Exploration and Optimization of Tellurium‐Based Thermoelectrics

The electrical conductivity, σ, is measured via the four‐point probe method (Figure 5.2). Current
is passed through the vertical electrodes (in alternating directions to average – further discussed
in 5.5) while is measured between the horizontal probes, as with . With the maintenance of a
constant, uniform current flow over the area through the length of the pellet, the physical length
between and allows one to observe the electrical potential difference and ascertain the
material’s resistance . With the following three relationships in Equation 5.1, can then be calculated
utilizing Ohm’s law and accurate pellet dimensions:
a
b ∙
Equation 5.1 (a) Ohm's Law (b) Specific resistivity
Figure 5.2 Four‐point probe method.
It should however be noted that practically, the measured voltage ( meas) possesses several
contributions to Ohm’s law (Equation 5.1 (a)): meas wire contact . Instrumentation within the
ZEM ensures that wire contact are minimized to ensure an accurate voltage measurement; this is
compensated for by utilizing an input impedance ≥1 G such that ≫ wire contact. The
aforementioned camera gives the values necessary for the dimensions included in the conductivity
units. This allows for accurate calculation of σ via Equation 5.1 (b).
In a recent two‐step international round‐robin study on n‐ and p‐type Bi2Te3, machines from
seven labs including the Kleinke lab revealed that measurements were not only reproducible on a
measurement‐to‐measurement basis, but also from a lab‐to‐lab basis. Seebeck measurement is the
most precise with a spread of approximately 4 % across the temperature range of 298 K to 573 K.
Measurement of σ was between 10 % and 12.5 % not only because of the measurement itself, but
the added error of measuring pellet dimensions and probe separation. [147] The error bars for the ZEM
plots featured in this work are therefore approximately as large as the displayed points.
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