Defect identification in semiconductors with positron annihilation: Experiment and theory

Filip Tuomisto and Ilja Makkonen

Rev. Mod. Phys. 85, 1583 – Published 14 November 2013

Abstract

Positron annihilation spectroscopy is particularly suitable for studying vacancy-type defects in semiconductors. Combining state-of-the-art experimental and theoretical methods allows for detailed identification of the defects and their chemical surroundings. Also charge states and defect levels in the band gap are accessible. In this review the main experimental and theoretical analysis techniques are described. The usage of these methods is illustrated through examples in technologically important elemental and compound semiconductors. Future challenges include the analysis of noncrystalline materials and of transient defect-related phenomena.

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Received 13 February 2013

DOI:https://doi.org/10.1103/RevModPhys.85.1583

Authors & Affiliations

Filip Tuomisto^*

Department of Applied Physics, Aalto University School of Science, Espoo, Finland

Ilja Makkonen^†

COMP Centre of Excellence, Helsinki Institute of Physics and Department of Applied Physics, Aalto University School of Science, Espoo, Finland

^*filip.tuomisto@aalto.fi
^†ilja.makkonen@aalto.fi

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Vol. 85, Iss. 4 — October - December 2013

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Figure 1
The number of papers published per year on positrons in condensed matter physics and materials research. The development of slow positron beams and of the theory of positrons in semiconductors and defects during the 1970s and 1980s predates the strong increase in research activity. Data from ISI Web of Science.Reuse & Permissions
Figure 2
Positron lifetime spectrum obtained with a typical spectrometer. The dashed and dotted lines show the detector resolution and the “ideal” spectrum. The inset shows a magnification of the $t = 0$ range.Reuse & Permissions
Figure 3
Two “raw” positron lifetime spectra measured in different samples. The spectra are shown without the left-hand-side background, as in practice the window for optimal analysis starts around $t \approx - 0.1 ns$ .Reuse & Permissions
Figure 4
Single- and two-component positron lifetime spectra after background subtraction (upper panel) and subsequent source effect subtraction (lower panel).Reuse & Permissions
Figure 5
Vacancy concentration sensitivity of the positron lifetime measurement in a system where $τ_{B} = 170$ and $τ_{V} = 230 ps$ . The highest sensitivity is midrange, where a small change in vacancy concentration produces a substantial change in the average positron lifetime.Reuse & Permissions
Figure 6
Doppler broadening spectra obtained with a single HPGe detector and with two HPGe detectors in coincidence. The high background in the single-HPGe-detector measurement can be subtracted; the functional form is dictated by the incomplete charge collection in the detector (dashed line). The resolution function of a typical HPGe detector is also shown for reference (dotted line).Reuse & Permissions
Figure 7
Folded experimental coincidence Doppler broadening spectra for the GaN lattice and Ga vacancy. Typical integration windows for the $S$ and $W$ parameters are shown (upper panel). Experimental and calculated “ratio curves” of the momentum densities (lower panel).Reuse & Permissions
Figure 8
Computational Doppler spectra of (a) $V$ , (b) $V − Sb$ , (c) $V − {Sb}_{2}$ , and (d) $V − P$ in Si. The thick (black) solid line shows the full spectrum. The contributions of individual Si core shells are shown with thin (black) solid lines, and dopant atoms’ core shell contributions by solid colored lines. Adapted from 381.Reuse & Permissions
Figure 9
An isosurface of the positron density for a positron localized at a Ga vacancy in GaN in a 96-atom supercell model. The Ga atoms are shown by light shaded and the N atoms by dark shaded spheres. Based on the calculations of 159. From 453.Reuse & Permissions
Figure 10
Positron lifetime spectra in as-grown and in 2-MeV electron-irradiated Si samples. Positrons annihilate in the as-grown sample with a single lifetime of 220 ps corresponding to delocalized positrons in the lattice. In the irradiated samples the experiments reveal vacancies with positron lifetimes of 250 ps ( $V − As$ pair in Cz Si:As sample doped with $[As] = 1020 {cm}^{- 3}$ ) and 300 ps (divacancy in undoped FZ Si sample). From 393.Reuse & Permissions
Figure 11
Experimental (markers) and calculated (solid curves) coincidence Doppler broadening spectra in vacancy-donor complexes in Si, showing the perfect match between theory and experiment. Adapted from 393.Reuse & Permissions
Figure 12
$S$ parameter depth profiles for F-implanted Si samples annealed at (a) $400 ° C$ for up to 67 h and (b) $700 ° C$ for up to 125 h. From 347.Reuse & Permissions
Figure 13
Coincidence Doppler broadening spectra, normalized to the spectrum for silicon, showing relative intensity vs electron momentum. Peaks in the data from annealed samples match the “fingerprint” of fluorine. From 414.Reuse & Permissions
Figure 14
Ratios of the annealed samples of relaxed 10% and 30% Ge and multilayer 30% Ge at $\sim 2 keV$ . Best fits are shown on top of data. Ratios of implanted ${SiO}_{2} / Si$ , $F / Si$ , $Ge / Si$ , and $V_{2}$ in $Si / Si$ are shown for reference. All spectra are divided by a Si spectrum. From 122.Reuse & Permissions
Figure 15
The average positron lifetime $τ_{av}$ and annihilation line-shape parameter $S$ in semi-insulating GaAs as functions of isochronal annealing temperature after 1.2-eV illumination at 25 K. The illumination transforms EL2 into the metastable state and corresponding changes in positron parameters are indicated by arrows. The open triangles with dashed lines below 100 K represent the reference levels where EL2 is in the stable state. The normalized infrared absorption coefficient is shown in the top panel. All measurements have been made in darkness at 25 K. From 233.Reuse & Permissions
Figure 16
Optical cross section for the creation of the metastable vacancy as a function of the photon energy in a SI GaAs sample. The data in the upper part are obtained from IR absorption measurements and in the lower part from positron lifetime measurements. Measurement temperature was 25 K. From 388.Reuse & Permissions
Figure 17
(a) Average positron lifetime $τ_{ave}$ and (b) defect-related lifetime $τ_{def}$ vs measurement temperature in Te-doped GaAs compared to a GaAs:Zn reference. Spectral decomposition was not reliable for $T > 350 K$ for the $5 \times 10^{16} {cm}^{- 3}$ doped sample ( $τ_{av}$ is close to $τ_{b}$ ). Lines are fits according to the temperature-dependent trapping model. From 141.Reuse & Permissions
Figure 18
(a) High-momentum part of the positron annihilation momentum distribution (normalized by taking the ratio to a GaAs:Zn reference) for the vacancies in GaAs:Te and GaAs:Si. The spectra (total area $3.5 \times 10^{7}$ counts) were brought to unity and scaled to full trapping at the vacancies before normalization. Lines result from smoothing and serve to guide the eye only. (b) Ratio of the momentum density to bulk GaAs for different vacancies in GaAs from theoretical calculations. The curves for $V_{Ga} − {Te}_{As}$ and $V_{As} − {Si}_{Ga}$ complexes are highlighted to emphasize the good agreement with the respective experimental data in GaAs:Te and GaAs:Si. The theoretical curves are not accurate for $p_{L} < 15 \times 10^{- 3} m_{0} c$ and hence are omitted. From 141.Reuse & Permissions
Figure 19
The average positron lifetime $τ_{av}$ and the lifetime component $τ_{2}$ vs measurement temperature for GaN bulk crystal. The lifetime component $τ_{2}$ could be decomposed only at $T > 200 K$ . The solid lines are drawn to guide the eye. From 390.Reuse & Permissions
Figure 20
Experimental coincidence Doppler ratio curves for irradiation-induced and two kinds of in-grown Ga vacancies. Adapted from 159.Reuse & Permissions
Figure 21
Ratio curves of the calculated momentum densities of annihilating $e − p$ pairs in selected vacancy complexes in InN. All spectra are convoluted with a Gaussian of 0.53 a.u. FWHM (except $V_{In}^{0.66 a . u .}$ , $FWHM = 0.66 a . u .$ ) and divided by the momentum-density spectrum of the InN lattice. From 371.Reuse & Permissions
Figure 22
Experimental coincidence Doppler spectra of the investigated samples in the layer (a), (b) and interface (c) region. The data have been divided by a suitable reference spectrum for the InN lattice. Computational ratio curves are shown for comparison. From 371.Reuse & Permissions
Figure 23
(a) The $(S, W)$ values corresponding to the annihilation of positrons in the delocalized state (defect free, DF) and that of positrons trapped by cation vacancies ( $V_{In}$ or $V_{Ga}$ ) calculated using ordered ${In}_{x} {Ga}_{1 x} N$ ( $x = 0, \dots, 1$ with steps of 0.1). The $(S, W)$ values for $V_{In} V_{N}$ and $V_{Ga} V_{N}$ in ${In}_{0.5} {Ga}_{0.5} N$ are also shown. Arrows show the effect of $V_{N}$ coupled with cation vacancies. (b) The $(S, W)$ value for the cation vacancies in $SQS − {In}_{0.5} {Ga}_{0.5} N$ [special-quasirandom structure SQS)] and experimentally obtained $S W$ relationship for ${In}_{x} {Ga}_{1 x} N$ . The $x$ values for the sample are shown. The $(S, W)$ values for MBE-grown GaN and HVPE-grown GaN are also shown. The dotted lines connecting the $(S, W)$ values for DF and cation vacancies show the effect of the trapping of positrons by the cation vacancies in ordered ${In}_{0.5} {Ga}_{0.5} N$ . From 467.Reuse & Permissions
Figure 24
Positron lifetime spectra measured for an electron-irradiated VP-grown ZnO sample (499), a typical spectrum for HT-grown ZnO (as well as for Li-enriched MG-grown ZnO samples) and the bulk lifetime spectrum as measured in the VP-grown ZnO reference sample. From 199.Reuse & Permissions
Figure 25
Coincidence Doppler broadening measurements for as-grown HT ZnO, as-grown MG ZnO, and Li-doped MG ZnO as compared to the theoretical values obtained for $V_{Zn}$ , ${Li}_{Zn}$ , and the ${Li}_{Zn} − H − {Li}_{Zn}$ complex. The experimental data obtained for $V_{Zn}$ are shown for comparison. From 199.Reuse & Permissions
Figure 26
Example of average positron lifetime measured with time-modulated illumination in a natural diamond sample.Reuse & Permissions
Figure 27
Schematic of a thin-film moderator in transmission geometry.Reuse & Permissions

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