Spectroscopy of the solid-state analogues of the hydrogen atom: donors and acceptors in semiconductors

Abstract

Under suitable circumstances imperfections in semiconductors can bind electrons (holes) with a binding energy small compared to the intrinsic energy gap of the host; the wavefunctions characterising the energy levels of the imperfection are extended over many lattice spacings. This review discusses the electronic energy levels of chemical impurities in the classic group IV elemental and the 111-V and 11-VI compound semiconductors. The large dielectric constant of the host, the anisotropic effective mass tensor and/or the small effective mass of the charge carrier are the factors which play a significant role in the description of the electronic energy levels; they can be viewed as scaled-down versions of the hydrogen atom with bound states having binding energies orders of magnitude smaller than those of the hydrogen atom. In this review we present the experimental results on the spectroscopy of donors and acceptors in semiconductors together with the theory necessary for their interpretation. We discuss the experimental results and the theory of the bound states of impurities in the context of the symmetry and the effective-mass parameters of the band extrema with which they are associated. Effects of external perturbation-piezo-and magneto-spectroscopy-are presented both from experimental and theoretical points of view. The review concludes with the experimental observations on the linewidths of the excitation spectra of donors and acceptors in semiconductors and an analysis of the causes underlying them.

Isotope effect on the lifetime of the 2p0state in phosphorus-doped silicon

“…1(a) ). 19 The 1s state splits into 1s(A 1 ) singlet, 1s(T 2 ) triplet, and 1s(E) doublet states, with the 1s(E) and 1s(T 2 ) states close to what is predicted by EMT and the 1s(A 1 ) ground state significantly lower. The decay of an electron is controlled by phonon-assisted relaxation and at a low temperature strongly depends on the energy gap to the nearest lower state.…”

Far infrared fourier transform spectroscopy of semiconductors

“…PTIS revealed a second hydrogenic set of lines increasing in strength with increasing sample temperature. Under uniaxial stress the lines of both series did not split as expected for shallow acceptors [1]. This unexpected behavior meant that the shallow acceptors could not be explained with effective mass theory and the band structure near ... k = 0 alone, but that an extra degree of freedom was required to model these centers.…”

“…The fifth valence electron of phosphorus is not required for bond formation with the four Si neighbors and it is bound with an energy of only 45.59 meV to the positive phosphorus core [1]. In an analogous manner, aluminum in a substitutional position forms a shallow acceptor binding a hole with an energy of 70.18 meV.…”

“…The we11-known equation for the groundstate binding energy of the hydrogen atom is modified by introducing the relative dielectric constant £r and by replacing free electron mass with the effective mass m*. The binding energy E of a "hydrogenic" system is: * E = = 13.6 eV _m __ 2 £r mo (1) and the Bohr radius becomes: semiconductor has a value > 10 which leads to a reduction of Eh d by y rogen more than two orders of magnitude. The effective mass, which needs to be appropriately averaged over all it-space directions, can be smaller than the free electron mass by factors of more than 3, further reducing E. The binding energies of hydrogenic donors and acceptors in Si, Ge,and GaAs range from a few meV to -100 meV or in wave numbers from about 10 cm-1 to 1000 cm-1 .…”

“…A comprehensive modern review of the hydrogen analogue in semiconductors, the shallow donors and acceptors ,has been written by Ramd~s and Rodriguez [1]. Here I simply summarize those major features of shallow levels which are important for the understanding of impurity spectra.…”