An amorphous silicon photodiode with 2 THz gain‐bandwidth product based on cycling excitation process

Sensitivity, frequency response, power consumption, and process compatibility are among the key considerations of detector technologies. Avalanche photodiodes (APDs) have the highest sensitivity among all semiconductor photodetectors because of the detectors' internal gain by impact ionization and are widely used in applications with low light intensity.^1–5 However, besides high operation voltage^1,2,6 (20–200 V) and difficulties in integration with the readout circuits,^7,8 APDs suffer from high excess noise under high avalanche gain⁹ and limited gain-bandwidth product.^2,3 Hence, most APDs operate in the relatively low gain regime.^1,2 The recent discovery of the cycling excitation process (CEP)¹⁰ offers a promising solution for these issues. On the premise that CEP effect uses Auger excitation involving localized states to relax the k-selection rule which limits the efficiency of carrier excitation, the design of the previous CEP photodetector consists of a heavily doped and heavily compensated p-n junction.^10,11 Having these compensating impurities as localized states to support the CEP process, efficient amplification of primary photocurrent has been achieved under low bias.^11,12 However, the delicate balance in doping compensation presents significant challenges in dark current and process compatibility. Furthermore, the gain-bandwidth product and the required material properties to produce the CEP effect remain unclear. Previous experimental results¹³ and density functional theory calculations¹⁴ have suggested that the high density of localized states and strong electron-phonon coupling are two properties that favor the CEP effect. We recognize that many disordered semiconductors possess such properties. In fact, one can treat the heavily doped, heavily compensated p-n junction as a method to turn crystalline silicon into a quasi-disordered material.

Following this rationale, we infer that amorphous silicon (a-Si), as a disordered material, can present the CEP effect too. Because of its bonding and topological disorder, amorphous silicon has long band tails of localized states¹⁵ which have a strong electron phonon interaction^16,17 as well. However, there are also deep states within its bandgap due to structural defects and dangling bonds. Although the deep states are also localized states, they are too deep to be excited by phonons and rely on field enhanced direct/indirect tunneling to move the localized carriers to the mobile bands. Therefore, we have treated the amorphous silicon with hydrogen plasma to passivate the dangling bonds of Si with H atoms to control the density of those deep states. We further introduce a small percentage of carbon (∼5%) into the hydrogenated amorphous silicon (a-Si:H) to increase the level of disorder¹⁸ and to tailor the phonon energy and strength of electron-phonon coupling.¹⁹ With this approach, we designed and fabricated devices with a 30 nm carbon-doped (C-doped) a-Si:H CEP layer sandwiched between a top transparent contact and an n⁺-Si substrate.

A schematic diagram of the device cross-section is shown in Fig. 1(a). Indium tin oxide (ITO) was used for the top contact as a transparent electrode. The top view of a 30 μm-diameter device with a ground-signal-ground (GSG) probe for high-speed measurements is shown in Fig. 1(b). The contact pad was isolated from the substrate by a 200 nm thick silicon dioxide layer [Fig. S1(c) in the supplementary material]. The device mesa other than the photosensitive area was covered by a 150 nm thick chromium/gold layer so that the incident light can only illuminate the active area (see supplementary material for details).

The approximate band diagram of the device under reverse bias is plotted in Fig. 1(c), which shows the band offsets and energy barriers between different layers. As shown in Fig. 1(d), all tested devices exhibit standard current-voltage characteristics of a diode. Under forward bias, our photodiodes are turned on at about 2 V due to a hole barrier of 1.2 eV from ITO to the a-Si:H layer and a 0.25 eV conduction band offset at the interface between a-Si:H and silicon (see supplementary material).

The CEP device with C-doped a-Si:H shows excellent photoresponse against dark current, as shown in Fig. 2. The photocurrent at zero bias is 17 nA (with a quantum efficiency of 8%). At 3 V reverse bias, the photocurrent is amplified to 8.57 μA with a gain of 504, and the dark current rises to 215 pA. The extrapolated primary dark current is around 0.5 pA.

Figure 3(a) shows the device dark current for various designs of the CEP active gain layer. The compensated silicon p-n junction devices have the highest dark current, mostly due to high tunneling current. The a-Si:H devices show much lower dark current because of their higher bandgap which suppresses tunneling. Doping the a-Si:H with ∼5% carbon further suppresses the dark current by more than three orders of magnitude. At -3 V bias, the dark current density of the 5% carbon-doped a-Si:H device is about 22 μA/cm².

To probe the intrinsic properties of the CEP effect in the amorphous silicon layer, we characterize the device under a laser wavelength of 405 nm because of its shallow absorption depth (<100 nm). This minimizes carrier diffusion in the n⁺-Si substrate as a side effect that could mask the intrinsic properties of the CEP process within the (C-doped) a-Si:H layer. The CEP photocurrent gain of the a-Si:H device and C-doped a-Si:H device are shown in Fig. 3(b). The gain is defined as the ratio of photocurrent under a given bias voltage to photocurrent under zero-bias where only the built-in field is present in the (C-doped) a-Si:H layer. The zero-bias external quantum efficiency of the C-doped a-Si:H devices is between 7.6% and 18% at a wavelength of 405 nm.

Figure 4(a) shows the frequency dependence of photocurrent gain under different bias voltages. The photocurrent gain drops to half of its low frequency value at 1 GHz to 1.5 GHz under all bias voltages. Since the cutoff frequency for photocurrent gain is almost independent of the bias voltage, it is likely that the cutoff frequency is due to RC roll-off instead of the intrinsic bandwidth limit of the cycling excitation process in the carbon-doped a-Si:H layer. Even so, one can make a conservative estimate of the gain-bandwidth product by taking 1.5 GHz as the intrinsic bandwidth of the device and a gain of 1500 under 4 V reverse bias. This yields a gain-bandwidth product of 2.25 THz for the carbon-doped a-Si:H device. The reported results are from the best device, and most devices we measured have shown a gain of greater than 1000 and a gain-bandwidth product of over 1 THz.

Besides the gain-bandwidth product, the excess noise factor is another important figure of merit for any amplification mechanism in photodetectors. For an ideal APD, the excess noise factor increases to 2.0 as gain approaches infinity. However, the excess noise factor for a practical APD is usually much greater than 2.0 under high gain.^1,2,9,22 Figure 4(b) shows the excess noise factor versus photocurrent amplification gain for a 30 μm-diameter carbon-doped a-Si:H CEP photodiode and a commercial silicon APD for comparison. The measured excess noise factor for the commercial silicon APD agrees well with McIntyre's model⁹ that assumes the k-factor to be 0.02 for silicon. On the other hand, the excess noise factor of the carbon-doped a-Si:H CEP photodiode is close to the curve of an ideal APD. The measured excess factor of carbon-doped a-Si:H CEP is 1.91 at a gain of 1526, more than 17 times lower than the silicon APD at the same gain.

Contradictory to the conventional wisdom, the low carrier mobility²⁰ (∼2 cm²/V-s)²¹ of a-Si does not prevent carriers from achieving sufficient kinetic energy required for Auger excitation. The mobility of a-Si is valid for a low field and a relatively large length. In the regime of a high field (∼10⁶ V/cm) and short distance (30 nm), carriers in a-Si can gain sufficient kinetic energy as all inelastic scatterings cannot relax the energy fast enough. The key for the efficient CEP effect, however, is for an energetic carrier to have a high probability of triggering the Auger excitation within a distance of a few nanometers, which is 10–100 times shorter than the required length for impact ionization. The enormous number of localized states in a-Si provides such an environment.

Furthermore, the ultrathin CEP layer reduces the timing uncertainty and, consequently, the excess noise of the gain process. APDs, on the contrary, have a much thicker multiplication region due to the low efficiency of impact ionization. Indeed, we have observed very different results from a previous study²² with a much thicker layer of a-Si. Further studies are still needed to fully understand such differences.

In addition, one may wonder whether the observed gain could be produced by photoconductivity. We have performed detailed analysis based on the Fowler-Nordheim tunneling model and Silvaco simulation to rule out the possibility that photoconductivity alone can explain the measured gain, gain-bandwidth product, and noise characteristics without including a highly efficient carrier multiplication process which we describe in the following paragraph.

As shown in Fig. 5(a), an energetic hole excites another hole from a conduction bandtail state to the valence band (or equivalently, excites an electron from the valence band to occupy a conduction bandtail state). Following this Auger excitation, a localized electron is created and is subsequently transferred to the conduction band [Fig. 5(b)] by absorption of a phonon or by field-enhanced tunneling. Similarly, the conduction band electron created in the above process can be accelerated and causes another Auger excitation, giving rise to an electron in the conduction band and a localized hole in the valence bandtail [Fig. 5(c)]. Again, the localized hole can be transferred into the valence band by phonon-absorption or field-assisted tunneling [Fig. 5(d)]. In this manner, the amplification process occurs in cycles to create photocurrent gain, within the 30 nm thin a-Si layer.

To summarize, we have demonstrated a carbon-doped, a-Si:H photodiode, applying the CEP effect. The device shows a gain-bandwidth product of over 2 THz and a low excess noise factor of 1.9. These desirable characteristics are achieved with extremely simple device structure and low-mobility material. On the premise of the proposed physics for the cycling excitation process, many other disordered materials including polymers may also be used to produce CEP photodetectors, opening more avenues for applications involving optical-to-electric signal conversion.

See supplementary material for the detailed device design, fabrication, and characterization, as well as the experimental setup and methods.

This work was performed in part at the San Diego Nanotechnology Infrastructure (SDNI) of UCSD, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which was supported by the National Science Foundation (Grant No. ECCS-1542148). The original concept and physics foundations of using the disordered material for the device were supported by the DARPA DETECT Program (No. W911NF-16-2-0183). The model of signal amplification and the gain characteristics for the cycling excitation process were supported by the Office of Naval Research (No. N00014-15-1-2211). The device process for dark current reduction and high-speed characterization were supported by DARPA MTO (No. N00014-16-1-3206).