Temperature-dependent $^{29}\mathrm{Si}$ incorporation during deposition of highly enriched $^{28}\mathrm{Si}$ films

Temperature-dependent ${}^{29}{Si}$ incorporation during deposition of highly enriched ${}^{28}{Si}$ films

K. J. Dwyer, H. S. Kim, D. S. Simons, and J. M. Pomeroy

Phys. Rev. Materials 1, 064603 – Published 16 November 2017

Abstract

In this study, we examine the mechanisms leading to ${}^{29}{Si}$ incorporation into highly enriched ${}^{28}{Si}$ films deposited by hyperthermal ion beams at elevated temperatures in the dilute presence of natural abundance silane $({SiH}_{4})$ gas. Enriched ${}^{28}{Si}$ is a critical material in the development of quantum information devices because ${}^{28}{Si}$ is free of nuclear spins that cause decoherence in a quantum system. We deposit epitaxial thin films of ${}^{28}{Si}$ enriched in situ beyond 99.999 98% ${}^{28}{Si}$ onto Si(100) using an ion-beam deposition system and seek to develop the ability to systematically vary the enrichment and measure the impact on quantum coherence. We use secondary ion mass spectrometry to measure the residual ${}^{29}{Si}$ isotope fraction in enriched samples deposited from $\approx 250^{\circ} C$ up to 800 °C. The ${}^{29}{Si}$ isotope fraction is found to increase from $< 1 \times 10^{- 6}$ at the lower temperatures, up to $> 4 \times 10^{- 6}$ at around 800 °C. From these data, we estimate the temperature dependence of the incorporation fraction $s$ of ${SiH}_{4}$ , which increases sharply from about $2.9 \times 10^{- 4}$ at 500 °C to $2.3 \times 10^{- 2}$ at 800 °C. We determine an activation energy of 1.00(8) eV associated with the abrupt increase in incorporation and conclude that below 500 °C, a temperature-independent mechanism such as activation from ion collisions with adsorbed ${SiH}_{4}$ molecules is the primary incorporation mechanism. Direct incorporation from the adsorbed state is found to be minimal.

Received 28 July 2017

DOI:https://doi.org/10.1103/PhysRevMaterials.1.064603

Physics Subject Headings (PhySH)

Adsorption Quantum computation

Semiconductors Thin films

Chemical vapor deposition Focused ion beam Molecular beam epitaxy Secondary ion mass spectrometry

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

K. J. Dwyer

Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20740, USA National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8423, USA

H. S. Kim

Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20740, USA and National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8423, USA

D. S. Simons

National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8371, USA

J. M. Pomeroy^*

National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8423, USA

^*joshua.pomeroy@nist.gov

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Vol. 1, Iss. 6 — November 2017

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Figure 1
Semilog SIMS depth profile of the 502 °C sample showing the isotope fractions $({}^{z}{Si} / {Si}_{tot})$ of ${}^{28}{Si}$ (circles), ${}^{29}{Si}$ (squares), and ${}^{30}{Si}$ (triangles). The sharp increase in ${}^{29}{Si}$ and ${}^{30}{Si}$ isotope fractions to the natural abundance levels (dotted lines) at 300 nm corresponds to reaching the substrate (gray shade). The average isotope fractions (from 40 to 280 nm) are shown as dashed lines. These averages lie below the visible data because many of the data were zero counts.
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Figure 2
Correlation plot of isotope fractions from SIMS vs ${SiH}_{4}$ flux ratio $d = F_{g} / F_{i}$ shown on a log-log scale for samples deposited at room temperature $(\approx 21^{\circ} C)$ ; ${}^{29}{Si}$ (squares) and ${}^{30}{Si}$ (triangles). The top axis is the flux ratio for the total gas flux during deposition. The gas sticking deposition model $c_{z}$ is fit to the ${}^{29}{Si}$ and ${}^{30}{Si}$ data (solid and dashed line respectively) and gives a value of $s = 6.8 (3) \times 10^{- 4}$ . $c_{z}$ is linearly proportional to $s$ over the range of the data, but asymptotes (see inset) to the natural abundance values when $F_{g} ≫ F_{i}$ (dash-dotted lines). To demonstrate the sensitivity to changes in the free parameter $s$ , $c_{30}$ for two other values of $s$ (blue dotted lines) are also shown. “LP” and “HP” denote data from two different experimental configurations; only the LP data are used for quantitative analysis. Horizontal error bars are dominated by the uncertainty in the pressure measurements, and vertical error bars represent the standard deviation of the SIMS data.
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Figure 3
${}^{29}{Si} / {}^{30}{Si}$ isotope ratios for samples deposited at room temperature (circles) and elevated temperatures (triangles). The ratios of these samples agree with the natural abundance ratio of 1.5 (line) indicating that the source of ${}^{29}{Si}$ and ${}^{30}{Si}$ is naturally abundant, probably the ${SiH}_{4}$ gas. Measurement numbers 28, 31, and 36, which lie above a ${}^{29}{Si} / {}^{30}{Si}$ ratio of 4, suffer from discrete counting noise in the SIMS measurements due to a total ${}^{30}{Si}$ count $< 10$ , which makes the ratio highly volatile. Error bars are derived from the standard deviation of the SIMS data.
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Figure 4
Adjusted isotope fraction $c_{z} (s_{T}^{n}, d_{502})$ vs temperature for ${}^{29}{Si}$ (squares) and ${}^{30}{Si}$ (triangles). The raw isotope fractions are adjusted to the deposition conditions $(F_{g}$ and $F_{i})$ of the 502 °C sample to account for differences in pressure and deposition rate among different samples. This shows the expected increase in isotope fraction at a given temperature for a sample deposited under the same conditions as the 502 °C sample. Horizontal error bars are due to uncertainty in the pyrometer calibration and temperature fluctuation during deposition, and vertical error bars represent the standard deviation of the SIMS data.
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Figure 5
Correlation plots of the generalized isotope fractions $({}^{z}{Si} / {Si}_{tot}) / a_{z}$ vs ${SiH}_{4}$ flux ratio shown on a linear scale for samples deposited at several elevated temperatures. The raw SIMS isotope fractions for ${}^{29}{Si}$ and ${}^{30}{Si}$ are each generalized using their natural abundance $a_{z}$ to get the estimated total adsorbed ${SiH}_{4}$ . Then $c_{tot}$ is fit to the data for each temperature (solid, dashed, dotted lines) to determine $s_{T}$ . The fits originate at the point (0, 0) because zero ${SiH}_{4}$ flux results in an adsorbed ${SiH}_{4}$ fraction of zero. Horizontal error bars are dominated by the uncertainty in the pressure measurements, and vertical error bars are derived from the standard deviation of the SIMS data.
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Figure 6
Incorporation fraction $s$ (circles) vs deposition temperature. $s$ is determined from the fits of $c_{tot}$ to the data for each temperature in Fig. 5. The fit to Eq. (6) is shown in the red dotted line with all parameters free. The inset presents the same data in Arrhenius form, $ln (s)$ vs 1/ $k_{B} T$ , with linear fits to the activation energies above and below 502 °C (1/ $k_{B} T \approx 15 e V^{- 1})$ . Using the energies determined in the inset as fixed inputs to Eq. (6), the model is refit and shown as the blue dashed line. Horizontal error bars are due to uncertainty in the pyrometer calibration and temperature fluctuation during deposition, and vertical error bars represent the standard deviation of the fit values of Fig. 5.
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Physical Review Materials

Temperature-dependent Si29 incorporation during deposition of highly enriched Si28 films

K. J. Dwyer, H. S. Kim, D. S. Simons, and J. M. Pomeroy

Phys. Rev. Materials 1, 064603 – Published 16 November 2017

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Temperature-dependent ${}^{29}{Si}$ incorporation during deposition of highly enriched ${}^{28}{Si}$ films