Plasmonic photodetectors based on asymmetric nanogap electrodes

Hot electrons excited by plasmon resonance in nanostructure can be employed to enhance the properties of photodetectors, even when the photon energy is lower than the bandgap of the semiconductor. However, current research has seldom considered how to realize the efficient collection of hot electrons, which restricts the responsivity of the device. In this paper, a type of plasmonic photodetector based on asymmetric nanogap electrodes is proposed. Owing to this structure, the device achieves responsivities as high as 0.45 and 0.25 mA/W for wavelengths of 1310 and 1550 nm, respectively. These insights can aid the realization of efficient plasmon-enhanced photodetectors for infrared detection.

I n recent years, the rapid development of optical communications, 1) signal processing, and sensor systems has proposed higher requirements for the performance of semiconductor photodetectors. 2) Photons with energies below the Si bandgap (E g = 1.12 eV) cannot be harvested by a Si photodetector, which limits its application to optical communications and infrared detection. 3) This limitation of the Si photodetectors can be relaxed by harvesting the energy of photoelectrons ejected from a metal. 4) Hot electrons excited by plasmon resonance in metallic nanoelectrodes can be converted into a photocurrent, 5) even when the photon energy is lower than the bandgap of the semiconductor. 6) There are two characteristics making the plasmonic photodetector an efficient device: the intense light-focusing properties of a plasmonic nanoantenna allow more photons to be coupled and absorbed by the device, 7) which means more photons can be converted into a photocurrent; 8) and efficient collection of the conductive carriers can be achieved by a certain device structure that makes use of the hot carriers produced in the relaxation of plasmons. 9) Recent studies have already revealed the potential importance of plasmon resonances in near-infrared optical absorption enhancement. 10) Halas et al. accomplished an active optical antenna device with Au resonant antennas fabricated on an n-type Si substrate, and achieved a tunable peak response at a wavelength range of 1250-1600 nm. 11) Nevertheless, the device structure can restrict the hot electron collection efficiency. As a result, the responsivities are on the order of µA=W. Jason Valentine et al. demonstrated a perfect absorber photodetector with ultrathin plasmonic nanostructures of 15 nm, and achieved responsivities on the order of mA=W in the communication band, 12) where the fabrication process is relatively complicated. Overall, these studies opened a pathway for the development of near-infrared Si photodetectors. However, a challenge in achieving high efficiencies is related to the efficient collection of the excited hot electrons. 13) In this work, a plasmonic photodetector with asymmetric nanogap electrodes is demonstrated, in which the travel length of carriers is short and the energy loss is small. Hence, high responsivities can be obtained in the near-infrared spectral region. Meanwhile, the device is easily fabricated and compatible with CMOS processes.  14) electron beam evaporation, and the lift-off process. 15) On the n-type Si substrate, asymmetric electrodes, including the plasmon and collection electrodes, are fabricated in the interdigital configuration. The narrow ones are the plasmon electrodes, while the wide ones are the collection electrodes. Schottky barriers are formed between the metal (Au) and the semiconductor (n-type Si). 16) The asymmetric nanostripe electrodes produce nonequilibrium photocurrents in the device. There are many more hot electrons induced in the plasmon electrodes than those induced in the collection electrodes. As demonstrated in Fig. 1(b), assuming the illumination is uniform and vertical, the photocurrent produced by the plasmon electrodes is I p ,  (a) Device structure. The dimension of the structure is illustrated on the topright. Here, W p is the width of the plasmon electrodes, W c is the width of the collection electrodes, G is the gap between the electrodes, and H is the height of the electrodes. (b) Band diagram of the device. The photocurrent is generated in five consecutive steps. and the one produced by the collection electrodes is I c . Then, the net current I can be expressed as I = I p − I c . Thus, the device is able to work without a bias voltage due to the asymmetric structure.
Furthermore, the band diagram in Fig. 1(b) illustrates the five physical steps to produce a photocurrent. First, photons of energy hν excite plasmon resonance in the metallic nanostructure, generating a large amount of hot carriers. This process can be analyzed based on the finite-difference time domain method (Lumerical FDTD Solutions), more details of the results will be presented later. Second, hot carriers arrive at the metal-semiconductor interface with a kinetic energy. Third, hot carriers transfer across the Schottky barrier and travel through the interface with a certain probability. 17) In the fourth step, a part of the surviving carriers travels across the gap in the semiconductor. By using nanogap electrodes, shorter travel distances in the semiconductor promote the carrier collection efficiency. Finally, the carriers reach a semiconductor-metal interface again and are collected as a photocurrent.
As depicted in Fig. 2, the constant energy outline contains all of the possible terminations of the allowed electron momenta at a given kinetic energy. In Au electrodes, the hot carriers emitted by photons have energy as below: 18) Here, ħ is the reduced Planck's constant, m Ã e is the effective mass of the electron, and k Au,x and k Au,z are the hot electron momenta in the xand the z-directions, respectively. The total momentum of a hot electron is equal to the quadratic sum of the momenta in the xand the z-directions: Once the electron is injected into the Si substrate, both its kinetic energy and momentum would change relatively. The kinetic energy is calculated as Again, the total momentum of the hot electrons in Si is calculated as the following: The hot electron momenta in the x-direction are fixed when electrons are injected into the semiconductor substrate from the metallic electrodes, which defines the escape cone for the electrons. Hot electrons can escape only when k Au,x < k Au,xmax , which limits the probability of emission to a solid angle Ω. Thus, regardless of the reflecting events, the emission probability is 19) PðEÞ ¼ However, despite the fact is that the hot electrons arriving at the metal=semiconductor interface can be reflected in the vast majority of cases, there is still a possibility for them to pass the Au-Si interface after multiple times of scattering events, and two assumptions are made based on this phenomenon: 20) (1) If the hot electrons cannot travel through the Au-Si interface, they will make it to the interface in an elastic collision; (2) The electrons cannot travel through the Auvacuum interface or escape into vacuum, but they can make it to the interface in an elastic collision. Then, taking the reflecting events into account, the emission probability of a hot carrier every time is presented in Fig. 3 and the probability of emission is evaluated as: N is the total number of round trips before the excess energy of the carrier is reduced to E = Φ B . It is given by where L is the mean free path of the electrons, H is the height of the electrodes, E 0 is the initial energy of the hot electrons, and Φ B is the Schottky barrier. The mechanism of the hot electrons traversing Si-Au interfaces is essentially the same with that of traversing Au-Si interfaces except for the travel direction. Moreover, the possibility of hot electrons injecting into the collection electrodes is defined as P ii .
The total internal quantum efficiency η itotal indicates the efficiency of hot carriers emitted into the semiconductor and collected by collection electrodes, which can be obtained by: The responsivity of the electrodes is given below: where h is Planck's constant. With the above equations, the probability of hot carriers injected into the Si substrate can be obtained. Figure 4 shows the field distributions of the device with the initial design that has the dimensions of H = 30 nm, W p = 150 nm, W c = 1 µm, and G = 50 nm. Figures 4(a) and 4(c) are the electric field and the magnetic field distributions of the plasmon electrodes, respectively. The electric field is inclined to distribute towards the edges of the electrodes, opposite to its magnetic field status, because 1=2λ SPP fits along the width of the electrodes, which is evidence of the existence of surface plasmon resonance. 21) Figures 4(b) and 4(d) are the two field distributions of the collection electrodes. Compared to the plasmon electrodes, the intensity of their electric field is significantly weakened. In the meantime, the 1 µm metallic electrodes no longer fit 1=2λ SPP .
Therefore, there are several maximums simultaneously in the magnetic field, and the plasmon resonance is reduced.
The light absorption is determined by the intensity of the electric field, as shown in this equation: 20) A ¼ This enables us to analyze the performance of the devices. As shown in Fig. 5, the relationships between the optical absorption and device dimensions are studied. In Fig. 5(a), the light absorption exhibits a cos 2 θ angular dependence and the position of the peak value is relevant for the physical size of the device.
In Fig. 5(b), when the wavelength is 1310 nm, the absorption is improved with the growth of H, and remains the same since H is more than 30 nm. On the contrary, the absorption is reduced with the growth of the electrode width, shown in Fig. 5(c), and the peak value appears with the electrode width W p = 90 nm and electrode height H = 25 nm. When the wavelength is 1550 nm, the changing trend of the curve of the absorption is different. It has a negative relationship with H, and has a positive relationship with the electrode width. The peak value appears with the electrode width W p = 150 nm and electrode height H = 20 nm. These provide valuable information for optimizing the device.
The relationship between electrode gap and absorption is shown in Fig. 5(d). When the nanogap is relatively small, its surface plasmon polaritons (SPP) will couple with the wavelength of 1310 nm, which enhances the electric field. For a gap is up to 200 nm, the coupling interaction of the nanogap and wavelength of 1550 nm is dominant, 22) which proves that the optimized gap widths for the wavelengths of 1310 and 1550 nm are different. However, a wide gap will increase the energy loss during the transition, and the transition time will become longer when the electrode gap is broadened. Consequently, proper electrode gaps are needed.
The collection electrode width W c plays an important role in influencing the absorption as well. The net current is the difference between the photocurrent produced by the plasmon electrodes (I p ) and the one produced by the collection electrodes (I c ). Without a bias voltage, it reduces to zero when the absorption of the two electrodes is the same. Thus, the photocurrent I c is expected to be kept as small as possible, and this can be realized via reducing the absorption of the collection electrodes. The relationship between the width W c and the absorption of the collection electrodes is depicted in Fig. 6. The absorption cannot be neglected when W c is smaller than 1 µm and I p is offset by I c , which leads to a decrease of   responsivity. The influence of plasmon resonant in collection electrodes is negligible since the width W c is more than 1 µm, and the offset effect is weakened. Meanwhile, the size of the device grows when W c increases. In this way, the collection electrodes with a width W c of 1 µm were chosen.
Consequently, with uniform vertical illumination, the absorption of the collection electrodes is much lower than that of the plasmon electrodes and can be ignored. Taking only the photocurrent produced by plasmonic electrodes into account will make the computation of the responsivity easier.
In Fig. 7, the spectral dependence of η itotal is revealed. Both η itotal and the emission probability decrease as the wavelength increases. As demonstrated in the picture on the topright corner, since the electrode height H is more than 20 nm, the emission probability as well as η itotal is independent of H and is only determined by the wavelength.
According to the analysis mentioned above, three types of devices with different dimensions are designed to meet the requirements of different work bands, Table I displays the parameters of these devices.
Device 1 is the initial design, and its responsivities at wavelengths of 1310 and 1550 nm are not ideal as depicted in Fig. 8. Device 2 is optimized specially for a wavelength of 1310 nm, and Device 3 is optimized specially for a wavelength of 1550 nm. These optimized structures have relatively high responsivities in the targeted wavebands. After optimization, the device can achieve responsivities as high as 0.45 and 0.25 mA=W for wavelengths of 1310 and 1550 nm, respectively. Consequently, we have optimized the device by changing its physical size according to the wavelength, and generated optimized devices.
In summary, a plasmonic Si photodetector with asymmetric nanogap electrodes is proposed and the physical mechanism of the photoelectric effect is studied. By decreasing the transmission length of the hot electrons to nanometer scales, the device achieves much higher responsivities with wavelengths of 1310 and 1550 nm. This ultracompact, CMOS-compatible Si based plasmonic photodetector can be readily integrated into on-chip optoelectronics, which will result in enhanced efficiencies and lower costs in optical communication systems.