Thermodynamical limits of diluted (magnetic) semiconductors

The incorporation of transition metal dopants in semiconductors above their solubility limit is the main challenge for the fabrication of diluted magnetic semiconductors. Dietl et al. have predicted the Curie temperature of different p-type conducting semiconductors alloyed with 5 at. % Mn [1]. This work motivated experimental efforts focused on the fabrication of highly diluted magnetic semiconductors. Unfortunately, such highly diluted magnetic semiconductors are metastable alloys and try to reach their thermodynamical equilibrium by the diffusion of the incorporated magnetic dopants leading to spinodal decomposition and secondary phase formation. There exist classical models which describe the kinetics of phase transitions and secondary phase formation for large clusters consisting of 100, 1000 or more atoms. However, electronic properties like carrier concentration strongly depend on the fraction of unclustered dopant atoms. Especially, in diluted magnetic semiconductors the formation of such clusters has to be prevented and growth techniques far from thermodynamical equilibrium are necessary.
Besides the LT-MBE process, the magnetic dopant implantation followed by pulsed laser annealing (PLA) appears to be a promising route for the fabrication of ferromagnetic semiconductors. The fast temperature quenching during PLA suppresses the diffusion of magnetic dopant atoms, i.e. diffusion via random hopping of these dopants is frozen and metastable diluted magnetic semiconductors are formed.
In this contribution we present the results from combined random-walk simulations and heat-flow calculations to describe the initial cluster formation for different magnetic semiconductors being characterized by a large variation of diffusion coefficients of the magnetic dopants. Under the assumption that the de-clustering probability of neighbouring dopants is lower than the clustering probability, we can explain the successful fabrication of GaAs:Mn and the impossibility to fabricate diluted ferromagnetic Si:Mn with LT-MBE or Mn implantation followed by PLA. Especially, our modelling approach can be used to estimate first clustering events during the re-crystallization after PLA. Within this picture, we conclude that for the preparation of diluted ferromagnetic semiconductors the basic diffusion parameters and the room temperature solubility of the magnetic dopants are reasonable parameters to estimate the chance for a successful preparation of different kinds of diluted systems.
[1] T. Dietl et al. Science 287 1019 (2000)