= Solution
A hydrogenic donor has the <effective Bohr radius of a hydrogenic donor>
$$
\boxed{a_B^*=\epsilon_r\frac{m_e}{m^*}a_0=80a_0=4.23\,\mathrm{nm},}
$$
using the external $a_0=0.52917721067\times10^{-10}\,\mathrm m$.<CODATA recommended values of the fundamental physical constants 2014 by National Institute of Standards and Technology>[Bohr radius]{ref} Increasing donor density causes donor states to overlap and screens their binding, allowing a metallic impurity system rather than isolated frozen-out donors.
Using the standard approximate <Mott criterion>, $n_D^{1/3}a_B^*\simeq0.25$, gives
$$
\boxed{n_{D,c}\sim\left(\frac{0.25}{a_B^*}\right)^3\simeq2.1\times10^{23}\,\mathrm{m^{-3}}=2.1\times10^{17}\,\mathrm{cm^{-3}}.}
$$
The factor 0.25 is an externally documented empirical criterion, not supplied exam data or an exact universal threshold.<The Mott criterion: So simple and yet so complex by Alexander Pergament and others>[Abstract and discussion of the effective-Bohr-radius criterion]{ref} An order-of-magnitude overlap argument without that prefactor would give $(a_B^*)^{-3}\simeq1.3\times10^{25}\,\mathrm{m^{-3}}$. Compensation, disorder and multivalley anisotropy affect a real material's transition; this estimate uses the scalar mass and permittivity actually supplied, without substituting other germanium parameters.
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