1. Introduction

A phosphorus donor doped in silicon is a promising candidate as a quantum bit (qubit) because the donor has long longitudinal and transverse relaxation times (T₁ and T₂) of nuclear and electron spins. The long coherent times elongate a memory time of a state in quantum information processing [1–4]. In addition, phosphorus in silicon is compatible with solid-state devices and integrated circuits in future quantum processors. Recently, the electron spin of phosphorus has been electrically detected with a single-electron transistor [2]. Phosphorus in silicon can also be used as an optically accessible quantum memory in a repeater put on long-distance quantum communication networks [5]. In this memory, the interactions between light and nuclear or electron spins of phosphorus are mediated by a donor bound exciton (BE) with Zeeman or hyperfine levels. In order to resolve these levels, the line width of the BE emission must be narrower than the Zeeman or hyperfine splitting energies of several μeV or less [6]. Present extensive studies have clarified that phosphorus BE emission in isotope-purified silicon exhibits quite narrow lines due to small inhomogeneous broadening [7,8], which is suitable to observe the splitting. However, the intrinsic small radiative transition rate of the BE makes it difficult to obtain a strong light-donor interaction, owing to the indirect-bandgap nature of silicon. In addition, so far the phosphorus BE emission has been observed only in silicon substrates doped phosphorus during crystal growth [7–9]. To improve the insufficient interaction, the donor should be placed in the center of an optical microcavity where the light-donor interaction can be enhanced by the Purcell effect [10]. It is also necessary that the donors are doped in a thin silicon layer because the typical microcavities such as photonic crystal cavities are fabricated in a thin silicon layer [11]. The doped phosphorus must be activated and well isolated from each other to suppress their dephasing.

Considering these requirements, ion implantation is a useful doping technique for fabricating the donor-embedded microcavities because the donor can be injected into the nanometer-scale region with precise control of the concentration and isotopes if an ion mask is used [12]. Photoluminescence (PL) studies for ion-implanted bulk silicon have been done to evaluate damages induced by implantation processes [13–15]. In addition, one can find several reports for BE emission from implanted impurities in natural and isotope-purified silicon substrates [16–18]. However, there has been very few reports for BE emission from implanted phosphorous in silicon substrates [19], and BE emission from phosphorus implanted into thin silicon layers has never been observed. The observation of the BE emission is crucial even for electrical device applications because the BE emission studies give us information about the detailed state of donors.

Here we report the first observation of clear BE emissions from phosphorus donors implanted into thin silicon layers, and also examined the implanted-donor state in detail. As a result, we have confirmed that implanted donors are electrically activated and isolated without severe damages. However, we have found that most of the activated donors form a cluster state even in a low dose range. This result is important for developing ion implantation techniques for the fabrication of silicon quantum devices with phosphorus qubits.

2. Experimental procedures

The samples were silicon-on-insulator (SOI) wafers, which had a 160-nm-thick undoped silicon layer with a (100) surface on a 2-μm thick buried oxide layer. The resistivity of the top silicon layer was > 700 Ωcm. The top silicon surface was always covered by only a native oxide. Phosphorus ions were injected into the entire silicon area with an acceleration voltage of 30 kV at room temperature. The projection range of the ions was 40 nm [20]. The ion dose amounts were 10¹⁰, 10¹¹, 10¹², and 10¹³ cm⁻². After the ion implantation, the samples were annealed in a high-temperature furnace to remove defects from silicon [21]. The annealing temperature and time were 1000 °C and 1 hour, respectively. No visible defects or dislocations could be observed in the annealed samples with a transmission electron microscope. A secondary ion mass spectroscopy (SIMS) analysis confirmed uniformity of the implanted phosphorus and loss of the donors induced by thermal diffusion and segregation during the annealing. A spreading resistance analysis (SRA) at room temperature and an X-band electron spin resonance (ESR) measurement at 20 K were performed to estimate the concentrations of the electrically activated and isolated donors, respectively.

The ion-implanted samples were mounted on the cold stage of a cryostat and cooled with liquid helium. The temperature of the stage was 4 K. The donor BE in the thin silicon layer was created by an ultraviolet pulsed laser with a wavelength of 373 nm, a repetition rate of 80 MHz, and a pulse duration of 10 ps. The incident optical power was 160 μW. A 50x objective lens focused the laser light and simultaneously collected emission from the samples. Since at least 93% of the incident optical power is absorbed by the top silicon layer [22], the PL emission collected by the lens dominantly comes from the excited top thin silicon layer [23]. The emission was guided to a spectrometer with an InGaAs detector array cooled by liquid nitrogen. The spectral resolution was 0.3 nm. When the emission lifetime was measured, the laser pulse was selected by a modulator for a repetition rate of 8 MHz. The emission from the sample was filtered with an optical spectrum analyzer and detected with a superconducting single photon detector with a time-to-amplitude converter. The time resolution of the system was 0.14 ns.

As a reference, two commercially available pre-doped SOI wafers (cSOI-1, 2) were also measured. The SOI wafers were fabricated with the wafer bonding technique using silicon substrates that were doped with phosphorus during the crystal growth [24].

3. Results and discussion

The SRA results are shown in Fig. 1 to reveal the electrical activation of the implanted phosphorus. Figures 1(a) to (c) show depth profiles of carrier concentration in implanted silicon layers. The carrier concentration corresponds to the concentration of the electrically activated phosphorus donor, assuming constant carrier mobility. These results show that the ion-implanted donors are electrically activated in all the silicon layers because the carriers, which are generated from the activated donors, are found in all the samples. However, their activation is neither uniform nor perfect. In Fig. 1(a), a depth profile of the implanted phosphorus obtained by SIMS analysis is also shown. The SIMS analyses for lower dose silicon layers were failed due to the insufficient sensitivity. Figure 1(a) shows that the carrier concentration is smaller around a Si/SiO₂ interface even though the SIMS analysis finds that the implanted phosphorus are uniformly dispersed in the entire silicon layer with their average concentration of 6.9×10¹⁷ cm⁻³. This means that the activation around the top surface is more efficient than that around the Si/SiO₂ interface. This non-uniformity of the activation becomes significant as decreasing the ion dose as seen in Figs. 1(b) and (c). However, since all activated donors in the thin silicon layers are excited and detected by PL measurements, the sheet concentration is more important than the depth profile for comparison. The sheet concentration of the activated donors n, which is obtained by the integration of the depth profile, is noted in Figs. 1(a) to (c).

 

Fig. 1 (a)-(c) Spreading resistance analysis of ion-implanted samples. The carrier concentration corresponds to the concentration of electrically activated phosphorus. The sheet concentrations of the activated donors n are noted with an error of 20%. The concentration of implanted phosphorus obtained by SIMS analysis is also shown in (a). (d) The fraction of the electrically activated phosphorus. The sample with an ion dose of 10¹⁰ cm⁻² could not be measured due to the detection limit.

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Figure 1(d) shows the activation fraction calculated by the ratio of the sheet concentrations of implanted and activated donors, those were derived from the SIMS and SRA analyses, respectively. The activation fraction is 42% at the highest ion dose, however the fraction falls to 0.3% as the ion dose decreases. The activation fraction depending on the ion dose has been reported previously [25,26]. There are two possible reasons for the reduction of the activation fraction. One is the loss of the implanted donors due to the thermal diffusion or the segregation at a Si/SiO₂ interface during the annealing. The dose amount calculated by the integration of the SIMS profile in Fig. 1(a) is ~1×10¹³ cm⁻², which agrees well with the desired dose set to an ion implanter. This result confirms no loss of the implanted donors. In addition, it is known that the segregation of phosphorus at a Si/SiO₂ interface takes place during the annealing and the segregated donors cannot be electrically activated [27]. However, the SIMS analysis shows a flat profile and no clear indication of the segregation in the highest dose sample. If the segregation is apparent, the concentration of the implanted donors increases around the interface. At the lower dose, we guess that there is no prominent segregation. Another possible reason is that phosphorus is not located at the substitutional site in silicon. The donor substitution can be promoted by silicon vacancies. Since the silicon vacancies introduced by the high-energy ions are fewer when the ion dose is smaller, the activation may be suppressed in the low dose samples. In order to increase the activation fraction, the co-implantation of silicon and phosphorus ions may be available because it creates an excess of silicon vacancies and promotes the substitution of phosphorus in the annealing process [26]. The SRA also shows that the activated donor concentrations for cSOI-1 and cSOI-2 are 5.1×10⁸ and 2.2×10⁹ cm⁻², respectively.

In order to examine the emission characteristics of the samples, we measured PL spectra as shown in Fig. 2 . It is well known that the BE of isolated phosphorus emits luminescence at a wavelength of 1079 nm without phonon coupling (no-phonon line or NP) [9]. The upper two curves in Fig. 2 are the PL spectra of the commercially available pre-doped SOI samples. They show clear emission lines at 1079 nm from the phosphorus BE and at 1136.6 nm from their transverse optical (TO) phonon replica.

 

Fig. 2 Photoluminescence spectra for SOIs with different ion doses. The emissions from commercially available pre-doped SOIs are shown for comparison. The ion dose and the activated donor concentration in parentheses are shown.

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The lowest curve was obtained with the undoped SOI wafer that was used for the ion implantation, which shows no indication of BE emission at 1079 nm. The PL spectra for the ion-implanted SOI samples are shown by four curves in the center of Fig. 2. Note that emission lines at 1079 nm are definitely observed for two samples with ion doses of 10¹¹ and 10¹² cm⁻². This result shows that these emissions come from the ion-implanted phosphorus that is activated and isolated in the thin silicon layers. As far as we know, this is the first observation of BE emission from ion-implanted phosphorous in thin silicon layers. In Fig. 2, no BE emission was observed at 1079 nm for the sample with an ion dose of 10¹⁰ cm⁻² probably because there were too few activated donors for detection. In the highest dose sample (10¹³ cm⁻²) the BE emission also disappeared, but another broad emission appeared at around 1090 nm. Similar broad emissions can be observed in the implanted samples with doses of 10¹¹ and 10¹² cm⁻². The origin of this broad emission is discussed later.

The sharp and broad emissions at 1135.9 and 1150 nm on the lower five spectra are the TO phonon replicas of the boron BE and the electron-hole droplet (EHD) emissions, respectively [9]. The undoped SOI contains a little boron as a residual impurity. Since the oscillator strength of boron BE is 5 times larger than that of phosphorus BE [28], the intense boron BE line can be observed at 1135.9 nm in the undoped and ion-implanted samples. In addition, the doped boron has their bound multiple exciton complex (BMEC) line at 1137.5 nm, which is labeled by b² in Fig. 2. In contrast, it is known that the PL intensity of boron BE no-phonon line at ~ 1079 nm is quite smaller than that of phosphorus one [9]. Thus, there is no emission line at ~ 1079 nm on the spectra for the undoped sample, and we can separate the emissions from boron and implanted phosphorus in the implanted samples. The emission intensities for the phonon replicas of boron BE and EHD exhibit almost no change in the ion-implanted samples.

Figure 3 shows the relation between the integrated intensity of the BE emission at 1079 nm and the concentration of the activated phosphorus which was deduced from Fig. 1. At the same concentration range centered around 10⁹ cm⁻², the BE emission intensity at 1079 nm for the ion-implanted samples is nearly 1/10 that of the pre-doped SOIs. The emission intensity I_PL is expressed by $I_{PL}={\eta }_R{N}_{BE}\approx {\eta }_R{N}_D$, where η_R and N_BE are the radiative quantum efficiency and the concentration of the phosphorus BE. At this excitation laser power, we can assume that N_BE is nearly equal to the concentration of the isolated active donors N_D because we found that the BE emission intensity was saturated, which shows that most of the donors trap the exciton. Here, we discuss two possible reasons why the BE emission intensity of the ion-implanted samples is weaker than that of the pre-doped samples. First, the BE emission can be weakened by the reduction of η_R due to nonradiative centers created by the ion implantation. ${\eta }_R={\Gamma }_R/({\Gamma }_R+{\Gamma }_{NR})\approx {\Gamma }_R/{\Gamma }_{NR}$, where Γ_R and Γ_NR are the radiative and nonradiative decay rates, respectively and Γ_NR >> Γ_R owing to the small radiative transition rate of silicon. The increase in the nonradiative decay rate reduces η_R. The second possible reason is the cluster state formed by an overlapped electronic wave function of the activated donors, which can reduce the number of isolated donors and the BE emission intensity at 1079 nm. The cluster state does not contribute to the sharp emission line at 1079 nm due to the delocalization of the BE [29].

 

Fig. 3 Integrated PL emission intensity of the isolated phosphorus BE at 1079 nm with different of the activated phosphorus concentrations. The integrated emission intensity of the broad lines at around 1090 nm is also shown. These intensities are calculated by the integration of the fitted Gaussian curves in Fig. 2.

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The nonradiative center was evaluated by the emission lifetime of EHD. Figure 4 shows the PL decay curves and the EHD lifetimes. At the highest dose, the lifetime reaches 8 ns. This short lifetime results from an additional nonradiative process. The possible nonradiative center is the defects caused by the ion injection that remain even after the annealing. In contrast, the lifetimes stay around 40 ns for activated donor concentrations below 10¹⁰ cm⁻². Note here that there is no difference between the lifetimes of samples with and without ion implantation, and the pre-doped SOIs. This means that the lifetime is dominated by the nonradiative recombination at the surface of silicon [30], and the additional nonradiative process induced by the ion implantation is negligible in the samples except at an ion dose of 10¹³ cm⁻². The stable boron BE emission intensity at ~1136 nm, as shown in Fig. 2, also supports this consideration. If the nonradiative process due to the ion implantation is prominent, the emission intensity of the boron BE should also be decreased.

 

Fig. 4 (a) PL decay for the EHD emission. The spectral window of the detection is 1147 ± 2.5 nm. The ion dose and the activated donor concentration in parentheses are shown. (b) Lifetime of the EHD emission with different samples. The dashed line is an eye guide.

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Next, we discuss the presence of a cluster state of the activated donors. The cluster state in silicon has been reported for phosphorus-doped silicon substrates by ESR measurement when the volume concentration of the active donors exceeded ~10¹⁷ cm⁻³ [6]. Since the SRA profile in Fig. 1(a) shows that the activated donor concentration of the highest dose sample is larger than 10¹⁷ cm⁻³, we performed ESR measurements for all ion-implanted samples to confirm the cluster state. Figure 5 shows the ESR spectrum for the sample with an ion dose of 10¹³ cm⁻². The signal from the cluster state of the activated donors was found in a magnetic field of 3375 G (g ~1.998), however there was no hyperfine splitting signal from the isolated phosphorus at 3354 and 3396 G [6]. The cluster concentration was estimated to be ~3 × 10¹² cm⁻² by curve fitting. Since the activated donor concentration obtained by the SRA is 4.2 × 10¹² cm⁻², the ESR result demonstrates that most of the activated donors are not isolated, but form their cluster state in the sample with an ion dose of 10¹³ cm⁻². This is consistent with there being no phosphorus BE emission at 1079 nm for this sample, as shown in Fig. 2.

 

Fig. 5 Electron spin resonance signal for a sample with an ion dose of 10¹³ cm⁻². This contains signals from the phosphorus cluster state at 3375 G (g ~ 1.998), silicon dangling bond at 3364 G (g ~2.005), and unidentified spin source at 3374 G (g ~ 1.999).

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Our ESR spectrometer could not detect spin signals from the cluster state in other samples with lower doses because of the spin detection limit of ~4×10¹¹ cm⁻². However, an indication of the cluster state can be found in the PL spectra as a broad emission peak. It is reported that the cluster state of the active donors shows a broad PL emission at around 1090 nm, which is result of the radiative recombination of the delocalized electrons in the donor cluster state and the holes in the valence band without phonon coupling [31,32]. This PL emission is red-shifted and broader than that of the isolated donors due to the band tailing of the donor state [29]. In Fig. 2, we can also find a similar broad emission at around 1090 nm for the samples with ion doses ranging from 10¹¹ to 10¹³ cm⁻². Thus we assume that the activated donors form cluster states even in the lower dose samples. The integrated intensity of the broad emission, which is plotted in Fig. 3, is an order of magnitude larger than the intensity at 1079 nm for the ion-implanted samples with ion doses of 10¹¹ and 10¹² cm⁻² (corresponding activated donor concentrations of 10⁸ and 10¹¹ cm⁻²). This means that the isolated donors might account for approximately 10% of the total amount of activated donors. The new evidence of the cluster state of the activated donors even in the low dose range (< 10¹² cm⁻²) is surprising because their activated donor concentrations are less than 10¹⁶ cm⁻³ as shown in the profiles of Figs. 1(b) and (c). These concentrations are sufficiently lower than the threshold for appearing the cluster state, which is commonly known as 10¹⁷ cm⁻³ [6].

Consequently, the BE emission intensity of the ion-implanted samples, which is weaker than that for the pre-doped sample, is not suppressed by the nonradiative centers created by the ion implantation, but can be reduced by the cluster state of the activated donors.

4. Conclusion

In this study, we have succeeded in detecting the BE emission from phosphorus implanted into thin silicon layers. The clear BE emission line at 1079 nm confirms that there were activated and isolated donors. However, their emission intensity was weaker than the pre-doped SOI samples. This reduction in the BE emission intensity for the implanted samples is not due to the nonradiative centers created by ion implantation, but can be explained in terms of a cluster state of the activated donors. If the cluster states can be suppressed, it will become possible to obtain a more intense BE emission from the isolated donors. In addition, the larger fraction of the isolated donors is suitable for the efficient light-donor interaction without dephasing. Our results provide important information about the state of ion-implanted donors and for developing an ion implantation technique for future optical quantum devices using the isolated phosphorus as a qubit.