Antenna-enhanced and polarization sensitive photoresponse in arrays of silicon P–i–N nanowires

The built-in field region responsible for short-circuit current generation in the SiNWs was imaged by EBIC using a low-noise current preamplifier in a scanning electron microscope. The acceleration voltage and beam current were 8 kV and 100 pA, respectively. A spatial map of the EBIC signal is shown in figure 2(A). Note that the region between the SiNWs corresponds to the reference (zero) level of the EBIC signal. Beginning at the boundary between the cathode and n-type region of the SiNW and moving toward the opposite terminal, the EBIC signal is negative for approximately 250 nm, positive for approximately 500 nm and again negative for approximately 250 nm, for each 1 μm long SiNW. The EBIC profile along a single NW (dashed line in figure 2(A)) is shown in figure 2(B). The width of the bright region at half of the peak EBIC signal is L = 470 ± 50 nm. Bright regions in cross-sectional imaging of junctions are associated with the built-in field where efficient separation of electron–hole pairs occurs [14]. Since the 470 ± 50 nm length of the bright central region matches expected 500 nm length of the intrinsic region, it can be readily attributed to electron/hole pair generation in the intrinsic region.

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The negative EBIC signal (i.e. the P and N regions of the SiNW) occurs by direct injection from the electron beam outside the region of the built-in field [14, 15]. An electron injected directly into the P region would immediately recombine, creating current flow from the anode that would be in the opposite direction to the current generated by electron/hole pair generation in the junction. Similarly, an electron generated in the cathode could recombine with an excess hole from the P region to produce the same response. Stochastic interaction of the electron beam with SiO₂ material spatially broadens [14] the electron beam 400 nm below the SiO₂ surface, where the SiNWs are located. In particular, this accounts for the blurred appearance of the EBIC image, in which the apparent width of the SiNWs exceeds their physical width.

Photocurrent I and responsivity $\mathcal {R}$ were measured for excitation wavelengths 1100 > λ > 400 nm for 500, 200 and 100 SiNW gratings with no externally applied bias. As shown schematically in figure 3(A), optical excitation was provided by a combination of broadband light source and optical spectrometer, which after collimation was focused onto the sample at normal incidence by an objective lens. An aperture was used to control the illuminated area of the sample, and an electromechanical shutter was used to gate the excitation. Measurements were carried out with both unpolarized and linearly polarized excitation. For the latter, electric field could be oriented at an arbitrary angle relative to the SiNW axis. Chips were mounted on an optical translation stage with three axes of motion. Finally, a moveable beam splitter (BS) was used to image the illuminated area of the sample on a charge coupled device (CCD) camera, as shown in figure 3(A). The diameter of the illuminated area was measured using the CCD to be d_m = 520 ± 10 μm. The aperture and translation stage were used in combination to scan the excitation over the large ohmic contacts and wirebonding pads, which, as expected, did not exhibit any short-circuit photoresponse.

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In the short-circuit configuration, I is related to the responsivity $\mathcal {R}$ (figure 3(B)) of the SiNW P–i–N junction grating. The total incident optical power P_m shown in figure 3(C) was measured using a calibrated bulk silicon diode. The raw responsivity, $\mathcal {R}_{\mathrm { raw}}=I/P_{\mathrm {m}}$, was first obtained for an unpolarized excitation. There is a large disparity between the illuminated area A_m = πd²_m/4 and active area A_a = NWL of N SiNW junctions. Here L = 470 nm is the width of the region where short-circuit generation occurs, as measured by EBIC in figure 2(B). Hence, we define and plot the responsivity $\mathcal {R} = \mathcal {R}_{\mathrm { raw}} A_{\mathrm {m}}/A_{\mathrm { a}}$ in figure 3(B) (curves are offset for clarity).

Three distinct peaks at λ ≈ 420, 490–500 and 540–560 nm are apparent in $\mathcal {R}$ for N = 500, 200 and 100 SiNWs. These three resonances are not present in the well-known absorption spectrum of bulk silicon [16] and are not the trivial resonances of the bare air/SiO₂/Si cavity. Owing to the small cross section of the SiNWs, these peaks cannot be ascribed leaky-mode resonances of individual NWs [8–10], which for d = 10 nm SiNWs in SiO₂ occur for λ < 200 nm. Electronic quantum confinement effects in the optical absorption spectrum are also highly unlikely at photon energies of the observed resonances since SiNWs do not have sufficiently small diameter required, typically d ≈ 2–3 nm [17].

However, as we will show, the observed resonances match predictions for scattering of incident radiation into the SiNW grating. Moreover, these resonances occur at wavelengths where radiation is strongly scattered by the SiNW grating, incurs phase from reflection by air/SiO₂ and SiO₂/Si interfaces and constructively interferes. The resonance quality factor Q determines the lifetime of photons in the cavity. For each of N = 500, 200 and 100 SiNW gratings, $\mathcal {R}\propto \mathcal {Q}_{\mathrm { abs}}$, where $\mathcal {Q}_{\mathrm { abs}}$ is the absorption efficiency, was fit to an exponential absorption background appropriate for bulk Si for energies smaller than the direct gap [16], modulated by resonances with center wavelength λ_i and full-width half-max δλ_i. Fits are plotted as solid lines alongside measured data in figure 3(B), while extracted curve-fitting parameters and associated uncertainties are summarized in table 1. The quality factor Q of the SiNW cavity is most consistent for the λ₁ ≈ 420 nm resonance, with Q = λ₁/δλ₁ = 11 ± 1, 12 ± 1, 9.6 ± 1 for N = 500, 200 and 100 SiNWs, respectively. Average Q for the three resonances are 13, 16 and 14 for N = 500, 200 and 100 SiNWs, respectively. The Q measured in experiments is an aggregate of different loss mechanisms Q_i obeying $Q=(\sum _i Q_i^{-1})^{-1}$. Since Q is essentially independent of N, we see that losses due to the finite number of SiNWs in the grating do not dominate.

The measured dependence of $\mathcal {R}\propto \mathcal{Q}_{\mathrm{abs}}$ on polarization angle θ is shown in figure 3(D) for the 200 SiNW grating at a wavelength 450 nm between the 420 and 510 nm resonances. It retains the sinusoidal dependence $\mathcal{Q}_{\mathrm { abs}} = \mathcal {Q}_{\mathrm { abs},\parallel }\cos (\theta ) + \mathcal {Q}_{\mathrm { abs},\perp }\sin (\theta )$ that is characteristic of single NWs [12]. We find $\mathcal {Q}_{\mathrm { abs},\parallel } > \mathcal {Q}_{\mathrm { abs},\perp }$, reflecting more efficient electric field penetration into the SiNW for polarization along the NW's axis compared with the perpendicular polarization. For a single SiNW we expect $\mathcal {Q}_{\mathrm { abs},\perp } / \mathcal {Q}_{\mathrm { abs},\parallel } \approx |2\epsilon _{{\mathrm { SiO}}_2} / (\epsilon _{\mathrm { Si}}+\epsilon _{{\mathrm { SiO}}_2})|^2 \approx 0.05$. This value is smaller than the measured ratio $\mathcal {Q}_{\mathrm { abs},\perp } / \mathcal{Q}_{\mathrm { abs},\parallel }\approx 0.5$ SiNW grating, i.e. the measured anisotropy falls short of the theoretical prediction.

To better understand the wavelengths and quality factors of the resonances, their dependence on the number of SiNWs in the grating and the polarization anisotropy, we consider the scattering of an incident electromagnetic plane wave E_i into the SiNW grating. The total field E(r,t) so obtained is directly related to $\mathcal {R}(\lambda )$ as follows. The time-averaged power dissipated in an electromagnetic field ${\bf E}({\bf r},t)={\bf E}({\bf r})\exp (\mathrm {i}\omega t)$ due to generation of electron–hole pairs in N parallel SiNWs is given by $P_{\mathrm { loss}}=\sum _j\frac {1}{2}\int _{V_j}\textrm {d}^3{\bf r}\epsilon _{\mathrm { im}}\omega \left |{\bf E}({\bf r})\right |^2$, where j = 1,...,N is the index of an SiNW with junction volume V_j, and _im is the imaginary part of the NW's complex dielectric permittivity,  = _re − i_im. The short-circuit current at the terminals of the SiNW is therefore I = eη_intP_loss/ℏω, where η_int is the number of charges collected by the contacts per absorbed photon. For a total incident power $P=\sum _j P_j$ on N NWs, the responsivity is therefore $\mathcal {R}=e\eta _{\mathrm { int}}\mathcal {Q}_{\mathrm { abs}}/\hbar \omega$, where

$$\begin{equation} \mathcal{Q}_{\rm abs}\equiv\frac{P_{\rm loss}}{P}=\frac{\epsilon_{\rm im}\omega}{W\epsilon_0c|{\bf E}_0|^2}\int_A\textrm{d}^2{\bf r}|{\bf E}({\bf r})|^2 \end{equation} \tag{ 1 }$$

is the absorption efficiency, A is the SiNW cross-section, $S =\frac {1}{2}|{\bf E}_{0}|^2\epsilon _0c$ is the intensity of optical excitation for an incident plane wave with electric field amplitude E₀ and P_j = WLS.

The electric field E(r) in equation (1) for the SiNW structure (figure 1(A)) was estimated by means of electromagnetic scattering calculations for plane waves at normal incidence to both finite and infinite gratings of infinitely long SiNWs for incident electric field parallel and perpendicular to the SiNWs. The finite element method (FEM) was used to calculate E(r) for the case of N → ∞ SiNWs using analytically formulated scattering boundary conditions for light incident from above the structure and periodic boundary conditions at surfaces defined by x = ± ℓ/2. The influence of finite number of N NWs in the array was explicitly addressed for N ⩽ 100, using the so-called perfectly matched layer boundary conditions. Details of the FEM scattering calculations are given in the supplementary information (available from stacks.iop.org/NJP/15/093029/mmedia). An analytic solution for the case N → ∞ and electric field parallel to SiNWs was derived for the limit where the SiNW diameter d satisfies d ≪ λ, and is presented in the supplementary information. The dielectric properties  = _re − i_im of the SiNWs and Si substrate were taken as those of the well-known bulk electronic structure of silicon [16].

For electric field parallel to SiNWs, calculated $\mathcal {Q}_{\mathrm { abs}}$ for an infinite grating (figure 4(A), solid line) reveals resonant enhancement for free-space wavelengths λ = 423, 490 and 544 nm for d = 10 nm cylindrical SiNWs. Each of these wavelengths is in good agreement (< 5% error), with each of the grating devices with N = 500, 200 and 100 SiNWs, as summarized in table 1. As shown in the supplementary information, calculated wavelengths for SiNWs were found to be independent of NW cross-sectional shape for a range of cylindrical diameters 10, 8 and 6 nm and triangular cross-sections (W,h) = (13,12 nm). This verifies that for SiNW diameters d/λ ∼ 1/30, the Rayleigh scattering limit can be applied to the structure.

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The SiNW grating is responsible for the observed resonances, rather than the air/SiO₂/Si cavity. Additional finite element scattering calculations in figure 4(A) (dashed line) show that a single NW in SiO₂ does not exhibit strong resonant absorption features, due to weak scattering by a single SiNW and poor quality factor of an empty air/SiO₂/Si cavity. Nevertheless, the interfaces of the air/SiO₂/Si cavity modify the resonance condition when the grating is present, which is an essential ingredient producing agreement between theory and experiments as shown in table 1. Indeed, calculated $\mathcal {Q}_{\mathrm { abs}}$ for otherwise identical SiNW gratings in an infinite SiO₂ medium without interfaces, shown in figure 4(A) (dash-dot), exhibits only a single resonance in the visible regime at the onset (θ = π/2) of the first-order diffraction, l sin(θ) = λ₀/n_SiO2. The analytical model for multiple scattering of radiation by SiNWs modified by the presence of dielectric interfaces presented in the supplementary information, is in excellent agreement with numerical calculations.

A crucial ingredient determining the sharpness of predicted resonances is that radiation scattered by the SiNW grating and SiO₂ interfaces picks up wavevector components 2πn/ℓ along the $\hat {x}$ direction (figure 1(A)) due to the grating's periodicity, giving multiple scattered radiation grazing incidence on the dielectric interfaces. Radiation is totally internally reflected by the air/SiO₂ interface for λ₀ > ℓ, and due to its grazing incidence and the high dielectric constant encountered, is strongly reflected at the SiO₂/Si interface.

The quality factors predicted for the 423, 490 and 544 nm resonances are given in table 1, which fall in the range Q ≈ 50–90. Photon loss from the calculated modes is mainly due to incomplete reflection at the SiO₂/Si interface. Absorption resonances calculated for a suspended SiO₂ film (air/SiO₂/air cavity) with embedded SiNWs are considerably sharper than those of the same structure supported by the Si substrate. In this situation, diffracted radiation is totally internally reflected at both SiO₂ interfaces. Details are provided in the supplementary information (available from stacks.iop.org/NJP/15/093029/mmedia).

The predicted quality factors are on average approximately five times higher than the corresponding experimental values. For the 420 nm resonance, theoretically predicted Q = 70 ± 10 is approximately seven times higher than the corresponding measured value. Since decreasing Q corresponds to decreasing photon lifetime in the cavity, the lower quality factor in experiments suggests a photon loss mechanism that is not accounted for in the calculation. Photon loss, both due to electron–hole pair generation in SiNWs and the silicon substrate, which for the latter occurs due to incomplete reflection at the SiO₂/Si interface, was considered in the theoretical calculation and are therefore not responsible for the discrepancy.

We evaluate several possible photon-loss mechanisms to determine the most likely cause of the discrepancy. Loss of photons from the mode by scattering into the continuum at the boundaries of the finite arrays can be easily eliminated as the cause. Theoretical calculations on finite arrays of N = 20 and 100 SiNWs described in the supplementary information give Q = 52 and 70, respectively, while experiments give Q ≈ 11, 12, 10 for N = 100, 200 and 500, that is, consistently smaller quality factors with no significant trend with respect to N. Calculations of $\mathcal {Q}_{\mathrm { abs}}$ were also carried out for an array with N = 100 SiNWs, incorporating fabrication disorder by adding a random variable to the SiNW position. Even for unrealistically large root-mean-square deviations up to 45 nm, Q could not be significantly suppressed. Halving the cross-sectional area of the SiNW also did not change Q significantly.

Having eliminated photon loss due to finite N and fabrication disorder as the cause of the discrepancy, we attribute the reduction of Q in experiments to end termination of the 1 μm long SiNWs at the electrically conductive ohmic contacts. The SiNWs are not of infinite length as assumed in calculations, and the metal surfaces of the ohmic contact would introduce significant scattering relative to the mode of an infinite length NW. We therefore expect that the quality factor of the resonances can be increased toward the theoretically predicted value by increasing the length of SiNW. Three-dimensional calculations including finite length and contact structures would therefore be of additional interest.

Photoresponse resonances of arrays of NW Rayleigh scatterers could be of interest when large-diameter NWs required for visible wavelength Mie scattering resonances [8–10] are undesirable. Geometrical resonances of the NW array presented herein are determined by the grating period and dielectric environment, and in the Rayleigh scattering limit (d ≪ λ) are independent of d. Large diameters required for visible wavelength Mie scattering resonances would, for example, be incompatible with the realization of electronic size quantization effects in NWs or NW quantum dots [2, 3]. Nevertheless, the multiple scattering resonances of one-dimensional gratings are not incompatible with larger-diameter NWs. Arrays of larger-diameter NWs would also exhibit geometrical resonances related to the array period, although further work is necessary to understand their properties.

When the number of charges collected by the measurement circuit per photon absorbed (η_int) exceeds unity, we say there is a gain g = η_int. The gain was estimated to be g ≈ 1 from $\mathcal {R}=e\eta _{\mathrm { int}}\mathcal {Q}_{\mathrm { abs}}/\hbar \omega$, using the measured off-resonance zero-bias responsivity $\mathcal {R}=0.075\,{\rm A}/{\rm W}$ (figure 3(B)) at λ = 450 nm and the corresponding estimated value of $\mathcal {Q}_{\mathrm { abs}}=0.020$ (figure 4(A)). This contrasts the biased NW photoconductors without P–N junctions, which frequently [18] have g > 1000. This gain is often attributed microscopically to fast trapping of either photo-generated electrons or holes at surface states, which enhances the lifetime τ of the other carrier. In this case, each carrier of the un-trapped species can effectively transit the device g = τ/τ_tr > 1 times from one contact to the other, where τ_tr is the carrier transit time. During this process each carrier of this species is replenished from an ohmic contact g − 1 times [18].

Examination of the band diagram in figure 1(B) shows that the replenishment process that produces gain in biased NW photoconductors is not possible near zero bias for a P–N junction NW. Electron (hole) replenishment is strongly blocked by the P (N) region's ohmic contact. While electron (hole) replenishment is possible by the N (P) region's ohmic contact, transport is blocked by the junctions' built-in potential. This is interesting since gain from this replenishment process comes at the expense of bandwidth, and quenching the gain should increase the intrinsic device speed [18]. If gain is desirable, the P–N junction could, in principle, be reverse biased into an avalanche multiplication regime. Furthermore, a grating of NWs without P–N or P–i–N junctions could still exhibit resonances of $\mathcal {Q}_{\mathrm { abs}}$ in combination with a photoconductive gain η_int = τ/τ_tr > 1 at finite bias. It is straightforward to show that the photoresponse would still be governed by $\mathcal {R}=e\eta _{\mathrm { int}}\mathcal {Q}_{\mathrm { abs}}/\hbar \omega$. Any effect of inhomogeneous electric field on carrier mobility would be absorbed into the transit time τ_tr, although such effects are unlikely in the ultra-small NWs employed here.

The absorption efficiency $\mathcal {Q}_{{\mathrm { abs}},\perp }$ was also calculated by the finite element scheme for electric field perpendicular to SiNWs and is shown alongside $\mathcal {Q}_{{\mathrm { abs}},\parallel }$ in figure 4(B). It is evident that the ideal grating's polarization anisotropy is $\mathcal {Q}_{\mathrm { abs},\perp } / \mathcal {Q}_{\mathrm { abs},\parallel } \approx 0.05$ off-resonance. Moreover, the resonances apparently disappear for the ${\bf H}\parallel \hat {z}$ case. Therefore, the ideal grating's polarization anisotropy is further enhanced on resonance, compared to a single NW. The absence of resonances for ${\bf H}\parallel \hat {z}$ is essential because in this case, multiple scattered radiation by an SiNW grating does not constructively interfere. However, the measured off-resonance polarization anisotropy $\mathcal {Q}_{{\mathrm { abs}},\perp }\approx 0.5\mathcal {Q}_{{\mathrm { abs}},\parallel }$ falls short of the predicted value. The discontinuity presented by the ohmic contacts (separated by only 1 μm) may be responsible for the smaller-than-predicted polarization anisotropy. Refinements to the sample design are likely to be necessary for improving both Q and for enhancing the anisotropy. The position of SiNWs within the mode's spatial field profile, shown in figure 4(C) for λ = 544 nm, could also be optimized.

Finally, we demonstrate the ability of SiNW gratings to enhance sensitivity and selectivity of photodetection at a single wavelength in the visible regime (λ₀ ≈ 400–700 nm). First, to reduce the number of resonances in the visible regime, the SiO₂ thickness is modified to 260 nm from 550 nm. For this dielectric thickness, resonances for red (λ₀ ≈ 610 nm), green (λ₀ ≈ 540 nm) and blue (λ₀ ≈ 460 nm) wavelengths are obtained for grating periods of ℓ = 460, 400 and 320 nm, respectively. The enhancement of photon density for each grating for d = 20 nm is shown in figure 4(D).