= Solution
Ordinary doped <semiconductor devices> need a regime where their <donor impurities> or <acceptor impurities> supply mobile <charge carriers> while intrinsic thermal excitation remains sufficiently small.
At low <temperature>, <donor impurities> or <acceptor impurities> may no longer be ionized. <Dopant freeze-out> reduces the <carrier density>, raises <electrical resistance> and changes the intended <carrier injection> and <p-n junction> response. At high <temperature> the <intrinsic carrier concentration> grows as
$$
\boxed{n_i\propto T^{3/2}e^{-E_g/(2k_BT)}}
$$
when <band effective masses> and <band gap> are treated as constant. Once it becomes comparable with the net doping density, it overwhelms the intended electron-hole imbalance; reverse leakage and dissipation increase and useful p/n control is lost.
The usual operating window lies between freeze-out and intrinsic conduction, with mobility and thermal management placing further practical limits. This is a statement about conventional doped-device operation, not a fundamental prohibition on engineered cryogenic or wide-bandgap devices.
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