Why dopant energy levels differ from one material to another? Dopant levels in Si, Ge and GaAs are very different from each other. Even "similar" materials such as Si and Ge exhibit different dopant energy levels.
(source: Pierret, Advanced Semiconductor Fundamentals, 2003)
What makes the energy levels of various dopants be so different when introduced into different materials?
 A: The model for shallow donors is a modification of the Bohr atom: an electron or hole bound to an ion in a medium. The binding energy is less than in hydrogen mostly because it scales with the relative permittivity squared $\varepsilon_r^2$ and with the effective mass ratio:
$$E_b = \frac{m^*/m_e}{\varepsilon_r^2} 13.6 \ {\rm eV}. $$
For silicon $\varepsilon_r = 12$, for germanium $\varepsilon_r = 16$. Effective masses of electrons and holes are smaller in germanium.
A: The dopant level is bound to the atom, and we can think of two different "ionization energies" that exist: one would be to freedom in the semiconductor's conduction band (call this $E_{d}$ - what we are interested in), and a larger one is the energy to complete freedom in the air (call this $E_{free}$). Electrons in the semiconductor can also be excited to complete freedom, this place being called the vacuum potential, and the energy required to do this is the electron affinity (often named $\chi_{s}$). Now, we use the vacuum potential as a global energy reference, so we have:
$E_{d} = E_{free}-\chi_{S}$
For the same dopant atom in different semiconductors, if $E_{free}$ stays relatively constant since it's a property mostly of just the dopant, the different $\chi_{S}$ for each semiconductor will cause $E_{d}$ to be different.
Keep in mind this is a bit of a simplified view for everything occuring in a semiconductor with dopants, but serves as qualitative explanation.
