  We show that a gap parameter can fully describe the merging of Dirac cones in
semi-Dirac materials from $K$- and $K^\prime$-points into the common $M$-point
in the Brillouin zone. We predict that the gap parameter manifests itself by
enhancing the thermoelectric figure of merit $zT$ as the chemical potential
crosses the gap followed by a sign change in the Seebeck coefficient around the
same point. Subsequently, we show that there is also a trade-off feature
between the maximum power delivered and the efficiency when the chemical
potential crosses the gap parameter. An optimal operating point that minimizes
the power-efficiency trade-off is consequently singled out for the best
thermoelectric performance. Our work paves the way for the use of 2D semi-Dirac
materials for thermoelectric applications.
