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Abstract
We reported significant improvements in device speed by reducing the quantum barrier (QB) thicknesses in the InGaN/GaN multiple quantum well (MQW) photodetectors (PDs). A 3-dB bandwidth of 700 MHz was achieved with a reverse bias of -6 V. Carrier escape lifetimes due to carrier trapping in the quantum wells (QWs) were obtained from both simulation and experimental fitting, identifying carrier trapping as the major speed limiting factor in the InGaN/GaN MQW PDs.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Visible light communication (VLC) has garnered significant interest in recent years as it offers a solution to the impending capacity crunch problem in the congested radio frequency (RF) spectrum [1–3]. The rapid advancements of VLC have created demand for high-speed and high-performance photodetectors (PDs) in the visible light spectrum [4,5]. InGaN-based PDs are promising candidates for the optical receivers in the VLC links as InGaN has a direct bandgap (0.61-3.4 eV) that can be flexibly tuned over the entire visible spectrum. The tunability enables wavelength-selective response which improves the signal-to-noise ratio of the receiver without external filters. Due to the wide bandgap, InGaN-based PDs also have a high breakdown voltage and a low intrinsic noise in comparison to the well-established silicon PDs [6]. Furthermore, their radiation hardness and high thermal stability allow them to operate under harsh conditions (e.g. outer space, underwater etc.) [7].
Most InGaN-based PDs use the multiple quantum well (MQW) structure design due to the difficulty of growing thick InGaN layer with high crystalline quality [8–20]. This design offers significant advantages in growth as it avoids strain-induced morphological instability and suppresses the formation of V-defects which act as leakage pathways. However, the 3-dB bandwidths of those devices range only from tens to hundreds of MHz which are lower than the bandwidths of most commercially available high-speed silicon PDs which are in the GHz range [13–20]. Since photogenerated carriers in the quantum wells (QWs) have to escape to reach the collecting electrodes, the bandwidths of MQW-based PDs are also limited by the carrier escape lifetimes on top of the usual RC time constant and carrier transit time. It has been reported lower than expected bandwidths were observed in Ge/SiGe MQW PDs due to carrier trapping [21]. However, the effect was more subtle in narrow bandgap materials such as Ge and Si as their conduction band and valence band offsets are smaller than that of wide-bandgap III-nitride materials.
In this paper, we demonstrated that reducing the quantum barrier (QB) thicknesses in the InGaN/GaN MQW structures improved the 3-dB bandwidth by decreasing the carrier escape lifetimes. To this end, InGaN/GaN MQW epitaxial structures with varying QB thicknesses were grown and fabricated into PDs with different device sizes. Following that, we reported the responsivity, dark current, and frequency response for the thickness series. Simulations were performed to calculate the carrier escape lifetimes due to carrier trapping in the QWs. The carrier escape lifetimes of the PDs were also extracted by considering the combined effects of the RC response, carrier trapping, and transit time to explain the observed trends.
2. Experimental
Three InGaN/GaN MQW epitaxial structures with varying GaN QB thicknesses were grown by metalorganic chemical vapor deposition (MOCVD) on c-plane sapphire substrates (Fig. 1(a)). The structure began with a 1.2 µm unintentionally doped (UID) GaN template layer and a 4.8 µm Si-doped n-GaN ([Si] = 5 × 1018 cm-3), followed by a 14 nm highly Si-doped n+-GaN layer ([Si] = 1 × 1019 cm-3). Then, an active region was grown, consisting of a 6 period UID InGaN/GaN MQW with 2.5 nm In0.14Ga0.86N QW. The GaN QB thicknesses were varied: 18 nm, 13.5 nm, and 9.5 nm in PD-A, PD-B, and PD-C, respectively. Above the active region was a 23 nm highly Mg-doped p+-Al0.1Ga0.9N layer ([Mg] = 1.5 × 1020 cm-3), followed by a 100 nm moderately doped Mg-doped p-GaN layer ([Mg] = 2 × 1019 cm-3) and a 17 nm highly Mg-doped p+-GaN contact layer ([Mg] = 1.5 × 1020 cm-3). The highly doped layers sandwiching the active region were used to improve carrier collection [22]. Furthermore, the AlGaN layer was used to suppress the dark current by hindering the minority carrier transport in the p-type region [12].
Fig. 1. (a) Schematic of the front illuminated InGaN/GaN MQW PDs. (b) Top-view SEM image of a 100×100 µm2 device.
Following the MOCVD growth, the wafers were fabricated into PDs with different mesa areas ranging from 20×20 µm2 to 100×100 µm2. First, a 110 nm layer of indium tin oxide (ITO) was deposited by electron-beam evaporation to form a transparent p-contact. Square mesas were then defined by reactive-ion etching the ITO and the epitaxial layers to reach the n-GaN layer. After that, a dielectric stack composed of silicon dioxide and aluminum oxide was deposited using ion beam deposition as a metal isolation layer. A 50 nm layer of silicon dioxide was then blanket deposited using atomic-layer deposition (ALD) for sidewall passivation [23]. After via opening, common Al/Ni/Au n- and p-metal contacts were deposited by electron-beam evaporation.
After fabrication, the spectral response and external quantum efficiency (EQE) of the devices were measured using an Oriel 300 W Xenon lamp with an Oriel 260 monochromator and were calibrated with a reference Si photodetector. The light was coupled into the device by using a lensed fiber. The photocurrent density versus voltage measurements were taken using a source meter (Keithley 2400) and a semiconductor parameter analyzer (HP 4155B). The optical-to-electrical (O-E) frequency response of the devices was then measured by using a network analyzer (PNA-X N5247) together with a 405 nm laser diode with 2 GHz 3-dB bandwidth.
3. Results and discussion
The measured spectral response and EQE of PD-A, PD-B, and PD-C at -4 V are shown in Fig. 2(a). Measurements were taken on PDs of size 100×100 µm2 but results are representative of PDs with different device sizes. The spectral response and EQE of all three devices were found to peak around 365 nm. The peak EQE increases with the thickness of the GaN QBs, as they contribute to the absorption. At >380 nm, all devices show similar spectral response and EQE since they have the same total thickness of the InGaN layers and the absorption mostly occurs in the QWs. The slightly higher responsivity of PD-B in this range is likely due to the small variations in thickness and/or indium composition in the QW layers across the samples. Representative dark and illuminated current density versus applied voltage (J-V) curves for PD-A are shown in Fig. 2(b). Under illumination, photocurrent saturation corresponding to maximized IQE occurs at a reverse bias as low as -1 V, indicating excellent carrier collection. The inset of Fig. 2(b) shows the dark current density of all 3 devices of size 100×100 µm2. The dark current (density) ranges from 1 pA to 4 nA (1×10−5 to 4×10−2 mA/cm2) with a bias from -1 V to -5 V. The devices with thinner QBs have slightly larger dark current due to higher thermionic emission or tunneling rates as well as poorer crystalline quality of the active region.
Fig. 2. (a) Spectral response and EQE of PD-A, PD-B, and PD-C of size 100×100 µm2 at -4 V. (b) Dark and illuminated (360 nm) J-V curves of PD-A of size 100×100 µm2. Inset: J-V curves for PD-A, PD-B, and PD-C under dark condition.
Figure 3(a) shows the frequency response of various device sizes for PD-C at -6 V. The 3-dB bandwidths of the PDs increase with decreasing device sizes due to the smaller RC time constant. Similar bandwidth dependence on device size was observed for PD-A and PD-B (measured but not shown). The bias dependent 3-dB bandwidths for PD-A, PD-B, and PD-C of size 20×20 µm2 are plotted in Fig. 3(b) showing that the bandwidths increase as the reverse bias increases from 0 V to -6 V. Furthermore, PDs with thinner QBs achieve higher bandwidths under the same bias voltages. At -6 V, the bandwidth of PD-C is more than double the bandwidth of PD-A. Finally, we note that the highest measured 3-dB bandwidth is 700 MHz for the smallest device (20×20 µm2) with the thinnest QBs (9.5 nm) under a reverse bias of -6 V.
Fig. 3. (a) O-E frequency response of PD-C of various device sizes at -6 V. (b) 3-dB bandwidth versus applied bias of PD-A, PD-B, and PD-C of size 20×20 µm2.
Various speed limiting factors are considered to understand the dependence of bandwidth on applied bias and QB thickness. Under illumination of a 405 nm light source, electron-hole pairs are photogenerated in the InGaN QWs. These carriers either escape the wells and contribute to the photocurrent or are lost through recombination. The possible escape mechanisms of the carriers include tunneling through the barrier and thermionic emission over the barrier as shown in the inset of Fig. 4(a). Once escaped, the electrons and holes drift in the opposite directions with respective drift velocities to the collecting electrodes. Electric fields in the GaN QB region are usually in excess of hundreds of kV/cm at moderate reverse bias. Due to these high electric fields in the QB region, carriers travel at velocities close to their saturation velocities (1.25×107 cm/s and 6.63×106 cm/s for electron and hole respectively) [24,25]. Therefore, apart from the RC time constant, the bandwidth of an MQW photodetector also depends on the carrier escape lifetimes (tunneling or thermionic emission) and the transit time of the carriers through the depletion region.
Fig. 4. Simulated thermionic emission (TE) and tunneling (T) lifetimes as a function of applied bias for (a) holes (b) and electrons. Inset: Carrier escape mechanisms.
For our structures, due to the thin depletion region, the transit-time-limited bandwidths (fTr) are calculated to be hundreds of GHz (>300 GHz). Assuming uniform illumination, the equation used is fTr = 0.67vp/L where vp and L are hole saturation velocity and active layer thickness respectively [26,27]. Since the measured bandwidths (<1 GHz) are orders of magnitude lower than the calculated fTr, the PDs in this work are not limited by the transit time. In other words, even though the depletion widths for all three structures are different, the calculated transit times are too small compared to other limiting lifetimes to explain the differing bandwidths.
To calculate the carrier escape lifetimes, simulations were performed by using a self-consistent Schrödinger-Poisson drift-diffusion solver. Our calculations used full theoretical polarization values and a conduction-to-valence-band offset ratio of 0.63:0.37 [28–30]. A Gaussian shape was used to describe the indium compositional profile in the QW instead of an ideal “tophat” function [31–33]. The full width at half maximum (FWHM) of the Gaussian profile was set to be the QW thickness. The electric field, band profile, and quantum-confined eigenstates of the three structures at different bias voltages were determined. Lifetimes for tunneling and thermionic emission were then calculated by using methods similar to [34] for electrons and heavy holes at 300 K. In the calculation, only carriers escaping from the lowest energy bound states, which represent the worst-case scenario, were considered. We note that even in the same structure, there are slight differences in the escape lifetimes from different QWs. The lifetimes, averaged over each quantum well, are plotted in Figs. 4(a)–4(b). As shown by the figures, all escape lifetimes decrease with increasing reserve bias. Besides that, it is also shown that the dominant escape mechanisms for holes and electrons are thermionic emission and tunneling respectively in the bias range of interest. More importantly, all escape lifetimes, regardless of carrier type and escape mechanism, are smaller for PDs with thinner QBs under the same bias voltages. The trends remain true even when an ideal but less realistic “tophat” function was used as the indium compositional profile as presented in [34].
Simulated energy band diagrams and electric fields of the PD structures were used to guide the interpretation of the results. Figure 5(a) shows the band diagrams and electric fields (inset) of PD-A and PD-C under a reverse bias of -4 V. The net electric fields in the QWs are negative due to the large polarization-induced electric fields which are in the opposite direction of the built-in field (defined as positive). Since PD-C has a smaller depletion width, which is mainly determined by the thickness of the UID active region, built-in and applied potentials are distributed over a smaller distance. Therefore, its electric fields are shifted in the positive direction, resulting in larger electric fields in the GaN QB region and smaller electric fields in the InGaN QW region. The difference in field strengths in PD-A and PD-C is around 0.5 MV/cm. As a result, the barrier height (measured relative to the ground state) in PD-C is lower than that in PD-A under the same applied bias as shown in Fig. 5(b). Increasing the applied reverse bias has the similar effect on the barrier height. The probability of the carriers tunneling through the barrier depends on the height and width of the classically forbidden triangular barrier while the thermionic emission lifetime grows exponentially with the barrier height. Since both tunneling and thermionic emission lifetimes decrease with decreasing barrier height, devices with thinner QBs and under larger reverse bias have smaller escape lifetimes as expected, resulting in higher 3-dB bandwidth.
Fig. 5. (a) Band diagrams and electric fields (inset) of PD-A and PD-C at -4 V. (b) Valence band edges near a QW in PD-A and PD-C at -4 V. The band edges are drawn superimposed for comparison. The barrier heights in PD-A and PD-C (ϕPD-A/C) are shown in the figure.
Escape lifetimes were also extracted by fitting the frequency response of the PDs. The net frequency response is the product of the circuit transfer function (Hckt) and the current source response (Hi) [35]. The PD is modeled as a lumped-element device with the equivalent circuit as shown in Fig. 6(a). The circuit parameters were de-embedded from the electrical reflection (S22) measurement. Figures 6(b)–6(d) shows the impedance of PD-C of size 20×20 µm2 on a Smith chart as well as its real and imaginary parts. The measured and modeled impedances were shown to be in good agreement. For this particular device, the extracted circuit parameters are 2.7 Ω, 2.7 pF, 21 kΩ and 2.0 nH for series resistance (RS), junction capacitance (CJ), junction resistance (Rd) and series inductance (LS), respectively. The circuit transfer function of the PD is given by:
where $\omega $ is the angular modulation frequency and ${Z_L}$ is the 50 Ω load resistance. For a p-side illuminated p-i-n photodiode, the current-source response is given by:Equation (3) was then fitted to the measured frequency response of PDs using the nonlinear least-square method. Figure 6(e) shows the measured and modeled frequency response of PD-C of size 20×20 µm2 at -6 V. On the same figure, we plotted the frequency response only considering the circuit transfer function which predicts a higher bandwidth. It shows that carrier trapping effect cannot be ignored when modeling the frequency response.
Fig. 6. (a) Equivalent circuit of the photodetector. (b) Measured and modeled impedance of PD-C (20×20 µm2) on Smith chart. (c)(d) The real and imaginary part of the impedance. (e) Measured and modeled frequency response of PD-C (20×20 µm2) considering only the circuit transfer function (dash-dot line) and both circuit transfer function and carrier trapping effect (dashed line).
The fitted hole escape lifetimes of PD-A, PD-B, and PD-C with various sizes from -4 V to -6 V are shown in Fig. 7. The extracted experimental hole escape lifetimes were found to be independent from device size. This was expected as escape lifetimes are only determined by the epitaxial structures and the bias voltages. They range from 0.3 ns to 1.5 ns at -4 V and 0.2 ns to 0.6 ns at -6 V. The simulated hole thermionic emission lifetimes that we obtained earlier are also shown in the same figure for comparison. In general, the experimental values are smaller than the simulated escape lifetimes. However, we emphasize that only carriers escaping from the lowest energy bound states were considered for the calculation of the simulated escape lifetimes. Therefore, they can be seen as the upper bound for the escape lifetimes. Nonetheless, similar to the simulated lifetimes, the experimental hole escape lifetimes decrease with increasing reverse bias and, more importantly, with decreasing QB thicknesses. This explains the higher 3-dB bandwidths measured in PDs with thinner QBs. Future work will include simulations of carrier escape including 3D natural alloy fluctuations using Localization Landscape theory [37,38].
Fig. 7. The extracted experimental hole escape lifetimes of PD-A, PD-B, and PD-C with different sizes (triangles). The simulated thermionic emission lifetimes for holes (from Fig. 4(a)) are also shown for comparison.
Both experimental and simulation results suggest that InGaN/GaN MQW PDs are limited by carrier escape lifetimes due to the carrier trapping in the QWs. Further speed improvements of InGaN/GaN MQW PDs should be done by reducing the carrier escape lifetimes. We have shown that having a thinner depletion region via reducing the QB thickness helps to decrease the barrier height for the carriers to escape. Even though similar effect can be achieved by increasing the reverse bias, it is preferable to operate the devices at low bias to minimize the dark current (background noise). Further reduction of the QB thickness can also improve the bandwidth but risks increasing the dark current. Another way to obtain smaller depletion widths is by reducing the number of periods in the MQW at the expense of the efficiency of the devices. To avoid sacrificing the efficiency, side-illuminated waveguide structures can be used if normal-incidence is not required for the application [16,20]. The large carrier escape lifetimes are primarily due to the large conduction and valence band offsets at the InGaN/GaN interfaces. Superlattice or compositional grading at each heterointerface is another way to eliminate carrier trapping effects although it leads to higher accumulative stress in the MQW structure [39]. Apart from the large band offsets, the devices, usually grown on c-plane substrates, also suffer from the polarization-induced electric fields in the QWs which oppose the built-in field. The resulting net electric field in the QW pushes the photogenerated carriers away from the barrier, resulting in a larger barrier height, thus larger escape lifetimes. To alleviate the effect of the polarization fields, devices can be grown on semipolar or nonpolar substrates to reduce or eliminate the polarization fields. At certain orientations (e.g. 20$\bar{2}$1), the polarization field switches direction and aids the carrier escape [28]. Similarly, N-polar (000$\bar{1}$) oriented devices should also be considered for the same reason [40].
4. Conclusion
In conclusion, we demonstrated that reducing the thickness of QBs in InGaN/GaN MQW PDs leads to improved 3-dB bandwidths, going as high as 700 MHz. The large carrier escape lifetimes due to carrier trapping in the QWs significantly limit the bandwidth of the devices. Further device speed improvement efforts should reduce the carrier escape lifetimes to enable high-speed applications in VLC.
Funding
Solid State Lighting and Energy Electronics Center, University of California Santa Barbara; UCSB-Collaborative Research in Engineering, Science and Technology (CREST) Malaysia project; Simons Foundation (601952); Air Force Office of Scientific Research (FA9550-19-1-10090); National Science Foundation (RAISE program A007231601); Ministry of Science and Technology, Taiwan (108-2628-E-002-010-MY3, Y.-R. W.).
Acknowledgments
The authors would like to thank Sergio Pinna, Brandon Isaac, and Kai Shek Qwah for helpful discussions. The authors gratefully acknowledge the support of the Solid State Lighting and Energy Electronics Center (SSLEEC) at UCSB. A portion of this work was performed in the UCSB Nanofabrication Facility, an open access laboratory. Use was made of the computational facilities administered by the Center for Scientific Computing at the CNSI and MRL (an NSF MRSEC; DMR-1720256) and purchased through NSF CNS-1725797.
Disclosures
The authors declare no conflicts of interest.
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