1. Introduction

The terahertz (THz) science and technology has been a significant research field during the past decades because of its promising applications ranging from THz radar [1], high-speed communications [2], to biological imaging [3], time domain spectroscopy (TDS) and scientific study [4–6]. Hence, the development of THz devices, such as sources, detectors and many other THz components, is urgent demand. During the past a few years, a lot of studies have been focused on the THz modulator. For the construction of active THz modulators, various types of materials or structures have been employed. By fabricating an organic/silicon composite, THz intensity modulation has been realized with cw-laser photoexcitation [7–10]. Combined photoexcitation and gate voltage, larger intensity modulation depth can be realized in organic/inorganic composite [11], graphene/Si hybrid structures [12,13]. All electric control of THz modulators has been realized in a graphene-based field-effect-transistor [14,15] and hybridization of metamaterials with pseudomorphic high electron mobility transistors [16]. A review article in [17] presents a good outline for the fabrication and performance of various THz modulators. Among these THz devices, an active electrically tunable THz device is desired for fast THz switching and easy control. In this paper, a new model based on heterojunction is proposed, and a novel all-electrically driven THz modulator was designed and fabricated. The measurement results demonstrate that the maximum modulation of 42% is realized with bias of 4.8 V, the modulation bandwidth up to 1.0 THz is obtained for the new device.

2. Model for a new terahertz modulator

It is well known that terahertz is very sensitive to conductivity of free carriers in semiconductor. In order to design an all electrical terahertz modulator, we put forward a new model to design a terahertz modulator in principle. It is well known that a heterojunction, made of two materials with dissimilar Fermi levels, is a building block of various electronic devices, which can be used to monitor the propagation of carriers effectively with forward and reverse bias. The depletion layer formed in the heterojunction is vital importance to control the diffusion and drift of majority and minority carriers in the heterojunction structure. If the heterojunction is fabricated with two very different materials: one is semiconductor having high carrier mobility, and the other is a semiconductor-like material with localized band structure, therefore having very low carrier mobility, and it is expected that the heterojunction formed with the two materials will behave a diode-like character for THz transmission, which therefore can be used to fabricate an all electrical THz modulator. Considering a terahertz modulator without photo-doping (all electric-driven), the carrier transportation in heterojunction under forward and reverse bias is mainly contributed by n-type or p-type dopants. A semiconductor film with low carrier mobility (LCM) is deposited on a lightly doped substrate with high carrier mobility (HCM), and a heterojunction is formed in the interface of the two semiconductors. Let us consider holes concentration changes (electrons concentration changes have similar behavior) under external bias across the heterojunction. The holes concentration in LCM layer without bias of heterojunction, P_n0(x_n), reads:

3. Fabrication and measurement of THz modulator

It is known that BiFeO₃ is a kind of semiconductor-like material with very low carrier mobility. Thus we design and fabricate a heterojunction which is made of BiFeO₃ (BFO) thin film on a lightly-doped p-type silicon substrate.

A heterojunction of polycrystalline BiFeO₃ thin film grown on (001) p-type silicon substrate by pulsed laser deposition was fabricated. For details, La and Nb codoped BiFeO₃ (namely Bi_0.8La_0.2Fe_0.99Nb_0.01O₃, for simplicity, we use “BFO” throughout the text) film on p-type silicon substrate was fabricated by pulsed laser deposition (PLD) technique. It should be mentioned that the La and Nb codoped BFO film shows a much better electrical polarization than that of intrinsic BFO film [18]. Third harmonic generation of a Nd doped yttrium aluminum garnet laser with a wavelength of 355 nm and a repetition rate of 10 Hz was used as the laser source. The thin films were initially deposited on (001)-Si substrate at 550 °C, then cooled down to room temperature following rapid thermal processing. During the deposition, the dynamic oxygen flow pressure was kept at 20 mTorr. The as-deposited BFO thin films on p-type (001)-Si have tetragonal structure determined by X-ray diffraction. The details of the sample fabrication have been reported elsewhere [19]. The thickness of BFO film is about 200 nm, the 0.4 mm-thick silicon substrate was lightly doped by boron to form p-type semiconductor [20] with dopant concentration~10¹⁴ cm⁻³. In order to investigate the active modulation of heterojunction on THz transmission, a terahertz time domain spectroscopy in transmission configuration was used. The output of a mode-locked Ti:sapphire laser, with pulse duration of 100 fs, centered wavelength of 800 nm, and repetition rate of 80 MHz (Mai Tai HP-1020, Spectra-Physics), was used to generate and detect the THz transient. The THz emitter and detector is a pair of low-temperature-grown GaAs photoconductive antennas. The effective bandwidth of the THz spectrum is from 0.2 to 2.0 THz, centered around 0.6 THz and the signal to noise ratio is better than 2000:1. The THz waves have a beam size of 3 mm at the sample position. Two rings silver electrodes were deposited on the BFO and Si surfaces, respectively. The ring silver electrode with width of 2 mm forms a square aperture with size of 6 × 6 mm, which allows the THz wave to pass through the heterojunction. The external dc bias with alterable magnitude and direction was applied to the BFO/Si heterojunction during THz transmission measurement, as shown schematically in Fig. 1(a).

 

Fig. 1 (a) Schematic diagram of BFO/Si sample, the red and blue colors represent BFO thin film and Si substrate, respectively. The silver electrode with ring shape is illustrated as yellow color. (b) THz time-domain signal at various bias voltages. The inset (up) shows the enlargement of secondary reflection signals (THz echo pulse), and the inset (down) illustrates the main THz transmission as well as the reflections occur at the two interface. (c) Bias voltage controlled amplitude changes of time-domain transmission peaks of the BFO/Si hybrid structure. The solid line is exponential fitting result.

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Figure 1(b) shows the transmitted terahertz waveforms with the bias of + 4.8 V (forward bias with electric field pointing to BFO film), −5.0 V (reverse bias with the E-field pointing to the Si substrate), and zero bias. The pronounced transmitted main THz pulse is followed by a secondary reflection pulse (or say “echo pulse”), and both of the pulses are bias dependent. It is clearly seen that reverse biases do not generate any changes to the THz transmission; In contrast, the forward bias leads to the enhancement of THz transmission (bleaching of THz transmission). Inset in Fig. 1(b) shows the enlargement of the secondary reflection, it can be seen that the rectifying effect is more pronounced in echo pulse than that in the main THz pulses because the echo pulse travels through the heterojunction two more times than the main pulse. Figure 1(c) represents the peak values of the time-domain signals from BFO/Si heterojunction biased from −5.0 to + 4.8 V, respectively. With reverse bias, the applied bias voltage does not cause any observable change in the THz transmission through the BFO/Si hybrid structure. On the other hand, when the forward bias is applied, at low biased voltage V_bias <2 V, there is almost no significant enhancement for the THz transmission. Interestingly, when forward biased voltage is higher than 2 V, the enhancement of THz transmission starts to appear, and the enhanced THz transmission increases exponentially with bias increases. It should be mentioned that the device can be damaged when the bias is higher than 6.0 V due to the large current.

In order to evaluate the property of the heterojunction, a modulation depth is introduced as defined in Eq. (6), in which V_g represents the applied bias voltage and f is the terahertz frequency. E(f, 0) stands for the THz transmission spectrum at zero bias voltage, and E(f, V_g) represents the THz transmission spectrum at forward or reverse bias voltage, V_g,

 

Fig. 2 (a) THz transmission spectra at bias voltage of −5, 0 and + 4.8 V. (b) THz spectra modulation depth at various bias voltages.

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4. Discussions

To address the diode-like THz transmission in the BFO/Si hybrid structure, energy band diagram is presented for isolated BFO and Si, as well as an ideal heterojunction of BFO/Si, which are presented in Fig. 3(a) and 3(b), respectively. It is known that BFO films with different substrates have different energy band gap ranging from 2.2 to 2.8 eV [21]. In our case, the band gap of 2.3 eV is taken for the BFO on p-type Si substrate. La and Nb codoped BFO film can be treated as an n-type semiconductor [19,20, 22]. We suppose that the BFO thin film’s Fermi energy level is close to the middle of the energy gap. The Fermi energy level of p-type Si is about ~45 meV [23] above the bottom of the valance band. In addition, the electron affinities for silicon and BFO are 4.01 [24] and 3.30 eV [21, 25], respectively, are taken to construct the band structure. Thus the work functions for silicon substrate and BFO are 5.08 eV and 4.45eV, respectively. Figure 3(b) shows the equilibrium band diagram of the BFO/Si heterojunction. Theoretically, built-in potential is found to be V_b = 0.63V, which is the difference between the work functions for the BFO and Si. And the built-in field (with the magnitude of V_b/e) is formed in the depletion layers pointing to Si substrate. In addition, the band offset of the conduction band is ∆E_c0 = 0.71 eV, and that of valence band is ∆E_v0 = 0.47eV. As a result, the heterojunction barriers heights seen by electrons and holes are 0.08 and 1.1 eV, respectively. Although much smaller barrier in conduction band, the current is dominated by holes due to the p-type Si used in the hybrid structure. Figure 3(c) shows current vs. applied bias characteristic of the Ag/BFO/Si/Ag structure at room temperature. As a comparison, bias dependence of THz peak spectra (~0.66 THz) transmission is also plotted in the figure. Once again, it can be seen from Fig. 3(c) that the gate voltage dependence of THz transmission shows exact tendency as that of I-V response in the Ag/BFO/Si/Ag hybrid structure. It should be mentioned that the Ag/BFO Schottky barrier may also contribute to the gate voltage dependence of THz transmission enhancement. Although Schottky barrier can change the carrier mobility, terahertz can’t transmit through the silver electrode. Thus the influence of the Ag/BFO interface on the THz transmission can be ruled out in our case.

 

Fig. 3 (a) Energy band diagram of isolated BFO and p-type silicon; (b) Energy band diagram of an ideal BFO/p-type Si heterojunction at thermal equilibrium. (c) Bias controlled amplitude changes of normalized THz peaks of the BFO/Si heterojunction (open diamond), and the current-voltage curve of the heterojunction is also plotted as open circles. The solid lines are the exponential fittings for the both experimental data.

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Based on the exponential fittings on the experimental data in Fig. 3(c), the turn-on voltage in Ag/BFO/Si/Ag is determined to be about 2.0 V, which is much higher than the theoretical value(~0V) [Appendix 2]. We infer that the deviation comes from the relatively high resistance in p-type Si substrate and BFO film used in our study. The ring electrodes on both surfaces of heterojunction are used for the I-V curve and bias dependent THz transmission measurement, the lateral resistance on surface of BFO film and silicon substrate can’t be ignored, especially the resistance of Si substrate is thought to be more dominate for the deviation due to low dopants (~10⁻¹⁴ cm⁻³) and large thickness (~0.4 mm). In order to fit the current-voltage experimental data, we introduce a correction factor γ to offset the voltage applied on the heterojunction [Appendix 2]. From the I-V curve fitting, correction factor with magnitude of γ = 0.05 is obtained, therefore γV≈0.1 V, which is very close the theoretical turn-on voltage (~0 V).

To further elaborate the mechanism, we could interpret the electric field modulation of THz transmission as that of an electronic “p-n” junction. Figure 4(a) shows schematically the built-in potential across the BFO/Si heterojunction with zero (solid black), forward (red dash) and reverse (blue dash) bias, in which the x_p and x_n denote the thickness of depletion layer in p-(silicon) and n-(BFO) regions, V_b and V_g denote for built-in and gate potential, respectively. Figure 4(b) presents schematically the influence of gate voltage on the diffusion of majority carrier (hole) from Si to BFO thin film. The difference of the reverse THz transmission (1/T_g-1/T₀) under various gate voltages is presented in Fig. 4(c), in which T_g and T₀ stand for the THz peak transmission (at 0.66 THz) with and without gate voltage. The solid line in Fig. 4(c) is the fitting result with exponential function.

 

Fig. 4 (a) The change of potential barrier at zero (black solid), forward (red dash), and reverse (blue dash) bias voltage for BFO/Si heterojunction. x_p and x_n denote the depletion width in Si and BFO region. (b) Illustration of holes diffusion in the BFO/Si heterojunction with forward bias. Forwards bias decreases the potential barrier and reduces the width of depletion layers, as a result, more holes can come across the barrier and accumulates at the BFO region. (c) Bias controlled R(f) response, and the solid line the exponential fitting result.

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As the thickness of BFO is much less than the wavelength of incident THz wave, and the BFO can be treated as a thin film, the transmission T(f) can be simply expressed as

According to both our theoretical model and experimental results, the performance of BFO/Si heterojunction can be improved by adjusting following two parameters: (i) The thickness of the BFO film, this is seen from the enhanced modulation depth in the “echo THz pulse” shown in the inset of Fig. 1(b). The thickness of a common heterojunction is about several micrometers, however, in our case, the thickness of BFO film is about 200 nm, it is expected that the THz modulation depth can be improved by increasing the thickness of BFO film. (ii) Carrier concentration in Si substrate, according to Eqs. (5) and (8), THz conductivity difference (Δσ) with and without bias voltage is proportional to the hole concentration in Si (P_p0), and higher P_p0 in Si, larger THz modulation depth is predicted. Of course, higher carrier concentration in Si will lead to much larger attenuation of THz transmission; therefore, a properly doped Si is optimum for a good performance of the device. Finally, we would like to point out that modulation speed of our device is quite low, ~tens of Hz only. Intrinsically, the modulation speed of a heterojunction is dominated by the turn-off time, which is approximately given by${\text{t}}_{\text{s}}\approx {\tau }_{\text{n}}\text{ln}2=0.68{\tau }_{\text{n}}$with τ_n the carrier lifetime [26]. For most of silicon p-n junction, t_s is ranged from hundreds of ns to a few µs depending on the ratio of forward and backward current [26]. The very slow modulation speed in our device is due to the large thickness of the silicon substrate used. The larger separation between two ring electrodes is indicative of larger capacitance of the heterojunction, which results in a slow response for our device. The modulation speed can reach megahertz by reducing the thickness of the silicon layer to a few µm to hundreds of nm. In short, the proposed model in this paper presents a proof-of-principle for designing and fabricating a new type of all electrical THz modulator.

5. Conclusions

In summary, we propose a new model for all electrical terahertz modulator, and we have designed and fabricated a BFO/Si hybrid structure by using PLD technology. A diode-like behavior for THz transmission appears in the Ag/BFO/Si/Ag heterojunction. The THz spectra modulation exhibited exponential bleaching and broadband characteristics with the applied bias V_g. The maximum modulation depth above 42% has been achieved with forward bias of 4.8 V. The forward bias causes the enhancement of THz transmission can be interpreted well with the proposed model that the substantial difference in carrier mobility of Si and BFO in the heterojunction. Thus it is prospected that, by increasing the hole concentration in Si substrate and BFO thickness on the one hand, the performance of the heterojunction is expected to be improved accordingly, on the other hand a novel heterojunction with higher rectifying feature can be realized with two semiconductors: one has very large carrier mobility, and the other has very low carrier mobility. Our studies pave the way for fabricating a novel all-electrical THz modulator with high performance.

Appendix

1. Modulation depth for second order reflection of THz pulses

Inset in Fig. 1(b) (in the text) presents the secondary reflection signals, it is seen that the applied bias shows more pronounced influence on the secondary reflection pulse than that of main transmission pulse. By using Eq. (6) in the text, we calculate the modulation depth of secondary reflection pulse, which is shown in Fig. 5. It is seen that modulation depth can reach as high as 180% under bias of 4.8 V, which is much higher than that (42%) of main transmission THz pulse. As interpreted in the text, the much larger modulation depth for the secondary reflection THz pulse is due to the fact that the secondary reflection THz pulse traveling twice distance than that of the main THz pulse.

 

Fig. 5 THz spectra modulation depth for the secondary reflection THz pulses under various bias voltages.

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2. Simulation details for Fig. 3(c) and Fig. 4(c)

For an ideal diode, the current density, J vs applied voltage, V_g, can be expressed as Eq. (SE1):

$$J=J_s({\text{e}}^{{}^{\frac{e{V}_g}{k_{B}T}}}\text{-}1),$$ (SE1)

where, e, k_B and T are electron charge, Boltzmann constant and Kelvin temperature with the e = 1.6x10⁻¹⁹ C and k_B = 1.38х10⁻²³ J/K, respectively. J_S is reverse saturation current density with${\text{J}}_{\text{s}}={\text{eD}}_{\text{p}}\frac{{\text{p}}_{\text{n}0}}{{\text{L}}_{\text{p}}}+{\text{eD}}_{\text{n}}\frac{{\text{n}}_{\text{p}0}}{{\text{L}}_{\text{n}}}={\text{eL}}_{\text{p}}\frac{{\text{p}}_{\text{n}0}}{{\text{t}}_{\text{p}}}+{\text{eL}}_{\text{n}}\frac{{\text{n}}_{\text{p}0}}{{\text{t}}_{\text{n}}}$. Theoretically, the turn-on voltage for an ideal diode is zero according to Eq. (SE1).

In order to reproduce the I-V curve shown in Fig. 3(c) (blue circle) in the text, Eq. (SE2) is used to fit the experimental data of Fig. 3(c),

$$I=A_0(e^{R_0{V}_g}-1),$$ (SE2)

the best-fitting leads to A₀ = 8.0х10⁻⁶, and $R_0=\frac{\text{γe}}{k_{B}T}=2.06$, a correction factor$\text{γ}$is introduced to fit the I-V curve of the BFO/Si heterojunction, and $\text{γ}=0.051$is obtained from the fitting. Our experimental measured turn-on voltage is about ~2.0 V, and therefore γV_g ≈0.1 V, which is very close the theoretical turn-on voltage (~0 V).

In addition, Eq. (8) (in the main text) is used to simulate the influence of applied voltage on the THz transmission, in which R(f) is defined as the difference between reverse THz transmission with and without applied voltage, i.e.

$$\begin{array}{l}\text{R}\left(f\right)=\frac{1}{\text{T}\left(f,{\text{V}}_{\text{g}}\right)}-\frac{1}{\text{T}\left(f,0\right)}=\frac{{\text{Z}}_0\text{d}}{1+{\text{n}}_{\text{sub}}}\text{Δσ}\\ \begin{array}{cc}& \end{array}=\frac{{\text{Z}}_0\text{d}}{1+{\text{n}}_{\text{sub}}}\left({\text{μ}}_1-{\text{μ}}_0\right){\text{p}}_{\text{p}0}\left({\text{x}}_{\text{p}}\right){\text{e}}^{\frac{-\Delta {\text{E}}_{\text{v}}}{{\text{K}}_{\text{B}}\text{T}}}({\text{e}}^{\frac{{\text{eV}}_{\text{g}}}{{\text{K}}_{\text{B}}\text{T}}}-1),\end{array}$$ (SE3)

in order to fit the experimental data of Fig. 4(c), again a correction factor, $\gamma \prime$ is introduced, and we have

$$R\left(f\right)=\frac{{\text{Z}}_0\text{d}}{1+{\text{n}}_{\text{sub}}}\left({\text{μ}}_1-{\text{μ}}_0\right){\text{p}}_{\text{p}0}\left({\text{x}}_{\text{p}}\right){\text{e}}^{\frac{-\Delta {\text{E}}_{\text{v}}}{{\text{K}}_{\text{B}}\text{T}}}({\text{e}}^{\frac{{\text{γ'eV}}_{\text{g}}}{{\text{K}}_{\text{B}}\text{T}}}-1),$$ (SE4)

similar as Eq. (SE2), R(f) is an exponential function of an applied voltage V_g, and an exponential function Eq. (SE5) is used to fit the Fig. 4(c) of text:

$$R\left({\text{V}}_{\text{g}}\right)=A_1(e^{R_1{V}_g}-1),$$ (SE5)

the best fitting parameters produce A₁ = −1.05х10⁻⁵, and $R_1=\frac{\text{γ'e}}{{\text{k}}_{\text{B}}\text{T}} =2.06$, as a result, we have R₁≈R₀, and$\text{γ}\approx \text{γ'}=0.051$ . It is seen that our two independent experimental measurements produce very close value of$\text{γ}$, which indicates that our experimental measurements are raliable.

Funding

National Natural Science Foundation of China (NSFC: 11674213, 11604202); Research Innovation Fund of the Shanghai Education Committee (14ZZ101); Young Eastern Scholar at Shanghai Institutions of Higher Learning (QD2015020).

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