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An alternative-grating gated AlGaN/GaN field-effect transistor (FET) is proposed by considering the slit regions to be covered by a highly doped semiconductor acting as supplemental gates. The plasmonic resonant absorption spectra are studied at THz frequencies using the FDTD method. The 2DEGs, under supplemental gates, modulated by a positive voltage, can make the excitation of the higher order plasmon modes under metallic fingers more efficient in comparison to ungated regions in common slit-grating gate transistors. Moreover, the supplemental gates can confine the electric field of dipole oscillation between metallic gate fingers under THz radiation. The competition of the near-field enhancement and screening effect of the supplemental gate fingers results in the intensity of the higher order plasmon resonances being maximized at increased doping concentration. Our results demonstrate the possibility of significant improvement in the excitation of plasmon resonances in FETs for THz detection.
©2013 Optical Society of America
1. Introduction
Recently, the terahertz (THz) response of field-effect transistors (FETs) [1–16] with a periodic metal grating gate [5–16] has been widely investigated. The metal grating gate placed in close proximity to the two dimensional (2D) electron channel is an efficient coupler between plasmons and THz radiation [17]. The frequency of gated plasma oscillations can be tuned efficiently by applying DC voltage to the grating-gate fingers. Thus, the gated controllable plasmon becomes one of the most attractive modes for THz radiation detection [18–20]. However, gated plasmons are still weakly coupled to THz radiation due to the strong screening effect of the gate electrode [20,21]. A method to more efficiently excite the gated plasmon modes, especially the higher order resonances, has attracted extensive attention. Popov et al. have demonstrated that the ungated regions of the common 2D electron channel play an important role of electric vibrators in efficiently exciting gated plasmons [20]. Further, the absorption spectrum of field-effect hetero-transistors (FEHTs) is calculated with separated 2D electron channels in which the ungated regions are replaced by lateral metal contacts [20,22,23]. In their work, higher order plasmon resonances up to a frequency of 15 THz are obtained and the absorption strength approaches the maximum of 0.25. This effect is the result of the electron liquid in the lateral metal contacts being more “rigid” than that in the 2DEGs. Therefore, the side metal contacts are more efficient electric vibrators exciting the gated plasmons. Based on such an idea, we design an alternative-grating gated AlGaN/GaN field-effect transistor by considering the slit regions of the structure to be covered by a highly doped semiconductor acting as supplemental gates. Thus, the supplemental gates can be used to make the “ungated” 2DEGs more “rigid” than the 2DEGs under vacuum slits by applying positive voltages.
2. Device description and analysis model
Figure 1 shows the schematic of a AlGaN/GaN FET with alternative-grating gates (AGG). Compared with the common slit-grating gates (SGG), our slit regions are occupied by a highly doped semiconductor acting as supplemental gates. The metallic (yellow, 1 μm wide) and supplemental (green, 0.1 μm wide) gated fingers are arranged alternatively to fully cover the barrier, but not fully screen the channel due to the semi-screened characteristic of doped semiconductor material. Here, the doped semiconductor material, as the supplemental gate, is highly doped GaN and the doping concentration is at the level of 1018 cm−3. According to our calculations, a higher concentration, i.e. 1019 cm−3, can cause serious screening of the supplemental gate so that the gated plasmons in the channel can be hardly excited. The voltage applied to the metallic gate can be transferred to the supplemental gate due to the Ohmic contact boundary between the metallic and supplemental finger. With this type of grating gate, the density of all the channel electrons can be modulated uniformly. Other parameters of AlGaN/GaN FETs are used in calculations as follows: areal density of 2DEGs at zero gate voltage N0 = 1.87 × 1013 cm−2, electron relaxation time τ = 2.27 × 10−13 s [20], electron effective mass m* = 0.2m0, barrier thickness d = 10 nm and barrier permittivity εb = 9 [20]. The plasmonic resonant absorption spectra of the transistor at THz frequencies are investigated by using a finite difference time domain (FDTD) method [13,24]. The Drude model [13,25,26] is used to describe the behaviors of 2DEGs and the supplemental gates. The gold fingers with electric conductivity 4.1 × 107 S·m−1 are considered as the perfectly conductive strips. Our further calculation shows that this assumption has a negligible effect on our results.
Fig. 1 The schematic of an alternative-grating gated AlGaN/GaN FET. The THz wave is incident from the top side with the polarization of electric field along the grating-gate periodicity.
The electromagnetic wave (EMW) solver “EMLAB” from “Sentaurus” was used for the calculation of the 2D FDTD method. According to the standard Yee algorithm [27], Maxwell’s equations are differentiated in the time–space dimension [9,14]. The frequency-dependent conductivity based on the Drude model is embedded into the EMW solver [9,13]. In the simulation, recursive convolution (RC) methods are used to handle dispersive media [28]. Additionally, periodic boundary conditions are imposed in the x direction for the grating gates, while perfect matched layers are imposed in the y direction [29].
For a thin barrier layer, the dispersion of gated plasmons in FETs with SGG has the following form [8,17,22],
where k = 2πn/L (n = 1, 2, 3···) when w << L. w and L are the slit width and the period of SGG, respectively. In this paper, w is narrow enough compared to L (see Fig. 1) such that the wave vector of gated plasmon basically satisfies the formula mentioned above. Under the gradual channel approximation, the areal density in the gated region can be expressed in a simple parallel-plate capacitor model aswhere Ug is the gate voltage and Uth is the channel depletion threshold voltage. Then the dispersion Eq. (1) becomes3. Results and discussions
Figure 2 shows the THz absorption spectra of AlGaN/GaN FETs for AGG (solid lines) at zero gate voltage. The doping concentration of the supplemental gate changes from 3.5 × 1018 cm−3 to 1.5 × 1018 cm−3 at a step of 0.5 × 1018 cm−3. For convenience of comparison, the absorption spectrum for common SGG (dashed line) is also calculated, as shown in Fig. 2. The resonant frequencies for the structure with SGG are in good agreement with that of Eq. (1). The equidistant characteristic of THz absorption peaks is also shown in the results of the AGG as evidence of the excitation of the gated plasmon modes, although the peaks have a small redshift in spectra. The small shift may result from the dielectric change of the supplemental gates induced by different doping concentrations. Figure 3 shows the plasmon-induced electric field distributions of the AGG device with a doping concentration 2.0 × 1018 cm−3. Figures 3(a), 3(b), 3(c) and 3(d) correspond to the 1st, 2nd, 3rd and 4th order resonant modes, respectively. It has been indicated that the electric field of channel plasmons can extend to the barrier and buffer layers without the metallic gates [30]. However, with the metallic gates, the induced imaging charge in the gates confines the field of channel plasmons to the barrier layer even without applied gate voltages. Furthermore, the spatial waveform of the plasmon mode occupies the entire period of the structure [8]. The maximum field intensity tends to be confined more closely to the edges of the metallic gate fingers as the order of plasmon modes increases.
Fig. 2 THz absorption spectra for AGG (solid lines) and SGG (dashed line) at zero gate voltage. The arrow marks the change of doping concentration from 3.5 × 1018 cm−3 to 1.5 × 1018 cm−3 at a step of 0.5 × 1018 cm−3. “S1” to “S6” are used to label the resonant peaks. Each symbol presents a series of peaks at the same resonant order. Absorption strength as a function of doping concentration at S6 is shown in the inset.
Fig. 3 Plasmon-induced electric field distributions (absolute value) along the channel (in one period) under THz wave excitation. (a), (b), (c) and (d) correspond to the resonant peaks S1, S2, S3 and S4 for AGG transistor with doping concentration of 2.0 × 1018 cm−3 (red line in Fig. 2), respectively.
It also can be seen from Fig. 2 that the absorption strengths of S1 to S3 for the common SGG are higher than that for AGG. Moreover, with increasing the doping density, the absorption strengths of S1 to S5 monotonically decrease. This effect may be due to the carrier screening effect of supplemental gates resulting in the weakening of gated plasmons coupling to the THz radiation. However, an abnormal change is obtained that the absorption peak of S6 for AGG exhibits a maximum at increased doping concentration (see the inset of Fig. 2). Here, the screening effect of the supplemental gates reduces the absorption of channel plasmons with increasing doping concentration. Therefore, the absorption peak is expected to decrease. However, for the higher order plasmon modes, the high resonant frequencies make the electric dipole oscillations very strong. When increasing the doping concentration, the electric fields of dipole oscillations near the channel become stronger. The maximum peak is the consequence of the competition between the screening effect and the near-field enhancement caused by the supplemental gates. This phenomenon will be explained below in detail.
When a positive voltage is applied to the AGG, the density of metallic and supplemental gated 2DEGs can be modulated simultaneously. The 2DEGs under the supplemental gates are more “rigid” in contrast to the common SGG transistor with a constant density of ungated 2DEGs thus efficiently exciting the metallic gated plasmons. Figures 4(a) and 4(b) show the THz absorption spectra for AGG (solid lines) and SGG (dashed line) with 3V and 5V gate voltages, respectively. For the AGG with doping concentration 1.5 × 1018 cm−3 and 2.0 × 1018 cm−3, the absorption strengths of S1 to S4 are very high and approach the maximum absorbance of 0.25. For the SGG, only the peak values of S1 and S2 are close to 0.25, and then the absorption strength decreases rapidly with increasing resonant orders. The enhancement factors, defined as the strength ratio of AGG and SGG structures, are 1.30 and 2.18 for S3 and S4 with 3V gate voltage, respectively. And with 5V voltage, the factors are 1.61 and 3.86 for S3 and S4, respectively. Furthermore, the higher order plasmon resonance S5 can also be excited efficiently for AGG in comparison with that for SGG.
Fig. 4 THz absorption spectra for AGG (solid lines) and SGG (dashed line) under 3V (a) and 5V (b) gate voltages. The arrow marks the change of doping concentration from 3.5 × 1018 cm−3 to 1.5 × 1018 cm−3 at a step of 0.5 × 1018 cm−3. “S1” to “S6” are used to label the resonant peaks. Each symbol presents a series of peaks at the same resonant order. The insets in (a) and (b) show the absorption strength as a function of doping concentration for S5 and S4, respectively.
As mentioned above, the absorption peaks of the lower orders exhibit little reduction with an increase in the doping concentration due to the carrier screening effect of supplemental gates. However, the absorption peaks of the higher orders are excited with increasing doping concentration and have higher strength. This is due to the fact that the resonant frequencies are not very high for the lower order plasmon modes, and the electric fields of the dipole oscillations between the metallic gates are weak. Thus, the carrier screening effect is dominant and reduces the absorbance. For the higher order plasmon modes, the high resonant frequencies make the electric fields of the dipole oscillations very strong. The supplemental gates between two adjoining metallic fingers provide a good conductive path in which the electric fields of dipole oscillation are well confined. The gates make the fields near the 2D channel stronger than that for SGG. In addition, the higher doping concentration the supplemental gates have, the more strongly the electric fields are confined. Thus, for the higher order plasmon modes, although the carrier screening effect still exists, the near-field enhancement effect is dominant and the higher order resonances are more efficiently excited. For clarity we only calculate the field distribution of dipole oscillation of the AGG structures for different doping concentrations without considering the 2DEG channel in order to indicate the near-field enhancement. The results are shown in Fig. 5 with AGG at a 5V gate voltage. The left inset (black line) presents the electric field for the AGG structure with a doping concentration of 1.5 × 1018 cm−3 at the 5th resonant frequency 11.86 THz. The right inset (red line) shows the electric field for the AGG structure with a doping concentration of 3.5 × 1018 cm−3 at the 5th resonant frequency 11.08 THz. It is seen that the electric field with low doping concentration is much lower and more spread than that with high doping concentration.
Fig. 5 The electric filed distribution of dipole oscillation along the white dashed line (see the insets) at 5V gate voltage. The white dashed line is the perpendicular bisector of the supplemental gate. The values of the X-coordinate correspond to that of Y-axis of the inset.
Moreover, the abnormal peaks appear at S6 for zero gate voltage, S5 for 3V and S4 for 5V (seeing the insets of Fig. 2 and Fig. 4). It is well known that a higher positive gate voltage can cause the higher 2DEGs density. In that case, the near-field enhancement can also be strengthened due to the increasing net dipole moment in the channel. Thus, at a certain gate voltage, the competition of the screening and near-field enhancement of supplemental gates results in the creation of the maximum peak at increased doping concentration. When increasing the gate voltage, the channel under the metallic gate can further intensify the effect of near-field enhancement. Finally, the combining localized strengthening of the electric fields causes the relevant peak of abnormal change to shift the excitation of lower orders. In addition, for SGG transistor, it is also found that the plasmon resonances can be excited up to 7th order at zero gate voltage (not shown in Fig. 2), 5th order at 3V and 4th order at 5V. Higher ratio of Ngated/Nungated, where Ngated and Nungated are the 2DEGs densities under the gated and ungated regions, respectively, can reduce the number of excited plasmon modes. For the AGG transistor, the supplemental gates can be used to modulate the 2D electron channel uniformly under a positive gate voltage resulting in higher orders of plasmon modes which can be excited. Therefore, according to the applications, the high performance THz response of field-effect transistors can be achieved by appropriately choosing the grating gate.
4. Conclusions
We have calculated the plasmonic resonant absorption spectra of AlGaN/GaN FETs with an alternative-grating gate at THz frequencies using the FDTD method. The supplemental gates are designed by covering the slit regions with a highly doped semiconductor. The 2DEGs under the supplemental gates, when modulated by a positive voltage, can make the excitation of the higher order plasmon modes under the metallic gates more efficient. Moreover, the supplemental gates can confine the electric field of dipole oscillation between metallic gate fingers under THz radiation. The competition between the near-field enhancement and screening effect of the supplemental gate fingers results in the intensity of the higher order plasmon resonances being maximized at increased doping concentration. Our results demonstrate the possibility of significant improvement in the excitation of plasmon resonances in FETs for THz detection.
Acknowledgments
The authors thank James Torley from the University of Colorado at Colorado Springs for critical reading of the manuscript. The work was supported by the State Key Program for Basic Research of China (2013CB632705), National Natural Science Foundation of China (11274331, 61006090, 61290301, 10990104, 60976092), and Shanghai Rising-Star Program.
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