  We consider the energy complexity of the leader election problem in the
single-hop radio network model, where each device has a unique identifier in
$\{1, 2, \ldots, N\}$. Energy is a scarce resource for small battery-powered
devices. For such devices, most of the energy is often spent on communication,
not on computation. To approximate the actual energy cost, the energy
complexity of an algorithm is defined as the maximum over all devices of the
number of time slots where the device transmits or listens. Much progress has
been made in understanding the energy complexity of leader election in radio
networks, but very little is known about the trade-off between time and energy.
  $\textbf{Time-energy trade-off:}$ For any $k \geq \log \log N$, we show that
a leader among at most $n$ devices can be elected deterministically in $O(k
\cdot n^{1+\epsilon}) + O(k \cdot N^{1/k})$ time and $O(k)$ energy if each
device can simultaneously transmit and listen, where $\epsilon > 0$ is any
small constant. This improves upon the previous $O(N)$-time $O(\log \log
N)$-energy algorithm by Chang et al. [STOC 2017]. We provide lower bounds to
show that the time-energy trade-off of our algorithm is near-optimal.
  $\textbf{Dense instances:}$ For the dense instances where the number of
devices is $n = \Theta(N)$, we design a deterministic leader election algorithm
using only $O(1)$ energy. This improves upon the $O(\log^* N)$-energy algorithm
by Jurdzi\'{n}ski et al. [PODC 2002] and the $O(\alpha(N))$-energy algorithm by
Chang et al. [STOC 2017]. More specifically, we show that the optimal
deterministic energy complexity of leader election is
$\Theta\left(\max\left\{1, \log \frac{N}{n}\right\}\right)$ if the devices
cannot simultaneously transmit and listen, and it is $\Theta\left(\max\left\{1,
\log \log \frac{N}{n}\right\}\right)$ if they can.
