Systematics of the activation energies for all the x-levels of group IIIB acceptors in silicon and germanium

A number of essential findings are presented here for the first time. Lyman-like empirical equations are presented, which successfully determined the activation energies of all the x-levels related to a Group IIIB acceptor doped into silicon or germanium crystals. For any two Group III element dopants with known activation energies, EA and EB, and where EA > EB, these equations determine exactly the activation energies of the four x-level acceptors of atom A. In addition, these equations correctly determined that the energy difference between adjacent x-levels of atom A is aways equal to the constant ED = (EA − EB)/2, where ED is equal to the activation energy loss per carbon atom that has bonded with acceptor A. Parameter ED governs all the systematics of x-levels. An important relationship discovered in this work is that the activation energy equation, EAxx = EB, is true. Discovery of this equation demonstrates for the first time that important relationships exist between the acceptors produced by different Group IIIB atoms. Employing the relationship EAxx = EB also means that ED = (EA − EAxx)/2 is true. As a result of this important fact, x-levels in crystals doped only by atom A, contrary to popular opinion, can form atom A’s x-levels when there is only unintended carbon atoms and even though no B atoms are present in the crystals. This fact has been repeatedly documented experimentally. That EAx occupies an energy level, which is equal to the mean of EA and EB, and that EAx does not depend on the existence of EB indicate that its activation energy may just be equal to a pre-existing energy level, which reveals itself via the mean rule calculation because it is a pre-existing energy level of a correlated set of the possible energy levels of the semiconductor crystal. The set of equations introduced herein was also utilized differently to successfully identify nine previously reported unidentified x-level acceptors seen in doped Ge and Si. Some of those identified were two and three carbon atom x-levels, a possibility authenticated here for the first time. A three-carbon atom x-level is identified in boron-doped germanium with an activation energy of EBoronxxx = 9.99 meV where EBoron = 10.47 meV. A two- and a three-carbon atom x-level were identified in gallium-doped silicon with activation energies of EGaxx = 42.7 meV and EGaxxx = 27.3 meV. For reference, literature values of EGax = 57 meV and of EGa = 72.7 meV are provided for a comparison. Note that the larger the number of carbon atoms an x-level contains, the smaller its activation energy. This may explain the many unidentifiable very shallow energy levels reported in the scientific literature.