coefficient of resonance frequency (TCRF_sampi_e platform) of the resonator element ( 10) for heating of the sample platform ( 1 1 ) without a sample is less than 20 ppm/K.

2. Thermogravimetric device ( 1 ) according to claim 1 , wherein the resonator element ( 10) comprises a base area ( 19) being attached to the frame (20), wherein the compensation means are provided by providing thermal isolation to thermally isolate the sample platform ( 1 1 ) and heater (50) from the base area ( 19) of the resonator element ( 10).

3. Thermogravimetric device according to claim 2, wherein the sample platform ( 1 1 ) is suspended from the frame (20) by a single beam (12).

4. Thermogravimetric device according to claim 2, wherein the sample platform

(I I) is suspended from the frame (20) by two or more beams ( 12, 13 , 14).

5. Thermogravimetric device according to claim 4, wherein the sample platform

( 1 1 ) is suspended from the frame by two or more beams ( 12, 13) connecting a first edge of the sample platform ( 1 1 ) with the frame (20).

6. Thermogravimetric device according to claim 4, wherein the sample platform

(11) is suspended from the frame by a first beam (12) and a second beam (14), the first beam (12) connecting a first edge of the platform (11) with the frame (20) and the second beam (14) connecting a second edge of the platform with the frame.

7. Thermogravimetric device according to any one of the claims 4 - 6, wherein one or more thermal actuators (30) interact with a first subset of beams (12, 12') and one or more resonance sensing elements (40) interact with a second subset of beams (14, 14'), the beams of the second subset not being part of the first subset.

8. Thermogravimetric device according to any one of the claims 1 - 2, wherein the sample platform is formed by a membrane that is suspended from the frame

substantially along its entire perimeter.

9. Thermogravimetric device according to any one of the preceding claims, wherein the thermal isolation between the heater (50) and the frame (20) is given by a factor GRL² of at least 20, wherein

- L is a distance between the sample platform (11) and the frame (20),

- G is the thermal conductance of gas around the resonator element (10) in W/K per meter of distance L,

- R is the average thermal resistance of the resonator element (10) expressed in K/W per meter of distance L.

10. Thermogravimetric device according to claim 9, wherein the factor GRL² is at least 50 or at least 100.

11. Thermogravimetric device 1 according to any one of the preceding claims, wherein the parts of the resonator element 10 in between the sample platform (11) and the frame (20) are substantially made of materials having a thermal conductivity of less than 5 W/Km.

12. Thermogravimetric device 1 according to any one of the preceding claims, wherein the sample platform (11) is suspended from the frame (20) by one or more beams (12, 13, 14) having a length between 10 and 2000 μιη, a width between 3 and 500 μιη and a thickness between 0.1 and 10 μιη.

13. Thermogravimetric device 1 according to any one of the preceding claims, wherein the resonator element (10) comprises a membrane connecting the sample platform (11) to the frame (20), the membrane having a length spanning the distance between the sample platform (11) and the frame (20) between 50 and 5000μιη, and having outer lateral dimensions between 100 and 10 ΟΟΟμιη and a thickness between 0.01 and ΙΟμιη.

14. Thermogravimetric device 1 according to any one of the preceding claims, wherein heat sink elements are provided at a distance between 3 - 300 μιη from the resonator element (10).

15. Thermogravimetric device 1 according to any one of the preceding claims, wherein the thermogravimetric device further comprises a housing or is incorporated in an enclosure that is arranged to be filled with a gas mixture having a heat conductivity above 26 mW/Km, or at least above 30 mW/Km, or at least above 40 mW/Km, at room temperature.

16 Thermogravimetric device 1 according to claim 15, wherein the gas mixture comprises additional gas components, formed by at least one of the group of neon and helium, the gas mixture comprises at least 10 volume% of the additional gas components.

17. Thermogravimetric device 1 according to any one of the preceding claims, wherein the resonator element comprises a hinge part (91) near the frame (20).

18. Thermogravimetric device 1 according to any one of the preceding claims, wherein the resonator element (10) comprises a first zone near the frame and a second zone in between the sample platform (11) and the first zone, the first zone (19) having a first thermal conductance and the second zone having a second thermal conductance, the first thermal conductance being higher than the second thermal conductance.

19. Thermogravimetric device 1 according to any one of the preceding claims, wherein at least one of the resonance sensing element (40) and the temperature-sensing element (60) is an optical element.

20. Thermogravimetric device 1 according to any one of the preceding claims, wherein the resonator element (10) comprises a first zone near the frame and a second zone in between the sample platform (11) and the first zone, wherein the first zone has a first flexural rigidity and the second zone having a second flexural rigidity, the first flexural rigidity being smaller than the second flexural rigidity.

21. Thermogravimetric device (1) according to any one of the preceding claims, wherein the resonator element (10) comprises a first zone (19) near the frame (20) and a second zone (24) in between the sample platform (11) and the first zone (19), wherein the compensation means are formed by providing a first zone (19) that is made of a stack of layers, the stack of layers at least comprising a first layer (81) with a negative Temperature Coefficient of the Young's Modulus and a second layer (82) with a positive Temperature Coefficient of the Young's Modulus.

22. Thermogravimetric device (1) according to any one of the preceding claims, wherein compensation means are provided by providing a base temperature control element (51) in the vicinity of the first zone (19) to establish a base temperature.