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Abstract
A fiber laser system emitting ultrashort femtosecond pulses at 1550 nm with configurable properties has been developed as an excitation source for the two-photon absorption transient current technique (TPA-TCT). The modules of the system are designed to provide the optical specifications required at the output for localized characterization of semiconductor radiation detectors: variation of pulse energy between 10 nJ and $10\;{\rm pJ}$, variation of the pulse repetition rate from 8.2 MHz to single shot, and variation of pulse duration between 300 and 600 fs. The validity of the system as an excitation source in the TPA-TCT is demonstrated by measuring spatially resolved excited charge carriers in a silicon detector.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
In the field of silicon detector development for high energy physics, the study of quantities as the charge collection or the electric field is important to understand the semiconductor device and evaluate its performance with irradiation. The transient current technique (TCT) is a widely used method for characterizing radiation detectors. Among other advantages, it allows determination of the efficiency of charge collection, full depletion voltage, sign of the space charge, or effective trapping time of the carriers in defects generated by radiation. These position it as one of the preferred techniques when studying the degradation of detectors operating in high radiation environments [1–4] and establish it as a standard tool for the characterization of unirradiated and irradiated silicon particle detectors.
With the TCT, the device under test (DUT) is illuminated with a pulsed laser source that generates electron–hole pairs inside the detector material. The drift current, resulting from the movement of the generated charge carriers in the biased silicon detector, is measured. Conventional TCT uses lasers with central wavelengths of 650 nm to 1100 nm, where silicon absorbs light by single photon absorption (SPA). SPA-TCT systems in the red wavelength regime have typical laser spot sizes of $5\;\unicode{x00B5}{\rm m}$ and are used to study electron and hole separation, because full light absorption is within the first $3\;\unicode{x00B5}{\rm m}$ to $10\;\unicode{x00B5}{\rm m}$ of the material thickness. A schematic of the typical application of red SPA-TCT is shown in Fig. 1(a). Near infrared SPA-TCT systems are used to mimic the ionization profile of a minimum ionizing particle (MIP) since they provide continuous ionization along the beam propagation direction [5]. The method also offers the possibility for illumination from the edge (e-TCT), which allows to study the DUT along its depth [Fig. 1(b)]. A two-dimensional resolution with typical spot sizes of $6\;\unicode{x00B5}{\rm m}$ to $10\;\unicode{x00B5}{\rm m}$ is achieved. The development in semiconductor to even smaller designs pushes the conventional SPA-TCT to its limits and demands higher resolving methods. Moreover, the increasingly complex implantation in silicon devices to small segmentations needs a true three-dimensional resolution.
Fig. 1. (a) Schematic of the usual illumination and charge generation in the red SPA-TCT. (b) Schematic of the near infrared SPA-TCT. Illumination from the top side, back side, and particular edge is usually performed. Charge is generated all along the beam propagation path. (c) Schematic of the TPA-TCT, showing the volume of excess charge carriers simplified as an ellipsoid. Illumination from the top side and back side is typically performed. Illumination from the edge is also possible, but often limited in depth by the high focusing.
Those demands can be covered by the two-photon absorption-TCT (TPA-TCT), where femtosecond pulsed lasers with wavelengths well above the bandgap energy of silicon ($\lambda \gt{1100}\;{\rm nm}$, photon energies lower than 1.12 eV) are used to exploit the process of TPA. For high enough intensities, electron–hole pairs are created by the simultaneous absorption of two photons at the focal point of the laser. This effect is nonlinear and depends quadratically on the intensity [6]. Figure 1(c) shows the method with typical applications schematically. Through highly focusing optics, the main generation of excess charge carriers is confined to a volume of typically $1\;\unicode{x00B5}{\rm m}\times 1\;\unicode{x00B5}{\rm m}\times 20\;\unicode{x00B5}{\rm m}$ around the focal point, and said point can be moved inside the silicon detector in all three spatial axes to achieve three-dimensional resolution. Then, the lateral resolution achieved with the TPA-TCT is approximately 10 times higher than for the SPA-TCT and true three-dimensional resolution is achieved.
In the context of the RD50 collaboration at CERN [7], the proof of concept of the TPA-TCT method was successfully carried out at the Singular Laser Facility of the UPV/EHU [8]. This first demonstration of the three-dimensional resolving capability of the TPA-TCT method was performed on pad-type n-in-p float-zone silicon diodes [9], and subsequently demonstrated on neutron irradiated diodes [10]. The application of TPA-TCT in an e-TCT configuration on depleted monolithic active pixel sensor diodes showed the full potential of the method, achieving an unprecedented spatial mapping of the semiconductor junction that is still unparalleled [6,11,12].
However, one practical limitation of these initial studies was the use of a high power femtosecond pulsed laser, even though the energy of the pulses employed in the TPA-TCT is well below 1 nJ. The validation of the TPA-TCT on silicon detectors was performed using a Ti:sapphire (Ti:Sa) solid-state laser as the light source and an optical parametric amplifier (OPA) to shift the emission wavelength to the $1.3\;\unicode{x00B5}{\rm m}$ range. The use of this light source has several limitations and disadvantages. First, a Ti:Sa laser does not emit at wavelengths where silicon is transparent; thus an OPA must be used to shift its wavelength. This method to obtain usable light is very inefficient and adds complexity to the experimental setup. Second, the energy per pulse is oversized for the energy requirements of TPA-TCT, and therefore, most of the generated photons are wasted. Third, Ti:Sa amplifiers involve the use of Pockels cells operating at high voltage, which introduce electromagnetic noise into the measurements. Finally, femtosecond laser sources based in Ti:Sa and OPA have high costs and alignment and maintenance difficulties due to their free-space laser structure and limited service life.
Instead, the modest pulse energy requirement of the TPA-TCT allows the use of a femtosecond pulsed laser based on a fiber optic architecture. In fact, there are fiber based lasers delivering fs pulses at $1.5\;\unicode{x00B5}{\rm m}$ that are used to generate TPA in other kinds of applications [13,14]. However, these sources do not present configurable properties or are out of the range requirements for TPA-TCT. In this work, we present the development and application of a fiber laser to the TPA-TCT, designed in the context of a dedicated project supported by the CERN Knowledge Transfer Fund to overcome the limitations presented by the Ti:Sa solid-state laser. This laser source has all the advantages of a fiber optic architecture: robustness, excellent thermal dissipation, high efficiency, and fiber output delivery. Particularly, the fiber laser has the following properties: emission wavelength of 1550 nm (within the transparency region of silicon) to allow 3D mapping; pulse duration and pulse energy of less than 300 fs and more than 10 nJ, respectively, to enable efficient two-photon excitation; average power and pulse-to-pulse amplitude standard deviation below $1\%$ to obtain direct measurements, avoiding mathematical corrections and reducing the derived error in the final data; and a low laser frequency option, down to single pulse, to avoid unwanted saturation in irradiated detectors.
A first prototype has been developed and is used to carry out validation tests as an excitation source in the TPA-TCT.
2. LASER SYSTEM
The system consists of three modules (see the block diagram in Fig. 2). The laser pulse source (LPS) is the source of laser pulses, with a repetition rate of 8.2 MHz, central emission wavelength of 1550 nm, and pulse width below 300 fs. The laser pulse management (LPM) module is used to select the energy of the pulses (from ${\lt}10\;{\rm pJ}$ to ${\gt}10\,\,\rm nJ$ measured at the system output) and repetition rate of the pulsed signal (from 8.2 MHz to single shot) and to arbitrarily commute the laser emission at a response time of ${\sim}1\,\,\rm ms$. The dispersion-scan (D-scan) module comprises a pair of wedges, one of them motorized to select the temporal duration of the pulses in the range of 300 fs to 600 fs. Pulse characterization at the output of the system is performed preferably at the fundamental repetition rate of the pulses, 8.2 MHz. Once characterized, pulse energy, pulse repetition rate, and pulse duration are tuned independently by LPM and D-scan modules.
Fig. 2. LPS, laser pulse source; LPM, laser pulse management module; D-scan, dispersion management module and characterization of the laser pulse by dispersion scanning.
A. Laser Pulse Source
The LPS is composed of several stages (see Fig. 3). First, a mode-locked fiber optic laser is used as the seed to provide pulses of high amplitude and phase stability, of 8.2 MHz fundamental repetition rate, ${\lt}300\,\,\rm fs$ FWHM duration, and 1.5 nJ pulse energy. The standard deviation of the average power achieved is less than $0.2\%$. Then, the chirped pulse amplification technique [15,16] is used to amplify the seed pulses, avoiding undesired nonlinear effects. The light delivered by the seed propagates in a stretcher stage through 40 m of dispersion compensating fiber, stretching the temporal duration of the pulses up to ${\gt}{50}\;{\rm ps}$. To reach the energy levels required by the TPA-TCT, ${E_p} \gt 10\,\,\rm nJ$ at the output of the system (${\sim}1\,\,\rm nJ$ reaching the DUT), the output signal of the stretcher stage is amplified through two stages. A first core-pumping amplification is carried out with an erbium-doped fiber to obtain a pre-amplified signal with optical signal-to-noise ratio ${\rm SNR} \gt 30\,\,\rm dB$, which enables even higher SNR for an optimized amplification in the next high power amplifying stage (${\rm SNR} \gt 50\,\,\rm dB$). This second amplifier is based in cladding-pumped erbium-ytterbium codoped fibers. Pulses of energy ${E_p} \gt 150\,\,\rm nJ$ are obtained at its output.
Finally, once the pulses have the appropriate energy, they are compressed down to the femtosecond range using a photonic bandgap hollow core (PBG-HC) fiber to avoid unwanted nonlinear effects. The final laser output provides pulses of energy ${E_p} \gt 30\,\,\rm nJ$ and duration $\Delta {\tau _{{\rm FWHM}}} \lt 300\,\,\rm fs$.
1. Oscillator
To design the oscillator, the needs of the target application and the technical limitations of some elements that form the later stages of the laser system have to be considered. On one hand, the oscillator must provide a pulsed signal at 1550 nm, with high pulse-to-pulse stability in phase and in amplitude, high SNR, and sufficient energy per pulse to amplify the pulses up to 10 nJ at the output of the system. On the other hand, the limited rise/fall time (80 ns) of the acousto-optic modulator used in a later stage for pulse repetition rate downconversion conditions the oscillator to work at repetition rates below 10 MHz. At a repetition rate of 10 MHz, the output average power of the oscillator for optimized amplification has been determined experimentally to be ${\gt}1\,\,\rm mW$. Such low repetition rates are not common in fiber-optic passively mode-locked cavities, which are typically of several tens or hundreds of MHz. To obtain a stable solitonic emission regime, the net group delay dispersion of the cavity must be close to zero, which is easier to achieve for shorter cavity lengths. Also, the oscillator is designed to autonomously reach the stable emission regime (self-starting). Taking all this into account, three different configurations have been designed solving the nonlinear Schrödinger equation with the split-step Fourier method [17,18]. The mathematical development of the simulations used in the oscillator design is explained in detail in [19]. From a theoretical point of view, the three configurations were viable, and the three of them were tested experimentally to find the one with the best performance. The first two cavities were designed with a dichroic mirror as one of the reflectors of the cavity, with different active fiber and passive fiber lengths. The dichroic mirror, in contrast to a fiber Bragg grating (FBG), has a much higher reflectance value at the output wavelength of the oscillator ($99\%$ against $7\%$) but also has a wider bandwidth (100 nm in contrast to 20 nm). This results in higher dependence on thermal effects since the narrow bandwidth of the FBG fixes the central wavelength with more precision. Furthermore, the FBG can be designed with the required amount of dispersion needed to have a net dispersion value for the cavity, which is anomalous and close to zero. Also, in one of the oscillators, 2 m of dispersion shifted fiber (PM2000D, Nufern) were added to achieve the adequate dispersion regime. Despite that, the first cavity was stable only at pulse repetition rates over 13.5 MHz, and the second one had high losses in splices between the passive and the dispersion shifted fiber, which hindered the reach of a positive gain regime. Figure 4 shows the structure of the passively mode-locked, polarization maintaining (PM), Fabry–Perot cavitiy proved as the configuration that meets all target specifications: emission centered wavelength at 1550 nm, average output power ${\gt}1\,\,\rm mW$, repetition rate ${\lt}10\,\,\rm MHz$, net dispersion ${\lt}0.04\,\,\rm ps/nm$, and self-starting consistency. A 976 nm 300 mW butterfly laser diode (BL976-SAG300, Thorlabs) is used as the pump. Its light is delivered through a PM wavelength division multiplexer (WDM-PM.1598, AFW Technologies) and sent to the chirped FBG (DMR-1550-20-7(-D0.1 $+$ 0)-P1, Teraxion) acting as one of the mirrors of the cavity. Its specifications are 1550 nm central wavelength, 20 nm bandwidth, ${-}0.12\,\,\rm ps/nm$ normal dispersion, 7% reflectance at 1550 nm, and $99\%$ transmittance at 976 nm. The total length of the passive fiber in which the grating is printed is 1.25 m (half of this length is part of the cavity). The laser cavity is composed of 80 cm of PM erbium-doped fiber (PM-ESF 7/125, Coherent) and 10 m of PM passive fiber (PM1550-XP, Coherent). After the passive fiber, a 90/10 polarizing fiber coupler (PFC-15-1-10-B-P-7-1-FB, AFW Technologies) is placed to have access to a $10\%$ auxiliary output for security checks. Also, a 70/30 PFC from the same supplier is used to divide the auxiliary output into a reference for the electronic components and a reference for the user. The second reflector is an InGaAs saturable absorber mirror (SAM-1550-37-2ps-1.3b-0, Batop) with modulation depth, saturation fluence, and recovery time of $37\%$, $30\,\,\unicode{x00B5} {{\rm J/cm}^2}$, and 2 ps, respectively. The laser output is the 1550 nm port of the PM WDM through a polarizing isolator (PISO-2-15-B-7-2-FB, AFW Technologies) to protect the cavity from backreflections that can cause instabilities and damage the oscillator.
Fig. 4. Oscillator structure. PWDM, polarizing wavelength division multiplexer; FBG, fiber Bragg grating; PISO, polarizing isolator; PFC, polarizing fiber coupler; SESAM, semiconductor saturable absorber mirror.
Fig. 5. (a) Oscillator optical spectrum. (b), (c) Autocorrelation traces with simulated pulse and ${\rm sech^2}$ fit, respectively. (d) Radio frequency spectrum and (e) oscilloscope trace of the photodetected signal of the oscillator.
Figure 5(a) shows the measured optical spectrum of the oscillator for a pump power of 210 mW. The spectral bandwidth at 10 dB from the maximum is 20.4 nm, the bandwidth at 3 dB is 14.9 nm, and the SNR is 40 dB. The optical spectrum was stable in long-term measurements: ${\lt}0.3\,\,\rm dB/nm$ in a 4 h long MAX HOLD (optical spectrum analyzer saves the higher signal value for each wavelength over time) versus MIN HOLD (optical spectrum analyzer saves the lower signal value for each wavelength over time) spectral measurement. The average output power was ${\lt}0.5\%$ in a 4 h long measurement. The temporal shape of the pulse was characterized with an autocorrelator (Femtochrome FR-103XL). The autocorrelation trace ($\Delta {\tau _{{\rm FWHM}}} = 219\,\,\rm fs$) and the simulated pulse are shown in Fig. 5(b). The experimental pulse width is calculated assuming a ${\rm sech^2}$ shape for this and every pulse in the following stages of the system. Figure 5(c) shows the same autocorrelation trace together with the ${\rm sech^2}$ fit. The average output power is 12.6 mW, and the pulse energy is 1.54 nJ. Figures 5(d) and 5(e) respectively show the radio frequency (RF) spectrum and the oscilloscope trace of the electrical signal at the trigger output of the LPM module (see Section 2.B). This trigger signal is obtained by photodetecting a replica of the optical signal of the oscillator, which is obtained from a tap of the LPM module and has an optical average power of ${\sim}100\,\,\unicode{x00B5} {\rm W}$. With the RF spectrum measurement, we check the quality of the signal to ensure that we have a clean tone at 8.2 MHz with no spurious frequencies. This is convenient because the trigger from the LPM module is used to synchronize different elements of the TPA-TCT experimental setup. The measured SNR of this trigger signal is ${\sim}30\,\,\rm dB$. Note that this measurement, limited by the low power of the replica signal, does not correspond to the SNR of the RF signal that would be obtained from direct photodetection of the oscillator output. At the time not accessible for measurement, having an optical power of 12.6 mW, the expected SNR for the oscillator under the same floor conditions of the analyzer would be ${\gt}50\,\,\rm dB$, as is the case for mode-locked fiber laser oscillators of the type [19,20].
2. Stretcher
The energy value required for the target application is defined as ${\sim}1\,\,\rm nJ$ reaching the DUT based on the estimations and measurements of the proof of concept mentioned in the Introduction [9,10]. To overcome losses introduced by the optical setup before the DUT, it is necessary to have pulses of energy around 10 nJ at the output of the system. The fundamental repetition rate of the oscillator is 8.2 MHz; therefore, the target average power at the system output is 82 mW. At the same time, a compression stage is required to compensate for the dispersion affecting the pulse temporal shape in previous fiber stages of the laser architecture. If not, the coherence of the pulses delivered by the source breaks, leading to a noise-like shape [21,22]. In the first version of this prototype [23], the pulse shape presented half of the energy in a 120 fs peak, while the other half formed a 1 ps pedestal because of the lack of an appropriate compression stage. The fiber compression stage designed to overcome this problem is what reduces the pedestal to $10\%$ of pulse energy, but at the same time, it introduces losses of ${\gt}70\%$. Taking this into account, a gain of ${\sim}20\,\,\rm dB$ is needed (from 12.6 mW at the oscillator output to 1230 mW at the amplifier output). To achieve these values avoiding undesired nonlinear effects, which would degrade the temporal coherence of the pulses and the shape of the spectrum, the chirped pulse amplification technique is used, which consists of stretching the pulses temporally before the amplifying stages to decrease the peak power of the pulses, thus avoiding nonlinear effects during the amplifying process. Once the target power is achieved, the pulse is recompressed through a linear medium. This technique is explained in detail in [24,25]. Without this amplifying stage, it is not possible to have 10 nJ at the output of the system.
The fibers of the oscillator and amplifier have anomalous dispersion at 1550 nm. The stretcher is built with 40 m of PM2000D, a dispersion shifted fiber with a normal dispersion value $D =-50\,\,\rm ps/nm \cdot km$ and mode field diameter ${\rm MFD} = 4\;\unicode{x00B5}{\rm m}$. Being stretched with normal dispersion, the pulses are compressed throughout the subsequent stages of the laser. In this way, the final compression stage is easier to construct, since the pulses at the output of the main amplifier are partially compressed. On the other hand, the pulses leave the oscillator with anomalous net dispersion. When it propagates through the normal dispersion fiber of the stretcher, the normal dispersion compensates for anomalous dispersion. At some point, the net dispersion value becomes zero. Then, a minimum temporal width is reached and, consequently, a maximum peak power that causes spectral broadening due to self-phase modulation. The spectrum is coherently broadened up to a bandwidth of 40.0 nm at 10 dB from the maximum (23.1 nm at 3 dB), supporting a transform limited pulse width of ${\lt}300\,\,\rm fs$ in subsequent compression stages (obtained from the Fourier transform of the spectrum trace).
Figure 6 shows the optical spectrum after a length of dispersion shifted fiber ${L_{\textit{PM}2000D}} = 40\,\,\rm m$ and the corresponding autocorrelation trace ($\Delta {\tau _{{\rm FWHM}}} = 51.7\,\,\rm ps$). The average output power is decreased to 5.2 mW due to the losses introduced by the fiber and the coupling between the cores of the oscillator output fiber and the dispersion shifted fiber (${\rm MFD}_{\textit{PM} - 1550XP} = 8\;\unicode{x00B5}{\rm m}$ and ${{\rm MFD}_{\textit{PM}2000D}} = 4\;\unicode{x00B5}{\rm m}$). Pulse energy ${E_{\!p}} = 0.61\,\,\rm nJ$.
3. Amplifier
After the stretcher, a double-stage amplifier is implemented with the goal of providing an energy per pulse of ${\gt}\!10\,\,\rm nJ$ at the output of the laser system. The structure of the amplifier is illustrated in Fig. 7.
The first stage is based on core-pumping amplification using 50 cm of PM erbium-doped fiber (PM-EFS 7/125, Coherent). A 976 nm butterfly laser diode that emits a maximum power of 300 mW is used as the pump. The objective of this first stage is to achieve a power gain of around 10 dB while maintaining a spectrum with high SNR and stable pulsed emission. The second stage is based on cladding-pumped amplification. The objective of this second stage is to achieve a power gain of around 15 dB. As an active medium, we use a PM erbium-ytterbium codoped double-clad fiber (PM-EYDF-12/130, Coherent). For pumping, a temperature stabilized 18 W diode has been used, which emits exactly at 976 nm due to wavelength stabilization provided by a volume Bragg grating placed at the output of the laser diode. During the experimentation process, it was observed that a small variation in the wavelength of the diode due to changes in the environment temperature (${\sim}0.2 {-} 0.5\,\,\rm nm$) entailed a large instability (${\gt}\!5\%$ in standard deviation during 4 h) of the pulse energy. Codoped fibers with erbium and ytterbium have a very sharp absorption peak centered at 976 nm, so small variations in the emission wavelength of the pump diode can translate into high instabilities of the energy of the pulse. After stabilizing the emission wavelength of the diode with the Bragg grating, this value was reduced to ${\lt}1\%$.
Fig. 7. Amplifier structure. PWDM, polarizing wavelength division multiplexer; FFC, fused fiber combiner; PISO, polarizing isolator.
Longer lengths of active fiber, despite decreasing the minimum pump power required, induced undesired nonlinear effects. The target power is achieved with 90 cm of active fiber and 4.4 W of pumping power. The spectrum and the pulse structure at the output of the second amplifying stage are shown in Figs. 8(a) and 8(b), respectively. The average output power is 1230 mW, the spectral bandwidth at 10 dB from the maximum is 40.1 nm (25.0 nm at 3 dB), and the pulse duration at FWHM is 51.4 ps.
Fig. 8. (a) Optical spectrum at the output of the second amplifying stage and (b) autocorrelation trace.
4. Fiber Compression
After the amplifying stage, a compression stage is implemented to compress the pulse without nonlinear effects. For the high peak powers to be handled (up to 100 kW), the proposed solution is to use a PBG-HC fiber since undesired nonlinear effects are avoided due to the low nonlinear coefficient of the air core. A pair of prisms or other bulk components could be used to compress the pulse to avoid nonlinear effects as well, but the fiber optic architecture gives us the advantage of splicing the previous stage to this one to transfer the light from one fiber to another. This translates into better stability, robustness, no need to perform periodical alignments between the stages, and the possibility of delivering output pulses through optical fiber in future updates of the system. The structure of the laser (oscillator, stretcher, and amplifier) is entirely built with PM elements. Hence, input to the PBG-HC fiber is linearly polarized. However, the PBG-HC fiber introduces different dispersions for each polarization mode, preventing the pulse from being compressed to its Fourier limit. This effect is known as polarization mode dispersion [26–28]. The solution implemented in this work is to introduce a Faraday rotator mirror (FRM) at the end of the PBG-HC fiber. FRMs receive the output beam from a single mode fiber and rotate the polarization state by ${90^ \circ}$ before reflecting it back through the same fiber. By doing so, a FRM acts as a phase conjugate mirror and cancels out any birefringent effects the beam experienced along the forward path [29,30].
To implement the FRM, a free-space stage consisting of a polarizing beam splitter and a half-wave plate is set up [Fig. 9(a)]. This allows linearly polarized light to be introduced directly into the PBG-HC fiber and to obtain the laser output with the polarization state rotated ${90^ \circ}$ and the pulses compressed to their Fourier limit. The present architecture of the source, designed under a fundamental repetition rate and energy requirements of ${\lt}10\,\,\rm MHz$ and ${\gt}\!150\,\,\rm nJ$ at the output of the amplifier, respectively, leads to an output spectrum for this stage with a Fourier limit of ${\sim}240\,\,\rm fs$.
Fig. 9. (a) Optimized compressor design. FRM, Faraday rotator mirror; PBG-HC, photonic bandgap hollow core. (b) Compressor output optical spectrum and (c) autocorrelation trace.
The compressor is composed of 19 m of PBG-HC fiber with anomalous dispersion of ${+}100\,\,{\rm ps}/{\rm nm\cdot km}$ at 1550 nm and a fiber pigtailed FRM (MFI-1550, Thorlabs). The fiber length of the PBG-HC is adjusted together with the length of PM2000D stretcher fiber so that the pair action over the pulses is optimized to obtain the minimum possible pulse duration. The spectrum and the autocorrelation trace at the output of the compressor are shown in Figs. 9(b) and 9(c), respectively. The average output power is 252 mW, the spectral bandwidth at 10 dB from the maximum is 34.0 nm (26.0 nm at 3 dB), and the FWHM pulse duration is 239 fs.
B. Laser Pulse Management Module
This stage allows selecting the energy of the pulses (from ${\lt}10\;{\rm pJ}$ to ${\gt}\!10\,\,\rm nJ$, measured at the output of the system), selecting the pulse repetition rate, and arbitrarily commuting the emission of the laser at a response time of ${\sim}1\,\,\rm ms$. It is composed of four main elements: first, a pulse picker is included to arbitrarily select the repetition rate of the equipment from 8.2 MHz to single shot. It is based on the switching effect of an acousto-optic modulator, of a high cutoff frequency (${\gt}10\,\,\rm MHz$), rise/fall times ($10 {-} 90\%$) ${\lt}80\,\,\rm ns$, $4\%$ of insertion losses, and a diffraction efficiency of $40\%$. Time referenced to a TTL sync signal obtained from the auxiliary output of the oscillator, the acousto-optic modulator downconverts the fundamental repetition rate of the pulse train to sub-multiple frequencies of the fundamental one. The modulator is placed after the CPA stages, so that the amplifier is always optimized for the fundamental repetition rate. Performing the frequency selection before amplifying would lead to different peak powers for each frequency, inducing undesired nonlinear effects for the range below ${\sim}1\,\,\rm MHz$. This would require different active fiber lengths and/or pump powers for the amplifier to optimize the pulse amplification at each frequency. Second, a variable neutral density filter with an optical density between zero and 4.0 is used to vary the energy of the pulses. This filter works in a reflective regime; therefore, thermal effects due to absorption are avoided, and the beam quality is preserved when the beam goes through the filter. Also, the filter has been selected to be as thin as possible (2 mm of fused silica) to minimize the dispersion effect on the pulse. From the point of view of the target application, the added dispersion ($115.08\;{{\rm fs}^2}$ for 2 mm of fused silica [31]) can be neglected. However, in the case that the laser system is used in an environment where such dispersion is critical, it can be compensated for through the dispersion management module. The automatic selection of pulse energy is carried out through a motorized electromechanical enclosure. Third, a highly sensitive InGaAs photodiode is incorporated as a monitor. Its function is to convert part of the optical beam into an electrical signal to provide a pulse count, reading of energy, and peak power of the pulses in real time. Last, an electromechanical shutter with a response time of ${\sim}1\,\,\rm ms$ to close and open the output of the laser beam is included. Commutation is performed automatically in synchronous reference with the optical pulse train. A scheme of the pulse management module is shown in Fig. 10.
Fig. 10. LPM module internal structure. AOM, acousto-optic modulator; NDF, neutral density filter; PD, photodiode; BS, beam splitter.
The power stability at room temperature of the signal at the output of the complete system has been analyzed, measuring its value every 5 s during 15 h (see Fig. 11). A standard deviation of $0.352\%$ is obtained, which is below the targeted stability ($1\%$) for reliable TPA-TCT.
Fig. 11. Average power of the output of the complete system as function of time, at room temperature.
Fig. 12. (a) Dispersion management stage composed of a D-scan and an autocorrelator. GDD, group delay dispersion. (b) Autocorrelation traces of the laser output after the LPM and D-scan modules for different insertion lengths of the dispersive element.
C. Dispersion Management Module, D-Scan
This stage is designed to tune and measure the pulse duration from ${\sim}300$ to 600 fs, providing a 300 fs range for studying TPA-TCT dependence on pulse duration. It is composed of two elements: a free-space device with two wedges and an autocorrelator [see Fig. 12(a)]. The free-space device works by introducing normal dispersion in the optical path of the beam through a high precision motor to vary the pulse duration. Said motor is used to move several millimeters one of the two wedges so that there is more or less dispersive material introduced in the optical path of the beam (from a minimum of 3 mm to a maximum of 13 mm). In this way, it is possible to vary the dispersion suffered by the pulse in a range between ${-}10800\;{{\rm fs}^2}$ and ${-}45000\;{{\rm fs}^2}$, while at the same time, the autocorrelator is used to measure the pulse duration at the output of the system for each position of the wedge. The transmission bandwidth of the dispersive material is large enough so as not to affect any other properties of the pulsed signal than the pulse duration. The autocorrelator (FR-103TPM, Femtochrome) performs the measurement at the sample plane, which is especially convenient since this gives the information of the pulse profile at the actual point of the semiconductor under test where the two-photon excitation happens. Figure 12(b) shows the autocorrelation traces obtained at the output of the LPM, in the configuration of minimum pulse width (stretcher fiber length of 36.6 m; see Fig. 13) for different insertion lengths of the motorized wedge, 3, 8, and 13 mm.
Fig. 13. Pulse temporal duration versus length of PM2000D fiber in the stretcher. Asterisk: minimum insertion length of dispersive material, 3 mm; squares: intermediate insertion length of dispersive material, 8 mm; crosses: maximum insertion length of dispersive material, 13 mm.
To optimize the dynamic range of the D-scan and obtain dispersion matching among the fiber stretcher stage, fiber compression stage, and dispersion management stage, a study of the dependence of pulse duration on the length of the fiber of the fiber stretcher has been made for different insertion lengths of the dispersive material of the D-scan. Figure 13 shows the temporal duration of the pulse as a function of length of fiber PM2000D in the fiber stretcher.
Fig. 14. Schematic of the TPA-TCT setup used at CERN. Figure taken from [36] with slight adaptations.
3. APPLICATION IN TPA-TCT
One of the benefits of TPA-TCT is the true three-dimensional resolution for testing silicon detectors. With conventional TCT with red, or near infrared (${\lt}1200\,\,\rm nm$) light, it is possible to fully resolve the tested device only by changing the illumination direction in different measurement configurations. Instead, TPA-TCT provides resolution along the beam propagation direction and thus allows for a three-dimensional scan of the device in a single measurement setup. The laser system explained in the previous sections is required to be the source for the TPA-TCT setup schematically shown in Fig. 14, since it has its central wavelength at 1550 nm, where the silicon transparency region lies, pulse energy at the output, pulse duration of ${\sim}10\,\,\rm nJ$, and ${\lt}600\,\,\rm fs$, which are estimated for efficient generation of two-photon excitation (taking into account the losses introduced by the optics of the setup). It is later experimentally shown that the estimated values are suitable for the TPA-TCT. The configurable properties allowed by the system modules, such as the tunability of the frequency between the fundamental repetition rate of 8.2 MHz and single shot, and selection of pulse energy between 10 pJ and 10 nJ, are necessary not only to minimize the damage that can be caused to the DUT and avoid material saturation, but also to provide the chance to study the dependence of the TPA on the energy of the pulses and the number of pulses reaching the DUT. Also the fiber output delivery maintains the gaussian shape of the beam with enough quality to properly focus the laser beam inside the DUT at the desired material depth.
In the tabletop TPA-TCT setup developed at CERN [23] (with a first version of this system, as explained at the beginning of Section 2.A.2) and shown in Fig. 14, the beam coming from the laser system is guided by free-space optics into a Faraday cage. The Faraday cage is used for electromagnetic shielding and provides suitable ambience for temperature and humidity control. Inside the Faraday cage, the light is split by a 50:50 beam splitter. One arm is guided to a highly focusing objective (numerical aperture $\textit{NA} = 0.5$ to 0.7) onto the DUT. The DUT is mounted to a temperature controlled chuck that is fixed to a six-axis movable stage. The other arm leads towards a TPA reference detector, which is a thick silicon PIN detector. The TPA reference serves as an additional energy reference to account for fluctuations in the laser pulse’s temporal profile, which are not detected by the energy monitor in the LPM module. The same beam splitter is used to guide the reflected light from the DUT towards an infrared camera setup. The infrared camera pictures the laser spot position on the DUT and is used to find structures of interest.
Fig. 15. Pulse energy against the collected charge in a $285\;\unicode{x00B5}{\rm m}$ thick PIN diode. The charge is given in units of MIP equivalents.
Figure 15 presents a measurement of the charge generated in a silicon detector when irradiated with the 1550 nm femtosecond pulses of the fiber laser system previously described. The charge collected in a $285\;\unicode{x00B5}{\rm m}$ thick PIN diode, given in units of the equivalent charge deposited by a MIP, is measured as a function of laser pulse energy. The pulse energy is varied by changing the orientation of the neutral density filter inside the LPM module and is measured with a commercial S401C thermal power sensor from Thorlabs. For the measurement, the laser pulse repetition rate is set to 200 Hz, an objective with $\textit{NA} = 0.5$ is used, the DUT is biased well above its depletion voltage, and it is temperature controlled to ${20^ \circ}\rm C$. The Faraday cage is continuously flushed with dry air during measurement. Concerning the repetition rate, the TPA-TCT requires the use of single pulses, and it has to be ensured that not multiple pulses arrive at the DUT during its recovery time. This in particular is important for irradiated devices because their recovery times can be orders of magnitude higher than for pristine devices [32]. For the measurements presented here, this means that repetition rates higher than 200 Hz could be used, but as there is no benefit gained from higher repetition rates, since they have no influence on the physics and impact only the readout speed, 200 Hz is used. For 200 Hz, the readout speed is not limited by the signal acquisition, but by the stage movement. As expected, the relation between pulse energy and the collected charge shows a purely quadratic behavior, proving that only TPA is present. It can be seen that charges of less than one MIP and above 250 MIPs equivalent are reached.
Besides the detector characterization, it was found that TPA-TCT and especially the setup with this 1550 nm femtosecond source are suitable to study electron–hole plasma inside silicon with the advantage of three-dimensional resolution. The appearance of plasma is usually an unwanted side effect for detector characterization at high pulse energies, because it influences detector quantities, e.g., charge collection time [33]. At pulse energies high enough to create a plasma, the charge carriers inside the plasma are shielded from the electric field of the DUT. Therefore, the carriers do not immediately start to drift towards their collecting electrode, which leads to a prolongation of their drift time. A corresponding measurement of the carrier drift time in a thick PIN detector against the laser pulse energy at different bias voltages is shown in Fig. 16.
Fig. 16. Pulse energy against the collection time in a thick PIN detector at different bias voltages.
For this measurement, the laser is focused to $\frac{3}{5}$ of the DUT’s thickness, and its repetition rate is set to 200 Hz. The clear prolongation of collection time with pulse energies above ${\sim}400\;{\rm pJ}$ is observed. The fact that energies within and outside the plasma regime are available proves that the estimated range is sufficient for the application in TPA-TCT, as the plasma regime is the upper limit of the useful energy deposition for the investigation of silicon detectors. For higher bias voltages (absolute values), the impact of plasma effects decreases, because the increased electric field inside the DUT erodes the shielding effect of the plasma faster. Plasma studies can as well be performed using SPA-TCT. However, due to the smaller ionization volume in TPA-TCT the criteria for plasma is met at much lower laser intensities.
Finally, one of the main advantages mentioned about this setup can be observed through the investigation of the charge collection in a segmented silicon detector. The so called interpad region of a $50\;\unicode{x00B5}{\rm m}$ thick multipad LGAD [34], manufactured by HPK [35], was studied. The interpad region is the space between two pixels, and it contains two different implantations: the junction termination extension (JTE) and the p-stop. The implantation of the DUT is schematically depicted in Fig. 17(a). It is of particular interest because the charge collection in the interpad region is a crucial parameter for the detector design development. Figure 17(b) presents the measurement result: a well-resolved 3D collection map. During measurement, the DUT is biased well above its depletion voltage, and the repetition rate of the system is set at 200 Hz. These 3D mapping scans take only a couple of hours of measurement time, and the scan shown here took about 2 h. The resolution of the TPA-TCT depends on the used focusing optics, which are in the end limited by the material of the DUT. The beam parameters used for the shown measurement are a beam waist of about $1.7\;\unicode{x00B5}{\rm m}$ and a Rayleigh length of about $20\;\unicode{x00B5}{\rm m}$, which translates to a resolution in $xy$ of ${\sim}3.4\;\unicode{x00B5}{\rm m}$ and in $z$ for silicon of ${\sim}40\;\unicode{x00B5}{\rm m}$. Structures smaller than the given resolution are still visible, and for those, resolution can be enhanced by the data analysis, but the raw data of these structures will have technique related artifacts.
Fig. 17. (a) Implantation of a multipad LGAD (after [39]). (b) Charge collection measurement of the interpad region of a multipad LGAD [37].
The different implantations are identified by overlaying the received charge collection map with a microscope image of the DUT [36,37]. It is visible that TPA-TCT resolves the three different implantations, which cannot be achieved with conventional TCT methods. The dimensions of the implants are resolved, and their charge collection behavior is visible: the pad region collects more charge compared to the JTE and p-stop region because of the gain layer inside the pad region. Moreover, a bended structure in the charge collection profile of the pad region is visible. The bending is caused by the implantation of the interpad region, which shapes the electric field [38]. The bended electric field causes the charge carriers, which are generated close to the bottom edge of the pad region, not to reach the multiplication layer, but to be collected at the JTE implant. This is an important effect when it comes to optimizing LGAD technology for an as high as possible ratio between the active and total areas.
4. CONCLUSION
In conclusion, we have presented a 1550 nm fiber laser system that delivers femtosecond pulses with configurable properties to be the excitation source for the TPA-TCT in silicon detector characterization. The configurable properties required from the system to study this technique are described, and the architecture of the modules used to achieve them is explained.
The experimental setup and several results of the TPA-TCT studies performed with this laser system are presented. We demonstrate with this kind of source the advantages of TPA compared to SPA for different pulse energies at very low frequencies. Compared to prior TPA-TCT setups, the presented laser system is easy to integrate in a tabletop setup. Its configurable properties allowed us to study the charge generation in silicon detectors as a function of the sensor position and pulse energy, experimentally showing the suitable range of pulse energy values. Also, studies of the plasma effect within the detector and characterization of segmented silicon detectors can be performed with three-dimensional resolution when using this laser system for TPA-TCT.
Funding
Ministerio de Ciencia e Innovación (PID2020-113705RB-C31, DI-15-07461, DI-17-09578); Generalitat Valenciana (IVACE-IMIDTA/2020/32); Bundesministerium für Bildung und Forschung—Wolfgang Gentner Program (05E18CHA); Horizon 2020 Framework Programme (H2020 Research and Innovation Program)—AIDA Innova project (101004761).
Acknowledgment
Part of this work was performed within the RD50 collaboration.
Disclosures
The authors declare no conflicts of interest.
Data availability
Due to the complexity of the data and to maintain an overview on usage, data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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