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Abstract
In this paper, we demonstrate that n-type heavily doped germanium (Ge) can serve as a sort of CMOS-compatible, permittivity crossover wavelength (at which the real part of permittivity changes sign) wide range adjustable epsilon-zero material in mid-infrared (MIR). The antimony (Sb) doped Ge films with high doping concentrations have been highly crystalline grown on silicon substrates with the molecular beam epitaxy (MBE) process. Our results reveal that the crossover wavelength of doped germanium is highly tunable by adjusting the carrier concentration and crystallinity of the films simultaneously. By optimizing dopant flux and substrate temperature, the maximum carrier concentration can be achieved as high as 1.6×1020 cm−3, resulting in a very short crossover wavelength of 4.31 µm, which is very difficult to realize in group IV semiconductors. The heavily doping process also enables it possible to observe the room temperature photoluminescence (PL) from direct band transition of germanium films.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The wavelength for certain materials whose real part of permittivity changes from positive to negative is called epsilon (ɛ) crossover wavelength (or epsilon zero wavelength), around which is known as epsilon-near-zero (ENZ) region [1,2]. The crossover wavelength is an important parameter for characterizing a series optical properties of materials, and hence influence their applications, such as plasmonics [3] and transformation optics [4]. In their ENZ region, the materials exhibit very small real part dielectric permittivity while changing the sign from positive to negative [5]. Photons of crossover frequencies would have a distinctive effect on the polarization of the electron cloud of the materials [6]. This will lead to some unconventional optical behavior and brand new applications for such materials [6,7]. The reported epsilon zero point media related phenomena include ultrafast light-induced large refractive index changes [8], novel optical response of plasmonic antennas [9] on ENZ substrates, electric and magnetic fields decoupling [10], and demonstration of superluminal phenomenon [11]. A series researches have been focused on nonlinear optics [5,8,12], metasurface [13] and plasmonics [14,15] based on the materials whose epsilon crossover wavelength is in visible (noble metals) [16] and near-infrared (transparent conductive oxides) ranges [4,17,18]. However, the research on the mid-infrared (MIR) materials whose epsilon zero point can be tuned are currently insufficient. In general, n-type semiconductors in which electrons are the majority carriers are capable of locating their epsilon zero wavelength in mid-infrared (MIR, 2.5-25µm [19]), such as n-type III-V semiconductors (InGaAs et al.) [20] as well as group IV elemental semiconductors (Si et al.) [21,22]. Compared with III-V semiconductors which are inherent defective in lower doping upper limit (1018∼1019 cm−3, the doping concentration is closely related to the epsilon crossover wavelength) [23] and incompatible to silicon platform Complementary Metal Oxide Semiconductor (CMOS) fabrication process, Group IV semiconductors are considered to be more promising in MIR because of a wide range of tunable epsilon crossover wavelength, low optical loss and compatibility with CMOS process [24,25].
Basically, Drude’s free electron model could be applied to describe the dispersion of permittivity [26]:
Among group IV n-type semiconductors, silicon and germanium are the commonly used matrix, while phosphorus and antimony are the main dopants [27]. There is no self-compensation effect of limiting the upper doping concentration commonly found in group III-V semiconductors, as a result, the doping concentration can reach to the magnitude of 1020 cm−3 in group IV materials. At the same doping concentration, the conductivity effective mass of germanium (around 0.12 m0) is smaller than that of silicon (around 0.26 m0) [27,28], that means to achieve the same epsilon crossover wavelength, germanium requires much lower doping concentration than silicon, and thus the loss due to free carrier absorption could be also effectively reduced [29]. Meanwhile, the dopant antimony has a higher electrical mobility than that of phosphorus in the same group IV semiconductor doping environment, leading to a smaller momentum scattering loss of antimony doped germanium than phosphorous doped germanium [27,30]. Therefore, antimony heavily doped germanium is expected to get a high quality short wavelength mid-infrared material [22].
As a qualified material whose epsilon zero point is located in MIR, doped germanium semiconductor has another advantage that it is fully compatible with silicon CMOS manufacturing process [31]. The success of hetero-epitaxial growth of germanium on silicon has provided integrated germanium photodetector [32], germanium waveguide [33] and germanium light source with excellent performance in the field of silicon photonics [34]. Although there exists lattice and thermal mismatches between germanium layers and silicon substrates, state-of-art germanium growth techniques (such as compositional grading buffer [35,36], cyclic post-annealing [37], epitaxial lateral overgrowth [38] or selective area depositions [39,40]) are capable of reducing threading dislocation density and generating Ge-on-Si epilayers with high crystal quality and low surface roughness, thereby significantly reducing the optical losses caused by structural defects and rough surface.
Among various mid-infrared epsilon-zero materials, group IV semiconductor phosphorus doped germanium and antimony doped germanium are worth mentioning [15,41]. Most reported phosphorous doped germanium films are grown with the chemical vapor deposition (CVD) process, and the measured carrier concentration is generally lower than 5×1019 cm−3 [42], resulting in an epsilon crossover wavelength longer than 8 µm. Combined with the laser thermal annealing (LTA) process, the doped phosphorus can be activated as much as possible [43], leading to the emergence of materials with effective carrier concentration as high as 2×1020 cm−3 and epsilon crossover wavelength of about 3 µm [21]. As for antimony doped germanium, the reported highest carrier density can reach 1020 cm−3 [44], although no reports of epsilon crossover wavelength tuning and corresponding performance studies were involved. We have reported that our doped germanium films can be applied in surface plasmon polariton (SPP) and localized surface plasmon polariton (LSPP) in mid-infrared. The research about SPP excitation, transmission and loss, local field enhancement and mid-infrared FTIR reflection signal enhancement has been described in detail in our recent published paper [45].
In this paper, we focus on study of growth process of antimony heavily doped Ge-on-Si films, our study revealed that the epsilon crossover wavelength of the material has a close relationship with the epitaxial process including substrate temperature and dopant flux. Antimony-doped epitaxial germanium films are therefore expected to be the materials with large tuning range and low optical loss around mid-infrared epsilon zero point.
2. Experiments
Antimony doped germanium films were deposited on silicon chips with the molecular beam epitaxy (MBE) mothod. The solid source MBE system was equipped with an electron beam evaporator for silicon growth (EVBB-63-5, MBE-Komponenten, Germany), two Knudsen cell sources (WEZ-63-35, MBE-Komponenten, Germany) for germanium and antimony evaporation, a Reflection high-energy electron diffraction (RHEED) system (RH 20 SS, Stable INSTRUMENTE, Germany) for in-situ surface morphology monitoring. The base pressure of MBE chamber was maintained under 2×10−10 Torr. Cleaned with standard RCA process, 2-inch silicon wafers were loaded into MBE chamber. After degassing and removing the residual oxide, 50 nm homo-epitaxial Si layers were deposited at 500 °C to smoothen the terraces on substrates. Antimony doped germanium films were grown on silicon substrates with a constant germanium deposition rate of 0.5 Å/s and a constant Sb flux of 1.4×1012 cm−2s−1, while the temperature of substrates varied from 150 °C (sample A), 250 °C (sample B) to 350 °C (sample C). The substrate temperature of sample D was maintained at 250 °C, but was grown at a lower antimony flux of 7.4×1012 cm−2s−1. Our results show that a too low temperature of substrate (lower than 150 °C) will not provide sufficient nucleation and surface migration energy for film crystallization. However, low temperature benefits higher activated carrier concentration by reducing the aggregation due to the large diffusion coefficient of antimony. In order to balance the carrier density and crystallinity, a virtual substrate was inserted between bottom silicon layer and upper Sb-doped germanium epilayer in sample A. The virtual substrate was composed of low temperature (LT) seed layer (50 nm), LT-HT intermediate layer (110 nm) as well as high temperature (HT) epilayer (840 nm). To achieve low density of threading dislocation (TD) and small surface roughness, the virtual substrate should be post-treated with a cyclic thermal annealing process between 750 and 900 °C for 10 times. As for other samples deposited at higher substrate temperatures without affecting crystallinity, they were directly hetero-eptaxial grown on silicon layer without a virtual substrate.
Cross section transmission electron microscopy (TEM) (200 KV, Tecnai G2) was employed to study the crystal quality and surface smoothness of heavily doped germanium films. Secondary ion mass spectrometer (SIMS) analysis (CAMECA ims-7f auto) was used to show the in-depth distribution profile of antimony concentrations (or called as chemical antimony concentrations) in germanium films. A Fourier Transform Infrared Spectroscopy (FTIR) (Bruker, VERTEX 70) with a microscope accessary (Hyperion 1000) was utilized to measure the mid-infrared reflectance spectra R(ω). Drude-Lorentz dispersion model could be chosen to extract complex permittivity of antimony doped germanium films by fitting FTIR data [46,47].
3. Results
Sample A (Tsub=150 °C) and sample C (Tsub=350 °C) are selected as typical samples for transmission electron microscopy (TEM) characterization. TEM images are shown in Figs. 1(a) and 1(c) for sample A, as well as in Figs. 1(b) and 1(d) for sample C, respectively. As indicated in Fig. 1(a), most threading dislocations in sample A are effectively confined in the vicinity of the Si/Ge interface, rather than penetrating through the upper area; at the same time, the root mean square (RMS) roughness of the doped germanium layer surface for sample A is relatively low, as shown in magnified “A” region of Fig. 1(a). A clear interface between doped germanium layer and intrinsic germanium layer is shown in magnified “B” region of Fig. 1(a) because of the doping process. The reciprocal lattice constant of doped germanium epilayer along (220) direction is measured to be 3.485 nm−1 according to the diffraction patterns in Fig. 1(c), which is very close to that of bulk germanium. Compared with the surface morphology of sample A, the surface of sample C has a larger RMS roughness, shown in magnified “C” region of Fig. 1(b). The doped germanium layer for sample C also clearly demonstrates the existence of twin crystal in magnified “D” region of Fig. 1(b). In addition, the electron diffraction pattern for sample C consists of multiple sets of diffraction spots and a discontinuous diffraction ring, which is displayed in Fig. 1(d), indicating the existence of poly-crystalline domains.
Fig. 1. Bright field cross sectional transmission electron microscope (BF-XTEM) and High resolution (HR)-TEM images of (a) Sb doped Ge films grown on Ge virtual substrate at deposition temperature of 150 °C (sample A) and (b) those grown on Si substrate at deposition temperature of 350 °C (sample C) with a constant Sb flux of 1.4×1012 cm−2s−1. Four outlined regions A, B, C and D are magnified to show more details respectively. Electron diffraction patterns of (c) sample A and (d) sample C are captured along [011] zone axis respectively.
Figure 2 represents the microstructure and elemental distribution of sample C. The cross sectional high-angle annular dark field (HAADF) scanning transmission electron microscope (STEM) image shows the dense threading dislocation networks in sample C in Fig. 2(a). The energy dispersive x-ray (EDX) element mappings of germanium and silicon elements shown in Figs. 2(b) and 2(c) demonstrate a distinct Si-Ge distribution interface, indicating less Si-Ge mixing even at growth temperature of 350 °C. The homogeneous distribution of antimony elements can be clearly seen in the entire region in Fig. 2(d), it is consistent with the results from the SIMS measurement. HR-TEM image in Fig. 2(e) shows clearly a grain boundary, along where oxygen element is assembled as indicated by EDX mapping in Fig. 2(f). The marked circles are the selected regions to show the fast Fourier transform (FFT) patterns (inset), the top and bottom regions are selected from different grains, while the middle region is from the area containing the grain boundary. The FFT patterns in the grains indicate different orientations of single crystal whereas the pattern taken along grain boundary is polycrystalline. Atom force microscope (AFM) measurement indicate the root mean square roughness is 0.965nm (sample A), 1.35nm (sample B) and 3.63nm (sample C), respectively. It shows that a low substrate temperature benefits to surface smoothness.
Fig. 2. Microstructure and elements distribution of sample C. (a) Cross sectional high-angle annular dark field (HAADF)-scanning transmission electron microscope (STEM) image of one selected region, and the energy dispersive x-ray (EDX) element mappings for (b) Ge, (c) Si, and (d) Sb elements in the same region. (e) HR-HAADF-STEM image and (f) the EDX element mappings for Ge, O elements, showing the aggregation of oxygen in grain boundary. The fast Fourier transform (FFT) patterns (inset) of different areas show different crystalline orientation.
In order to analyze the crystallinity of germanium films on silicon and demonstrate their epitaxial relationship in a large size region, we perform the electron backscattered diffraction (EBSD) measurement for sample B, whose substrate deposition temperature is 250°C. Figure 3(a) is the inversed pole figure (IPF) image mapped in a 200 µm ×200 µm scale, the whole area is shown in uniform red, implying a single (001) orientation. Pole figures (PF) in different orientations shown in Fig. 3(b) provide a direct proof of epitaxial relationship between the deposited film and the substrate.
Fig. 3. (a) Inversed pole figure (IPF) image of a 200 µm × 200 µm area of sample B. The coloration indicates crystalline orientation referring to the inserted legend. (b) Polar figure (PF) of sample B in different directions.
The doping concentrations of the Sb atoms are analyzed by secondary ion mass spectrometer (SIMS) and Hall measurements. Figure 4(a) shows the SIMS depth profile of Sb-doped germanium layer grown on silicon substrate with Sb-flux of 2.9×1012 cm−2s−1 and substrate temperature of 250 °C. The distributions of antimony, germanium and silicon atoms along depth are constant and homogeneous, and the depth profile at the interface is very sharp, implying a stable and interdiffusion-free doping process. The amount of antimony added is determined as 3.91×1020 cm−3 while its slight variation is probably due to fluctuations of Sb-flux during the growth process. Figure 4(b) shows SIMS measurements for samples with different substrate temperature at a constant antimony flux of 1.4×1012 cm−2s−1 (black, red and blue solid lines represent for sample A, sample B, sample C, respectively) and with different antimony flux at a constant substrate temperature of 250 °C (sample B of 1.4 × 1012 cm−2s−1 and sample D of 7.4×1011 cm−2s−1). The antimony content shown in flux-constant samples series remain almost unchanged as around 2 ×1020 cm−3, regardless of substrate temperatures. This means that chemical antimony concentrations obtained by SIMS measurements are insensitive to crystallinity and surface segregation of epitaxial layers. We also used the etched-pit density (EPD) method to estimate the treading dislocation density (TDD). The TDD of sample A is counted as 1.5×107 cm−2, and that of sample C is 1.2×108 cm−2. The result indicates that a lower substrate temperature will decrease threading dislocation numbers, and a virtual substrate (sample A) is beneficial to higher crystalline quality.
Fig. 4. (a) SIMS depth profile of the Sb doped Ge layer grown on Si substrate. Left scale: Sb concentration; right scale: Si or Ge secondary ion intensity. Calibration of Sb concentration is performed by measuring a standard Ge layer with known Sb areal density. (b) Sb concentration determined by SIMS measurements for different growth temperatures and different Sb flux. Sample A, B and C are all of 1.4×1012 cm−2s−1 but different temperature (150°C, 250°C, 350°C, respectively). Due to the error of film thickness monitoring, the thickness of doped layer at 150 °C (sample A) is smaller than that of other samples.
The measured FTIR spectra in the MIR range of 2.5-16 µm for samples A, B, C and D are shown in Fig. 5(a). As the wavelength gets shorter, the reflectivity curve of each sample show a similar sharp decline and forms the first dip, the dip locates in the position where the real part of permittivity equals to 1 (the minimum reflectivity is caused by the interference effect ɛ′ = 1) [41], which is very close to the epsilon zero point. The dip position of each curve shows a tendency of substrate temperature dependence, the lower the substrate temperature, the shorter the dip position, this means in addition to the doping concentration, the deposition parameters are also an effective route for the epsilon crossover wavelength tuning. By fitting the reflectivity spectra with Drude-Lorentz dispersion model, the wavelength dependent real and imaginary part of permittivity of those samples can be extracted. As shown in Fig. 5(b), the epsilon zero point of sample A, B, C and D is around 4.31 µm, 5.43 µm, 7.89 µm and 7.95 µm, respectively. With the help of fitting calculation, the plasma frequency of Drude dispersion model (Eq. (1)) is achieved, thus we can calculate the carrier densities of these samples with
The calculated free carrier densities of sample A, B, C and D are 1.56×1020 cm−3, 8.99×1019 cm−3, 1.11×1019 cm−3 and 3.85×1019 cm−3, the calculated active carrier density (compared to the chemical doping concentration shown by SIMS) of each sample is very close to the data obtained by our Hall measurements results (shown in Table 1).Fig. 5. (a) The absolute reflectivity measured (black dots) and calculated data by fitting (solid line). (b) Complex permittivities obtained by fitting the reflectivity data with Drude-Lorentz formula. Red, green, blue and purple lines represent for sample A, B, C and D, respectively. The y = 0 label is plotted by dot line, and the epsilon crossover wavelength λ* is labeled by dot line, too. (c). The permittivity, refractive index (n and k) around epsilon crossover wavelength of sample A and C is extracted and shown in (c) as examples, where ENZ region is highlighted in grey zone.
Table 1. Some parameters of commonly used III-V and IV n-type semiconductors reported so far
In the process of semiconductor doping, effective activated carrier concentration is affected by many factors. In our solid source MBE growth system, substrate temperature plays an important role at both improving the crystallization quality and turning as many chemical dopants as possible into active carriers. Unlike the hetero-epitaxial growth of un-doped germanium on silicon, such as the classical two-step method, which often requires a substrate temperature of more than 350 °C, the growth of antimony-doped germanium with high carrier concentration requires a lower substrate temperature to prevent antimony segregation, which is due to its high diffusion coefficient. While germanium epitaxial growth requires a certain substrate temperature to meet the needs of crystallization. So optimizing substrate temperature becomes the key to obtain high antimony doping concentration and high crystal quality at the same time. Since MBE is a growth method that allows low temperature doping, an extremely high active carrier concentration of 1020 cm−3 could be realized for Sb doped germanium films, which is difficult to achieve in chemical vapor deposition process. Our results show that with the introduction of a virtual substrate, the effective doping concentration of antimony at 150 °C can reach more than 1.5×1020 cm−3, while the germanium film still maintains a high crystalline quality. Even without the virtual substrate, a 250 °C substrate can still bring the doping concentration close to the order of 1020 cm−3.
The optical loss of doped germanium films could be expressed in terms of the imaginary part of permittivity (ɛ'’), shown as dash line in Fig. 5(b). If the contribution of Lorentz oscillators is not taken into account, it can be known from Eq. (1) that again, the imaginary part of permittivity is correlated with carrier concentration and mobility. Since carrier performance is closely related to epitaxy process, the optimal selection of flux and substrate temperature will therefore affect the optical loss of materials at epsilon zero point. Comparing sample A, B and C grown at the same flux but at different substrate temperatures, the optical loss of sample B is smaller than that of sample A and C. The imaginary parts of permittivity (ɛ'’) increase with its free carrier concentration (ɛ'’ (A) > ɛ'’ (B)), in addition, crystallinity of n-type germanium films plays an important role in the optical losses (ɛ'’ (C) > ɛ'’ (B)). While comparing samples B and D with the same substrate temperature, but with different flux, the lower carrier density of sample D will result in a relatively lower optical loss at the same wavelength.
When the material works at the epsilon zero point, its optical loss is inevitable. From the relationship between permittivity and refractive index (n) as well as extinction coefficient (k), it can be known that refractive index equals extinction coefficient at epsilon crossover wavelength, so reducing both refractive index and extinction coefficient becomes the only way for material to reduce optical loss. The optical coefficient (n, k) dispersion curves of sample A and sample C are also shown in Fig. 5(b). The intersection of refractive index and extinction coefficient curves is exactly the epsilon crossover wavelength. With higher doping concentration and carrier mobility, sample A with better crystallization not only has shorter epsilon crossover wavelength than sample C, but also has lower refractive index and extinction coefficient at its epsilon zero point (nA=kA=0.925@4.31µm, nC=kC=2.683@7.89µm)
Table 1 lists some parameters of commonly used III-V and IV n-type semiconductors reported so far, they are carrier concentration (n), effective mass (m*), epsilon crossover wavelength λ*, and CMOS compatibility. Among the other semiconductors as well as 2D graphene listed in Table 1, our antimony doped germanium film with carrier density of 1.6×1020 cm−3 possesses the shortest mid-infrared epsilon crossover wavelength of 4.31 µm. In addition to very high carrier density, both the low electron effective mass m* of 0.12 m0 for germanium and large mobility of 224 cm2/(V·s) for antimony dopants contribute to the shortest epsilon crossover wavelength.
We also measure the room temperature photoluminescence (PL) spectra of sample B and sample C to demonstrate the effect of crystallization on light emission, as shown in Fig. 6(a). The excitation light source is CW laser with wavelength of 532 nm. Direct band gap luminescence in antimony heavily doped germanium is observed for sample B at 1550 nm ∼1600 nm (0.775 eV∼0.8 eV, considering that out InGaAs detector in the PL measurement is limited to ∼1600 nm), while no luminescence was observed in sample C.
Fig. 6. (a) Photoluminescence (PL) spectrum of samples at room temperature. The green and blue lines represent for sample B and C, respectively. The insets in right column (b) and (c) are RHEED monitor image of sample B and C, respectively. The stripe in (b) indicates a good crystallinity, while the ring pattern reveals that sample C is polycystal.
As an indirect bandgap semiconductor, germanium's direct band gap is only 134 meV narrower than its indirect band gap, which makes it possible to modulate the electronic structure by tensile strain or doping. For the doping level higher than 1×1020 cm−3, the Fermi level would be deep in the conduction band, germanium with such high doping level will behave as the quasi-direct band gap semiconductor. Taking into account the probability of the radiative recombination for the direct and indirect transitions, the Γ valence band transition would therefore dominate. Meanwhile, the radiative recombination is greatly related to the crystallinity, defects as dislocations, grain boundaries will greatly reduce the possibility of interband radiative transition.
In Fig. 6, sample B and C has great difference in crystallinity. The two insets show real-time RHEED patterns when B and C grow, where stripe and ring pattern illustrate that sample B grows as single crystal while sample C grows as polycrystal, respectively. Thus, the direct transition related PL spectra of sample B means that it is entirely possible to obtain high quality heavily doped semiconductor materials with the right deposition process.
4. Conclusion
In this work, Sb-doped Ge-on-Si epilayers are systematically studied as a prime candidate for epsilon crossover wavelength tuning material in mid-infrared range. TEM, SIMS and PL measurements provide convincing evidence of superior crystallinity and extremely high doping concentrations. The epsilon zero wavelength of the germanium films is directly determined by carrier concentration and crystallinity-related electron mobility. The germanium epilayers are in-situ doped with antimony in the concentrations ranging from 7.8×1018 cm−3 to 1.6×1020cm−3, which corresponds to the epsilon crossover wavelengths in the range of 4.31∼7.89 µm, demonstrating that Sb-doped Ge-on-Si epilayers can serve as a high quality platform whose epsilon zero point is widely tunable in the MIR range.
Funding
National Natural Science Foundation of China (61575176); National Basic Research Program of China (973 Program) (2013CB632104); State Key Laboratory of Modern Optical Instrumentation (MOI20170001).
Acknowledgments
Z. W. thanks Zemin Xu and Ke Wu for their helpful discussions, Xiangdong Tan for vacumm technical assistance and Hao Luo for support in FTIR measurements.
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