1. Introduction

Influence of THz and mid-far IR radiation, probing charge, structural and mesoscopic states of matter, on functional materials, electrical circuits and living organisms is still remaining rather uncovered, partially, because of historical challenges in detection and visualization of transmitted, reflected and scattered radiation in this spectral range [1,2] (Reststrahlen region [3]). Highly demanded availability of cheap, robust and sensitive photodetectors in this range, potentially, based on advanced silicon (Si) photonics [4,5], could lead to remarkable breakthroughs in our novel perception of the surrounding world.

Crystalline intrinsic Si, being very abundant, rather cheap and highly transparent material in the range of 1-1000 micrometers [6], appears as a primary candidate material platform of IR and THz photonics, comparing to germanium and III-V and II-VI compounds. Si doping by different impurities [7,8], introducing shallow and deep optical centers, allows to modify its IR absorption. However, to ensure high IR-photosensitivity, such doping should be high (>10$^{20}$ impurity atoms/cm³, hyperdoping) [9,10]. Such hyperdoping is challenging, since high relative content of impurity atoms perturbs the Si crystalline lattice, leading to local amorphization and degradation of optical and electrical performance [11–13], and requiring ultrashort-pulse laser hyperdoping and subsequent annealing to quench hyperdoped Si states with tremendous non-equilibrium solubility of impurities [14–17]. Importantly, it is high intermediate concentration of impurity that drives its aggregation in Si and related mid-IR broadband absorption, with stronger aggregation providing absorption deeper in IR region. However, ultimate spectral limits for photosensitivity extension into IR region for hyperdoped Si were not explored yet and advanced IR-sensitive Si photo-elements were demonstrated only in the range below 2 micrometers [18–24], comparing to the demonstrated IR-absorption range up to 10 micrometers [9–13,17]. Hence, comprehensive near-far IR photoconductivity (PC) studies of p-n junctions based on as-fabricated hyperdoped – either annealed, or non-annealed – Si could be crucial differential intermediate tests of both their IR-sensitivity and related electrical performance prior potential harnessing in optoelectronic integration [16–24]. Strong liquid-helium cooling of the hyperdoped samples is required in this case to obtain mid-far IR ($\lambda \approx$ 2-20 $\mathrm{\mu}$m) spectra of shallow impurity centers ($E \approx$ 50-400 meV) [25–27], while avoiding their considerable bleaching via thermal ionization at $kT \sim E$ and photoconductivity damping via electron-phonon scattering at $kT \sim \hbar \Omega$ (freezing of low-energy phonons with frequencies $\Omega$).

2. Materials, procedures and methods

In this work, the functional IR-sensitive p-n junction photoelement was fabricated by femtosecond-laser induced n-type sulfur-hyperdoping [17,28,29] a submicron-thick surface layer of a p-doped ($\sim$10¹⁵ B-atoms/cm³, specific resistivity $\approx$ 20 $\Omega \cdot$cm) 0.38-mm thick commercial Si(111) wafer substrate, irradiated in a raster-scan manner (100 lines/mm, 1 m/s) in liquid carbon disulfide CS₂ medium in a glass beaker by 1030-nm, 300-fs 7-$\mu$J pulses, coming at the 100-kHz repetition rate and focused onto the sample surface (the peak surface laser fluence $\approx$ 1 J/cm²), as described elsewhere [30]. Its subsequent annealing, similarly to [14], was performed in a muffle oven in ambient air at the temperature of 1150 $^\circ$C during 30 minutes and quasi-static quenching directly inside the turned off, closed oven accompanied by 10’-ultrasonic cleaning to delaminate the surface oxide layer, according to the procedure described elsewhere [29].

Scanning electron microscopy (SEM) visualization of the ablated surface topographies was performed using a microscope TESCAN VEGA, equipped by an energy-dispersion x-ray (EDX) spectrometer, for preliminary in-depth chemical micro-analysis by varying the kinetic electron energy in the incident beam in the range of 4-30 keV. Chemical bonding of silicon, sulfur and carbon atoms across a 1-mm wide of the modified surface layer was studied by means of x-ray photoelectron spectroscopy (XPS). The photoelectron spectra were acquired with Mg-K$\alpha$ line of an analytical module, including a XPS spectrometer with an electron energy analyzer, providing the energy accuracy of 0.1 eV and composition accuracy of 0.15 at. % (84.00-eV Au 4a7/2 line as the standard). According to our EDX characterization, the resulting n-doped layer contained about 0.4 at. % of sulfur, which was distributed, besides the surface oxidized sulfite/sulfate forms (60-70 at. %), in the dissolved atomic (S⁰) and segregated cluster (Sn^2-) forms ($\approx$ 30-40 at. %) in the nanocrystalline surface layer (Figs. 1(a),b).

 

Fig. 1. (a) Functional layout of the n-p junction made by n-hyperdoped layer on the p-doped Si substrate and corresponding EDX elemental maps (prior ultrasonic cleaning). (b) XPS spectrum of S$_{2p}$-band of sulfur, its deconvolution and assignment after [31]. (c) image of the PC element. (d) IR-PC acquisition arrangement: globar, KBr splitter, sample, electrical scheme, Bruker spectrometer.

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Detailed imaging and structural characterization of the layer cross-section were performed by means of transmission electron microscopy (TEM, accelerating voltage – 200 kV, point-to-point resolution – 0.19 nm) using JEOL JEM-2100F equipped by an energy-dispersion x-ray spectroscopy (EDX) module. Cross-sectional specimens for TEM were prepared in a common way, involving mechanical grinding and subsequent thinning of a sample by Ar⁺ ion milling at 4 keV ion energy. Selected area electron diffraction (SAED) patterns were obtained using a 100-nm selective aperture. Elemental maps were acquired in a scanning (STEM) mode, using 1-nm spot size for enhanced spectrum collection rates.

During fabrication of the photoconductive (PC) element, the sulfur-hyperdoped/annealed sample was mounted into a diode case (Fig. 1(c)), where back and front electrodes were 100-nm thick gold films, deposited via magnetron sputtering. The back (substrate) side of the sample was fully covered by gold to provide the large contact area. The laser-treated front side was partially covered by the metal layer. Rear and front electrical contracts were glued with silver paste. In this way, a PC sample with a vertical arrangement and large photosensitive contact area equal to 5x5 mm² was obtained. Relatively high conductivity of the sulfur-hyperdoped layer provided good lateral current distribution.

Mid-IR photoconductivity experiment was carried out using a Bruker IFS 125 HR all-range high-resolution vacuum Fourier spectrometer (Fig. 1(d)). A Cryomech PT 403 closed-cycle helium cryostat was used for sample cooling in the temperature range of 5-300 K, controlling the temperature by means of a Lakeshore 335 controller and a silicon sensor. A KBr optical window was used as the entrance window of the cryostat. As a radiation source was used a globar with a KBr beam-splitter. To register the photoconductivity in the spectral range of 2-25 $\mathrm{\mu}$m, a self-made electronic circuit with a preamplifier was used, the signal from which was fed by the analog output of the spectrometer. The PC spectra were obtained with different voltage biases in the range from -10 V to +10 V, indicating no dependence of the PC spectra on the voltage value or sign. To correct the signal on the blackbody emission, as well as to take into account various spectral features of the optical components of the spectrometer, measurements were carried out with similar optical components and parameters, where the DLaTGS linear pyroelectric detector served as a radiation detector. The sulfur-hyperdoped/annealed mounted sample was tested by IR-PC spectroscopy in the temperature range of 5-105 K, blocking/splitting the visible part of incident light by a KBr splitter. To prevent distortion of the photoconduction signal due to non-linear responses, the following checks were performed. First, we checked the shape of the signal when the sample was irradiated with different intensities of light. Second, the signal was investigated at different rates of modulation of radiation by a Fourier spectrometer (from 1 to 30 kHz). Once nonlinear processes depend on time and intensity, these check would allow us to evaluate the possible nonlinear distortion of the signal. However, we did not observe any noticeable changes in the spectra.

3. Results and discussion

3.1 Broadband (2-21 $\mu$m) structured photoconductivity of liquid-helium cooled hyperdoped Si: spectral assignment of sulfur centers

The typical acquired broad-range (60-500 meV, 2.4-20.8 $\mathrm{\mu}$m, 480-4200 cm^-1) PC spectrum of the hyperdoped Si is shown in Fig. 2, where the accessory rocking (450 cm^-1), bending (800 cm^-1) and stretching (1075 cm^-1) Si-O-Si bands and other contaminants are absent [32]. Comparing to room-temperature broad and continuous near-mid-IR absorption spectra of weaker hyperdoped Si samples in the most of previous studies (see the bibliography in [9–13]) due to the deep cooling this spectrum demonstrates a number of well-resolved spectral bands, which can be readily assigned as follows [25–27]. Besides the common mid-IR bands of atomic-like S$^+$ and S$^0$ centers (ground-state binding energy E$_{S+}$ = 614 meV, E$_{S0}$ = 318 meV) [25], the interesting feature in Fig. 2 is the set of rather strong and well-resolved spectral bands in the range $\lambda \approx$5-20 $\mathrm{\mu}$m. These bands apparently indicate the rarely observed, usually very weak absorption of S-clusters S$_2^0$, S$_2^+$, S$_c^0$(X$_{1-5}$) and S$_c^+$(X$_1$), as well as absorption of the anticipated similar centers S$_c^+$(X$_{2-5}$), which are, by the analogy with S$_2^+$ and S$_c^+$(X$_1$), two-fold higher energy (the overall binding energy range $\approx$ 50-250 meV) [25–27]. Here, these PC band can be observed in mid-far IR PC spectra due to the liquid-helium cooling and high abundance of the highly aggregated cluster forms of sulfur atoms. In its turn, such high atomic aggregation became possible due to the high overall concentration of sulfur impurity in the n-doped surface layer, including also accessory sulfur sediments on the surface and nanograin boundaries, which could be minimized, e.g., by dissolution upon high-temperature (>1100 $^\circ$C) [14–17] annealing.

 

Fig. 2. PC spectrum of the photoelement at 5 K temperature with spectral assignment of the spectral bands after [25–27]. The anticipated spectral positions of unknown centers S$_c^+$(X$_{2-5}$), which could be twice higher in energy regarding the position of corresponding neutral centers, are shown with the question mark.

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Hence, at the liquid-helium temperatures, preventing bleaching of shallow states of highly-aggregated charged and neutral sulfur-donor centers via their thermal ionization and electron-phonon scattering, broad near-far IR photoconductivity spectrum of the hyperdoped Si demonstrates a large set of their corresponding spectral bands. The observed extraordinary extension of the spectral photoconductivity response toward far-IR was assigned, first, to high dopant concentration, providing near-far-IR absorbing highly-aggregated of sulfur cluster centers [13,17,28,29]. Other driving factors are dopant annealing conditions [14–17], and the low operation temperatures, as shown below.

3.2 Temperature effects in mid-IR photoconductivity of hyperdoped Si: quantum-level damping via electron-phonon interaction in different sulfur aggregation states

Temperature effects on photoconductivity of the hyperdoped Si were studied in the range of 5-105 K for the most intense part of its mid-IR PC spectrum presented in Fig. 2 (Fig. 3, wavenumbers $\mathrm{\nu}$ = 1200-8000 cm^-1, $\lambda \approx$ 1.25-8.3 $\mathrm{\mu}$m). The influence of temperature is expected to damp and broaden these present spectral bands with interactions of the corresponding shallow donor electronic states with thermally-excited low-energy lattice phonons [33] and their depopulation via thermal ionization [34].

 

Fig. 3. Color PC spectra of hyperdoped Si at different temperatures in the range of 5-105 K with the spectral assignment after [25–27]. The yellow bilateral arrows indicate the lower-temperature (< 35 K, upper arrow) and higher-temperature (> 85 K, bottom arrow) ranges of PC damping, with the anticipated spectral positions of unknown centers S$_c^+$(X$_{2-5}$) shown with the question mark.

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Indeed, in Fig. 3 a strong decrease in the PC spectral intensity is observed versus the increasing temperature, starting at the lower temperatures T < 35 K in the low-wavenumber range and then extending to the high-wavenumber range at higher temperatures T > 85 K. Specifically, one can highlight two main trends in the temperature dependence of the PC bands: 1) the total drop at the lower temperatures T < 35 K till the noise level for the low-wavenumber centers S$_2^0$, S$_c^+$(X$_3$), the simultaneous partial drop for the medium-wavenumber centers S$_c^+$(X$_{1,2}$), S$_2^+$ and the subsequent persistence at this level till $\approx$ 85 K; 2) the final drop to the noise level for all these centers S$_c^+$(X$_{1,2}$), S$_2^+$ and even high-wavenumber centers S$^0$, S$^+$. These trends are overviewed in Fig. 4(a) as a function of temperature.

 

Fig. 4. (a) PC spectral intensity $\Phi _i$ for the different sulfur-donor centers versus T (left axis), right axis - phonon occupation numbers at $\varepsilon _1 \approx$ 4 meV and $\varepsilon _2 \approx$ 20 meV). (b) Dependences ln$\{1-\Phi _i/\Phi _{i,max}\}- 1/$kT with their linear fitting curves and activation energies $\varepsilon _i$ as the linear slopes (b).

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In a fair assumption that the observed thermally-induced changes in the photoelectrical properties of the hyperdoped Si are barrier-like processes with certain center-specific activation energies $\varepsilon _i$, the PC intensities were presented in ln$\Phi _i$ -1/T coordinates and linearly fitted to evaluate these magnitudes $\varepsilon _i$ (Fig. 4(b)). The derived activation energies demonstrate two characteristic values $\varepsilon _1$ = 4.2$\pm$0.3 meV and $\varepsilon _2$ = 20$\pm$2 meV, effective in the temperatures ranges <35 K ($kT$ < 3 meV) and > 85 K ($kT$ > 7 meV), respectively, while are still much lower, than the electron binding energies of the centers E $\approx$ 50-600 meV, and comparable to the corresponding values $kT$ (Fig. 3). Therefore, one should look at other sulfur-related lower-energy excitations in the material, e.g., intra-center phonons and local vibrational modes.

Particularly, the activation energy $\varepsilon _1 \approx$ 4 meV could be directly related to the lowest energy phonon ($\hbar \Omega _{min} \approx$ 4 meV) in a crystalline lattice of face-centered orthorhombic sulfur unit cell (space group D$_{2h}^{24}$ (Fddd)) [35], which has the population factor [36]

In contrast, at higher temperatures > 85 K much higher activation energy $\approx$ 20 meV comes into play in the PC response (Figs. 3,4). Again, its magnitude is much lower, than the electron binding energies of the centers E $\approx$ 50-600 meV [25–27], or even zone-edge phonon energies in crystalline Si (12-16 and 55-63 meV for the acoustic and optical modes, respectively) [37]. Meanwhile, it is still related to the same PC spectral bands in Fig. 3, indicating close relation to their underlying sulfur centers. Specifically, one can relate this five-fold higher activation energy to the lowest energy of Raman-active vibrations $\nu _8$(e$_2$) of sulfur molecular octagons ($\hbar \Omega _{mean} \approx$ 20 meV) in the orthorhombic crystalline sulfur [35]. Moreover, according to Fig. 4(b), such molecular-like sulfur vibrations could be also related to substitutional S-ion in the S$^+$, S$_2^+$-centers or S-atom in S$^0$-center, and to sulfur atoms bound to surrounding Si atoms, since vibrational spectroscopy of sulfur impurity in Si is not well explored yet.

Overall, the unexpectedly strong effect of the limited (5-35 or 85-105 K) temperature variation on the spectrally-resolved photoconductivity characteristics of the sulfur-donor hyper-doped Si was observed. Its detailed characterization in terms of thermal activation energies indicates that quantum-level, single-particle thermal excitation of the lowest-energy phonon modes in the embedded sulfur nanocrystallites is underlying the observed two-step deactivation of the IR-photoconductivity through electron-phonon scattering. More enlightening and detailed picture of broader IR-THz-range spectral (1-1000 $\mathrm{\mu}$m) PC response and related temperature effects for a large number of samples with variable abundance of different sulfur-donor centers is in progress and will be presented in our forthcoming publications.

4. Conclusions

Crystalline, moderately p-doped silicon wafer, strongly laser-hyperdoped in its sub-micrometer surface layer by donor sulfur, demonstrates very broad near-far IR (2-21 $\mathrm{\mu}$m) photoconductivity spectra of its donor centers in different charge and sulfur aggregation states, well-resolved at the liquid-helium temperatures. At higher temperatures in the range of 5-105 K, two-step deactivation of the photoconductivity response occurs via electron-phonon scattering due to thermal population of the lowest-energy sulfur lattice phonon (< 35 K) and the related lowest-energy molecular-like sulfur vibration mode (85-105 K). The minimal temperature variation in the ranges of 5-35 and 85-105 K, providing the strong PC damping, indicates its efficient and spectrally-specific temperature control in the hyperdoped Si for potential broad-IR and even THz applications.