M Guionie

Marc Brunel

Anthony Carré

Hen Goulc'

Ludovic Loas

François Frein

Emmanuel Bondu

Benoit Pinsard

Mehdi Cadier

Marco Alouini

Romanelli

Phase locking of dual-polarization DFB fiber lasers through pump-power modulation

  => usually single-frequency, but dual-polarization oscillation possible -Birefringence due to photo-inscription of the FBG Question: use the beat note for microwave photonics? Aim: characterization and stabilization of a DFFL, here preliminary work on pump-power beat frequency tuning and locking M. Guionie, 1 M. Brunel, 1 A. Carré, 1 G. Loas, 1 L. Frein, 1 F. Bondu, 1 E. Pinsard, 2 B. Cadier, 2 M. Alouini, 1 M. Romanelli, 1 and M.Vallet 1 1 Institut FOTON, Université de Rennes 1-CNRS, Rennes 2 iXblue Photonics, Lannion Phase locking of dual-polarization DFB fiber lasers through pump-power modulation Beat frequency tuning and locking Er-Yb DFFL Typical DFB fiber laser Effective length 2 < L eff < 10 mm Birefringence ~10 -5 => f b ~ 1GHz FFP High Er 3+ doping, 976 nm or 1480 nm pumping Various samples tested (L, R 1 , R 2 , κ, φ), λ = 1.54 µm Stable dual-frequency oscillation 0.9 < f b < 1.5 GHz (≠ samples) experimentally -simple phase-locked loop demonstrated for DFFL -compensates for slow drifts (< 3 kHz) Next… -Further loop optimization for phase noise reduction -Dual-polarization laser simulation -Study DBR architecture -PZT actuator for higher beat notes (10 GHz range)


M Guionie

Ludovic Frein

François Bondu

Anthony Carré

Hen Goulc'

Emmanuel Loas

Benoît Pinsard

Mehdi Cadier

Marco Alouini

Marc Romanelli

Vallet

G Loas

E Pinsard

B Cadier

M Vallet

M Brunel

Dual polarization DFB fiber lasers as optical phase-locked microwave sources in the 1-10 GHz range

Keywords: Fiber lasers, microwave sources, dual-frequency, DFB

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Since their first demonstration in 1964, performances of fiber lasers have been improved in many ways (e.g. reduced linewidth, high output power). Besides their beam quality due to the confinement of laser radiation in the structure, their major advantages are compactness, ruggedness, and ease of integration. Fiber lasers are hence appealing sources for a wide variety of applications [START_REF] Fu | Review of recent progress on single-frequency fiber lasers[END_REF] . Distributed feedback (DFB) fiber lasers are usually known to be single frequency but it has long been observed that DFB lasers can sustain the oscillation of two orthogonal polarizations at different frequencies [START_REF] Loh | 1.55µm phase-shifted distributed feedback fibre laser[END_REF][START_REF] Philipsen | Polarisation control of DFB fibre laser using UV-induced birefringent phase-shift[END_REF][START_REF] Ronnekleiv | Polarization characteristics of fiber DFB lasers related to sensing applications[END_REF] . Such dual-frequency DFB fiber lasers were used as sensors [START_REF] Hadeler | Distributed-feedback fiber laser sensor for simultaneous strain and temperature measurements operating in the radio-frequency domain[END_REF][START_REF] Jin | Strain-insensitive temperature sensing with a dual polarization fiber grating laser[END_REF] , and may be promising as heterodyne sources in the field of microwave photonics [START_REF] Leng | A new method for microwave generation and data transmission using DFB laser based on fiber Bragg gratings[END_REF][START_REF] Maxin | Dual-frequency distributed feedback fibre laser for microwave signals generation[END_REF][START_REF] Yuan | Implementation of a widely tunable microwave signal generator based on dual-polarization fiber grating laser[END_REF][START_REF] Liang | Stabilization of microwave signal generated by a dual-polarization DBR fiber laser via optical feedback[END_REF] .However, in the context of optical distribution of local oscillators for instance, we can wonder whether DFB fiber laser can be used to realize a stable continuous-wave microwave source. Stabilization of the beat frequency against a reference is then mandatory. Elasto-optical effects, induced by torsion [START_REF] Maxin | Dual-frequency distributed feedback fibre laser for microwave signals generation[END_REF] or compression [START_REF] Yuan | Implementation of a widely tunable microwave signal generator based on dual-polarization fiber grating laser[END_REF] , have already been used to control the beat frequency of dual-polarization fiber lasers, but phase-locked stabilization to a reference oscillator has never been performed. More precisely, we are interested in an optical phase-locked loop (OPLL) where the DFB fiber laser acts as a voltage-controlled oscillator (VCO) driven by the laser pump power.

Pump-induced thermal effects may become useful for noise reduction or locking in the case of diode-pumped shortcavity solid-state lasers. For example, phase-locking microchip lasers was demonstrated with a feedback on the pumppower of one laser with respect to the other [START_REF] Keszenheimer | Phase locking of 1.32-μm microchip lasers through the use of pump-diode modulation[END_REF] . Besides, simultaneous intensity and frequency noise reduction was obtained in a non-planar ring oscillator [START_REF] Heurs | Simultaneously suppressing frequency and intensity noise in a Nd: YAG nonplanar ring oscillator by means of the current-lock technique[END_REF] . Also, locking a single-frequency erbium microchip laser to a molecular line was realized by a simple modulation-demodulation technique through the pump power [START_REF] Brunel | Wavelength locking of CW and Q-switched Er 3+ microchip lasers to acetylene absorption lines using pump-power modulation[END_REF] . In all these examples, small temperature variations lead to important frequency shifts due to the thermo-optical effect in the short cavity. The low dimensions also leads to reasonable kHz lock-in bandwidths [START_REF] Keszenheimer | Phase locking of 1.32-μm microchip lasers through the use of pump-diode modulation[END_REF][START_REF] Brunel | Wavelength locking of CW and Q-switched Er 3+ microchip lasers to acetylene absorption lines using pump-power modulation[END_REF] . While in Ref. 14 the role of pump-induced thermal effects on the frequency switching in ytterbium-doped DBR fiber lasers was demonstrated theoretically and experimentally, the pump-induced beat tuning effect has not been exploited previously in fiber lasers. Here we focus on erbium-doped DFB fiber lasers emitting in the 1.5 µm wavelength region. We find experimentally that minute differential refractive index changes provided by the pump power offer a satisfactory VCO effect, in both amplitude and bandwidth, which in turn permit to build a robust servo-locking loop.

We first detail in Section 2 the experimental set-up for OPLL and laser characteristics, with emphasis on the beat note study, of a laser operating with a 1 GHz frequency difference. Section 3 is then devoted to the OPLL based on pump-power control. In Section 4 and 5 we extend the same principle to a laser emitting a 10 GHz beat note and on Er 3+ :Yb 3+ -codoped lasers respectively. Finally, conclusions are given in Section 6.

DUAL-POLARIZATION DFB FIBER LASERS

The experimental set-up for OPLL is shown in Figure 1. We have investigated different samples of erbium-doped and erbium-ytterbium co-doped silica fiber lasers, all being made with a distributed-feedback (DFB) structure. The Bragg gratings are photo-induced using the phase-mask technique with a pulsed, un-polarized, UV laser. The dual-polarization lasers studied here bear different grating profiles that are detailed below. In particular we will show results obtained with samples emitting beat notes at around 1 GHz (labeled 1G), at 10 GHz (labeled 10G) and at 300 MHz (labeled 0.3G). The lasers are spliced to single-mode fibers (cut-off 900 nm) on both sides. The lasers are pumped at 980 nm on the output coupler side through a 980/1550 wavelength-division multiplexer. The laser output is transmitted through an isolator, a polarization controller (PC), and a polarizer, to the analysis instruments. The system is entirely single-mode (non PM) fibered. In the following, we concentrate our analysis on the dual-frequency performance of the DFB lasers, in order to define a suitable phase-locked loopfor beat note stabilization, either at 1 GHz, 10 GHz or 300 MHz. Let us detail the characteristics of sample 1G. The active medium is made with a 35 mm-long erbium-doped fiber, whose cladding diameter is 80 μm, and whose absorption is 11.3 dB/m at 1530 nm (the concentration is low enough to prevent any self-pulsing operation). The FBG is photo-induced at 193 nm, its central wavelength is λ B = 1547.3 nm, its length is L B = 30.5 mm, and its strength is κ= 390 m -1 . The resulting calculated effective length is L eff = 2.6 mm. A π phase-shift is made at 18 mm from the beginning of the grating, leading to mirror intensity transmissions of -57 dB and -34 dB. Due to the photo-induced birefringence of the fiber, the phase-shifted grating sustains two polarization-resolved resonances at the center of the stop band. This is verified experimentally by characterizing the spectral transmission of the component without pumping, using a high-resolution optical spectrum analyzer (OSA) containing a built-in tunable laser source. As can be seen in Figure 2(a), the polarization-mode wavelength difference is 8 pm (1 GHz), while the width of the stop band is 200 pm (25 GHz). Note that the weakness of the two resonances is here due to absorption of the tunable probe by the un-pumped erbium ions. The wavelength difference Δλ can be directly linked to the birefringence Δn by Δλ/λ B =Δn/n. We can thus deduce Δn= 7.5 10 -6 . This value is typical of DFB fiber lasers based on standard, i.e. non-PM, fiber, in agreement with the typical residual anisotropy induced by the photo-inscription process [START_REF] Erdogan | Characterization of UV-induced birefringence in photosensitive Ge-doped silica optical fibers[END_REF] . Depending on the sample under test, birefringence values between 6.8 10 -6 (0.9 GHz) and 1.1 10 -5 (1.5 GHz) have been found.

The fiber laser is pumped by a laser diode emitting 145 mW at 980 nm. The pump power at laser threshold is 2 mW and the laser emits at 1547 nm a total output power of 100 µW at 120 mW pumping power. The emitted optical spectrum corresponds to the dual-resonance bands of the FBG, and the frequency difference is measured to be 1.02 GHz at room temperature (Figure 2(b)). We verify that the two orthogonally polarized optical modes have the same pump threshold and are emitted with quite balanced powers (Figure 2(c)). The PC setting is chosen such that behind the polarizer, the high-bandwidth photodiode detects the dual-polarization beat note. Figure 3(a-b) presents the electrical spectrum of the beat over different spans and resolution bandwidths of the electrical spectrum analyzer (ESA). We verify that pure dualfrequency operation gives the radio-frequency tone at 1 GHz (Figure 3(a)). A zoom in this peak shows the free-running 3 kHz line-width of the beat note (Figure 3(b)). We observe a very stable beat power, with a typical 3% amplitude fluctuation (rms) over a few hours.

OPTICAL PHASE-LOCKED LOOP

OPLL design at 1GHz

We first investigate the temperature tuning. The DFB fiber laser temperature is controlled by means of a thermo-electric Peltier device. Using the high-resolution OSA, we measure a thermal response of about 4 pm/K for each optical frequency in the 14-30°C temperature range. The beat frequency also depends on temperature. We monitor the beat thermal drift using the ESA, and find that the thermal response depends on the operating point (temperature and pump power). The important point is that, at a fixed pump power, the beat frequency stays within ±4 MHz in a ±5 K temperature range around room temperature. In laboratory environment, without any temperature control, the drift is thus limited to about 2 MHz over a few hours. Second, we measure tuning characteristics provided by the pump power level.

In contrast with the outside temperature control, it appears that the pump power gives a robust and reproducible means to control the beat frequency. Indeed, we find a DC response of the beat frequency to pump current change of -7 kHz/mA, as shown in Figure 3(c)-(d), quite independently of the laser temperature (linear fits yield slopes between -6.7 and -7.3 kHz/mA). Considering our pump diode, the power-to-frequency tuning curve then has a typical slope of -20 kHz/mW. It follows that pump power variations could be sufficient to counteract the environmental drifts. In the context of a phase-locked loop (PLL), the laser is a "voltage"-controlled oscillator (VCO) at the beat frequency, where "voltage" accounts for the pump power. The VCO gain is mainly related to the thermal heating induced by pump absorption. As a result, the VCO effect is expected to be limited in bandwidth. Nevertheless, as will be seen in the following, it allows us to build an efficient PLL.

The OPLL is implemented as follows. The 11 GHz-bandwidth photodiode is followed by a DC block, a 3 dB attenuator, and by a 30 dB-gain amplifier. This RF signal is mixed with the local oscillator (LO) provided by a synthesizer at 1 GHz whose output power is 10 dBm. At the mixer output, the error signal feeds a loop filter with proportional gain and integrator stages whose parameters are freely adjustable. The resulting signal is added to the DC current driving the pump diode (see Figure 1). In our set-up the diode driver has a gain of 0.65 A/V. Our loop filter consists in a proportional gain of 23 dB. It is worthwhile to mention that the laser itself acts as an integrator stage since it converts the correction signal into a frequency shift.

Results

When the loop is closed, the beat note can be locked. Figure 4(a) shows the stabilized spectrum. The measured linewidth is 1 Hz (Full-Width at Half-Maximum), limited by the resolution bandwidth of our ESA. We measure a 1.5 MHz tracking range. Under our laboratory conditions, the beat then stays locked for days.

The open-loop transfer function can then be observed from closed-loop measurement using a low-signal network analyzer. This instrument is inserted between the mixer output and the loop filter input. The resulting Bode diagram is shown in Figure 4 decrease is due to the thermal response of the FBG laser, where the non-radiative relaxation of erbium ions in the fiber core is dominant. Indeed, we verified independently that the other loop elements have a flat gain up to at least 200 kHz. Thus the loop bandwidth (unit gain frequency) can be adjusted with the loop proportional gain. Under our experimental conditions, we can push the loop bandwidth (unit-gain frequency) up to 22 kHz. The corresponding phase noise is displayed in Figure 4(c). We measure a typical -65 dBc/Hz at 100 Hz offset and almost -80 dBc/Hz at 10 kHz offset from carrier. The small bump at around 300 kHz comes from the laser relaxation oscillations (intensity noise). For comparison the orange curve in Figure 4(c) plots the direct LO measurement. The beat and LO phase noises are almost equal at low frequencies, showing the stabilization and noise reduction effect of the OPLL. Besides, we observe a slight resonance at the unit-gain frequency (22 kHz) showing that the loop is close to the stability limit in this case. Finally, the loop gain also depends on the pump current, because the beat note amplitude is proportional to the laser output power. This is evidenced in Figure 4(d), where phase noise spectra at 60 mA and 270 mA of pump current are shown. The noise floor is reduced at higher power, but the loop resonance peak then gets stronger.

Calculation method for the free-running phase noise

In order to compare the closed-loop phase noise with the free-running beat note phase noise, we proceed as follows. We note that the free-running phase noise is not directly measurable by our phase noise measurement bench, because the fluctuations of the carrier frequency are too large at low frequency. However, we can deduce it from (i) the open-loop transfer function and (ii) the stabilized phase noise spectrum. . Block diagram of Figure 5 shows the complete loop. The error signal ε at the output of the mixer is proportional to the difference between the synthesizer phaseφ LO and the closed-loop phase of the VCOφ stab . M 0 is the peak value of the mixer gain (in V/rad). C is the transfer function of the loop filter (PID). u is the correction signal at the VCO input. A 0 is the VCO gain in MHz/V. The transfer function of the loop is then given by:

. Go has been measured

(Figure 4(b)), and the power spectral densities Sφ LO and Sφ stab of the local oscillator and stabilized VCO, respectively, can be retrieved from the phase noise spectra (Figure 4(c)). One can then deduce the power spectral density of the freerunning VCO (labeled Sφ free ) from the following equation:

Sj stab = 1 1+ G bo 2 Sj free + G bo 1+G bo 2 Sj LO , (1)
where Sφ LO , Sφ stab , and Sφ free are in rad/Hz². Since it can be assumed that we finally find:

Sf free = 1+ G bo 2 Sf stab .
(2) Figure 6. Phase noise spectra (black, locked beat note; red, free beat note; dotted, logarithmic adjustment with a slope of -28.7 dB/dec). We used Equation ( 2) to calculate the phase noise of free-running beat note. Figure 6 compares free-running and stabilized phase noises of our laser under the same conditions. It is interesting to note that the fit to the free-running beat noise yields a slope close to -30 dB per decade, in agreement with previous studies 8 .

LOCKING AT 10 GHZ

In this section we briefly discuss the extension to our pump-based OPLL to a dual-frequency fiber laser presenting a higher-frequency beat note. We consider another DFB sample, labeled 10G, that is based on the same glass as sample 1G, but has notable processing differences. The active medium is made with a 50 mm-long erbium-doped fiber, whose cladding diameter is 125 µm, and whose absorption is 11.1 dB/m at 1530 nm. The FBG is photo-induced at 248 nm, its central wavelength is λ B = 1533 nm, its length is L B = 41 mm, and its strength is κ = 275 m -1 . The resulting calculated effective length is L eff = 3.3 mm. A π phase-shift is made at 27 mm from the beginning of the grating, leading to mirror intensity transmissions of -59 dB and -28 dB. While the birefringence is of the same order of magnitude as sample 1G, we have observed dual-frequency operation with one frequency at the center of the stop band, as usual, and another at the edge of the stop band, 10.2 GHz apart (see the optical transfer function in Figure7(a), and the emitted optical spectrum in Figure 7(b)). Figure 7(a) shows the polarization-resolved transfer function, with dotted lines showing the resonances that are observed to oscillate when the DFB is pumped. The beat note is reproduced in Figure 8, within a 26 GHz window in Figure 8(a), and a close-up in Figure 8(b) showing a kHz-scale free-running linewidth similar to the 1G sample. While the reason for this 10 GHz-beat oscillation is still unclear, we use this sample as a test device for a microwave OPLL based on the pump-power effect. Laser 10G presents roughly the same pump threshold and output power as laser 1G. An important difference is that the VCO gain is measured to be 0.5 MHz/mA in this case, which is much higher than for sample 1G. We then used a low noise, low gain (1 mA/V) diode driver. We also had to upgrade both mixer and LO for operation at 10 GHz. Loop filter adjustments then lead to a proportional gain of 35 dB. As in case 1G, the laser beat at 10 GHz can be efficiently captured and locked, as shown in Figure 9 where one can measure an open-loop 50 dB gain at low frequency and a unit-gain frequency of 37 kHz. In these conditions, the phase noise spectrum is displayed in Figure 9(c). The close-to-carrier phase noise is limited by the LO, while the intermediate frequency band shows lower phase noise than before, due to the low-noise diode driver. A phase noise plateau is measured at -75 dBc/Hz below 20 kHz offset from carrier. Finally the tracking range is 4 MHz, which again permits to maintain the beat locked for days in the laboratory environment. As for 1G, we calculate the phase noise of free beat note laser (Figure 9(c)). We observe at 1 kHz a 40 dB reduction of the phase noise with the PLL.

Er:YbDUAL-FREQUENCY FIBER LASERS

In this section, we present some results obtained with a DFB fiber laser based on Er 3+ :Yb 3+ -codoping. The active medium is made with a 30 mm-long doped fiber, whose cladding diameter is 125 µm. The FBG is photo-induced at 193 nm, its central wavelength is λ B = 1548 nm, its length is L B = 28 mm, and its strength is κ = 362 m -1 . The resulting calculated effective length is L eff = 2.8 mm. A π phase-shift is made at 16 mm from the beginning of the grating, leading to mirror intensity transmissions of -43 dB and -32 dB. Yb 3+ doping prevents from Er-Erion clustering, leading to a higher Er doping concentrations without self-pulsing effects, and hence to higher output power [START_REF] Kringlebotn | Er 3+: Yb 3+-codoped fiber distributedfeedback laser[END_REF][START_REF] Loh | High performance single frequency fiber grating-based erbium: ytterbium-codoped fiber lasers[END_REF][START_REF] Mo | Microwave Signal Generation From a Dual-Wavelength Single-Frequency Highly Er^3+/Yb^3+ Co-Doped Phosphate Fiber Laser[END_REF] . The output power of these laser samples is in the 7 mW range (to be compared to 100 µW for the erbium-doped lasers described above). Figure 10(a) shows that the output power is saturated beyond 7mW. We find experimentally that the laser emission spectrum consists in orthogonally polarized lines separated by 2.4 pm (0.3 GHz). Lower birefringence than sample 1G may be due to different sample compositions. For example, Figure 10(b)-(c) shows the beat note spectrum at 300 MHz and its tuning curve via the pump power. We measured a slope of 50 kHz/mA. Besides, laser 0.3G presents the same pump threshold as laser 1G and 10G. Because of the VCO gain, as 10G, we used a low noise, low gain (1 mA/V) diode driver. We also used the same mixer as 1G and the same LO as 10G stabilization. The best loop stability is obtained when the filter mixed proportional gain, an integrator and a differentiator. In the same way as 1G and 10G, the laser 0.3G can be efficiently captured and locked, as shown in Figure 11(a). The Bode diagram of the open-loop transfer function is shown in Figure 11(b), where one can read an open-loop 56 dB gain at low frequency and a unit-gain frequency of 28 kHz. In these conditions, we measure the phase noise which is displayed in Figure 11(c). We observe a phase noise plateau around -80 dBc/Hz with a minimum at -95 dBc/Hz. For frequencies smaller than 100 Hz, the phase noise is limited by the LO. As for 1G and 10G, we calculate the phase noise of free-running beat note laser (Figure 11(c)). We observe at 10 kHz a 18 dB reduction of phase noise with PLL.

CONCLUSION

Our experiments area demonstration of beat note phase-noise reduction in dual-frequency DFB erbium-doped and erbium-ytterbium co-doped fiber lasers. We have implemented a simple optical phase-locked loop on dual-frequency DFB lasers that uses the pump power as the laser actuator. Beat notes at 1 GHz and 10 GHz were successfully stabilized on the long-term, with a phase noise as low as -75 dBc/Hz at 100 Hz offset frequency. Beat note at 300 MHz were also successfully stabilized with a phase noise as low as -95 dBc/Hz at 100 Hz, with different PID loop parameters. The method may apply to other compact dual-polarization fiber lasers such as DBR structures [START_REF] Guan | Electrically Tunable Microwave Generation Using Compact Dual-Polarization Fiber Laser[END_REF][START_REF] Tan | Multi-octave tunable RF signal generation based on a dual-polarization fiber grating laser[END_REF] or polarization-maintaining fiber-based lasers [START_REF] Liu | Dual-Wavelength Single-Longitudinal-Mode Polarization-Maintaining Fiber Laser and Its Application in Microwave Generation[END_REF] . Since the locking mechanism is based on the pump-power to signal frequency conversion, it could be interesting to compare 976 nm and 1470 nm pumping bands. Such dual-frequency stabilized lasers could provide allfibered and integrated components for microwave photonics applications.

Figure 1 .

 1 Figure 1. Optical phase-locked loop (OPLL) experimental set-up. DFFL: dual-frequency fiber laser; WDM, pump-signal coupler; PC, polarization controller; LO, local oscillator.

Figure 2 .

 2 Figure 2.Optical spectra of sample 1G.(a) Un-pumped DFB transmission spectrum. Insert: zoom on the dual-mode structure. (b) Laser spectrum showing the two frequencies with a 1 GHz (8 pm) difference; pump power 59 mW (130 mA). (c) Total power (black) and resolved in polarization (red and blue curves). The threshold power is about 2 mW.

Figure 3 .

 3 Figure 3. DFFL beat note at 1 GHz. (a) Span 13.6 GHz, RBW 3 MHz, spurious harmonics due to detection electronics, pump power 114 mW (250 mA). (b) Span 200 kHz, RBW 2 kHz, sweep time 100 ms. (c) Pump-power induced tuning: from right to left 45 mW (100 mA), 94 mW (200 mA), 144 mW(300 mA). (d)Beat note vs pump current at different laser temperatures.

Figure 4 .

 4 Figure 4. Locked beat note at 1 GHz. (a) Electrical spectrum (blue, single sweep; black average 10); Span 1 kHz, RBW 1 Hz, VBW 10 Hz, sweep 4.2 s. (b) Open-loop transfer function (red, gain; grey, phase). (c) Phase noise spectra (red, locked beat note; orange, LO). Pump power 92 mW (200 mA). (d) Phase noise spectra of 1G at two different pump current (red, 60 mA (25 mW); brown, 270 mA (123 mW)).

  (b), giving insight to the low-frequency behavior of the pump-controlled oscillator. The smooth gain

Figure 5 .

 5 Figure 5. Model of the OPLL.

Figure 7 .

 7 Figure 7. Optical spectrum of sample 10 G. (a) Transmission spectrum of cross polarization (un-pumped). (b) Emitted laser spectrum.

Figure 8 .

 8 Figure 8. Beat note spectrum at 10 GHz. (a) Span 26 GHz, RBW 3 MHz. (b) Span 1.6 MHz, RBW 20 kHz.

  (a). The openloop transfer function can be observed from in-loop measurement. The resulting Bode diagram is shown in Figure 9(b),

Figure 9 .

 9 Figure 9. 10 GHz beat stabilization. (a) Electrical spectrum; Span 1 kHz ; RBW 1 Hz ; VBW 1 Hz.(b) Open-loop transfer function (red, gain; grey, phase). (c) Phase noise spectra (red, stabilized beat note; orange, measurement noise floor; grey, free-running beat note; dotted, logarithmic adjustment with a slope of -27.4 dB/dec).

Figure 10 .

 10 Figure 10. DFFL beat note at 0.3 GHz. (a) Total laser power curves. (b) Beat note spectrum at 300 MHz; Span 5 MHz ; RBW 50 kHz ; VBW 50 kHz; side-bands at around ±600 kHz offset are due to relaxation oscillation intensity noise. (c) Pump-power induced tuning.

Figure 11 .

 11 Figure 11. 300 MHz beat stabilization. (a) Electrical spectrum; Span 200 Hz ; RBW 1 Hz ; VBW 1 Hz. (b) Open-loop transfer function (red, gain; grey, phase). (c) Phase noise spectra (red, stabilized beat note; orange, measurement noise floor; grey, free beat note; dotted, logarithmic adjustment with a slope of -28.4 dB/dec).

FUNDING

DGA (ANR-16-ASTR-0016); Région Bretagne, FEDER, Rennes Metropole (CPER SOPHIE-Photonique).


Ing-Song Yu
email: isyu@gms.ndhu.edu.tw

Shao-Chun Wu

Lucile Dumont

Julien Cardin

Christophe Labbé

Fabrice Gourbilleau

Christophe Labb E B

Monolithic crystalline silicon solar cells with SiN layers doped with Tb3+ and Yb3+ rare-earth ions

Keywords:

Introduction

Energy crisis and global warming are two important issues in twenty-first century. Solar energy is one of the solutions to solve these problems. Now, many materials are proposed for photovoltaic technologies such as Si, GaAs, CdTe and CIGS. [START_REF] Green | Solar cell efficiency tables (Version 45)[END_REF] In industry, crystalline silicon (c-Si) solar cell is still the mainstream among the various technologies of solar cells. The conversion efficiency of c-Si solar cells can be improved by reducing optical loss, carrier recombination loss and electrical loss. So far, the best experimental c-Si solar cells fabricated in the laboratories have achieved conversion efficiency of 25%. [START_REF] Green | The path to 25% silicon solar cell efficiency: history of silicon cell evaluation[END_REF][START_REF] Saga | Advances in crystalline silicon solar cell technology for industrial mass production[END_REF] Beside these above mentioned loss mechanisms, the main energy loss of c-Si for converting solar energy to electricity is the mismatch of the solar spectrum and the band gap energy of Si. The sub-bandgap photons (E < 1.1 eV) cannot be absorbed by Si solar cells. The excess energy of high energetic photons (E > 1.1 eV) is lost via non-radiative relaxation in the form of heat. The fundamental spectral loss that limits the theoretical maximum efficiency of single junction Si device is around 31%, which is known as the Shockley-Queisser efficiency limit. [START_REF] Shockley | Detailed balance limit of efficiency of p-n junction solar cells[END_REF] To break this limitation, several methods were proposed, such as tandem solar cells, intermediate-band cells, hot carrier cells and spectrum conversion. All those methods are clustered in the third generation photovoltaic cells. [START_REF] Brown | Third generation photovoltaics[END_REF] To increase conversion efficiency of a single junction solar cell, such as c-Si solar cells, spectrum conversion is a good method to modify solar spectrum by means of down-conversion (i.e. quantum cutting), down-shifting or up-conversion. Down-conversion is the process of splitting one high energy photon into more than one lower energy photons which can be absorbed by the cell. Downshifting is the process of absorbing one high energy photon and releasing one lower energy photons for better absorption. Upconversion is the process to combine two low energy photons into one absorbable photon by the Si solar cell. Traditional single junction c-Si solar cells are fabricated by thermal diffusion and screen printing processes for a low-cost approach. External quantum efficiency (EQE) of c-Si solar cells is still poor at shortwavelength range (from 300 to 500 nm) because of the recombination at the surface layer with heavily phosphorus-doped emitter and increased reflectance and absorption from antireflection coating (ARC). However, luminescent down-conversion and downshifting materials have been proposed for improving the poor spectral response of c-Si solar cells to short wavelength light. These materials can also decrease slightly the operational temperature due to electron-hole pair thermalization losses in the cells. 6e9 Rare-earth ions (lanthanide ions) doped materials can absorb and emit light via the energy levels of the active ions. Those rareearth ions may be praseodymium (Pr 3þ ), erbium (Er 3þ ), europium (Eu 3þ ), samarium (Sm 3þ ), cerium (Ce 3þ ) and terbium (Tb 3þ ) in different host materials. These luminescent materials have been used in the lighting, display panel, photocatalytic and photovoltaic technologies. 10e17 For a better integration with c-Si solar cell process, rare-earth ions were inserted in a specific oxide or nitride environment. In the material, those rare-earth ions are mostly stable as divalent or trivalent cations and can efficiently convert UV radiation into visible light as down-shifting layers. [START_REF] An | Highly efficient infrared quantum cutting in Tb 3þ -Yb 3þ codoped silicon oxynitride for solar cell applications[END_REF] Besides, downconversion layers using rare earth ion pairs can provide the energy transfer from one rare-earth ion to another one such as in the Tb 3þ eYb 3þ , Pr 3þ eYb 3þ or Nd 3þ eYb 3þ codoped systems. 19e23 Thus the down-shifting and down-conversion layers can theoretically be used to improve the performance of c-Si solar cell by reducing the thermalization process.

As we know, silicon nitride (SiN x ) thin film has been used as ARC layer at the front side of p-type c-Si solar cells in industry. [START_REF] Zhou | Low temperature SiN x :H films deposited by inductively coupled plasma for solar cell applications[END_REF] In this report, Tb 3þ -doped and Tb 3þ -Yb 3þ -codoped SiN x thin films were deposited by reactive radio frequency magnetron co-sputtering using three different metallic targets: silicon, terbium, and ytterbium, under a mixture of argon and nitrogen plasma. In addition, SiN x :Tb 3þ thin film was integrated into c-Si solar cell as the downshifting layer. SiN x :Tb 3þ -Yb 3þ thin film was integrated into c-Si solar cell as the down-conversion layer. Finally, a monolithic c-Si solar cell with spectrum conversion layers was demonstrated, and the enhanced performance of c-Si solar cells with these layers was investigated.

Experimental

In this work, SiN x , SiN x :Tb 3þ and SiN x :Tb 3þ -Yb 3þ layers were deposited by reactive magnetron co-sputtering in nitrogen-rich plasma. For the deposition parameters, the power density applied on the Si target was fixed at 4.5 W/cm 2 , and the gas fluxes were 1.35 Â 10 À2 Pa$m 3 /s for argon and 3.38 Â 10 À3 Pa$m 3 /s for nitrogen. The deposition operated at plasma pressure 0.40 Pa, and the substrate temperature was fixed at 200 C. The doping of rare-earth ions was controlled by the power densities separately applied on the terbium and ytterbium metal targets. The deposition time was adjusted to obtain 80 nm-thick films which requires an ARC layer with a refractive index around 2.2 (at 1.95 eV). The optimized photoluminescence emission in the visible range for the Tb 3þ ions or in the infrared one for the Yb 3þ ions has been achieved after an annealing process at 850 C. The composition of the produced layers was determined by Rutherford backscattering spectroscopy (RBS) while refractive index and thickness were deduced from ellipsometry spectroscopy experiments. Fourier transform infrared measurement (FTIR) was employed to investigate the SieN bond in the layers.

Fig. 1 shows the process flow of monolithic c-Si solar cells with two different spectrum conversion layers. First, 200-mm p-type Si wafer was cleaned by KOH solution to remove the saw damage as well as for surface texturing. Second, Si doped phosphorus was conducted by thermal diffusion at 850 C for 30 min. Then, isolation etching process was provided to remove the edge and backside ntype Si. Then, samples were cut into the size of 3.5 cm  3.5 cm. Prior to spectrum conversion layers deposition, the samples were cleaned by HF solution to remove native oxide layer on the surface. Three different thin films were then deposited by sputtering [START_REF] An | Fabrication and photoluminescence properties of Tb-doped nitrogen-rich silicon nitride films[END_REF] and followed by a thermal annealing process to recover the nonradiative paths in these layers. Finally, the metallization of c-Si solar cells, consisting in a screen-printing of metals and a co-firing process, was conducted. After these processes, a monolithic c-Si solar cell with spectrum conversion layers was obtained as is shown by the schematic diagram in Fig. 2. This report consists of three parts: the characterization of spectrum conversion layers, optical properties of spectrum conversion layers on c-Si solar cells, and the performances of solar cells with these layers.

Results and discussion

3.1. Characterizations of SiN x , SiN x :Tb 3þ and SiN x :Tb 3þ -Yb 3þ layers

The results of the RBS measurements for those three samples are shown in Table 1. The composition of SiN x in the three layers is close to the stoichiometric composition (Si 3 N 4 ) even when rareearth ions are added. The doping concentrations of Tb 3þ and Yb 3þ ions in the matrix achieved by RBS analysis are also exhibited in Table 1.

Fig. 3 shows the refractive index at 1.95 eV for the three layers. The blue line represents the refractive index of the stoichiometric silicon nitride, Si 3 N 4 . We can find that the refractive index increases when the matrix is doped with one or two types of rare-earth ions. The doping of 1.5 at% terbium in the SiN x matrix raises refractive index 0.02. The doping of 7.8 at% rare-earth ions leads to an increase of the refractive index 0.14. These are still in the acceptable range (from 2.0 to 2.2) for the application in c-Si solar cells.

The FTIR analysis was conducted on the three samples and the results are shown in Fig. 4. The two peaks present the longitudinal optical (LO) and the transversal optical (TO) modes of the asymmetric SieN bond. The position of the TO peak does not vary between the samples. The LO peak's position shifts to the low wavenumbers when rare-earth ions are inserted in the SiN x matrix. This shift may be attributed to a decrease in the silicon content compared with the nitrogen one, or to an increasing stress in the matrix due to the increasing insertion of rare-earth ions in the matrix. [START_REF] Huang | Structure and composition studies for silicon nitride thin films deposited by single ion beam sputter deposition[END_REF] In addition, the range of wavenumber between those two peaks (1100e900 cm À1 ) may be related to the lattice vibration that is a signature of the matrix disorder. Fig. 4 shows that the intensity difference between this part of the spectrum and the two peaks became smaller when one then two types of rare-earth ions are incorporated in the matrix. Thus, the shift of the LO peak towards the low wavenumbers should be attributed to the increase of disorder due to the insertion of rare-earth ions.

Microstructures and optical properties of these layers on textured emitter

After the fabrication of c-Si solar cells, these layers were integrated in monolithic c-Si solar cells. Fig. 5 shows the images of cross-section transmission electron microscopy. The microstructure of SiN x doped with Tb 3þ -Yb 3þ thin films can be observed on the textured Si surface by TEM observations. The layers were uniformly coated on the textured emitter of c-Si solar cells with the thickness around 70 nm.

The optical properties of these layers can be characterized by photoluminescence, and reflectance measurements. In Fig. 6, the emission of SiN x layer is very weak compared with the doped layers. However, it emits from and below 488 nm allowing the energy transfer from the matrix to the terbium ions. Such sensitization effect of rare-earth ions allow to overcome their low absorption cross section as already demonstrated in such a nitride based matrix. In addition, it has been determined that this transfer most likely occurs toward the high energy levels of the terbium ions before undertaking relaxation to the 5 D 4 energy level as shown by An et al. [START_REF] An | Fabrication and photoluminescence properties of Tb-doped nitrogen-rich silicon nitride films[END_REF][START_REF] An | Highly efficient infrared quantum cutting in Tb 3þ -Yb 3þ codoped silicon oxynitride for solar cell applications[END_REF] Tb 3þ ions in the SiN x matrix emit from 500 to 630 nm as displayed in Fig. 6 which exhibits the four characteristic peaks of the terbium at 629, 594, 550 and 493 nm that correspond to the 5 D 4 to 7 F 3 , 7 F 4 , 7 F 5 , and 7 F 6 energy transfers. The UV light can thus be absorbed by matrix and then transferred to the Tb 3þ ions that will then transfer the converted light to the Si. Therefore, SiN x :Tb 3þ can be a down-shifting layer for c-Si solar cell. For the SiN x :Tb 3þ -Yb 3þ thin film, this layer only presents the characteristic peak of the Yb 3þ at 990 nm which originates from the 2 F 5/2 to 2 F 7/2 energy transfer. The spectra show a mechanism of spectral down-conversion, energy transfer from one rare-earth ion to two other rare-earth ions. Thus, SiN x codoped with Tb 3þ -Yb 3þ ions can be a down-conversion layer for c-Si solar cell.

The reflectivity of these layers on textured emitter is important for c-Si solar cells because these layers also play the role of an ARC layer. Fig. 7 shows the reflectance as a function of the wavelength. The minimum of reflectance is between 400 and 500 nm. The reflectance increases at shorter wavelength, and a bump rising of reflectance at around 1050 nm is observed. To overall justify the ARC performance of our layers for solar cells, we can calculate the weighed average reflectance (WAR) at AM1.5G in the range of 300 and 1200 nm. The WAR value of these layers on the textured Si is around 6%, which shows the good light harvesting as ARC layers for c-Si solar cells. [START_REF] Park | Improvement on surface texturing of single crystalline silicon for solar cells by saw-damage etching using an acidic solution[END_REF][START_REF] Yu | Surface passivation and antireflection behavior of ALD TiO 2 on n-type silicon for solar cells[END_REF]

Performances of c-Si solar cells with these three layers

In previous section, the optical properties of rare-earth ion doped SiN x layers on textured emitters can be spectrum conversion and ARC layers for c-Si solar cells. We move forward to realize the performance of monolithic c-Si solar cells with these layers. After the process of metallization, external quantum efficiency (EQE) measurement was employed to get the short-circuit current density (J sc ), and pseudo IeV curve without the effect of series resistance could be obtained by Sinton's Suns V oc measurement. [START_REF]Open photovoltaics analysis platform[END_REF][START_REF] Kerr | Generalized analysis of quasi-steady-state and transient decay open circuit voltage measurements[END_REF] Fig. 8 shows the IeV curves of three cells, and inset is the zoom of curves. The photovoltaic performances of these cells are summarized in Table 2. To compare with the c-Si solar cell without rareearth ion doping, the performances of c-Si solar cell with SiN x doped with Tb 3þ or codoped with Tb 3þ eYb 3þ have enhancement in short-circuit current density and open-circuit voltage (V oc ). The conversion efficiency is from 17.13% to 17.31% for the down-shifting layer (SiN x doped with Tb 3þ ). The conversion efficiency is from 17.13% to 17.36% for the down-conversion layer (SiN x codoped with Tb 3þ eYb 3þ ).

The performance enhancement of Si solar cells both comes from the anti-reflection and spectrum conversion effects of these films.

From the WAR values of three different layers as 6.04%, 6.20% and 5.86%, the corresponding weighed average transmission of 93.96%, 93.80% and 94.14% can be obtained. To normalize the effect of antireflection coating, the ratios of conversion efficiency to transmission can be calculated as 18.23%, 18.45% and 18.44%, respectively. The SiN x films doped with Tb 3þ or codoped with Tb 3þ eYb 3þ can enhance the performance of c-Si solar cells due to the effect of spectrum conversion.

Conclusions

A monolithic c-Si solar cell with spectrum conversion layers was demonstrated with Tb 3þ doped SiN x and Tb 3þ -Yb 3þ codoped SiN x thin films. These thin films can not only play the role as antireflection coating, but also improve the performances of c-Si solar cells due to the spectrum conversion effects (down-shifting and down-conversion). From the characterizations of these films, their composition and refractive index are close to stoichiometric Si 3 N 4 . The layers with the thickness of 70 nm are uniformly coated on the textured emitter of c-Si solar cells. For the down-shifting layer, the UV light can be absorbed by matrix and then transfer to the Tb 3þ ions. For down-conversion effect layer, energy transfers from one rare-earth ion to two other rare-earth ions from the PL measurements.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Process flow of c-Si solar cells with spectrum conversion layers.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Refractive index of three layers at 1.95 eV deduced from Ellipsometry analysis.

Fig. 5 .

 5 Fig. 5. TEM images of SiN x doped with Tb 3þ -Yb 3þ on textured emitters.

Fig. 6 .

 6 Fig.6. PL measurements equipped with a 325 nm laser for the three layers on textured emitters of solar cells.

Fig. 7 .

 7 Fig. 7. Reflectance of three layers deposited on textured emitters.

Fig. 8 .

 8 Fig. 8. Pseudo I-V curves for three c-Si solar cells with SiN x , SiN x :Tb 3þ and SiN x :Tb 3þ -Yb 3þ layers, respectively.

Table 1

 1 The composition analysis of SiN x and doped SiN x layers by RBS (at%).

	Samples	Si	N	Tb	Yb
	SiN x	43	57	e	e
	SiN x :Tb 3þ	42	56	1.5	e
	SiN x :Tb 3þ -Yb 3þ	39.5	52.7	5.8	2

Table 2

 2 Photovoltaic performances of c-Si solar cells with SiN x , SiN x :Tb 3þ and SiN x :Tb 3þ -Yb 3þ layers.

	Samples	J sc	V oc	Pseudo	Pseudo	Efficiency to
		(mA/cm 2 )	(V)	FF (%)	Efficiency	normalized
					(%)	transmission (%)
	SiN x	32.091	0.546 0.804	17.13	18.23
	SiN x :Tb 3þ	32.098	0.552 0.803	17.31	18.45
	SiN x :Tb 3þ -Yb 3þ 32.165	0.552 0.806	17.36	18.44

supported by Ministry of Science and Technology, Taiwan (MOST 105-2911-I-259-501), the French Agence Nationale de Recherche through the GENESE Project (ANR-13-BSS09-0020-01), and the French Ministry of Research through the ORCHID Project (33572XF).


Julien Labbe

Cardin

C-H Liang

Y-T An

W Jin

D-C Meng

D-P Wang

C-A Chen

K-Z Liu

A W Kleyn

C Labbé

J Cardin

F Gourbilleau

Correlation between composition, microstructure, and emission properties in Nd-doped Si-rich Si oxynitride films: investigation into the nature of the sensitizer

Keywords: neodymium, rare earth, Si-rich Si oxynitride, thin film, non-resonant excitation, photoluminescence

HAL is

Introduction

Silicon photonics has attracted considerable attention since it has a potential application in microelectronics and more recently in silicon-based materials for energy conversion [1][2][3]. For this reason, systems composed of rare earth (RE) ions incorporated in silicon-based host matrices have been intensively investigated [4][5][6][7][8]. In such systems, the presence of sensitizers such as silicon nanoparticles (Si-nps) can allow an increase of the effective excitation cross section of RE ions by several orders of magnitude [9,10]. However, an effective sensitization process is governed by energy transfer (ET) mechanism that is strongly distance dependent. This ET is either a Coulombic type (Förster) or carrier exchange based (Dexter), with an interaction distance ranging from some nanometers for Förster-approach [11] to below a nanometer for Dexter-interaction [START_REF] Al | Nanoparticles de silicium et ion erbium pour lámplification optique[END_REF]. A large distance between the sensitizer and the RE ion, as well as the clustering of RE ions (formation of RE 2 O 3 for example) in the Si-based host matrix are considered as two major factors that could limit the coupling of RE ions with the sensitizer. This situation requires, therefore, some nano-engineering of the material composition (i) through growing a high density of sensitizers in order to enhance the RE-related emission, (ii) by increasing the concentration of RE ions before the concentration quenching effect becomes dominant [7].

The Er-doped Si-rich Si oxide (Er-SRSO) system has been widely studied. Early results stated that the ET between Si-nps and Er 3+ ions is optimal for crystallized Si-nps [START_REF] Chryssou | [END_REF], but amorphous Si-nps were later shown to play an efficient sensitizing role towards the Er ions as well [14,15], demonstrating that crystallization is not a prerequisite. From such results, it was found that crystallized Si-nps appear in general at high temperature 1100 °C, and the amorphous one at about 900 °C or below. This former would favor a coalescence of Si-nps as well as the formation of Er 2 O 3 , which consequently decrease the number of sensitizers, and increase the distance between them and the Er 3+ ions. The consequence is an observed quenching of the RE emission [16]. At low annealing temperature (<900 °C), our previous work has evidenced the presence of Si-based sensitizers issue from the agglomeration of less than 15 Si atoms [16]. This allows to obtain a high density of sensitizers uniformly distributed leading thus to a high fraction (22%) of optically active Er 3+ ions effectively coupled to sensitizers [17]. Up to now, the achievement of net gain from such an Er-SRSO system is, however, rather rare or even shown as impossible [18,19].

An alternative system, Nd-doped Si-rich Si nitride (Nd-SRSN), attracts strong interest in recent years. In contrast to the three-level electronic 4f structure for the Er 3+ ion, in the case of the Nd 3+ ion it is easier to achieve net gain due to its four-level configuration considering the 4 F 3/2 → 4 I 11/2 transition leading to a 1.06 μm emission. Our simulation work has demonstrated that a significant positive net gain up to 30 dB cm -1 can be achieved with the Nd-doped SRSO waveguide [19]. For the host matrix, the SRSN matrix has a much higher threshold for RE ions agglomeration than the oxide case. This may be due to low diffusion coefficients for RE ions in a nitride matrix [20,21]. This means that more optically active RE ions may potentially be present in SRSN than in SRSO matrices. Moreover, Li et al have observed a maximum Nd 3+ photoluminescence (PL) intensity corresponding to a Si concentration of 45% [22]. These authors proposed that localized states present in high density in the band-tails act as effective sensitizers to Nd 3+ ions for such oxygen-free Nd-SRSN sample. Marcus et al have observed that RE ions tend to be surrounded by oxygen atoms, an arrangement considered as crucial for the optical activation of RE ions in glasses, and particularly for efficient emission [23,24]. This statement implies the importance to carefully incorporate a small amount of oxygen in the host matrix. However, the work on Nd-doped Si-rich Si oxynitride (Nd-SRSON) system is quite scarce. The sensitizer nature requires a deeper analysis to see whether there is a difference comparing to other Si-based systems.

In our previous work on Tb-doped N-rich Si oxynitride (Tb-NRSON), we have confirmed that both band-tails and + N 4 defect states can play the role of sensitizers towards Tb 3+ ions [3]. Herein, we propose to study a different system, Nd-SRSON sample. It consists of an Nd-doped oxynitride Si-based matrix in which we have incorporated a Si excess. This study aims at (i) optimizing the Nd 3+ emission through variation of deposition parameters for tuning the sample composition and annealing conditions for controlling the sample microstructure, and (ii) elucidating the Nd 3+ ions excitation mechanisms correlated with composition and microstructure. This work has not only to do with waveguide applications in the case of Nd 3+ ions, but also with the REdoped Si-based systems as frequency conversion layers, see for example [21,25,26].

Experiment

The films of about 400 nm thick were deposited by radio frequency magnetron co-sputtering of two confocal cathodes (Si and Nd 2 O 3 ) driven by plasma constituting of a mixture of nitrogen and argon. The p-type mono-crystalline Si or fused silica substrates were used and maintained at 200 °C during the growth. Films deposited on fused silica as substrate were developed only for Raman measurements, other experiments were carried out on films grown on Si substrate. The plasma power densities for Si and Nd 2 O 3 targets were fixed at 4.44 and 0.44 W cm -2 , respectively. The ratio of N 2 to Ar gas flux (r N ) was varied from 7.0% to 13.3%, while the gas pressure of the plasma was kept constant at 2 mTorr. Such deposition parameters allow one to incorporate a Si excess in the films. Thus, these later are named as Nd-SRSON, which will be confirmed below by the characterizations of their composition. After deposition, the films were submitted to a thermal annealing treatment under N 2 ambient for 1 min durations, and different temperatures ranging from 600 °C to 1100 °C. The chemical composition, microstructure, and optical properties of as-deposited and annealed films were studied by x-ray photoelectron spectroscopy (XPS), Fourier transform infrared (FTIR), Raman, ellipsometry, transmission electron microscopy (TEM), PL and photoluminescence in excitation (PLE) spectroscopies.

The XPS measurements were performed in an ultra-high vacuum PHI-5000 VPII system with a base pressure lower than 5×10 -8 Pa using a mono-chromatic Mg kα radiation at 1253.6 eV. The layer surface was cleaned (sputtered) by 2 keV Ar + bombardment for 2 min before the measurements. The binding energy was calibrated by using the value of contaminant carbon C1s=284.8 eV as reference. For FTIR measurements, the spectra were recorded at 65°incidence angle in the 500-4000 cm -1 range using a Nicolet Nexus 470 spectrometer. In case of Raman characterization, the incident laser wavelength was 532 nm. The ellipsometry experiments were carried out by means of an UVISEL Jobin-Yvon ellipsometer with an incident angle of 66.2°. The experimental spectra were recorded on a 1.5-5 eV range with 0.01 eV resolution. The absorption coefficient, refractive index, and thickness were deduced from the experimental data by fitting with the new amorphous dispersion formula which is derived from the Forouhi-Bloomer model for amorphous semiconductors using the DeltaPsi2 software [27]. The model takes into account the use of crystalline Si substrate, an amorphous Si oxynitride, a rough surface layer composed of a mixture of void space and Si oxynitride. The TEM measurements were performed in bright and dark field modes on a cross-sectional sample using a JEOL 2010F (200 kV) microscope. The PL experiments were carried out using the 488 nm-line of a CW Argon laser (Innova 90 C Coherent), which is a non-resonant wavelength for Nd 3+ ions [28]. Finally, the PLE spectra were collected by means of Jobin-Yvon Fluorolog spectrophotometer using a Xe lamp as excitation source. The PLE spectra shown below have been calibrated to the spectrum of the Xe lamp used.

Results and discussion

Effect of composition

As nondestructive techniques, both FTIR spectroscopy and spectroscopic ellipsometry were adopted to study the microstructural and optical properties of dielectric films. Figure 1(a) shows the evolution of the FTIR spectra recorded for asdeposited films prepared with the indicative r N . Two main vibrations bands are clearly visible, peaking at about 830 cm -1 and between 970 and 1150 cm -1 . They correspond to the transverse and longitudinal optical (TO and LO) vibrations bands from Si-N bond, respectively. All spectra are normalized to the intensity of TO Si-N band. The TO Si-N band position slightly changes with r N , whereas the evolutions of LO Si-N position and intensity are more pronounced. The LO Si-N peak position, obtained by fitting with Gaussian formula, is displayed in figure 1(b). Thus, a significant blue-shift of LO Si-N peak position and a concomitant increase of its intensity with r N can be noticed. Such behavior is ascribed to a remarkable increase of Si-N bonds and thus confirms an enhancement of N content in the host matrix [29]. As presented in figure 1(c), each value of the absorption coefficient is lower than 10 3 cm -1 in the 1.0-1.5 eV range. For higher energies from 1.5 to 4.5 eV, it can reach some tens of 10 4 cm -1 . As noticed, all these curves are between those of amorphous Si 3 N 4 and Si materials. The absorption coefficient curve for the sample with r N =13.3% is close to that of amorphous Si 3 N 4 , while with decreasing r N the absorption coefficient increases towards the value of amorphous Si. Moreover, the refractive index shown in figure 1(d) decreases with r N which demonstrates that the increase of the nitrogen content in the plasma diminishes the Si incorporation in the Si3N4 matrix. This evolution is in agreement with the FTIR results confirming that r N is an effective parameter to carefully tune the layer composition, i.e. the Si/N ratio.

Figures 2(a)-(c) present the PL spectra for Nd-doped in stoichiometric SiO 2 , Si 3 N 4 , and SRSON matrices. No PL signal was observed from the former two matrices, while the latter exhibits a remarkable peak at about 920 nm. This suggests an excess of Si in the matrix is required to achieve PL signal. Thereafter, the PL spectra dependence on nitrogen rate r N used to prepare the samples are shown in figure 2(d). To note that, all these spectra come from the samples with annealing at 750 °C, which corresponds to an optimal temperature as described below. No emission is seen from 500 to 800 nm for any r N value. However, one can clearly observe a PL peak centered at 920 nm ascribed to the 4 F 3/2 -4 I 9/2 transition in the Nd 3+ ions [30]. Such an emission achieved with a non-resonant excitation wavelength (488 nm) for the Nd 3+ ions confirms the presence of sensitizers towards this RE ions in the host matrix. The integrated PL intensity of Nd 3+ (inset of figure 2(d)) gradually increases with the r N increases from 7.0% to 10.5%, then falls down for higher r N values (from 11.1 to 13.3%). The Nd content is assumed to remain constant since the applied power density on the Nd 2 O 3 cathode was the same for all these samples. Thus, the evolution of Nd 3+ PL intensity is probably determined by the Si/N ratio. As estimated by XPS measurements, the optimized sample (for r N =10.5%) was found to contain 47.4, 46.2, 5.7, 0.8 at% for Si, N, O, Nd element, respectively. The Si concentration is excessive comparing to those in Si 3 N 4 and SiO 2 , thus the sample is called Nd-doped Si-rich Si oxynitride (Nd-SRSON).

Effect of microstructure

To further understand the PL dependence, it is important to investigate the effect of microstructure influenced by thermal annealing conditions. The optimized layer (r N =10.5%) has been studied by FTIR and Raman spectroscopes, TEM and XPS experiments. Figure 3(a) shows the layer microstructure evolution for different annealing temperatures ranging from 600 °C to 1100 °C using FTIR experiments. All spectra are normalized to the TO Si-N band intensity. In contrast to the asdeposited sample, the LO Si-N peak intensity increases and shifts towards higher wavenumbers for annealed samples. For the former, such a behavior means that the number of Si-N bonds increases due to annealing. This implies the presence of some N dangling bonds in the as-deposited matrix, which recombine with Si atoms upon annealing. Moreover, the LO Si-N peak intensity approaches near saturation after annealing at 600 °C. This suggests that an achievement of the recombination of N· dangling bonds with Si to form Si-N bond does not require higher temperatures such as 1100 °C. By the way, the intensity of LO Si-N -TO Si-N bands overlapping at about 1010 cm -1 is gradually attenuated with increasing temperature. This behavior suggests that the host matrix becomes more ordered by the atomic rearrangement. The peak centered at 1250 cm -1 is attributed to a Si-O bond. Such a peak appears after annealing and its intensity increases with temperature. This is probably due to a phase separation within the matrix induced by the thermal treatment. . This suggests that the Si-nps density is very low for these two thin films. With T A increase especially at 1100 °C, the spectra show a remarkable peak. It attests the increase of amorphous Si-nps number within the host matrix [31]. It also confirms a structural rearrangement of the matrix and/or a phase separation in the Nd-SRSON materials under such a high annealing temperature. The absence of a peak at about 521 cm -1 indicates that no crystalline Si-nps have been formed upon 1100 °C-annealing temperature process. The TEM results are shown in figures 3(c) and (d). The observations exclude the presence of crystal in the film annealed at 1100 °C. This agrees well with the Raman experiments and strongly confirms that the Si atoms assemble during annealing as amorphous species.

The XPS spectra can provide the chemical surrounding, i.e. atomic binding condition in the samples. For the Si element, according to the random bonding model, each Si atom coordinates to four atoms in the SRSON matrix and forms tetrahedral units Si-Si k N x O y (k+x+y=4; k, x, y=0, 1, 2, 3, 4). Figure 4 shows the Si 2p XPS spectra and components peaks for the optimal sample as-deposited (figure 4(b)) and annealed at the indicated temperature (figures 4(c), (d)). The Si 2p XPS spectrum of Si wafer used as substrate is also added for comparison (figure 4(a)). Four component peaks were obtained after a de-convolution process. Two peaks centered at 103.8 and 99.2 eV have been experimentally observed and respectively attributed to Si-O 4 and Si-Si 4 species [32][33][34]. For the former, the peak intensity is quite low for the as-deposited layer and shows an enhancement upon annealing. This suggests the O atoms in as-deposited layers are located in a metastable state, rearrange locally and thus form Si-O bonds during annealing. For the later, the peak intensity is rather low for the as-deposited film. It is slightly enhanced by annealing at 750 °C, while it significantly increases at 1100 °C. This agrees well with Raman results and again evidences that a phase separation occurred after high temperature annealing. In case of the other two components peaking at 101.9 and 100.8 eV, they are assigned to the tetrahedrons containing Si-Si bonds, i.e. k′=1, 2, or 3 in Si-Si k′ N x O y formula (k′ +x+y=4; x, y=0, 1, 2, 3) according to the calculation by Cova et al [35]. In comparison with the case of k=0, such Si-Si k' N x O y species are named in this paper as Si-rich tetrahedrons. The tetrahedron corresponded to 100.8 eV has a higher k′ value than that for 101.9 eV. As noticed, these two components from Si-rich tetrahedrons mainly occupy the Si 2p peak area for the asdeposited sample. Their intensities relative to Si-Si 4 species show a little decrease after a 750 °C annealing treatment and a remarkable decrease at 1100 °C one. For this later case it indicates the decomposition of Si-rich tetrahedrons and thus the formation of Si-Si 4 species.

In case of N 1 s binding energy region (figure 5(a)), the peak centered at 397.8 eV is observed for the as-deposited sample and presents a red shift for annealed ones. This shift means that the N oxidation state decreases after annealing [36,37]. Since the oxidation state is dependent on the coordination number in the system, which mainly contains N and Si atoms, one would thus infer the existence of an N-SiN x (x<3) species with dangling bonds in the as-deposited sample. During annealing, the N-SiN x (x<3) species converts to an N-Si 3 leading to a passivation of the N· dangling bond [38]. In case of O 1 s binding energy region (figure 5(b)), the peak locates at about 532.9 eV for the asdeposited sample and gradually shifts to lower binding energy upon annealing. Note that the 1100 °C-annealed sample shows a broader band that can be fitted into two components peaking at 532.5 and 530.7 eV. The shift of the former component from 532.9 to 532.5 eV is explained by the conversion from O·-Si species into O-Si 2 species [39,40]. This leads to an enhancement of Si-O bond number with annealing temperature, which is consistent with FTIR results (figure 3). The other component at 530.7 eV is assigned to an O-Nd bond [41]. It indicates the change of Nd surroundings under high temperature annealing. As displayed in figure 5(c) for Nd 3d5/2 binding energy region, the 1100 °C-annealed sample shows a higher energy peak in contrast to both as-deposited and 750 °C-annealed samples. This peak is attributed to Nd-O bond, while the shift is interpreted by the increase of Nd oxidation state [42]. The PL spectra are displayed in figure 6 for as-deposited and annealed films. The Nd 3+ emission was recorded and its intensity versus T A is shown in the inset. In contrast to the asdeposited sample, the annealing treatment significantly enhances Nd 3+ PL intensity even at low T A =600 °C. When increasing T A , the PL intensity is improved by a factor of more than 10 before collapsing at 1100 °C. This behavior corresponds to the evolutions of matrix microstructure and chemical surrounding for Nd 3+ ions, which determine the fraction of efficient coupling between sensitizers and Nd 3+ ions. The samples show a high Nd 3+ PL intensity in a quite wide range of moderate annealing temperatures ranging from 750 °C to 1000 °C. This is obtained by a concomitant effect of the recovering of non-radiative defects, the evolution of sensitizers' number and optically active Nd 3+ density.

ET mechanisms

From ellipsometry data analyzed by means of new amorphous dispersion model, the energy band gap was estimated for various r N in this study. The band gap energy, as shown in figure 7(a), varies from 2.1 to 4.6 eV with r N varying from 7% to 13.3%. Such band gap enlargement is related to less Si incorporation in the Si 3 N 4 matrix. This causes the matrix to become more ordered and the band-tails concomitantly shrink [43]. For r N =10.5% the band gap energy was found equal to about 4.0 eV, which is much higher than the excitation energy at 2.54 eV. Furthermore, PL excitation (PLE) measurement collected at 920 nm was carried out on the optimized sample annealed at 750 °C and the obtained spectrum is shown in figure 7(b). As seen, the PLE intensity is weak for energy lower than 2.8 eV by comparison with the higher energy range (2.8-4.0 eV) where the PLE intensity increases with a slope shape. Such shape is a characteristic of band-tails to band-tails absorption mechanism in an amorphous silicon oxynitride matrix [25]. These spectra present a blue-shift with T A increase. This shift is related to the passivation of defect density as well as to the shrinking of band-tails in the matrix. The matrix band gap and tails are schematically illustrated in figure 7(c). As seen, the excitation energy 2.54 eV used in this work does not reach the conduction band. Therefore, the sensitization of Nd 3+ ions is not directly due to an ET occurring from exciton generated between conduction and valence band.

As discussed on figures 1 and 2, excessive Si in the matrix is required to form Si agglomerates and thus achieve Nd 3+ -emission under a non-resonant excitation (488 nm) [44,45]. These agglomerates, according to the TEM, Raman, and XPS experimental results, are amorphous and small for the optimized sample. This agrees well with our previous work demonstrating that a few Si atoms are enough to act as RE sensitizer [16]. Furthermore, the Si agglomerates at atomic scale, as observed by Salh et al, are optically active and display green-yellow emission [46]. The exciton emitting green-yellow light is likely to couple with the nearby Nd 3+ ion [47]. Indeed, the visible emission was not observed in our case for the Nd 3+ doped layers while a clear PL peak at 920 nm was present via a non-resonant wavelength excitation. This infrared PL at the expense of visible emission suggests the occurrence of efficient ET from atomic scale Si agglomerates to Nd 3+ ions.

Following the discussion on the nature of the sensitizer, the correlation between the composition, microstructure, and emission properties are described here. Excess Si atoms are needed to create the atomic scale Si agglomerates. However, high Si/N ratio would result in a formation of large Si agglomerates. These latter are ineffective to transfer energy to Nd 3+ ions [48]. Therefore, the Nd 3+ -PL intensity shows a maximum value at a moderate Si/N ratio. Moreover, the nonradiative defects such as N and O should be recovered to achieve a high PL intensity. Annealing treatment shows a good approach to promote N· and O· recombination with Si, as evidenced by both XPS and FTIR results. Whereas, annealing at high temperature 1100 °C, too large Si agglomerates are grown by a decomposition of Si-rich tetrahedrons species. It would also result in the clustering of Nd ions, which favors an energy cross-relaxation process. This will reduce the effective sensitizers and/or emitter centers. Such behaviors demonstrate the importance of controlling deposition parameter and annealing temperature to optimize sample composition and microstructure in order to (i) favor the generation of effective sensitizers, (ii) recover the non-radiative defects, (iii) promote the highest coupling number between sensitizers and lanthanide ions.

Conclusion

The correlation between the composition, microstructure, and emission properties of Nd-SRSON films have been studied in detail. The maximum PL intensity of Nd 3+ ions was obtained from the films (i) deposited by reactive magnetron co-sputtering of pure Si and Nd 2 O 3 cathodes under mixed (N 2 /Ar=10.5%) plasmas, and (ii) post-annealed at 750°C-1000 °C. This, as demonstrated above, corresponds to the best environment for the achievement of dense effective sensitizers and for a passivation of non-radiative defects such as N· and O· dangling bonds. The optical measurements confirm that the excitation process of Nd 3+ ions did not involve the valence-conduction band but the excitation rate is enhanced by atomic scale Si agglomerations. The overall analysis involves six types of optical measurements. This seems an effective methodology to monitor the evolution of composition and microstructure, such as Si agglomerations and nonradiative defects. This approach exhibits a great advantage to study atomic sensitizers towards RE ions and thus achieve favorable emission.

Figure 1 .

 1 Figure 1. (a) FTIR spectra recorded with an incidence angle of 65°for different r N values, (b) the position of LO peak obtained by fitting the FTIR spectra as a function of r N , (c) absorption coefficient versus energy, and (d) refractive index given at 1.95 eV versus r N for as-deposited layers. In (c) absorption coefficients of pure amorphous Si 3 N 4 and Si are added for comparison purpose. The absorption coefficients for pure Si and r N =7.0% are multiplied by 1/10 and 2/5, respectively.

Figure 2 .

 2 Figure 2. PL spectra for Nd-doped in the indicative matrix (a) SiO 2 , (b) Si 3 N 4 , (c) SRSON prepared with r N =10.5%, and (d) Si-rich Si oxynitride with different r N ranging from 7.0% to 13.3%; in (d) the inset shows the integrated 920 nm peak intensity versus r N and the right depicts the origin of 920 nm peak from 4 F 3/2 -4 I 9/2 transition in the Nd 3+ ions.

Figure 3 (

 3 Figure 3(b) reports the Raman experiments performed on corresponding as-deposited, 750 °C-, 900 °Cand 1100 °Cannealed samples. Both as-deposited and 750 °C-annealed samples present a weak band at about 480 cm -1. This suggests that the Si-nps density is very low for these two thin films. With T A increase especially at 1100 °C, the spectra show a remarkable peak. It attests the increase of amorphous Si-nps number within the host matrix[31]. It also confirms a structural rearrangement of the matrix and/or a phase separation in the Nd-SRSON materials under such a high annealing temperature. The absence of a peak at about 521 cm -1 indicates that no crystalline Si-nps have been formed upon 1100 °C-annealing temperature process. The TEM results are shown in figures 3(c) and (d). The observations exclude the presence of crystal in the film annealed at 1100 °C. This agrees well with the Raman experiments and strongly confirms that the Si atoms assemble during annealing as amorphous species.

Figure 3 .

 3 Figure 3. (a) FTIR spectra recorded with an incidence angle of 65°and (b) Raman spectra for the optimal Nd-SRSON layer as-deposited (AD) and annealed at the indicated temperatures, TEM pictures for 1100 °C-annealed film taken in bright (c) and dark (d) field modes.

Figure 5 (

 5 d), as a conclusion for 5(a)-(c), schematically depicts the evolution of chemical surrounding for N, O, and Nd. It illustrates the passivation of dangling bond upon thermal annealing.

Figure 4 .

 4 Figure 4. The raw Si 2p3/2 spectra data (open circles) and component peaks (filled area) obtained from the fit of the high-resolution XPS spectra in the Si 2p3/2 region for the optimized sample (for r N =10.5%) annealed at the indicated temperature ((b-d)) and Si wafer (a).

Figure 5 .

 5 Figure 5. High-resolution XPS spectra for (a) N 1 s, (b) O 1 s, and (c) Nd 3d5/2 binding energy region for the optimized sample (r N =10.5%) annealed at the indicated temperature, (d) drawing of evolution of chemical surrounding for N, O, and Nd elements.

Figure 6 .

 6 Figure 6. PL spectra of as-deposited (AD) and annealed samples (at indicated T A , annealing temperature). The left inset shows the integrated PL intensity for 920 nm peak versus temperature and the right one depicts the origin of 920 nm peak from 4 F 3/2 -4 I 9/2 transition in the Nd 3+ ions.

Figure 7 .

 7 Figure 7. (a) r N used to prepared samples versus band gap estimated by the new amorphous dispersion model, the 750 °C-annealed optimized samples (r N =10.5%) corresponds to a band gap of 4.0 eV; (b) PLE spectra detected at 920 nm for optimized samples (r N =10.5%) annealed at 750 °C. The inset shows the PLE spectra evolution for indicative values of T A ; (c) schematic illustration of the excitation photon with 2.54 eV compared to the matrix band gap and tails.

Acknowledgments

This work was financially supported by the Natural Science Foundation of China (Grant Nos. 11504343 and 51701194) and the French National Research Agency (Grant No. ANR-08-NANO-005).

ORCID iDs

Y-T An https:/ /orcid.org/0000-0003-3280-9579