Spectral narrowing of sub-bandgap absorbance and emissivity in highly doped silicon

Doping-engineered silicon is a vertatile material, well-suitable for exploring new optical properties and applications in infrared spectral region below its bandgap. In this paper, we report on a doping-induced spectral narrowing phenomenon in silicon’s sub-bandgap absorbance and emissivity. By measuring silicon samples with doping concentration varied between <1012 cm−3 and 4.4 × 1019 cm−3, we reveal that, besides the increased amplitude in absorption and emissivity, doping induces a spectral narrowing feature in both mid-infrared absorption and emission, which indicates a trade-off existing for silicon doping level in consideration of efficiency and bandwidth. The spectral narrowing effect occurs around the plasma wavelength, where the silicon changes from dielectric-like property to metal-like property with a negative permittivity. These results are helpful in further understanding free-carrier responses in silicon, and are potentially useful for developing silicon-based materials for mid-infrared applications, such as broadband bolometric sensing, thermal energy harvesting and radiative cooling etc.


Introduction
Silicon, the most important material in modern semiconductor industry, offers a versatile and promising platform for both fundamental and applied explorations in the field of optoelectronics [1,2]. Based on optical interband transition, tremendous progresses have been made in silicon-based optoelectronic devices including high performance photodiodes, solar cells, biochemical sensors and photocatalytic devices [3][4][5][6]. Besides the above-bandgap applications in visible and near-infrared spectral regions, silicon recently also has attracted much attention in mid-infrared below its bandgap [7,8]. The below-bandgap optical properties of silicon is mainly dominated by free-carriers from dopants. Depending on the doping concentration, silicon can be engineered to be fully transparent or totally absorptive, enabling an agility in material and device designs. Using high-resistivity silicon, a variety of important optical components were demonstrated including low-loss waveguides, high-Q resonators and high-speed modulators [9][10][11][12], which indicate silicon's great potential for mid-infrared integrated photonics [13]. On the other hand, in highly doped silicon materials, interesting properties such as plasma spectral filtering and surface plasmon resonance were revealed in the mid-infrared region below silicon bandgap [14][15][16][17].
Broadband absorbance and emissivity are among the engineered properties of silicon, which have attracted considerate interest for applications in infrared sensing, thermophotovoltaics and radiative cooling [18][19][20]. Early in 1967, T. Satō observed high emissivity of silicon over a flat spectrum from 0.4 to 15 μm at elevated sample temperatures [21]. Meanwhile, C. H. Liebert reported a dropping behaviour of emissivity of silicon at long wavelength region [22]. More recently, broadband absorption and thermal emission have been widely reported in black silicon fabricated into various microstructures [23][24][25][26]. Although doping has been shown to play a critical role in these reported broadband absorbance and emissivity, its understanding is not yet complete as these studies correspond to some selected doping levels of silicon and consider only either absorbance or emissivity. In this paper, we investigate the effect of doping on both absorbance and emissivity of silicon in a systematic manner, and discover a spectral narrowing feature in both absorbance and emissivity near the plasma edge. A series of n-type silicon samples with doping concentration varied from <10 12 to 4.4×10 19 cm −3 are characterized with Fourier-transform infrared (FTIR) spectroscopy. Our measurements reveal a dopinginduced spectral narrowing feature in commonly reported broadband subbandgap absorption and thermal emission of silicon. The spectral narrowing is shown to occur around the plasma wavelength associated with free-carriers and originates from the transition of silicon from dielectric-like property to metal-like property with a negative permittivity. These results are helpful for fully understanding free-carrier dominated optical properties of doped silicon.

Experiments
We used six single-side polished n-type Si(100) samples, whose phosphorus doping concentrations were systematially varied as listed in table 1. The sample area size is 2 cm×2 cm. Resistivity of the samples was measured with standard four point probe technique [27], which changes from 0.0016 to more than 10 000 Ωcm. Using the relation of resistivity versus donor density for n-type silicon as given in [28], doping concentrations of the samples were extracted, which decreases from 4.4×10 19 to less than 10 12 cm −3 .
Optical absorption and emissivity of the silicon samples were characterized with a FTIR spectrometer configured into two different schemes. For the optical absorption measurement as sketched in figure 1(a), an integrating sphere was equipped with the FTIR as reported in our recent work [29]. Inner surface of the integrating sphere is coated with a high reflectance diffuse gold coating. This setup enables the measurement of hemispherical total reflectance (R total ), and total transmittance (T total ). Absorption of the sample is obtained as 1−R total −T total . In reflection measurement, the incident light is directed to illuminate the sample placed on the top reflection port at an angle of 12°. The reflection from a reference diffuse gold mirror is used as the background spectrum. In transmission measurement, the sample is placed in the transmission port facing the incident beam, and the transmitted light is collected by the integrating sphere. Incident light entering the integrating sphere through the open transmission port is used as the background spectrum.
For the emissivity measurement as shown in figure 1(b), we followed the method described in [30]. The sample was placed in a cryostat, whose temperature is controllable from 30°C to 300°C above room temperature. Thermal emission of the sample was first spatially filtered with a circular aperture of 7 mm diameter, and then was collected and directed to the FTIR spectrometer with a ZnSe lens of 8 inch focal length. Thermal emission of a calibrated blackbody at the same temperature was used as the reference spectrum. To rule out thermal background, emission from room temperature environment was measured and subtracted from the sample and blackbody emission spectra.  Figure 1. Schematics of (a) absorption and (b) emissivity measurement setups.

Results and analysis
Our measured reflection, transmission and absorption spectra of the silicon samples are shown in figure 2.
Reflectivity of the intrinsic sample S1 increases from 16% to about 35% as the wavelength increases. Meanwhile, its transmission gradually decreases from 90% to about 55%. Its absorption is negligibly small for wavelengths from 1.5 to 8 μm and takes a value of about 10%-32% within the band from 8 to 18 μm as originated from silicon lattice absorption as reported in [31]. As the doping increases up to 1.8×10 18 cm −3 , reflection of the sample S4 becomes flat in spectrum with a slightly decreased amplitude of about 25%. At the same time, its transmission significantly drops. It decreases from 34% to zero as the wavelength increases up to 8 μm. The resulted absorption exhibits a strong absorption of more than 60% within the band from 4 to 10 μm. As the doping further increases to 3.1×10 19 cm −3 in sample S5, interestingly, its reflection first slightly decreases up to 10 μm wavelength, and then rapidly increases in the range of longer wavelengths. Correspondingly, its absorption is above 73% over the band of 1.5-10 μm, but decreases rapidly for wavelengths beyond 10 μm. This spectral narrowing phenomenon suggests that a trade-off exists for the doping level in silicon when considering both the absorption efficiency and bandwidth. As the doping increases to 4.4×10 19 cm −3 for sample S6, the wavelength position where the spectral narrowing occurs shifts to a shorter wavelength of 8 μm. Figure 3 shows the measured emission spectra and emissivity of the silicon samples at 125°C. This temperature was chosen to have distinguishable sample emission signal above the environmental background, but still low enough to prevent thermal excitation of free-carriers in silicon. It is seen that thermal emission of the samples spans a wavelength range from 3.6 to 18 μm. Emission intensities of the silicon samples are larger than that of thermal background, but less than that of the blackbody emission. The obtained emissivity of the samples increases as the doping increases. In particular, the intrinsic sample S1 has a low emissivity of less than 0.19. As the doping increases to 1.8×10 18 cm −3 for sample S4, the emissivity dramatically increases with an amplitude of more than 0.6 and becomes flat. As the doping further increases to above 10 19 cm −3 for samples S5 and S6, their emissivities further increases in amplitude, but rolls off around the wavelengths of 10 μm and 8 μm,  respectively. This doping-induced spectral narrowing is similar to that measured in optical absorption as described earlier.
The above observed doping-induced spectral narrowing effect originates from free-carrier responses [32]. To better understand its mechanism and properties, we simulated absorption of the silicon samples with different doping concentrations using the transfer matrix method [33]. Thickness of the samples was assumed to be 500 μm. The complex permittivity of silicon is described with the Drude model, i.e. [34] e w e e w where w represents the angular frequency, ω p and γ are the screened plasma frequency [25,35] and scattering rate, respectively, which can be written as w e e = ¥ Ne m 2 here, ε 0 is the vacuum permittivity, ε ∞ =11.7 is the dielectric constant at high frequency limit, and e is the electron charge, m * is the effective mass of electron, which equals 0.27 times the mass of free electron in vacuum, and N represents the electron concentration. μ is the carrier mobility, which is related to electron concentration N via an empirical relation [36] m m m m m where the parameters are μ 1 =68.5 .711, and β=1.98. Figure 4(a) shows the calculated free-carrier absorption of the silicon samples with different doping concentrations. For intrinsic undoped silicon S1, the absorption is zero. As the doping increases, the absorption dramatically increases, and evolves into a flat spectrum above 4.2 μm with amplitude of about 70% for sample S4 with a doping level of 1.8×10 18 cm −3 . As the doping level further increases to 3.1×10 19 cm −3 and 4.4×10 19 cm −3 for S5 and S6, besides the increased amplitude, the absorption start to exhibit a rolling-down behaviour at the wavelengths of 10 μm and 8 μm, respectively, which agree with our observed spectral narrowing feature in absorption and emissivity measurements. Similar dropping in emissivity of silicon was also observed by C. H. Liebert in [22]. However, its physical origin was not identified. Here, we attribute the spectral narrowing behaviour to the plasma edge effect. Figure 4(b) shows the calculated plasma wavelength λ p of the five doped silicon samples. The plasma wavelength of the S5 and S6 samples are 10.67 μm and 8.95 μm, which well match the positions where spectral narrowing occur as shown in figures 2(c) and 3(b). Therefore, our observed spectra narrowing phenomenon occurs around the plasma wavelength. Physically, the doping-induced spectral narrowing can be understood from the change of silicon from dielectric-like property to metal-like property. Figures 4(c) and (d) show the calculated refractive indices of the six silicon samples. It is seen that near the plasma wavelength, real part of the silicon refractive index changes from positive to negative, which is characteristic of a metallic property and leads to the measured rise in reflectance and decreased absorption for wavelengths above the plasma wavelength. It is noted that similar plasma edge effect has been observed in reflection spectrum of silicon in [14], which is characterized with a sharp rise in reflectivity. Here, we show that for absorbance and emissivity, the plasma edge effect leads to significant drop in their values. Therefore, when considering both efficiency and spectral performance of silicon materials in applications such as infrared sensing or radiative cooling [37,38], a trade-off doping level needs to be taken. Finally, it is worthy to note that Fabry-Perot interference fringes arised from the 500 μm sample thickness are present in above calculated results as shown in the purple and green shading area in figure 4(a), while they are absent in our measured results in figure 2. This discrepancy resulted from our used spectral resolution of 4 cm −1 , which is insufficient to resolve the interference features.

Conclusion
We investigated the effect of doping on sub-bandgap optical absorption and emissivity of silicon. By measuring a series of silicon samples with different doping concentrations, we observed a spectral narrowing feature in the commonly reported doping-induced broadband and strong absorption and thermal emission in silicon. This spectral narrowing phenomenon occurred around the plasma wavelength determined by the free-carrier concentration and resulted from transition behaviour of silicon from dielectric-like property to metal-like property with a negative permittivity. These results suggest that a trade-off exists for silicon doping level when considering both absorption/emission efficiency and bandwidth. Since the spectral narrowing happens within a finite spectral region around the plasma wavelength in a gradual manner instead of an abrupt one, it could be suppressed to some extent via scattering-enhanced effect by introducing sub-wavelength structures such as nanopores and nanopillars into silicon.