We have developed an automated setup for simultaneous measurement of Seebeck coefficient S(T) and electrical resistivity ρ(T) of thin film samples from room temperature to ∼650 °C. S and ρ are extracted from current–voltage (I-V) measurements obtained using a semiconductor parameter analyzer and temperature measurements obtained using commercial thermocouples. The slope and the x-axis intercept of the I-V characteristics represent the sample conductance G and the Seebeck voltage, respectively. The measured G(T) can be scaled to ρ(T) by the geometry factor obtained from the room temperature resistivity measurement of the film. The setup uses resistive or inductive heating to control the temperature and temperature gradient on the sample. Inductive heating is achieved with steel plates that surround the test area and a water cooled copper pipe coil underneath that generates an AC magnetic field. The measurements can be performed using resistive heating only or inductive heating only, or a combination of both depending on the desired heating ranges. Inductive heating provides a more uniform heating of the test area, does not require contacts to the sample holder, can be used up to the Curie temperature of the particular magnetic material, and the temperature gradients can be adjusted by the relative positions of the coil and sample. Example results obtained for low doped single-crystal silicon with inductive heating only and with resistive heating only are presented.

In electronic materials, the energy exchanges between free charge carriers and the lattice and its environment give rise to thermoelectric phenomena—Seebeck, Peltier, and Thomson effects—that can be utilized for power generation or solid-state cooling. The thermoelectric properties of a material are captured in its Seebeck coefficient (S), a fundamental transport parameter of a material that depends on the specific mechanisms of interaction between the charge carriers and the lattice, impurities, and defects. The Seebeck coefficient is directly related to the Peltier coefficient ∏ (∏ = ST) and Thomson coefficient β (β = TdS/dT).1 The Seebeck effect was discovered in 1821 by Seebeck. A temperature difference ΔT between two points on a material, at a given ambient temperature, leads to a potential difference V0 between the two points. The linear approximation of the relation between V0 and ΔT (valid under small temperature gradients) represents the Seebeck coefficient S of the material at that temperature, S(T) = − V0/ΔT.

Thermoelectric devices used for waste heat recovery (from industrial or automotive processes) typically operate at high temperatures and across large temperature ranges (e.g., automotive catalytic converters thermoelectric generators operate between ∼400 and 800 °C). Some electronic devices such as phase-change memories, in which a nano-volume of a phase-change material is repeatedly melted and re-solidified, also operate at remarkably high and wide temperature ranges (e.g., between room temperature and ∼600 °C for GeSbTe) and under large current densities which make for significant thermoelectric effects. There is also growing interest in using thermoelectric solid state cooling in microelectronic chips. While most thermoelectric characterization has been on bulk materials, there is an increasing need for thermoelectric thin film characterization for new applications and also to understand inherent thermoelectric effects in high-temperature micro/nanoelectronic devices.

The measurement of Seebeck coefficient is simple in concept but not straightforward to implement due to the difficulties in accurately measuring the temperature and voltage at the same location on a sample. High-temperature and thin-film measurements have additional difficulties of maintaining good thermal and electrical contacts while preserving the physical integrity of the samples. High temperature measurements of bulk samples have been reported up to ∼1000 °C2,3 but thin films or device level measurements have been limited to ∼400-500 °C.4,5

In this work, we report the development of an automated setup for simultaneous measurement of Seebeck coefficient and electrical resistivity of thin film samples from room temperature to ∼650 °C based on the differential method with small temperature gradients.6 The temperature and temperature gradients are controlled using resistive or inductive heating. The Seebeck coefficient and electrical resistivity are obtained from current-voltage (I-V) characteristics measured with a semiconductor parameter analyzer and temperature measurements measured with commercial thermocouples.

The measurement setup is shown in Figure 1. The sample holder is a non-magnetic (brass) chuck of 87 mm diameter and 10 mm height, put on top of two steel plates and supported by a high temperature glass-ceramic base. For resistive heating, two cartridge heaters, each of 6.35 mm diameter and 300 W power, are inserted in either side of the chuck and controlled individually using a relay card to heat and establish a temperature gradient in the sample. The distance between the two heaters is ∼70 mm which is large enough to generate a temperature difference of ∼±20 °C by heating one side more than the other. The temperature difference is controlled and stabilized by adjusting the on/off time periods for each heater. For inductive heating, a water cooled copper planar coil positioned underneath the chuck and supported by a motorized stage is used to generate a high frequency (160 KHz) AC magnetic field that heats the steel C-shaped plates surrounding the test area which in turn heats the non-magnetic chuck by direct contact (Fig. 1). The water cooled planar coil was made using spiral copper tube isolated with Kapton tape and can withstand chuck temperatures ∼800 °C. The switching of the inductive heater is controlled through the relay card to achieve the desired sample temperature. The temperature gradient along the sample is adjusted by the position of the coil underneath the chuck. Within a certain range (∼3 cm right or left from the center) the temperature gradient was found to be in direct relation with the number of steps completed by the stepper motor in either direction. To avoid possible interferences and to exclude any magnetic field effects on the sample or probes materials (e.g., bismuth–antimony alloys in thermocouples)7 the inductive heater is turned off through the relay card during each measurement.

FIG. 1.

Schematics of the high-temperature Seebeck coefficient and resistivity measurement setup. Two C-shaped surrounding steel plates form an enclosure for heat confinement and probe arms heating (with either resistive or inductive heating). The top view image shows the probe tip on the surface of the sample centered with the thermocouple probed spot. The actual setup has 4 probe arms and 4 thermocouples so that two samples can be measured at the same time. Resistive or inductive heating can be used. With inductive heating, the non-magnetic chuck (brass alloy) is heated by contact to the steel plate which in turn is heated by the AC magnetic field generated by the water cooled copper pipe coil underneath.

FIG. 1.

Schematics of the high-temperature Seebeck coefficient and resistivity measurement setup. Two C-shaped surrounding steel plates form an enclosure for heat confinement and probe arms heating (with either resistive or inductive heating). The top view image shows the probe tip on the surface of the sample centered with the thermocouple probed spot. The actual setup has 4 probe arms and 4 thermocouples so that two samples can be measured at the same time. Resistive or inductive heating can be used. With inductive heating, the non-magnetic chuck (brass alloy) is heated by contact to the steel plate which in turn is heated by the AC magnetic field generated by the water cooled copper pipe coil underneath.

Close modal

The probe arms are attached to the chuck (not shown) to reduce contact problems due to vibrations. Tapered tungsten probes of 2.4 μm tip radius and 45° angle (Cascade Microtech PTT-24/4-25 tungsten needles) are attached to the probe arms and gently pressed against the surface of the sample to form electrical contacts (Fig. 1). Two omega K-type thermocouples of 0.5 mm diameter tip are clamped laterally to each side of the sample at a distance set using a 10 μm resolution caliper. The electrical probes are then carefully aligned to be centered with the thermocouple probed spots and the distance is checked with the caliper and adjusted to be the same as that between the thermocouples (Fig. 1). For some samples, lithographically patterned metal contacts were also used to set the distance between the probes. A distance of 20 mm between the two sides of the sample is sufficient to achieve a temperature difference ΔT ∼ 10 °C. The L shaped probe arms are screwed to a ceramic glass plate (for electric isolation) then attached to the chuck to minimize the effect of vibrations on the electrical contacts. The signal and ground lines of coaxial cables are then connected directly to the corners of the probe arms.

An I/O USB card is used to obtain the temperature data with a sampling rate of 10 measurements/s. Measurements are performed in a glass enclosed chamber under low vacuum (∼20 kPa) covered by a second glass outer shield with nitrogen flow in between to minimize the oxidation of the chuck, sample, and probe tips (Fig. 2(a)).

FIG. 2.

Photographs of the developed high-temperature Seebeck coefficient and resistivity measurement setup showing the vacuum chamber (a) and the chuck, electrical probes, and thermocouples arrangement, without thermal paste (cleaned to show the alignment between the electrical probes and thermocouples) (b) and with thermal paste to improve adhesion and thermal contact between the thermocouple leads and the chuck (c).

FIG. 2.

Photographs of the developed high-temperature Seebeck coefficient and resistivity measurement setup showing the vacuum chamber (a) and the chuck, electrical probes, and thermocouples arrangement, without thermal paste (cleaned to show the alignment between the electrical probes and thermocouples) (b) and with thermal paste to improve adhesion and thermal contact between the thermocouple leads and the chuck (c).

Close modal

The sample is placed in-between and relatively far from the two cartridge heaters, where the temperature is expected to vary linearly (Fig. 1), and the average temperature of the sample (at which each S(T) point is obtained) is assumed to be the average between the temperatures of the two sides.

The temperature of the probe arms was measured to be ∼18% less than the temperature of the sample, ∼55 °C difference at ∼300 °C. Without the surrounding C-shape heating plates (Figs. 1 and 2(a)), this difference was approximately twice as large. This oven-like heating of the test area (probe arms as well as the thermocouples leads) allows the probe tips temperature to be very close to the sample temperature reducing the error in the measured Seebeck coefficient that arises from the local cooling of the probed spots.

The temperature measurements using the thermocouples were compared to those obtained using a Resistance Temperature Detector (OMEGA RTD) and the difference was approximately 1%. The errors in the measured temperatures provided by the manufacturers are ±0.15 °C at 0 °C for the RTD and ±2.2 °C or 0.75% (whichever is greater) for the K type thermocouple.8 The melting points of tin/lead alloy (188 °C) and GST (585 °C) were also used to verify the measured temperature values and found to be in good agreement (within ±1.5 °C).

The voltage measurements are taken at the thin film surface whilst the temperature is measured at the chuck surface. This temperature difference however is not expected to be significant since the samples are very thin compared to the chuck (∼500 μm thick substrate and ∼1 cm thick chuck) and are pressed against the chuck surface. Heat transfer simulations using finite element solver COMSOL Multiphysics show that the difference in temperature between the surface of the chuck and the surface of the sample (δT) is very small, less than 5 × 10−3 °C up to 650 °C (Fig. 3). The heat source was set at the bottom of the C-shaped surrounding plates (Fig. 3 top inset). The temperature difference δT increases with increasing chuck temperature; however, it is negligible compared to the thermocouples’ error.

FIG. 3.

COMSOL simulation results for the difference in temperature between the surface of the chuck and the surface of the sample as a function of chuck temperature. The temperature values were obtained 60 s after setting the heat source temperature. Top-left inset shows the cross section of the setup showing the heat sources at the bottom of each C-shaped steel plate. To simulate the experimental conditions, the test area is surrounded by a box filled with nitrogen with surface-to-ambient radiating boundaries set to room temperature.

FIG. 3.

COMSOL simulation results for the difference in temperature between the surface of the chuck and the surface of the sample as a function of chuck temperature. The temperature values were obtained 60 s after setting the heat source temperature. Top-left inset shows the cross section of the setup showing the heat sources at the bottom of each C-shaped steel plate. To simulate the experimental conditions, the test area is surrounded by a box filled with nitrogen with surface-to-ambient radiating boundaries set to room temperature.

Close modal

The measurements can be performed using resistive heating only to cover the low temperature range (30–200 °C) since it results in larger ΔTs or inductive heating only for higher temperatures (above 200 °C) since it offers more power to achieve higher temperatures. Combination of both resistive heating and inductive heating allows reliable measurements across a wide temperature range. The particular geometry and materials used for inductive heating in our setup allow chuck temperatures to reach ∼800 °C. At lower temperatures larger temperature gradients are obtained with the resistive heaters, whereas at higher temperatures with inductive heating. Both inductive heating and resistive heating are controlled using a temperature regulation algorithm (Fig. 4) to achieve the target temperature and temperature gradient while minimizing overshoots. In our case, below 80% of the target temperature, the heaters run at maximum power; after 80%, the power is reduced to limit overshoot and is turned off when 99% of the target temperature is reached to reduce the environmental noise on the measurements at the target temperature.

FIG. 4.

Algorithm for temperature control in our setup. When inductive heater is used alone, ΔT is generated by moving the coil right or left. When the inductive heater is used along with cartridge heaters, the coil is fixed in the center and ΔT is generated by adjusting the on/off cycles of the two resistive heaters.

FIG. 4.

Algorithm for temperature control in our setup. When inductive heater is used alone, ΔT is generated by moving the coil right or left. When the inductive heater is used along with cartridge heaters, the coil is fixed in the center and ΔT is generated by adjusting the on/off cycles of the two resistive heaters.

Close modal

The temperature difference between the two points on the sample is adjusted to cover the −10 °C to +10 °C range in small steps to determine the Seebeck coefficient based on many (ΔT, ΔV) points (Fig. 6(b)). I-V characteristics are acquired around the target temperature to obtain the resistance and Seebeck coefficient as the open-circuit voltage (x-axis intercept). The control and data acquisition for the electrical and temperature measurements are performed using a LabVIEW interface.

FIG. 6.

(a) R(T), resistance vs. temperature and (b) S(T), Seebeck coefficient versus temperature, obtained for the single-crystal low-doped silicon sample (n-type, phosphorous, n = (7.4 ± 0.3) × 1015 cm−3 and mobility μ = 1310 ± 24 cm2/V s) using resistive heating only and inductive heating only. Solid lines in (b) are the calculated S-T curves for n-type single-crystal silicon with carrier density n = 7.35 × 1015 cm−3 for scattering factor r varying from −0.5 (lattice scattering dominated) to 0.5 (impurity scattering dominated).1,11

FIG. 6.

(a) R(T), resistance vs. temperature and (b) S(T), Seebeck coefficient versus temperature, obtained for the single-crystal low-doped silicon sample (n-type, phosphorous, n = (7.4 ± 0.3) × 1015 cm−3 and mobility μ = 1310 ± 24 cm2/V s) using resistive heating only and inductive heating only. Solid lines in (b) are the calculated S-T curves for n-type single-crystal silicon with carrier density n = 7.35 × 1015 cm−3 for scattering factor r varying from −0.5 (lattice scattering dominated) to 0.5 (impurity scattering dominated).1,11

Close modal

A small temperature difference (−10 °C < ΔT < 10 °C) between two points B and C on a semiconductor as depicted in Figure 1 will lead to a potential difference,

VBC=STBTC,
(1)

where S is the Seebeck coefficient of the semiconductor and TB and TC are the temperatures at the contacts at points B and C, respectively. The measured voltage V also includes the potentials generated within the metal conductors,

V=VAB+VBC+VCD.
(2)

Since the two conductors are of the same material

V=SmT0TB+STBTC+SmTCT0,
(3)
V=SmTCTB+STBTC,
(4)

where T0 is the ambient temperature at A and D. Since the Seebeck coefficient of most metals is on the order of few μV/K, much smaller than that of semiconductors, typically on the order of few hundred μV/K,9 the metal Seebeck voltage term in (4) can usually be neglected and the semiconductor Seebeck coefficient is given by

V=STBTC.
(5)

The error introduced by neglecting the metals’ Seebeck voltage is usually less than 1%.2 The average temperature and the temperature gradient are given by Tavg = (TB + TC)/2 and ΔT = TB − TC.

Figures 5 and 6 show example results obtained for a sample of single crystal low doped silicon (n-type, Phosphorous) with carrier density n = (7.4 ± 0.3) × 1015 cm−3 and mobility μ = 1310 ± 24 cm2/V s as obtained from our room temperature Hall measurements done on a homemade 4 probe measurement setup. The measured electron mobility and carrier concentration results are in good agreement with the measured and calculated data reported by Masetti et al.10 Particular data shown here is for 500 μm thick sample used for comparison with the available literature data. The sample was annealed at 620 °C for 15 min prior to the measurements. The I-V characteristics obtained with the semiconductor parameter analyzer at each temperature and temperature gradient provide us with the resistance of the sample and the open-circuit Seebeck voltage (Fig. 5(a), for T = 200 °C and Fig. 5(b), for T = 500 °C), simultaneously. The I-V characteristics were obtained for ΔTs between −10 °C and 10 °C, at each average temperature (from room temperature up to ∼600 °C when the electrical contacts were lost). When using inductive heating only, and at lower temperatures (up to ∼200 °C), moving the inductive coil right and left led to max ΔT of ∼±5 °C across the sample (Fig. 5(c), inductive heating) and resulted in higher fluctuations in S(T) data in this region (Fig. 6(b)).

FIG. 5.

Example data obtained for a single-crystal low-doped silicon sample (n-type, Phosphorous, n = (7.4 ± 0.3) × 1015 cm−3 and mobility μ = 1310 ± 24 cm2/V s) using resistive heating only and inductive heating only. The sample was annealed at 620 °C for 15 min prior to the measurements. I-V characteristics from which the resistances and open-circuit voltages are obtained, at 200 °C (a) and at 500 °C (b). Open-circuit voltage versus temperature difference at T = 200 °C (c) and at T = 500 °C (d) to obtain the Seebeck coefficient.

FIG. 5.

Example data obtained for a single-crystal low-doped silicon sample (n-type, Phosphorous, n = (7.4 ± 0.3) × 1015 cm−3 and mobility μ = 1310 ± 24 cm2/V s) using resistive heating only and inductive heating only. The sample was annealed at 620 °C for 15 min prior to the measurements. I-V characteristics from which the resistances and open-circuit voltages are obtained, at 200 °C (a) and at 500 °C (b). Open-circuit voltage versus temperature difference at T = 200 °C (c) and at T = 500 °C (d) to obtain the Seebeck coefficient.

Close modal

Although using the slope of the I-V characteristic avoids the error in the calculated sample resistance due to probe tip-sample Peltier contributions (y-axis intercept) the contact resistances between the tips and the sample still introduce a small error in the resistance especially if the conductivity of the sample is very high. This series contact resistance can be found and subtracted from the total resistance by repeating the measurements with different probe distances (not done here). The errors in the linear fit parameters (slope and intercept) are taken into account for error propagation to obtain the error in S. The variation of V0 versus ΔT at 200 °C and 500 °C are shown in Figures 5(c) and 5(d). The open circuit voltages measured directly with an Agilent 34401A multimeter were found to be in good agreement with the x-intercepts of the I-V characteristics obtained with the parameter analyzer (±0.05 mV). The slope obtained from a linear fit of the open-circuit voltage V0 versus the temperature gradient gives the Seebeck coefficient. The procedure is repeated at different average temperatures to obtain the temperature dependent resistance R(T) and Seebeck coefficient S(T) (Fig. 6). The error bars on S in the S-T graph correspond to the standard error of the slopes of the linear fits of V0 vs. ΔT data while the error bars on R in the R(T) graph correspond to the standard deviation of the slopes obtained from multiple I-Vs at the target temperature (∼50 I-Vs at lower temperatures and at least 23 I-Vs at 400 °C and above). The error bars on T in both the R(T) and S(T) graphs correspond to the standard deviation of the temperature data at each target average temperature (∼0.65% of the mean value). The sudden jump in the R(T) characteristic observed at ∼300 °C with inductive heating (Fig. 6(a)) is likely due to a change in the contact resistance as the measurement was interrupted at this temperature. Changes in the contact resistance with temperature do not affect the S(T) characteristics since S is obtained from the open-circuit voltages across the sample.

The measurement speed is limited by the temperature regulation algorithm and the number of data points to be taken around each target temperature which depend on the acceptable tolerance for temperature overshoots and errors in the obtained S and T. With our current temperature regulation algorithm, the measurement progresses slower at low temperatures because of the thermal inertia of the chuck. The example measurements presented here took ∼9 h using resistive heating only and ∼11 h using inductive heating only. The R(T) characteristics can be scaled to resistivity versus temperature by the geometry factor of the sample which can be obtained at room temperature using the Van der Pauw technique for the measurement of resistivity.12 

We have developed a high temperature setup for measurement of Seebeck coefficient and electrical resistivity of thin-film samples based on simultaneous extraction of resistance and open-circuit voltages from current-voltage measurements obtained with a semiconductor parameter analyzer and using inductive or resistive heating. Two C-shaped steel plates—heated inductively or by direct contact with a resistively heated chuck—surround and create an oven-like heating of the test area. The measurements are performed under low vacuum to reduce oxidation. The setup allows heating up to ∼800 °C but currently the electrical contacts are limiting the measurements to ∼620-650 °C.

A main source of error in Seebeck coefficient measurements is the difference between the temperature of the points where temperature and voltage are measured. In our setup, since the thermocouple tips are clamped to the chuck surface, this difference corresponds to the difference between the temperature of the top and bottom surfaces of the sample at a given location on the chuck and does not affect the temperature difference used to calculate the Seebeck coefficient (although it introduces a negligible shift in the average temperature for 500 μm thick wafer substrates). Another major source of error in Seebeck measurements is the cooling of the voltage measurement point by the measurement probe (cold-finger effect) which is minimized in our setup by heating the surrounding environment using the C-shaped plates and also by using very small (2.5 μm radius) probe tips to measure the voltage. The systematic error of a voltage offset at ΔT = 0 noticed during high temperature measurements (also observed by others and still not well understood)13,3 is avoided by using a linear fit of V0 vs. ΔT for a large number of points. Standardization and calibration of the thermocouples can further reduce errors and improve the accuracy of the measurements.

Inductive heating delivers more uniform heating of the test area (through even heating of the surrounding C-shaped steel plates, versus contact heating for resistive heating), requires no contacts which reduces the wiring to the chamber considerably, can be used up to the Curie temperature of the magnetic material used, and the thermal gradients can be adjusted by moving the coil with respect to the chuck. Although with our particular inductive heating setup small temperature gradients in one of the directions could not be achieved, different geometries and materials can in principle be used to obtain the desired heating characteristics.

This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-FG02-10ER46774. Lhacene Adnane and Nicholas Williams were also supported by the U.S. Department of Education through a GAANN Fellowship (Graduate Assistance in Areas of National Need).

1.
G. S.
Nolas
,
J.
Sharp
, and
J.
Goldsmid
,
Thermoelectrics: Basic Principles and New Materials Developments
(
Springer Science & Business Media
,
2001
).
2.
Z.
Zhou
and
C.
Uher
,
Rev. Sci. Instrum.
76
,
023901
(
2005
).
3.
S.
Iwanaga
,
E. S.
Toberer
,
A.
LaLonde
, and
G. J.
Snyder
,
Rev. Sci. Instrum.
82
,
063905
(
2011
).
4.
S. R.
Sarath kumar
and
S.
Kasiviswanathan
,
Rev. Sci. Instrum.
79
,
024302
(
2008
).
5.
J.
Ravichandran
,
J. T.
Kardel
,
M. L.
Scullin
,
J.-H.
Bahk
,
H.
Heijmerikx
,
J. E.
Bowers
, and
A.
Majumdar
,
Rev. Sci. Instrum.
82
,
015108
(
2011
).
6.
R. R.
Heikes
and
R. W.
Ure
,
Thermoelectricity: Science and Engineering
(
Interscience Publishers
,
1961
).
7.
R.
Wolfe
and
G. E.
Smith
,
Appl. Phys. Lett.
1
,
5
(
1962
).
8.
See www.omega.com for information about OMEGA K type thermocouples and RTDs.
9.
K.
Seeger
,
Semiconductor Physics: An Introduction
(
Springer Science & Business Media
,
2004
).
10.
G.
Masetti
,
M.
Severi
, and
S.
Solmi
,
IEEE Trans. Electron Devices
30
,
764
769
(
1983
).
11.
G.
Bakan
,
N.
Khan
,
H.
Silva
, and
A.
Gokirmak
,
Sci. Rep.
3
,
2724
(
2013
).
12.
L. J.
Van der Pauw
, “
A method of measuring the resistivity and Hall coefficient on lamellae of arbitrary shape
,”
Philips Tech. Rev.
20
,
220
224
(
1958
).
13.
J.
Martin
,
T.
Tritt
, and
C.
Uher
,
J. Appl. Phys.
108
,
121101
(
2010
).