Thermoelectric and Thermoresistive Effect in Bi2Se3: A Novel Dual-Mode Temperature and Heat Flux Sensor

Here we present a sensor concept for simultaneous heat flux and temperature acquisition based on the thermoelectric and thermoresistive effect in n-type orthorhombic Bi2Se3. Measurements were performed in the 283–343 K temperature range. Temperature sensitivities as high as −36700 ppm/K (equivalent to a beta-value of 3260 K) and heat flux sensitivities of <inline-formula> <tex-math notation="LaTeX">$0.125 ~\mu \text{V}$ </tex-math></inline-formula>/(W/<inline-formula> <tex-math notation="LaTeX">$\text{m}^{2})^{}$ </tex-math></inline-formula> were determined. The temperature and heat flux accuracies were found to be ± 0.6 K and ± 20 W (through a 1cm x 1cm area, equiv. to ± 1 K) and the resolution was determined to be around 0.05 K. The underlying physical mechanisms were further investigated and a deep donor level with ionization energy of 0.292 eV was identified leading to a strong temperature-dependence of donor ionization. The presented device architecture has the potential to be utilized in applications where dual-mode simultaneous temperature and heat flux measurements are beneficial. [2023-0093]


I. INTRODUCTION
I N TIMES of global climate changes and energy crisis, monitoring temperature -which is one of the most important physical quantities in our environment [1], [2], [3] -as well as heat flux [4] is becoming indispensable.Some examples include: monitoring earth surface heat flux to determine the earth's energy balance [5], [6]; assessing and optimizing thermal energy storages such as sensible heat storage technologies [7], [8]; monitoring and optimizing of building materials [9], [10] or the optimization of food supply chains where deficiencies in the cold-chain and inappropriate packaging are some of the key reasons for significant losses and waste [11], [12], [13], [14].
Measuring heat flux is typically achieved via the thermoelectric effect.However, as a thermocouple sensor is only able to measure temperature differences, an additional cold junction reference temperature sensor is required.Moreover, the thermoelectric material properties may be temperaturedependent, making it necessary to measure and compensate temperature [15], [16].Although combinations of thermopiles for heat flux acquisition with thermocouple temperature sensors exist [15], [17], the ability to read-out both heat flux and temperature with the same sensor would be very advantageous.
Thermoelectric semiconductors exhibit rich physics that could be exploited for multi-modal sensing, e.g.heat flux and temperature.Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 all belong to the material family of chalcogenides that are semiconductors with at least one group 16 chalcogen element such as sulfur (S), selenium (Se) or tellurium (Te) [18].They are frequently utilized in thermoelectric energy conversion due to reasons such as a typically low thermal conductivity that arises from the heavy atoms involved and ability to manipulate by doping towards n-type or p-type behavior [19].
We previously reported the successful electrochemical synthesis of tens of micro-meter thick stoichiometric n-type Bi 2 Se 3 pillars of the orthorhombic phase which were characterized for thermoelectric and electrical properties at room temperature [20].
Here, we demonstrate a dual-mode temperature and heat flux sensor based on the simultaneous thermoelectric and thermoresistive effect in the same Bi 2 Se 3 material, investigated in the 283-343 K temperature range.The device is fabricated with microfabrication processes and the active sensor material is synthesized via electrochemical deposition (ECD).ECD is attractive because it offers a low-cost, simple synthesis solution at room temperature [20] while it can easily be integrated into existing microfabrication processes and therefore, has a large upscaling potential [21].In this work, the sensor outputs that are based on the thermoelectric and thermoresistive effect are displayed after which the potential for sensing applications is assessed by evaluating the sensor performance with respect to sensitivity, accuracy and resolution for both, temperature and heat flux acquisition.Last, the underlying physical mechanisms are explained based on the Arrhenius equation and the beta-value.

II. EXPERIMENTAL
The Bi 2 Se 3 -based structures were fabricated with conventional microfabrication processes.The test-structures containing the Bi 2 Se 3 micropillars (see Fig. 1b) were fabricated and characterized in order to help explain the underlying physical mechanisms responsible for the sensor behavior whereas  sensor response and sensor performance were evaluated on the Bi 2 Se 3 -based sensor devices (see Fig. 1c).

A. Synthesis of Bi 2 Se 3 Micropillars
The active material Bi 2 Se 3 was synthesized via electrochemical deposition from an electrolyte containing dissolved Bi(NO 3 ) 3 and SeO 2 in diluted HNO 3 .Depositions were performed onto an E-beam evaporated seedlayer consisting of 20nm Ti and 120nm Au on top of a Si wafer.The growth of Bi 2 Se 3 was confined to photolithographically patterned SU-8 templates 100 µm in diameter and 45 µm in thickness.After electrochemical depositions with growth rate of around 1.25 µm/hr, the surface was planarized by hand with a suspension containing approximately 3 µm-sized Al 2 O 3 particles.Metal top contacts were evaporated through a shadow mask composed of 10nm Cr and 150nm Au after performing an Ar-ion etch in the same chamber for surface cleaning purposes.Further processing details can be found in our previous work [20].

B. Synthesis of Bi 2 Se 3 Based Devices
Thermoelectric generators and heat flux sensors commonly consist of a multitude of thermocouples that are electrically connected in series while thermally connected in parallel [22], [23], [24], [25], [26].In order to explore the potential of Bi 2 Se 3 based sensors for temperature and heat flux measurements, a process for such a device was developed here where the electrodeposition process for Bi 2 Se 3 can be integrated, see Fig. 1a.A silicon substrate with 2 µm thermally oxidized SiO 2 was employed as a substrate layer.A metal stack of Cr/Au/Cr 10/120/10 nm was E-beam evaporated on top and structured using photolithography combined with wetetch (1).Chrome was utilized to enhance the adhesion to the SiO 2 layers below and above.Next, SiO 2 was deposited on the metal using PECVD and structured with photolithography and wet-etch in buffered oxide etch (BHF) (2).This layer served as a protection during the ECD.Subsequently, the photoresist SU-8 was deposited and lithographically structured yielding a permanent 45 µm thick template for the ECD (3).The template contained molds of 100 µm in diameter for the plating process of Bi 2 Se 3 and 50 µm in diameter for plating of Cu respectively and etching trenches to disconnect the bottom contact lines at the end.The diameter for the latter was smaller in order to reduce the impact of Cu on the thermal resistance of the thermopiles.The wafer was then diced into 2 cm x 2 cm chips.The first plating step of Bi 2 Se 3 was performed on chip level into the first set of molds (4).The previously structured SiO 2 ensured that no deposition occurred into the other structures.Afterwards, the sample surface was carefully polished (5), and a temporary protection resist was applied and structured to protect the Bi 2 Se 3 material while the second type hole was freed from the SiO 2 by dipping the chip in BHF (6).These were filled with copper in a plating process utilizing a high speed copper electroplating solution (Sigma Aldrich) that contained dissolved copper ions Cu 2+ from Copper(II) sulfate pentahydrate CuSO 4 •5H 2 O as well as sulfuric acid H 2 SO 4 and chloride.The reduction reaction of Cu is given as: Cu 2+ + 2e − → Cu solid .The deposition was performed at −0.25 V for 15 min, which sufficed to completely fill the holes and result in slight overgrowth (7).Then, the temporary resist was removed in Acetone and Isopropyl alcohol and the surface was once again polished manually to level off the layers (8).Another temporary protection resist was applied and structured to protect the electrodeposited material and to etch SiO 2 and the metal layers on the etching lines (9).After the temporary protection layer was removed, the surface was cleaned with an Ar-ion etch step and top contacts consisting of Cr/Au 50/150 nm were deposited through a shadow mask, yielding a device ready for characterization (10), see Fig. 1d.
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C. Electrical and Thermoelectric Measurements
Fig. 1b and 1c schematically illustrate the measurement setup used to acquire electrical and thermoelectric measurements where the samples were clamped in between two copper plates as shown.Electrical isolation was guaranteed with Kapton tape that was permanently attached to the copper plates as illustrated.Electrical connections to the sample were made by means of gold coated probetips.For the pillar design, the bottom electrode was shared by all pillars whereas top electrodes were uniquely defined for every pillar (Fig. 1b).In case of the TEG chain, bottom contacts were structured, and the device was electrically contacted from the top using two large metal pads (Fig. 1c).The copper plates contained two RTD PT1000 sensors located closely to the sample and two Peltier elements on either side.A PID mechanism was implemented to control the temperature T meas,top and T meas,bot of the two RTD sensors embedded in the copper plates where T meas =T meas,top − T meas,bot .Electrical resistance measurements were performed with a Keithley current source 6221 connected to a Keithley nanovoltmeter where a pulsed delta method was applied with a fixed source current of ± 10 µA.The IV sweep was measured with a Keithley 2400 Sourcemeter where the starting and end voltage was set to 0 V and the sweep started in positive direction.The Seebeck voltage was read out with a Keithley 2000 Multimeter.In case of an n-type semiconductor, under a temperature gradient, the e − majority carriers will thermally diffuse to the cold end, leading to a negatively charged cold end compared to the hot end.Connecting the positive test probe to the cold side and the negative one to the hot side will thus result in a negative measured open circuit potential which is the chosen sign convention throughout this paper.
For the characterization, the mean temperature T m where T m = (T top + T bot )/2 was incrementally ramped up from 283 K to 343 K in steps of 5 K.For every mean temperature step, T = T top − T bot was ramped from 0 K to 10 K.As T refers to the actual temperature drop across the device under test (DUT) throughout this paper, a calibration procedure was introduced in order to derive T from T meas .In the first routine, the thermal resistance of the Kapton tape was determined by means of a differential heat flux measurement.In the second routine, a heater was clamped in the setup and the temperature at the surface of the heater (determined with two additional temperature sensors) was compared to the temperature measured by the temperature sensors integrated in the measurement setup.The difference was assumed as the temperature drop across the interface.To ensure repeatable measurements, a thin film pressure sensor was used to obtain similar clamping conditions from one to the next measurement (SI S.1.contains further details on the setup characterization).

III. RESULTS AND DISCUSSION
Section A presents measurements of the thermoresistive and thermoelectric sensor output response, Section B further investigates the sensor performance with respect to sensitivity, accuracy and resolution and Section C discusses physical mechanisms underlying the observed sensor behavior.

A. Sensor Response
The temperature dependent resistance R T eg of the Bi 2 Se 3 -based devices is plotted in Fig. 2a as a function of the mean temperature T m for different temperature differences T across the device.We observe an exponential drop in resistance with increasing temperature, see (1), which is in line with thermally activated semiconductor behavior [27], [28], [29] as will be elaborated later-on.On the other hand, R T eg varies only slightly with respect to T , as visible in the inset of Fig. 2a.
In Fig. 2b, the open circuit potential V T eg arising from the thermoelectric effect is plotted as a function of the mean temperature T m for different temperature differences T across the device.The magnitude of V T eg is negative and its amplitude increases linearly with increasing T , which, according to the sign convention defined earlier implies n-type behavior and is in line with what we previously reported [20].The decrease of the absolute value of V T eg with increasing T m suggests a decrease in the Seebeck coefficient.temperature coefficient of resistance (NTCR) materials, that is given by [29] and [30]: With R the resistance in [ ], T the temperature in [K], β the beta-value in [K] and R 0 the resistance at T 0 .In Fig. 3a, the experimental data for T = 0 K is fitted with the Arrhenius equation.T 0 and R 0 are set to 313 K and 57.580 k respectively.The equation is plotted for β = 3260 K which results in a temperature discrepancy below 1 K between data and model across the full temperature range as can be seen in the inset of Fig. 3a.The beta-value determines how steeply the exponential resistance temperature characteristic falls and is hence a common parameter to determine the sensitivity of a thermistor with higher, absolute beta-values implying higher sensitivities [29], [30].Values of β for thermistor applications should be in the order of 2000 to 5000 K [3], [28], [31].As can be seen, the Bi 2 Se 3 -based device architecture presented here falls well within that range and is hence a promising candidate for NTC thermistor applications around room temperature from a sensitivity point of view.
In addition to the beta-value, the temperature coefficient of resistance (TCR) is another metric to quantify device sensitivity [29], [30].It is typically given in ppm/K or in %/K (1% = 10000 ppm) and can be derived by differentiating R(T ) with respect to the temperature: The T C R for metals is usually positive, the one of semiconductors negative [29].Furthermore, the relation between the T C R and β is given by: In Fig. 3b, the T C R is plotted as a function of T m .From the plot it can be seen that the sensitivity is higher for lower temperatures which is in line with the exponential behaviour in Fig. 3a.
In Table I, the sensitivity expressed through the beta-value as well as the TCR of three commercial thermistors is compared to the Bi 2 Se 3 -based devices.It becomes apparent that the sensitivity performance presented here competes well with commercial bulk NTC devices.
Next, the sensitivity of the voltage signal is analyzed.The heat flux is derived according to: With K the thermal resistance of the integrated thermopiles in [K/W] which was approximated by means of a differential measurement and found to be 0.0515 K/W (see SI S.1.for methodology).The sensitivity is defined as the slope of the transfer characteristic of V T eg (Q) and displayed in Fig. 4. A decrease for increasing mean temperature can be seen which is displayed in the inset of Fig. 4. A linear fitting Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE II COMPARISON OF BI 2 SE 3 -DEVICE SENSITIVITY COMPARED TO
COMMERCIAL HEAT FLUX SENSORS function describes the temperature dependent sensitivity where the derived sensitivity at room temperature is found to be 0.125 µV/(W/m 2 ).According to Table II, the sensitivity of the demonstrated sensor is smaller than commercial heat flux sensors.For high sensitivities, V T eg must be maximized and K should be large while not being larger than the thermal resistance of the environment to be measured in order to ensure the flow of the heat through the sensor element primarily [35].
In the current study, the reason for the lower sensitivity is the high thermal conductivity of the copper pillars which dominates the overall device thermal resistance.The low thermal resistance has further implications such as relatively high heat fluxes through the sensor as for example shown in Fig. 5c.
2) Accuracy: In order to investigate the accuracy, the sensor is exposed to an arbitrary input sequence with varying temperature and temperature differences, performed in the measurement setup as outlined in the experimental section.The resistance and voltage response to the input sequence is shown in Fig. 5a.The advantage of utilizing the measurement setup is that on top of the sensor output data, the temperature setpoints are stored which are subsequently used to compare the values derived from the sensor output with the actual temperature setpoint data and quantify the sensor accuracy with respect to the reference sensors.To obtain T m , the Arrhenius equation is solved according to: A first approximation of the mean temperature T m is derived using (5).Upon careful inspection of the inset of Fig. 2a, it can be seen that fitting the model coefficients for T = 0 K means that for T > 0 K, the model overestimates T * m .Hence, in particular the setpoints with high output voltage (see Fig. 5a) will have an inaccuracy in terms of the derived mean temperature.Without correcting for this, the measuring accuracy is around ± 0.8 K (see SI S.2. for visualization).
For this reason, a calibration is introduced in order to obtain a device-specific correction function.This is done by collecting the actual temperature as a function of R T eg (see Fig. 2 inset).Next, the actual temperature is subtracted from T m ( T = 0) according to T corr = T m ( T = 0) − T ( T ̸ = 0).The resulting temperature correction T corr linearly depends on T according to: T is not a sensor output signal but it can be expressed as a function of the sensor output V T eg .This requires an additional device-specific calibration where V T eg is monitored as a function of T .The resulting dependence is linear as well and, solved for T , is given by: In summary, the new formula for expressing the corrected mean temperature depends on both sensor output signals T m,calibr R T eg , V T eg and by inserting ( 7) into ( 6) and subtracting it from (5), is written as: Both, the mean temperature measured with the reference sensors as well as the derived mean temperature T m,calibr are plotted in Fig. 5b (top).The difference between the two is furthermore visualized in Fig. 5b (bot) where the discrepancy is utilized to define the sensor accuracy.Upon close inspection of Fig. 5a, spikes in the sensor response can be seen which arise due to the change in setpoint where the system requires approximately 80 s to adapt to the new setpoints.For this reason, we consider only data-points after the 80 s period for defining the sensor accuracy.
After the introduced correction as shown in ( 8), the measurement accuracy is improved to around ± 0.6 K.A part of the remaining inaccuracy is a systematic error arising from the offset in the beta function (see Fig. 3a inset), which becomes particularly significant further away from where T 0 was defined.
Fig. 5c (top) depicts the reference and calibrated heat flux response.The reference heat flux Q Re f is determined through knowledge of T and the thermal resistance K .The calibrated response is derived from the voltage signal together with the temperature-dependent sensitivity fitting function S that is given by (see Fig. 4 inset): Since T m is expressed through R T eg , the heat flux output signal is itself dependent on both sensor outputs: Q calibr V T eg, R T eg .In comparison to other heat flux sensors, the temperature correction is performed through the same sensor.The heat flux accuracy (see Fig. 5c bottom) is around ± 20 W/cm 2 which is equivalent to an accuracy in T of around ± 1 K (right axis) in terms of temperature difference.
3) Resolution: Fig. 6a and 6b give an indication for the sensor's resolution which was assessed around room temperature.For the thermoresistive performance, T = 0K and T m was increased by small amounts δT, see Fig. 6a top.For the thermoelectric performance, T ̸ = 0K small differences in temperature were applied across the device, see Fig. 6b, top.It can be seen that the sensor is able to resolve temperature changes as low as 0.05 K through the thermoresistive response and temperature differences as low as 0.05 K through the thermoelectric response which is equivalent to 1 W/cm 2 .

C. Physical Mechanisms
In order to understand the underlying physical mechanisms of the sensor output characteristic, Bi 2 Se 3 micropillars are investigated.These were fabricated in a different process run compared to the Bi 2 Se 3 devices (different month & separate electrolyte).The resistance-temperature characteristic can be seen in Fig. 7a which is comparable to the device observations in Fig. 2. Fig. 7d displays the IV-sweep of the structure for a voltage range of ± 0.5 V that results in a current range covering the selected source current for resistance measurements (±10 µA).The linearity and symmetry of the IV-sweeps supports that the electrical contacts are ohmic (see SI S.3.for an IV characteristic covering an extended potential range).Based on these observations, the exponential decrease in resistance must hence come from the mechanisms taking place in the bulk of the semiconductor material Bi 2 Se 3 .Bi 2 Se 3 is expected to be of n-type nature due to the domination of donor-type defects such as Se vacancies V Se and anti-site defects Se Bi [38], [39].This is confirmed by the negative Seebeck coefficient, see Fig. 7c, which was determined from the open circuit voltage V OC (measurement equivalent to Fig. 2b) and the knowledge about T , according to α = V OC T .On the band diagram level, the Fermi level will hence be located closer to the conduction band edge.A simple, widely used model for the electrical conductivity σ in semiconductors is: with ρ the electrical resistivity, n and p the free electron and hole concentrations, e the electrical charge, µ n and µ h the electron and hole mobility respectively.The second term of the equation is omitted for metals where charge carriers are mostly electrons [27].Furthermore, in metals, the free electron Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.concentration n is almost independent of temperature whereas scattering decreases the electron mobility µ n .Overall, the conductivity of metals decreases with increasing temperature.On the other hand, the temperature behavior of conductivity in semiconductors is more complex and the amount of free charge carriers is strongly temperature dependent [27], [28], [29], [40].In case of extrinsic semiconductors, dopant atoms induce new impurity levels inside the forbidden bandgap.Focusing on n-type semiconductors, these donor levels are energetically closer to the conduction band than to the valence band.Three distinct temperature regions are typically recognized: the partial ionization region at low temperatures , extrinsic (or full ionization) at intermediate and intrinsic at high temperatures [40], [41].Here, we define partial ionization as the region in between the freeze-out at 0 K where little thermal energy is available to excite electrons into the conduction band and the point of complete ionization where all donor impurities are ionized.
In the intrinsic region, the concentration of charge carriers n i resembles the one of intrinsic semiconductors and is dominated by the thermal excitation of electrons from the valence to the conduction band, described as: with T the temperature in [K], k B the Boltzmann constant (8.62 × 10 −5 eV/K) and E g the energy bandgap in [eV] [27], [40], [41].At intermediate temperatures, the semiconductor is found in the extrinsic region where the electron concentration remains constant.In the partial ionization region, the exponential increase in carrier concentration is dominated by the thermal excitation of donor electrons into the conduction band.In Fig. 7b, the natural logarithm of the Arrhenius equation is plotted where β = 3400 K which is in close agreement to the beta-value obtained for the Bi 2 Se 3 / Cu -based thermopile (% difference = 4.2%).The linearity in the plot indicates that in this temperature range, only one physical mechanism is dominating the resistance-temperature behavior in the given temperature range.In the intrinsic region, β = [30] (see Fig. 7e for nomenclature).
For the former, one obtains an energy gap E g of 0.584 eV for Bi 2 Se 3 .This is unlikely as band gaps of this size in orthorhombic Bi 2 Se 3 are not known.The rhombohedral phase of Bi 2 Se 3 was found to have small bandgaps of 0.2 -0.3 eV [38], [39], [42] while orthorhombic Bi 2 Se 3 as the material investigated here was reported to have bandgaps between 0.9 -1.2 eV [43], [44].
E g − E d = 0.292 eV is in close agreement with a donor level of 0.32 eV that was previously identified around room temperature [43].This in combination with a large bandgap would furthermore explain the overall rather low semiconductor conductivity of 8.6 S/m around room temperature [20].
Full ionization occurs around room temperature for shallow donors such as phosphorous atoms inserted into silicon where the ionization energy E g − E d is only around 0.045 eV [41].Incomplete ionization of dopants at room temperature is a well-known phenomenon of deep lying donor levels that occurs in particular in wide-bandgap semiconductors such as SiC, GaN and diamond [45], [46].Hence, the strongly temperature-dependent resistance characteristic in our study is likely related to a deep lying donor level around 0.292 eV below the conduction band edge.We assume that the defect state comes from the dominating selenium vacancies that create positive point charges and excess electrons, determining the n-type behavior of the material [38].
The high magnitude of the Seebeck coefficient between -170 and -220 µV/K (see Fig. 7c) can furthermore be explained by the magnitude of E d which results in relatively low carrier concentrations that lead to a low electrical conductivity but is favorable for a large Seebeck coefficient [47].In this context, the reduction the Seebeck coefficient for higher mean temperatures is due to the higher probability of occupied energy states above the Fermi-level as temperature increases which has a negative effect on the magnitude of the Seebeck effect [48].

IV. CONCLUSION
To conclude, we demonstrated thermoelectric and thermoresistive properties in Bi 2 Se 3 pillars and Bi 2 Se 3 -based devices in the temperature range between 283 K and 343 K.The underlying physical mechanism responsible for the strong thermoresistive effect is likely a deep lying donor level ∼0.3 eV below the conduction band, leading to incomplete ionization in the measured temperature range.Simultaneously, a high Seebeck coefficient was found.In addition, beta values of 3260 K compare well to state-of-the-art thermistors.
Exploring the effects in Bi 2 Se 3 over larger temperature ranges could extend the applicability of this sensor concept.Further investigations could focus on optimizing both thermal and electrical device performance.For example, in order to reduce the heat flux through the device, the thermal resistance associated to the copper pillars would need to be reduced.In addition, the impact of interface thermal resistances in real world scenarios would have to be assessed.
The device response to temperature and heat flux in the 283-343 K temperature range is very promising for integrated dual-mode sensors in a multitude of applications such as earth surface monitoring, thermal energy storage, building materials or supply chains.

Fig. 1 .
Fig. 1. a) Process flow for thermoelectric device fabrication b) Experimental setup for thermoelectric and electrical measurements for pillar characterization c) for device characterization, dimensions not to scale d) top view of fabricated TEG chip and zoom on the active area.

Fig. 2 .
Fig. 2. Sensor output as a function of the mean temperature T m and the temperature difference T a) thermoresistive output b) thermoelectric output.

B. Sensor Performance 1 )
Sensitivity: The measured resistance-temperature characteristic fits the well-known Arrhenius equation for negative Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

Fig. 3 .
Fig. 3. Sensitivity analysis for thermoresistive output signal a) fitting of experimental data with the Arrhenius equation; inset: temperature discrepancy between fitted model and experiment b) Derived TCR.

Fig. 5 .
Fig. 5. Accuracy analysis a) Raw sensor output of resistance (top) and voltage (bottom) of Bi 2 Se 3 device for an arbitrary measurement sequence b) Reference temperature profile T m,Re f vs. derived temperature profile T m,calibr (top) and accuracy indication (bot) c) Reference heat flux profile Q Re f vs. derived heat flux profile Q calibr (top) and accuracy indication (bot).

Fig. 6 .
Fig. 6.Resolution a) top: resistance response to changing sensor inputs, bottom: corresponding calibrated sensor input based on conversion operations b) top: voltage response to changing sensor inputs, bottom: calibrated sensor input.

TABLE I COMPARISON
OF BI 2 SE 3 SENSITIVITY TO COMMERCIAL LEADED BULK NTC THERMISTORS Fig. 4. Sensitivity analysis for thermoelectric output voltage displaying the voltage-heat flux transfer characteristic; inset: derived sensitivity and linear fitting function in dependence of T m .