= Solution
In a weakly doped <n-type semiconductor>, the mobile <electrons> occupy states near the bottom of the <conduction band>. Their local band curvature is positive, so \b[their <band effective mass> is positive and approximately constant sufficiently near that minimum]. For the usual $\beta<0$ convention, expand about $k=0$:
$$
E_k\simeq\alpha+2\beta-\beta a^2k^2,
\qquad
\boxed{m_e^*\simeq\frac{\hbar^2}{2|\beta|a^2}>0.}
$$
Stronger overlap gives larger $|\beta|$, greater curvature and a smaller <mass> within this model. Positive $\beta$ simply places the minimum at the zone boundary and again gives a positive edge <mass>. A negative <electron mass> near a band maximum instead motivates the positive-mass <electron hole> description; it is not the usual conduction-edge situation for an <n-type semiconductor>. No numerical comparison with $m_e$ follows without values of $a$ and $\beta$.
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