Breaking the Doping Limit in Silicon by Deep Impurities

n-type doping in $\mathrm{Si}$ by shallow impurities, such as $\mathrm{P}$, $\mathrm{As}$, and $\mathrm{Sb}$, exhibits an intrinsic limit due to the Fermi-level pinning via defect complexes at high doping concentrations. Here, we demonstrate that doping $\mathrm{Si}$ with the deep chalcogen donor $\mathrm{Te}$ by nonequilibrium processing can exceed this limit and yield higher electron concentrations. In contrast to shallow impurities, the interstitial $\mathrm{Te}$ fraction decreases with increasing doping concentration and substitutional $\mathrm{Te}$ dimers become the dominant configuration as effective donors, leading to a nonsaturating carrier concentration as well as to an insulator-to-metal transition. First-principles calculations reveal that the $\mathrm{Te}$ dimers possess the lowest formation energy and donate two electrons per dimer to the conduction band. These results provide an alternative insight into the physics of deep impurities and lead to a possible solution for the ultrahigh electron concentration needed in today’s $\mathrm{Si}$-based nanoelectronics.

Figure 1

(a) The carrier concentration of $\mathrm{Te}$-hyperdoped $\mathrm{Si}$ samples measured by the Hall effect at 300 K as a function of doping concentration. The carrier concentration approaches 10²¹ cm⁻³. Previously published results for $\mathrm{As}$, P, and $\mathrm{Sb}$ heavily doped $\mathrm{Si}$ are also included as references (the error bar represents the difference between reported values). Our results overcome the limit of free-electron concentration (approximately 5–6.5 × 10²⁰ cm⁻³) obtained by the conventional n-type dopants in $\mathrm{Si}$. Saturation in terms of the doping level is not observed within the range of $\mathrm{Te}$ concentrations, which are several orders of magnitude above the solid solubility limit of $\mathrm{Te}$ in $\mathrm{Si}$. (b) The resistivity of PLM-treated $\mathrm{Te}$-hyperdoped $\mathrm{Si}$ samples as a function of doping concentration measured at 300 K. Previous published works for $\mathrm{As}$, P, and $\mathrm{Sb}$ heavily doped $\mathrm{Si}$ are also included as reference. (c) The carrier mobility of PLM-treated $\mathrm{Te}$-hyperdoped $\mathrm{Si}$ samples as a function of doping concentration measured at 300 K.

Figure 2

(a),(b),(c) Angular distributions about the 〈100〉 axes for 1.7 MeV ${\mathrm{He}}^{+}$ scattered from $\mathrm{Te}$ (red circles) and $\mathrm{Si}$ (black squares) for the selected samples with different $\mathrm{Te}$ concentrations. The angular scan of substitutional $\mathrm{Te}$ will overlap with that of $\mathrm{Si}$ as reported. A peak is expected to arise in the middle of the angular scan for interstitial $\mathrm{Te}$ ions. The angular scan of substitutional but slightly displaced $\mathrm{Te}$ atoms is expected to be narrow and shallow. (d) The interstitial fraction of $\mathrm{Te}$ as a function of the concentration as calculated from the angular scan results.

Figure 3

Experimental two-dimensional backscattered-yield patterns of the sample $\mathrm{Te}$-2.5% obtained from RBS-C spectra. The patterns are extracted from the integral backscattering signal from $\mathrm{Te}$ [(a), (c), and (e)] and $\mathrm{Si}$ [(b), (d), and (f)] in the vicinity of the 〈100〉, 〈110〉, and 〈111〉 directions. The patterns for the $\mathrm{Si}$ and the $\mathrm{Te}$ signals match well with each other, indicating that the majority of $\mathrm{Te}$ impurities are substitutional.

Figure 4

(a) Normalized (per atom) formation energy $(\mathrm{\Delta }{E}_F/n_{\mathrm{Te}}^{\mathrm{SC}})$ of an isolated substitutional $\mathrm{Te}$ (circles) and a $\mathrm{Te}$-$\mathrm{Te}$ dimer (diamonds) as a function of $\mathrm{Te}$ concentration, computed via ab initio calculations. Inset: Formation energy of high-symmetry interstitial sites (T and H denoted with squares and stars, respectively) as a function of $\mathrm{Te}$ concentration; lines are a guide for the eye. Ab initio calculations of density of states (DOS) at a $\mathrm{Te}$ concentration x = 1.56% for a single $\mathrm{Te}$ dopant (b) and a ${\mathrm{Te}}_{\mathrm{Si}}$-${\mathrm{Te}}_{\mathrm{Si}}$ dimer (c). The sum of the DOS projections on the $\mathrm{Te}$ atomic orbitals is also displayed. The zero of the energy scales (dashed lines) corresponds to the Fermi energy.

Figure 5

The temperature-dependent conductivity of $\mathrm{Te}$-hyperdoped $\mathrm{Si}$ in the temperature range of 2–300 K. Samples with lower $\mathrm{Te}$ concentrations ($\mathrm{Te}$-0.25% and $\mathrm{Te}$-0.50%) show a strong temperature-dependent conductivity, indicative of the insulating state. Samples with higher concentrations ($\mathrm{Te}$-2.0% and $\mathrm{Te}$-2.5%) exhibit a conductivity comparatively insensitive to temperature down to 2 K, indicating an impurity-mediated transition to the metalliclike state.

Figure 6

The conductivity of sample $\mathrm{Te}$-0.25% as a function of inverse temperature. The red solid lines show the fits of data to Eq. (C3), yielding an activation energy of 46.5 meV.

Figure 7

A sequence of 1.7-MeV $\mathrm{He}$ RBS-C spectra of as-implanted and PLM-treated $\mathrm{Te}$-hyperdoped $\mathrm{Si}$ layers with different $\mathrm{Te}$ concentrations. The inset shows the magnification of random and channeling $\mathrm{Te}$ signals for the as-implanted and PLM-treated layers.

Figure 8

The RBS random spectra and the fitting by the simnra code for sample $\mathrm{Te}$-1.5% before and after the PLM treatment.

Figure 9

The schematic structure of the $\mathrm{Si}$ matrix. (a) The solid black circle represents the impurity atom and the empty black circles stand for the host material atoms. The RBS-C angular scans for an impurity in the $\mathrm{Si}$ host material, at the substitutional site and interstitial site (channel center), are shown in (b) [50]. (c) Positions of major sites in the $\mathrm{Si}$ lattice [hexagonal (H), tetrahedral (T), bond-centered (BC), antibonding (AB), split (SP), DS and DT sites (sites displaced from these high-symmetry sites)], shown in the 110 plane [74].

Figure 10

(a)–(r) The angular scans about the 〈100〉 [(a)–(f)], 〈110〉 [(g)-(l)], and 〈111〉 [(m)–(r)] axes for all the $\mathrm{Te}$-hyperdoped $\mathrm{Si}$ samples. Angular distributions have been normalized in a random direction. The red circles correspond to $\mathrm{Te}$ atoms and black squares to $\mathrm{Si}$; smooth curves are drawn through the symbols.