Electron Paramagnetic Resonance Studies of a System with Orbital Degeneracy: The Lithium Donor in Silicon

Abstract

Electron-paramagnetic-resonance (EPR) and electron-nuclear double-resonance (ENDOR) spectra are reported for the first time for the isolated interstitial lithium shallow-donor center in silicon. In zero applied stress the EPR spectrum is complicated because of the fivefold orbital degeneracy ($\mathrm{doublet} E+\mathrm{triplet} {T}_{2}$) of the donor ground state which results from the inverted valley-orbit splitting (singlet ${A}_{1}$ higher by 1.8 meV). Below 2.5\ifmmode^\circ\else\textdegree\fi{}K this spectrum contains a number of strongly anisotropic lines, the effective $g$ values of which are all \ensuremath{\gtrsim}2.000 at the experimental frequencies ${\ensuremath{\nu}}_{0}=10, 14, \mathrm{and} 20$ kMc/sec and vary linearly in ${{\ensuremath{\nu}}_{0}}^{\ensuremath{-}2}$. This spectrum is extremely sensitive to small applied stresses; its structure simplifies above 2.5\ifmmode^\circ\else\textdegree\fi{}K as a result of relaxation effects. These features may be accounted for by postulating a very weak spin-orbit interaction (in the range \ensuremath{\sim}0.01 to \ensuremath{\sim}0.05 ${\mathrm{cm}}^{\ensuremath{-}1}$) among the ${T}_{2}$ states and between the $E$ and ${T}_{2}$ states. Also, splittings of these states caused by random crystal strains [(\ensuremath{\sim}1-2) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$] in our samples must be larger than the spin-orbit splitting but smaller than $h{\ensuremath{\nu}}_{0}$. Under strong uniaxial compression along [001] or tension along [110], the EPR spectrum simplifies to a single line having axial symmetry about [001] with ${g}_{\mathrm{II}}=1.9997\ifmmode\pm\else\textpm\fi{}0.0001$, ${g}_{\ensuremath{\perp}}=1.9987\ifmmode\pm\else\textpm\fi{}0.0001$, in agreement now with the predictions of the independent-valley model for a nondegenerate ground state representing the antisymmetric combination of valleys on the $z$ axis. ENDOR spectra of ${\mathrm{Li}}^{7}$, ${\mathrm{Li}}^{6}$, and ${\mathrm{Si}}^{29}$ have been observed under these stress conditions in the range 1.3-4\ifmmode^\circ\else\textdegree\fi{}K and are interpreted in terms of a lifetime-averaged hyperfine interaction of the ${T}_{2}z$ ground state and the lowest excited electronic state (which represents the symmetric combination of the $z$ valleys in the limit of large stress). The ${\mathrm{Li}}^{7}$ hyperfine interaction is found to vary from $\frac{A}{h}\ensuremath{\simeq}0.01$ Mc/sec at 1.3\ifmmode^\circ\else\textdegree\fi{}K to \ensuremath{\sim}0.10 Mc/sec at 4\ifmmode^\circ\else\textdegree\fi{}K, from which data a value $\frac{{A}_{0}}{h}=2.3\ifmmode\pm\else\textpm\fi{}0.5$ Mc/sec is inferred for the hyperfine interaction of the excited singlet state in zero stress. The various parameters of the experimental spectrum are interpreted in terms of effective-mass theory, augmented by the spin-orbit interaction and other necessary refinements of our theoretical model. The EPR data show that the lithium is definitely not in the hexagonal interstitial site, but rather is in the tetrahedral site (or possibly slightly displaced from the tetrahedral site). Analysis of stress dependence of the EPR and ENDOR data gives a value ${\ensuremath{\Xi}}_{u}=+11.4\ifmmode\pm\else\textpm\fi{}1.1$ eV for the deformation-potential parameter of the conduction-band minima.