Infrared absorption cross sections, and oscillator strengths of interstitial and substitutional double donors in silicon

Infrared absorption cross sections and corresponding oscillator strengths of several intracenter transitions of double donors in silicon, interstitial magnesium (Mg; group IIA) and substitutional chalcogens (Ch = S; Se; group VI), were determined for impurity densities in the ranges $1\times {10}^{14}–1.6\times {10}^{15}\mathrm{atoms}/\mathrm{c}{\mathrm{m}}^3$ for Mg and $2\times {10}^{13}–2\times {10}^{16}\mathrm{atoms}/\mathrm{c}{\mathrm{m}}^3$ for chalcogens. The concentrations of electrically active atomic and diatomic donor centers were derived from the Hall effect measurements. The experimental integrated cross sections were obtained from low-temperature impurity absorption spectra. The oscillator strengths of related donor transitions were derived and compared with those for shallow single donors in silicon, both determined experimentally and predicted theoretically. The transitions of oscillator strengths of double donors follow the decreasing trend with decreasing radius of donor ground states and increasing an impurity binding energy.

Figure 1

Examples of temperature dependences of a free electron concentration in Si samples doped by chalcogens and magnesium. The dots are experimental data, the solid lines are calculated fitting curves. The lowest (black) concentration values in all tables on the right side indicate the residual dopant in the original Si crystals, before the diffusion doping. D, A stay for shallow (single-electron) donor and acceptor centers, respectively.

Figure 2

An example of treatment of a sample absorption spectrum for reduction of the two-phonon absorption band (TPA, $>700\mathrm{c}{\mathrm{m}}^{–1}$) overlapping with Mg neutral donor intracenter transitions in Si: (a) transmission spectrum of the Si:Mg no. 158-1 sample. Inset: Interferogram of the spectrum; (b) absorption spectra of Mg-doped and undoped Si samples, shifted for a better view; (c) a difference spectrum of the Si:Mg sample after subtracting the spectrum of undoped Si.

Figure 3

Examples of calibrated absorption spectra for samples with multiple donor centers in Si: (a) Si:Mg no. 85-3, neutral Mg* and ${Mg}^0$ double donors; (b), (c) Si:Se no. 42-06, neutral atomic and diatomic selenium double donors; (d), (e) Si:S no. 66-8b, neutral atomic and diatomic sulfur double donors.

Figure 4

Experimental dependences of integrated absorption for the two most intense intracenter transitions (from the ground state into $2p_0$ and $2p_{\pm }$ states) of neutral double donors in Si on concentrations of the centers (a), (b) selenium-doped Si; (c), (d) sulfur-doped Si; (e), (f) magnesium-doped Si. Note that the concentration of the Mg* center was estimated using the general trend for the oscillator strength dependences on the double donor transition energy [see Figs. 5 and 5] and using either sum of multiple transitions into the $2p_0$ or $2p_{\pm }$ ${\mathrm{Mg}}^{*}$ states. It is given for the reference purpose only, not for the accurate derivation of the Mg* parameters. The dashed lines are the best fit by eye to the experimentally derived data points.

Figure 5

Experimental (exp) and theoretical (th) dependences of oscillator strengths and their ratios for most intense intracenter transitions (from the ground center state into $2p_0$, $2p_{\pm }$ and $3p_{\pm }$ states) of double (DD) and single (D) donors in Si: (a), (b) on optical density of samples, as well as on the transition energy (c)–(f), in comparison with the transition intensities in absorption spectra of Si:Mg no. 158 (e) and Si:Se no. 42-10a (f) samples. Experimental data for single donors [D exp in (c), (d)]: pink (open and hollow) are from Refs. [41, 42], respectively; green – this work. Lorentzian fits for the overlapping transitions pairs (the lower energy into the $2p_{\pm }$ and $3p_0$ states and the higher energy of $4p_0$ and $3p_{\pm }$) are shown.