1. Introduction

The unique electrical and optical properties and their combination make graphene very attractive in pursuit of high-performance electro-optical or photonic devices, in particular for modulation applications [1–8]. This is fundamentally enabled by the readily tunable Fermi level for a Dirac linear band, which can be transformed into the variation of conductivity or absorption characteristics in a wide frequency range from terahertz to visible light. In practice, tuning of the Fermi level or charge density of graphene is mostly conducted by capacitive charging through a gate voltage [9, 10]. For this purpose, the structure of film capacitors has been widely employed. In addition, Schottky barrier with p-n type junction effect can be formed across the interface of the graphene-semiconductor heterostructure due to the charge diffusion driven by the differences of charge concentration and chemical potential [11–14]. This junction accompanied with the capacitive boundary charging effect can be applied to tune the Fermi level of graphene as well. This relative simple architecture may bring about many practical applications for graphene-based photonic devices, such as recently demonstrated in light harvesting for solar cells [15, 16]. As another important application, more recently, Li el al. found a double-layer graphene on a silicon substrate could give rise to a diode transmission behavior for terahertz waves that led to a large transmission modulation ratio about 83% under the laser pump [14], accompanied a p-n junction type transmission behavior with the bias voltage. This structure affords a simple but equally promising way to design terahertz modulators compared with the previously proposed metamaterials based on Au-Si Schottky diodes [17]. However, regarding the underlying mechanism for the diode behavior, the same authors gave a different explanation in a later paper [18], where this asymmetrical transmission was regarded due to the charge density change in the silicon substrate modulated by a Schottky diode formed between the bottom electrode and silicon interface while the top graphene sheet just acted as a transparent electrode. A further experiment investigation will be necessary to understand this interesting effect.

In present work, we extend the graphene-silicon heterostructure into the far-infrared regime with the aims to further understand the related physics behind the diode transmission and more importantly to explore their application potentials in infrared optics. Experimentally, we find this heterostructure could give rise to large transmission modulation with wavenumbers up to 2000 cm⁻¹, possessing the significance for practical applications [19]. Our electric and optical measurement results point to the existence of a graphene-silicon interface diode responsible for the asymmetrical infrared transmission behavior. These findings are believed not only physically meaningful but also practically helpful for the configuration of graphene-based infrared devices with multiple controlling functions [20, 21].

2. Experiment section

Fabrication the sample

Figure 1(a) depicts our sample structure and measurement setup. The sample consists of a high-resistivity (ρ > 1000 Ω·cm) silicon substrate (naturally doped n-type, size 30 × 30 × 0.5 mm³) and a double-layer graphene sheet (ACS MATERIAL) grown by chemical vapor deposition. For electrodes, we deposit on both top and bottom surfaces of the sample with Cr(10 nm)/Au(200 nm) films patterned into quadrilateral ring shapes (side length = 25 mm and strip width = 2 mm).

 

Fig. 1 (a) Schematics of the sample structure and measurement setup. Battery represents the polarity of the applied bias voltage. (b) Graphene-silicon Schottky junction and charge distribution. An internally-built electric field (pointing from silicon to graphene) is assumed near the graphene-silicon interface due to the diffussion of carriers. (c) and (d) Spectrum of transmission modulation ratio ΔT for the pure silicon substrate and the heterostructure sample pumped at different light powers, respectively. Inset in (c) and (d): measured transmittance spectra at different pump powers.

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Measurements

Pump source is a continuous wave (CW) green laser (532 nm) obliquely illuminating the sample surface at 45° with the normal from the top or bottom side [22]. The spot diameter of the pump beam on the sample surface is about 3 mm. The pump light will increase the sample temperature and a few minutes waiting to reach a thermally stable state is required before next measurement. Probe light [blue beam in Fig. 1(a)] is perpendicularly incident with a beam size nearly equal to that of the pump light. The transmittance of the heterostructure is measured using Fourier Transform Infrared Spectroscopy (FTIR) (Bruker VERTEX70). To better understand the pump-probe effect and the diode transmission behavior, we explore the influence of the relative positions of the pump and probe beams with four different setups: The pump light illuminates the sample from the top graphene side with the beam spot overlapped with (A) or separated from (B) the probe beam; The pump light illuminates the sample from the bottom silicon side with the beam spot overlapped with (C) or separated from (D) the probe beam. We also examine the transmission properties of the sample in the terahertz regime by a THz time-domain spectrometer (Z-omega Z3).

3. Results and discussion

Firstly, we measured the transmittance of the sample without bias voltage under different pump light powers in 400-4000 cm⁻¹. In our measurement, the silicon substrate has been regarded as the part of the sample and the transmittance is the ratio of the received energy with and without the sample. To show the pump influence, we define the parameter of transmission modulation ratio ∆T = [T(p)-T(0)]/T(0) where T(p) is the transmittance at the pump power p and T(0) the transmittance without pump. In Fig. 1(c), we first give the measured results for the pure silicon substrate at different pump powers. The inset plots the transmittance spectra that rise up with wavenumber. The noises appearing near 1800 and 3800 cm⁻¹ come from the molecular resonance spectra of water vapors. Increasing the pump power will decrease the transmittance of silicon visibly at small wavenumbers (< 2000 cm⁻¹) but with limited modulation ratios ∆T < 1 in our measurement range. After covering silicon by a double-layer graphene sheet, as shown in Fig. 1(d), the modulation ratio is largely enhanced, in particular for smaller wavenumbers. This effect decreases and becomes less obvious when the wavenumber increases and reaches the range 1000-2000 cm⁻¹ with the transition value dependent on the pump power. This accords with the intrinsic property of graphene that has minimum interaction with external light in the mid-infrared regime due to the Pauli block [23, 24]. From the comparison, it is clear that the graphene layer plays a key role in modulating the infrared light transmission. To simplify the illustration, hereafter, the wavenumber 1000 cm⁻¹ is chosen to examine the relationship between transmittance vs. pump light and bias voltage. At this frequency, covering the silicon substrate with graphene will enhance the transmission modulation ratio by more than 5 times, i.e., from 0.532% to 2.91% pumped by 750 mW green laser (see Table 1).

Table 1. Transmission modulation ratio and short-circuit current for different pump manners^a

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Figure 2(a) shows the current-voltage (I-V) curves of the sample under different pump powers. The bias voltage is positive when the anode is applied on the graphene side, as shown in the left inset of Fig. 2(a). Typical p-n junction rectifying effect is observed from these I-V curves [12, 13, 25]. The current rises up rapidly under the positive bias compared with the slow change under the negative bias. This particular change of the current with respect to the polarity of the bias voltage is opposite to the result reported by Du et al [18], where they contributed it to the Schottky junction formed between the silicon and bottom electrode. The difference could happen since the I-V characteristic depends on many practical parameters such as the interface state, Fermi levels and work functions. According to the current result, it is more reasonable to assume that this Schottky barrier arises from the graphene-silicon interface, which accords with most of the previous results [14], reported for similar graphene-silicon heterostructure [25–27]. Like normal metals [28, 29], doped graphene’s work function is usually larger than that of silicon [15]. Consequently, electrons will tend to move from silicon into graphene by forming a space charge region in the silicon near the interface as schematically shown in Fig. 1(b). Assisted by the built-in electric field, we observe the enhanced photocurrent at zero bias voltage with the increase of pump light power that will generate more photoexcited carriers. In addition, we need to mention that the temperature of the sample increases in our measurement when the pump power becomes large. At 750 mW, it rises up about 20 °C, which could modulate the I-V curves by exciting thermalized carriers and influencing the Schottky barrier. Since the amplitude of the temperature change is small, the photoexcited carriers will be dominant in charging the capacitive barrier.

 

Fig. 2 Measured results with pump light illuminating the sample from the top graphene side. (a) I-V curves of the sample when the pump light superimposes with the probe light. (b) I-V curves when pump light is offset from the probe light by 5 mm. Insets in (a) and (b): sketch of the pump and probe beams (left) and zoom-in of the I-V curve near 0 V (right). (c) and (d) Transmittance vs bias voltage under different pump powers without and with offsetting the pump beam, which correspond to the experimental setup described in the insets of (a) and (b), respectively. Wavenumber of the probe light is 1000 cm⁻¹.

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Figure 2(c) gives the measured transmittance at 1000 cm⁻¹ of the heterostructure changing with the bias voltage at different pump powers. Without laser pump, the transmittance shows very small variations with the bias field. It quickly decreases when the pump light is applied with power increasing from 120 to 750 mW and shows an asymmetrical dependence on the sign of the bias voltage. These results are closely related with the charge density of the graphene layer mediated by the change of the capacitive Schottky barrier. With the enhancement of pump power, more photoexcited carriers will be generated near the junction and then transferred into the graphene layer with the help of the built-in field or even without it, which will raise the Fermi level and conductivity of graphene consequently enhancing the backscattering effect for infrared light. In the pumping process, the enhancement of sample temperature will increase the density of the thermalized carriers and Schottky barrier [25], which also contributes to the reduction of the overall transmittance. Increasing the positive bias voltage will narrow the space-charge region and reduce the built-in field. The capacitive charging effect for graphene will be weakened as manifested by the enhancement of transmittance. Once the local insulating Schottky barrier disappears at about 2 V, the bias voltage will be applied totally to the 0.5 mm-thick high-resistance silicon substrate. The average field experienced by the photoexcited carriers (or the capacity to separate the photon-excited electron-hole pairs) will be significantly decreased, which may be the reason for the observed saturation of transmittance at higher positive voltages. On the other side, increasing the negative bias voltage will strengthen the built-in field and then enhance the charging effect of the graphene layer, as evidenced by the quick reduction of the total transmittance in Fig. 2(c). After −1 V, the transmittance will approach a constant value dependent on the pump power, which may be attributed to the saturation of the net charge densities separated from the photoexcited electron-hole pairs.

In order to further understand the Schottky charge accumulation process and the localization characters of the light pumping effect, we offset the pump light beam from the probe beam by 5 mm and check the change of transmittance, as schematically shown in the left inset of Fig. 2(b). The I-V characters plotted in Fig. 2(b) have no obvious difference with those in Fig. 2(a). The photocurrents under the same pump powers have the same order of magnitudes (see Table 1). Displacement of the pump beam doesn’t affect the optical-electric properties of the graphene-silicon heterostructure or the Schottky junction. But the optical spectrum, as shown in Fig. 2(d), the transmission modulation ratio upon the laser pump is obviously reduced in large degrees compared with the beam-coincident case given in Fig. 2(c) (also summarized in Table 1). In this case, we still observe a very weak asymmetrical transmission with the polarity of the bias voltage. From these results, the localization of the charging effect is clearly evidenced although the top electrode is only a two-atoms-thick conductive layer. The influence of the longitudinal charge diffusion driven by the density gradient seems very limited in our long-wavelength discussion. But for shorter wavelengths, it may be different, as recently shown by Yu et al’s experiment that the transmission modulation ratio of a graphene-covered silicon waveguide exhibited a very weak dependence on the position of the pump beam for a 1550-nm probe light [30]. The inter-band electron transition happening in the near infrared will make the graphene-light interaction more sensitive to the charge density of graphene [31, 32].

The penetration depth of pump green light (532 nm) inside silicon is about 1 µm [22]. To confirm the above analysis, it will be interesting to measure the transmittance when pumping the sample from the bottom silicon side that has a 500 µm distance from the top heterostructure. Figure 3(a) gives the I-V curves at this case with pump beam overlapping with the probe beam on the bottom surface. They show similar diode behaviors with those given Fig. 2(a) but have a negligible short-circuit current (at zero bias) irrespective to the change of the pump power. The transmission modulation ratio in Fig. 3(c) becomes much smaller than those given in Fig. 2(c). Because of the distance, the photoexcited carriers at the bottom boundary could not be effectively separated and delivered to the top boundary that has the Schottky diode junction. In this case, the graphene layer will be only slightly affected by the pump light and even the bias voltage. The final results will be similar with those by pumping pure silicon substrates. To further dislocate the pump beam from the probe light, as shown in Fig. 3(b), the opt-electric properties are almost the same as those in Fig. 3(a) but the transmission modulation ratio is further diminished due to the lateral localization of the carriers, as shown in Fig. 3(d).

 

Fig. 3 Measured results with the pump light illuminating the sample from the bottom silicon side. (a) I-V curves of the sample when the pump light superimposes with the probe light. (b) I-V curves when the pump light is offset from the probe light by 5 mm. Insets in (a) and (b): sketch of the pump and probe beams (left) and zoom-in of the I-V curves near 0 V (right). (c) and (d) Transmittance vs bias voltage under different pump powers without and with offsetting the pump beam. Wavenumber of the probe light is 1000 cm⁻¹.

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Table 1 summarizes the modulation values of transmission under different pump manners at specific pump light powers and bias voltages at 1000 cm⁻¹. ΔT describes the modulation ratio with and without pump and ΔRT is the relative modulation ratio between the 5 V and −5 V bias voltages. Photocurrents produced by pumping the graphene side of the sample are about one-order larger than those by pumping the silicon side under 750 mW pump power irrespective to the lateral pump positions. Among the different pump manners, the largest transmission modulation ratio ΔT = 2.9% is obtained for case A, i.e., when the pump light irradiates the sample from the graphene side with overlapped beam spots. It exposes the role of the graphene-silicon Schottky diode junction in enhancing ΔT. When pumped from the bottom silicon side (Case C), the modulation ratio 0.46% is very close to the value 0.53% for a pure silicon substrate as given in Fig. 1(c), since the effect of the Schottky junction is not excited in this case. For the same reason, the relative modulation ratio ΔRT for the three other cases except for case A is less sensitive to the change of the pump light power.

To validate the above discussions on the modulation behavior and the Schottky junction, we also extend the measurement downward to terahertz frequencies where graphene’s tuning effect will be more obvious [14]. Figure 4(a) gives the transmittance of the measured pulse peak through the heterostructure with respect to the bias voltage at different pump light powers. The sample shows similar transmission features in both terahertz and infrared regions, as graphene is commonly controlled by the intraband transition or a Drude mode in these frequency bands. But at a few THz frequencies, the modulation ratio of transmission substantially increases and reaches 32% for the pulse peak. But for a pure silicon substrate, this value is only 2.5% at the maximum pump power of 750 mW as plotted in Fig. 4(b). These results re-confirm the role of the graphene-silicon Schottky junction in enhancing the transmission modulation ratio. Note the THz modulation ratio obtained here is much smaller than that reported in [14]. That means the quality of our sample and the infrared modulation effect could be further enhanced.

 

Fig. 4 Measured transmission at Terahertz time-domain. (a) Transmittance of the pulse peak vs bias voltage under different pump light powers. (b) Transmittance of the pulse peak pump power for a 500-µm-thick bare silicon substrate without bias voltage. For the THz measurement, the pump and probe light beams are coincident in positions.

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4. Conclusion

In conclusion, we explore the graphene-silicon Schottky junction effect and its role in the modulation of wave transmission in the far-infrared region with the pump light and the bias voltage. The generation of photoexcited carriers is the dominant factor to reshape the Fermi level of graphene either through capacitive charging or direct electron transfer. The latter process explains the dependence of the positively saturated transmittance on the pump power. Introducing plasmonic metallic patterns may help to reduce the requirement for high pump power by increasing the extrinsic quantum efficiency for absorption. The bias voltage is another major parameter to vividly tune the charging effect and graphene’s Fermi level assisted by the interface diode junction. Its tunability could be further enhanced by increasing the quality of the Schottky junction [13], while it is challenging for the current experiment applying centimeters-sized samples. Although the overall tuning efficiency is much smaller than terahertz frequencies, this unique structure still provides a promising way for far-infrared optics to modulate the wave propagation that could be incorporated into metamaterial designs or other photonic devices with enhanced functionalities. Our quite recent work shows that if coupled with a high-quality waveguide mode with controlled small radiation loss, the single graphene-silicon junction could give rise to very strong modulation on the reflectance of a metamaterial absorber in far infrared. Proper design is quite important to enlarge the application area of this weak interaction effect.