Unlocking extreme doping and strain in epitaxial monocrystalline silicon

Abstract

Hyperdoping, overcoming the solubility limit of dopants in a crystalline semiconductor, is a fertile method for the enhancement of the electrical, structural and optical devices' performances and for the exploration of exotic phases such as superconductivity. We demonstrate an unprecedented control on the dopant concentration and lattice deformation via nanosecond laser doping in epitaxial boron doped silicon, achieving record carrier concentrations (8 at.%) and lattice deformations (3 %). Probing the microscopical hyperdoping limitations, we show that the relevant mechanisms are caught by a simple combinatorial model, which quantitatively explains both the experimental carrier concentration and lattice deformation evolution. First principle calculations complete and support such simple model. Indeed, at the high doping levels now attainable, the maximum carrier concentration is inherently limited by the probability of two or three substitutional dopants occupying neighboring lattice sites, forming partially inactive complexes that we detail. This description is valid in the case of perfect layers with no crystallographic defects and a fully substitutional dopant occupation, highlighting the quality of the epitaxial layers realized.

Figures (5)

• Figure 1: Doping of hyperdoped SiB by GILD: (a) Gas Immersion Laser Doping : (i) chemisorption of (BCl3) gas on the Si surface, (ii) pulsed laser melting inducing a downwards melting front (iii) epitaxial rapid solidification trapping B atoms within the crystalline lattice. (b) SIMS concentration profile of a layer $170\pm5nm$ thick for various number of laser shots N. (c) Atomic concentration $C_B = \frac{D_B}{d}$, with $D_B$ the integrated dose of the SIMS profiles and d the thickness, vs the injected concentration at each laser shot $C_{inj}\sim \frac{D_{surf}\times N}{d}$. The red line highlights the perfect equality between $C_B$ and $C_{inj}$.
• Figure 2: Comparison of the carrier density vs the B atomic concentration achieved by various annealing methods : white crossed squares : RTA solmi1990; black triangles : FLA jain2004yeong2008nishikawa2011do2014; white squares : non-melt NLA earles2004cristiano2016sharp2006; dark grey stars : NCs zhou2015bpatra2019hunter2019 ; grey diamond : MBE glass2000 ; purple circle : GILD (this work). For the latter two doping techniques, filled markers are attributed to pseudomorphic grown layers and unfilled markers to (partially) relaxed layers. The inset image shows a picture of the Hall cross geometry.
• Figure 3: (a) $\mathrm{h(C_B)}$ of hyper-doped SiB layers synthesized by GILD with thickness $d=23$ to $170\,$nm. The vertical dashed lines highlight the 100$\%$ activation concentration range, the onset of strain relaxation and the onset of saturation. As the relaxation onset slightly depends on the thickness, and for clarity, for each series pseudomorphic layers are shown in full circles, relaxed ones in empty circles. The fine black line represents the evolution expected for 100$\%$ activation ($h=C_B$). Four theoretical models are compared to the experiments: the concentrations of B monomers (black dotted line B1, eq.\ref{['eqB1']}) and B monomers and trimers (pink dotted line, B1+B3) expected from a simple binomial model, and the first principle simulations accounting for complexes with 1 to 3 B atoms for the diffusion shell S1 (DFT S1, light blue dotted line) and S1.5 (DFT S1.5, blue line), discussed in sec. \ref{['dft']}. (b) Bright field STEM images on top show: (left) a fully strained pseudomorphic layer, perfectly crystalline with no defects; (middle) a partially relaxed layer with B-poor pile-up regions; (right) a fully saturated layer showing evidence of B aggregates at the interfaces. The B-poor pile-up regions are due to cellular breakdown, where relaxation process induce the appearance of compositional column-shaped defects at high crystallisation rates and high concentrations. (c) Non-active concentration $C_{NA} = C_B - h$ vs total concentration $C_B$ compared to a quadratic power law (dotted black line) and to the expectations of the first principle simulations for complexes with 1 to 3 B atoms and the diffusion shell S1.5 (blue line).
• Figure 4: (a) In-plane lattice parameter $a_{//}$, extracted from both XRD-RSM maps (filled markers) and STEM-GPA images (unfilled markers). (b) Out-of-plane lattice parameter $a_{\perp}$ (XRD-RSM maps only). The red line has a slope of $\sim - 6.5\times10^{-24}\,$nm$\,$cm$^3$. (c) Lattice parameter $a_{SiB}$. The inset shows a closer view over the first $6\times10^{20}cm^{-3}$ and compares this work to MBE vailionis1999sardela1994baribeau1991 and RP-CVD boureau2018hartmann2020 growth techniques. Each data item corresponds to fully activated layers. (d) Difference between the measured lattice parameter and the one expected for a fully monomer concentration, compared to a third power law.
• Figure 5: (a) First-principles simulations of the formation energy of distinct types of charge-neutral B complexes involving 1 to 3 atoms as a function of B doping concentration $C_B$. The probability of each complex is evaluated as a function of its formation energy with Boltzmann weights. Through the calculated complex electrical activity, the expected hole concentration is calculated. (b) Schematic representation - inspired from Ref.luo2003 - of the different B-complexes with the electrical contribution as well as their average formation energy.