  We have measured diffusion thermopower in a two-dimensional electron gas at
low temperature ($T$=40 mK) in the field range 0 $<B<$ 3.4 T, by employing the
current heating technique. A Hall bar device is designed for this purpose,
which contains two crossing Hall bars, one for the measurement and the other
used as a heater, and is equipped with a metallic front gate to control the
resistivity of the areas to be heated. In the low magnetic field regime
($B\leq$ 1 T), we obtain the transverse thermopower $S_{yx}$ that
quantitatively agrees with the $S_{yx}$ calculated from resistivities using the
generalized Mott formula. In the quantum Hall regime ($B\geq$ 1T), we find that
$S_{yx}$ signal appears only when both the measured and the heater area are in
the resistive (inter-quantum Hall transition) region. Anomalous gate-voltage
dependence is observed above $\sim$1.8 T, where spin-splitting in the measured
area becomes apparent.
