Terahertz Optoelectronic Switching with Surface ... - OSA Publishing

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Terahertz Optoelectronic Switching with Surface Plasmon Polariton Diode Raj K Vinnakota and Dentcho A. Genov* College of Engineering and Science, Louisiana Tech University, Ruston, LA 71272 *e-mail: [email protected]

Abstract: We present a GaAs based optoelectronic switch that operates at exceptionally large signal modulation rates of 98% and switching rates up to THz. Applications in designing fundamental logic elements, NAND and NOR gates, are identified. OCIS codes: (250.0250) Optoelectronics; (230.2090) Electro-optical devices; (240.6680) Surface plasmons

1. Introduction The Surface Plasmon Polaritons (SPPs), spatially confined transverse magnetic (TM) electromagnetic modes propagating at the metal-dielectric interfaces, offer the bandwidths of photonic devices and physical dimensions shared with nanoscale electronics [1-4]. The potential of plasmonics to bridge the gap between electronics and photonics is now well recognized by the scientific community with a large number of investigators working in the field of plasmonics [5]. In 2008 Brongersma et al. demonstrated all-optical switch based on SPP waveguide that uses metallic (passive) nanostructures coupled with active PMMA films with photochromic molecules [6]. Unfortunately, the switching rates of the photochromic molecules were low (~20ns) [6]. The same group also proposed extremely compact gain-assisted plasmonic switch consisting of a gold-air-gold plasmonic waveguide side-coupled to a cavity filled with a semiconductor (InGaAsP) gain material [7]. A metal-oxide-Si field effect plasmonic modulators and alloptical modulation by plasmonic excitation of CdSe quantum dots have been investigated showing moderate transmission modulation at visible and telecommunication frequencies [8-9]. Recently, a THz all-optical switch based on a carbon nanotube metamaterial has been proposed, however the device shows a rather low transmission modulation of less than 10% [10]. In this paper we present a new optoelectronic device which we refer to as a Surface Plasmon Polariton Diode (SPPD). The SPPD demonstrates active control of SPPs at the interface between highly doped 𝒏-type and 𝒑-type semiconductors. While the propagation of SPPs on metal surfaces is well understood, not much attention has been paid on the fact that due to the extremely high plasma frequencies inherent to noble metals (for silver 𝝎𝒑 = 𝟗 𝐞𝐕) there is a substantial bandwidths mismatch with electronics that cannot be easily bridged. Here we show that use of highly doped semiconductor material (GaAs) can serve three distinct purposes: (i) act as a metal-like interface allowing SPP propagation, (ii) provide fast optoelectronic SPP switching facilitated by a p-n junction, and (iii) facilitates tunable operational frequency range. More importantly, due to strong localization of the SPP at the p-n junction, the SPPD can exhibit extremely fast (up to 1THz) switching rates, has relatively small size and can be used to develop the fundamental logic for prospective use in optoelectronic data processing. 2. SPPD principle of operation A basic schematic of the proposed Surface Plasmon Polariton Diode (SPPD) is shown in Fig 1(a). It consists of a highly doped p-n junction and an active drift-diffusion region formed between two control electrodes. The basic operational characteristics of the SPPD follow. For frequencies below the plasma frequency, 𝜔𝑝 = 𝑒√𝑛/𝑚𝜀0 , all semiconductors behave as metals and can be tuned by doping, increasing the equilibrium conduction electron concentration 𝑛 , or by applying an external bias. At zero applied voltage the n- region acts as a metallic layer (with permittivity 𝜀𝑛 < 0 ) while the p- region acts as a dielectric (𝜀𝑝 > 0). This allows SPPs to propagate along the interface establishing the “ON” state of the device. In the presence of external voltage, surpassing a certain critical voltage, 𝑉𝑐 = 2𝑘𝐵 𝑇ln(𝜔/ 𝜔𝑝0 ), where 𝜔𝑝0 is the plasma frequency of the intrinsic p-layer, the optical properties of the p-type layer can be dramatically altered due to injection of conduction electrons within the active drift-diffusion zone, as the concentration surpasses the critical value, 𝑛𝑐 ≈ 𝑛0 𝑒 𝑉𝑐/𝑉𝑇 (where 𝑉𝑇 = 𝑘𝐵 𝑇/𝑞 = 0.0026𝑉 is the thermal voltage), will result in inducing metal like permittivity (𝜀𝑝 < 0) resulting in “OFF” state. The SPPD switching, can be qualitatively described using the Wentzel-Kramers-Brillouin (WKB) method, which implemented for the SPP transmittance across the drift-diffusion region yields: 𝒘

𝑻(𝑽) = |𝒆𝒊 ∫𝟎

𝒌𝒔𝒑𝒑 (𝒙,𝑽)𝒅𝒙

𝟐

| ≈ 𝒆−𝟐𝒘𝐈𝐦[𝒌𝒔𝒑𝒑 (𝑽)]

(𝟏)

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where 𝒘 is the length of the active drift-diffusion region (roughly corresponding to the length of top electrode), and the SPP wave vector, 𝒌𝒔𝒑𝒑 , which is generally position and voltage dependent due to the spatially inhomogeneous minority carrier concentration in the p-type layer. For a given frequency of operation, 𝝎, and sufficiently low minority carrier concentration 𝒌𝒔𝒑𝒑 ∈ ℝ and 𝑻 ≈ 𝟏. When 𝑽 > 𝑽𝒄 , the permittivity of the p-doped layer becomes negative (𝜺𝒑 (𝝎) < 𝟎) and the SPP are evanescent in the drift-diffusion region. Consequently the transmittance exponentially decreases with an increase in the applied voltage (see dashed line in Fig. 1(b)).The SPPD characteristics are studied by performing simulations with a self-consistent numerical model that merges the electronic response, obtained from a finite difference (FD) integrated circuits semiconductor code (SENTAURUS, Synopsys Inc.), and the optical response simulated with a commercial electromagnetic code (COMSOL). 3. SPPD response times The prime interest of the SPPD is the speed at which the optical properties of the p-layer switches between dielectric (𝜀𝑝 > 0) to metallic (𝜀𝑝 < 0). The temporal response of the SPPD depends on the injection rate of electrons from the n-type into the p-type layer and thus on both applied voltage and doping concentrations. Figure 1(c,d) shows the SPPD temporal responses, where a forward bias (𝑉 > 𝑉𝑐 ) is applied across the drift-diffusion zone for a period of 5ps and a zero bias follows for 10ps. Under a forward bias, within few picoseconds the concentration close to metallurgic junction surpasses the critical value, 𝑛𝑐 , establishing the “OFF” state of the device. Once the applied bias is removed the excess electrons in the p-layer are removed by the net carrier outflow from the quasi-neutral region via diffusion and their concentration falls below the critical value in approximately 5ps, re-establishing the “ON” state. The temporal analyses depicts that the ON time 𝜏ON of the device is diffusion limited and the OFF time 𝜏OFF , however, is 𝑝 𝑝 governed by the drift of the electrons in the p-type with an effective velocity 𝑣𝑑 ≈ 𝜇𝑒 (𝑉 − 𝑉𝑏𝑖 )/𝑑 , where 𝜇𝑒 is the minority carrier drift mobility in p-layer [11], 𝑑 is the thickness of that layer and 𝑉𝑏𝑖 is the build-in potential. The effects of applied voltage and doping on the response times can be quantitatively estimated as follows. The SPPD OFF time is inversely proportional to the drift velocity and the applied bias and can be estimated as 𝜏OFF = 𝑙𝑠𝑝𝑝 /𝑣𝑑 , where 2 𝑙𝑠𝑝𝑝 = (1/2)/√𝑘𝑠𝑝𝑝 − 𝜀𝑝 𝑘02 is the SPP penetration depth in the p-type layer. Using dimensional analysis we can 2 write 𝜏ON = 𝑙𝑠𝑝𝑝 /(𝐹𝐷𝑛 ), where 𝐹 ≈ 4 is a shape factor near-independent on the parameters under investigation, 𝐷𝑛 = 𝑛 (𝑘𝑇/𝑞)𝜇𝑒 is the diffusion co-efficient of the electron in the p-region, 𝜇𝑒𝑛 is the electron mobility. The results indicate that extremely fast switching can be achieved corresponding to data rates of 100GHz and higher.

Fig. 1. (a) Basic schematic of a Surface Plasmon Polarition Diode (SPPD). (b) The transmittance curves obtained using the integrated finite difference semiconductor and optical module (solid blue line) and the WKB approximation (dashed red line), show exponential decrease of the output signal for 𝑉 > 𝑉𝑐 = 1.57 V. In the calculations the operation frequency is set at 35THz, the thickness of the p-type layer is 𝑑 = 0.5𝜇𝑚 and the overall length of the active drift-diffusion region is fixed at 𝑤 = 2𝜇𝑚. (c) Electron concentration. (d) SPP propagation across the SPPD driftdiffusion zone at two different times.

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