Mid-IR optical properties of silicon doped InP

: InP is one of the most important materials for optoelectronics as a direct bandgap semiconductor, which can also be regarded as a low loss alternative plasmonic material for mid-infrared (mid-IR). The InP films studied in this work were grown by metal-organic vapor phase epitaxy (MOVPE). The effect of growth conditions on the optical and electrical properties of silicon doped InP (InP:Si) in the wavelength range from 3 to 40 µm was studied. The carrier concentration of up to 3.9 × 10 19 cm − 3 is achieved by optimizing the growth conditions. The dielectric function, effective mass of electrons and plasma frequency were determined by Fourier transform infrared spectroscopy (FTIR) for different carrier density levels. The plasma frequency can be tuned effectively via doping from 18.43 to 50.5 THz. Based on the experimental results, a semi-empirical formula for the plasma frequency, as a function of carrier concentration, is derived. Comparison to other semiconductors shows superior plasmonic performance of InP:Si in terms of propagation length and surface confinement.


Introduction
Plasmonics is a growing field within nanophotonics which deals with excitation of the collective oscillations of free charges, known as plasmons, in a conductive material, resulting in a drastically enhanced electromagnetic field in the vicinity of the material interface. Plasmons can be excited by exposing subwavelength conductive particles to an external electromagnetic field, resulting in localized plasmon-polaritons (LPP) or by coupling the external field to the oscillating charges near the surface of the material, resulting in a highly confined surface wave propagating along the interface between the conductive and dielectric media, known as surface plasmon-polaritons (SPP) [1]. High confinement of this enhanced field provides higher local optical density of states and leads to applications such as plasmonenhanced photovoltaics [2], biosensing [3], Raman spectroscopy [4] and photocatalysis [5]. Furthermore, SPP's enable subwavelength spatial confinement of light, due to their dispersion properties. This very important property of SPP's is used in many fields including subwavelength waveguiding [6] and optical superlenses [7]. Metals such as Au, Ag and Cu are considered as traditional plasmonic materials for the visible range. However, when it comes to the mid-and far-infrared (IR) ranges, which are the hosts for many applications such as chemo-sensing [8] and thermal imaging [9], metals suffer from high optical losses and poor spatial confinement of SPP's. In addition, CMOS incompatibility of the noble metals is a challenge in the fabrication process of nanophotonic devices.
Alternative plasmonic materials such as graphene, ceramics, conductive oxides and semiconductors have been introduced to address these shortcomings [10,11]. Semiconductors play a key role in this context, owing to their high carrier mobility and low optical losses [12]. In addition, tunability of their optical properties via doping or charge depletion [13] adds an additional degree of freedom for engineering photonic device elements. InP as a direct bandgap III-V semiconductor is one of the most common materials in optoelectronic applications [ . In addition, highly doped InP can be considered as a plasmonic material with superior plasmonic properties compared to majority of other semiconductors in the mid-IR range owing to lower losses [20]. Furthermore, easy integration and compatibility with conventional III-V optoelectronic devices and their fabrication processes make InP a promising candidate as a perspective plasmonic material aiming for the mid-IR range.
Dielectric function of a material yields key information for understanding of its plasmonic behavior. Optical properties of undoped InP in ultra-violet, visible and near-IR ranges were investigated by different research groups [21][22][23][24][25][26]. Jayasinghe et al.
[27] studied the dielectric function and plasma frequency of p-doped InP in the IR range. The maximum carrier concentration considered was 2.4 × 10 19 cm −3 pertaining to a plasma wavelength of 15.4 µm. The large plasma wavelength in this case is due to the high effective mass of the holes. Zheng et al. [28] was able to achieve free electron concentrations as high as 1.1 × 10 20 cm −3 in InP:Si, using molecular beam epitaxy (MBE). The electrical and optical properties were measured by the Hall-effect and photoluminescence, respectively. El-Nahass et al. MOVPE is a powerful and flexible technology for epitaxial growth of compound semiconductors. It is widely used now due to the ability of instantaneous control over the partial pressure and flow rates of the precursor gasses which results in well-defined growth of a wide variety of semiconductor materials [31]. The free carrier concentration in the grown semiconductors is an important parameter which needs to be carefully controlled by choosing proper growth conditions such as the ratio of the precursor gasses, growth temperature and overall pressure of the growth chamber. Si is commonly used as a donor in MOVPE grown InP and the effect of growth conditions on its incorporation efficiency has been investigated [32][33][34][35][36][37][38][39]. In this regard, to the authors' best knowledge, the highest reported carrier concentration in MOVPE grown InP:Si has been reported as 2.6 × 10 19 cm −3 [40].
In our previous works [20,41] we have shown that highly doped InP can support SPPs, and its plasmonic properties can be effectively tuned by adjusting the free carrier concentration. The aim of the present work is to provide a database of the growth conditions and mid-IR optical properties of InP:Si with different doping levels. Influence of the growth parameters, namely the precursor's ratio and the dopant's flux, on the carrier concentration and self-compensation in InP:Si, measured by the Hall-effect measurement (van der Pauw method) and time-of-flight secondary ion mass spectrometry (TOF-SIMS), is investigated. Furthermore, the dielectric function of the grown material with different carrier concentrations is determined using IR reflectance spectroscopy. The effect of the carrier concentration on the effective mass of electrons, plasma frequency and electrons plasma damping is discussed.

Experiment and discussion
The samples were grown on single-side polished (1 0 0) semi-insulating InP:Fe substrates in a low pressure MOVPE TurboDisc® reactor, with hydrogen (H 2 ) as a carrier gas, using phosphine (PH 3 ), trimethylindium (TMIn) and disilane (Si 2 H 6 ) as the precursors for phosphorus, indium and silicon, respectively. The growth temperature, controlled by emissivity corrected pyrometers, was 610 °C. The carrier disk rotates with 1000 rpm inside the growth reactor chamber, transforming a laminar flow pattern of supplied precursor gasses into the circumferential flows and forms the so called boundary layer on top of the wafer surface. This boundary layer provides diffusion driven transport of precursors to the growing surface which results in uniform growth with a predictable rate. The growth conditions, namely the phosphorus to indium precursors' molar ratio and the disilane flux were adjusted, resulting in different free carrier concentrations.
Free carrier concentration of the samples was determined by Hall-effect measurements, which were carried out at room temperature using the van der Pauw method with a variable magnetic field (from zero up to 1.5 T).
Disilane is commonly used as the precursor for Si doping of MOVPE grown InP whose dissociation is described by a two-step process as 2 6 2 4 Si H SiH SiH → + SiH SiH H → + (2) where Si in SiH 2 will react on the surface of the epilayer and contribute to doping. At temperatures below 700 °C, the decomposition efficiency of silane (SiH 4 ) is very low and therefore the Si incorporation rate is mainly determined by Eq. (1) where TMIn P is the saturated vapor pressure of TMIn in the bubbler, hydrogen F is the hydrogen flux, bubbler total p is the total overpressure within the bubbler (500 mbar) and α is the efficiency of the bubbler which can be assumed to be unity with a good accuracy [31]. The molar flux of TMIn can readily be calculated using TMIn F and the ideal gas law. Molar fluxes of PH 3 , which is supplied directly from a gas source, as well as disilane, which is supplied as a 200 ppm diluted gas in hydrogen, can also be calculated using the ideal gas law.
All the samples were grown at 610 °C and an overall chamber pressure of 60 Torr. Table  1 summarizes the growth conditions, the resulting carrier concentration and mobility of the samples. Figure 1 shows the carrier concentration versus the disilane to TMIn molar flux ratio for two groups of samples with different V/III molar ratios. The carrier concentration is proportional to the disilane to TMIn molar flux ratio up to a threshold point where the excess Si precipitates on the surface of the sample and deteriorates it (Fig. 2). As explained above, a higher V/III ratio results in slightly higher carrier concentrations.
In order for the Si atoms to contribute as donors they should be incorporated into the sublattice of the IIIrd group, but in some cases, Si atoms may be incorporated to the sub-lattice of the Vth group and act as acceptors, or sit in interstitial sites of the crystal. This phenomenon, which is one of the barriers against high doping of InP, is known as self-compensation [42].
The concentration of Si atoms was determined using TOF-SIMS and subsequently compared to the free carrier concentration in the grown samples. In this regard a reference sample was ion implanted with a known amount of 28 Si in order to calibrate the TOF-SIMS response to the concentration. TOF-SIMS depth profiling analysis was performed on the grown InP:Si samples. The erosion rate was calculated to be 15.6 nm/min by measuring the resulting crater depth for the thickest epilayer using a Dektak 3030 surface profile measuring system (Sloan Technology Corp.) and relating the depth to the sputter time. The Si concentrations were extracted from depth profiles through the entire epilayer and the error bars are typically based on 50-100 in-depth measuring points. The TOF-SIMS measurement results with associated error bars are presented in Fig. 1. For all samples, the difference between the Si concentration measured by TOF-SIMS and the donors concentration measured by the Hall method is smaller than the error bars, which shows that the compensation ratio (ratio of the ionized acceptors to the ionized donor concentration) is smaller than the measurement limit.

Dielectric function
In order to use a material for optical applications, one needs to know its dielectric function which defines the material dispersion in the wavelength range of interest. In this section, the dielectric function of the grown samples at different carrier concentrations is determined after characterization of the material in the mid-IR range. The reflectance spectra of the samples under normal incidence were calculated using the intensity transfer matrix method [43]. The purpose of this method is to ignore the Fabry-Perot interference fringes originating from the thick substrate while the interference fringes from the epilayer are retained. The Drude-Lorentz (D-L) model was applied as the dielectric function for both doped and semi-insulating InP, where the Drude term accounts for the contribution of free electrons and the Lorentzians account for the contribution of phonons to the optical dispersion of the material: Here ε ∞ , p ω , γ and i are the high-frequency dielectric constant, plasma frequency, electrons plasma damping and imaginary unit ( 1 − ) respectively. j S , , The reflectance spectra of the samples at near-normal incidence (12°) were measured from 3 to 40 µm, using a VERTEX 70 FTIR spectrometer from Bruker. The measurements were repeated on five different points on each sample and normalized to the reflection from the aluminum mirror of the sample holder. Afterwards, the calculated reflectance spectra were fitted to the experimental data in order to find the parameters of the D-L dielectric functions. The fitting was done using the Levenberg-Marquardt algorithm [44], weighted with the inverse of the standard error for each measured point. This procedure was first carried out for the bare InP:Fe substrate and then the fitted parameters of the substrate were used to calculate and fit the reflectance from the grown samples. In all cases, ε ∞ is considered to have a constant value equal to 9.55 [42]. Figure 3 shows the measured and the fitted reflectance spectra of the bare semi-insulating InP:Fe substrate. The rough backside of the substrate and also optical losses of the InP:Fe, diminish the reflection from backside of the samples.
where n, e, 0 ε and * m are the free electron concentration, electron charge, vacuum permittivity and effective mass of electrons, respectively. The theoretical value of * m for ntype InP proposed in [45] is used to calculate p ω .
Basing on the experimental results, we derived a semi-empirical formula for the plasma frequency of InP:Si as a function of the free carrier concentration (n) in the range between 0.35 to 4 × 10 19 cm −3 :   Figure 7 shows the effective mass of electrons as a function of the carrier concentration calculated from Eq. (6) using the fitted values for p ω versus the theoretically calculated effective mass [45]. The discrepancy between the fitted and theoretical values for p ω in Fig. 6 can be attributed to the flaws in the theoretical formula for * m , for example the effect of nonparabolicity of the conduction band [45], together with the fitting errors and also the errors in the Hall measurements. These sources of error also explain the discrepancies in Fig. 7.
Fluctuations in the values of γ with respect to the free carrier concentration (Table 2) are correlated with the fluctuations in the mobility values measured by the Hall-effect (Table 1).

Comparison to other semiconductors
In order to compare the mid-IR plasmonic properties of InP:Si to other semiconductors whose data are available in the literature, we have chosen the following compositions: p-doped Si, ndoped Si [46], n-doped InSb [47] and n-doped InAs [48] with plasma wavelengths close to sample 9 (5.93 µm).
The propagation length of surface plasmons p L , is given by comparison to noble metals, in the mid-IR range, both real and imaginary parts of the permittivity of InP:Si are two orders of magnitude smaller which leads to better confinement of SPPs in expense of a shorter propagation length. Nevertheless, tuanability of the plasma wavelength and damping is a very important feature of semiconductors which cannot be achieved in metals.

Conclusion
We have studied InP:Si samples grown by MOVPE. In particular, the effect of the growth conditions, namely the dopant flow rate and the V/III ratio, on the free carrier concentration has been studied. Using the optimal growth conditions, the maximal free carrier concentration of 3.9 × 10 19 cm −3 is achieved. The total concentration of Si atoms, measured by TOF-SIMS, was compared to the free carrier concentration, measured by the Hall technique, and it was found that the compensation ratio in the grown samples is smaller than the measurement error. Reflectance of the samples in 3-40 µm wavelength range has been measured using FTIR, and used to retrieve the dielectric function of InP:Si by curve-fitting. The maximum plasma frequency is found to be 50.5 THz. Using the fitted plasma frequency, the effective mass of electrons is determined for different carrier concentrations. The semi-empirical Eq. (7), which accounts for the changes in the band structure of the InP upon Si doping, can be used to estimate realistic values for p ω versus carrier concentration in the range between 0.35 to 4 × 10 19 cm −3 .
Owing to its lower losses, InP:Si has higher figures of merit, which quantify the tradeoff between SPP confinement and propagation length, in comparison to the other doped semiconductors with a similar plasma frequency, whose data are available in the literature.
This paper provides information about the electrical and the optical properties of InP:Si and the MOVPE growth guidelines to be used for design and fabrication of optoelectronic and plasmonic devices.