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Functional Nanostructured Materials (including low-D carbon)
Enhanced Photoresponsivity of a GaAs Nanowire MetalSemiconductor-Metal Photodetector by Adjusting the Fermi Level Xue Chen, Dengkui Wang, Tuo Wang, Zhenyu Yang, Xuming Zou, Peng Wang, Wenjin Luo, Qing Li, Lei Liao, Weida Hu, and Zhipeng Wei ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b07891 • Publication Date (Web): 15 Aug 2019 Downloaded from pubs.acs.org on August 20, 2019
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Enhanced Photoresponsivity of a GaAs Nanowire Metal-Semiconductor-Metal Photodetector by Adjusting the Fermi Level Xue Chen,† Dengkui Wang,† Tuo Wang,† Zhenyu Yang,‡ Xuming Zou,♯ Peng Wang,‖ Wenjin Luo,‖ Qing Li,‖ Lei Liao,*,
‡, ♯
Weida Hu,‖ and Zhipeng Wei*,
†
†State
Key Laboratory of High Power Semiconductor Lasers, Changchun
University of Science and Technology, Changchun 130022, China ‡Key
Laboratory of Artificial Micro- and Nano-Structures of Ministry of
Education School of Physics and Technology, Wuhan University, Wuhan 430072, China ♯Key
Laboratory for Micro/Nano-Optoelectronic Devices of Ministry of
Education School of Physics and Electronics, Hunan University, Changsha 410082, China ‖State
Key Laboratory of Infrared Physics, Shanghai Institute of Technical
Physics, Chinese Academy of Sciences, Shanghai 200083, China KEYWORDS: GaAs nanowire photodetector; doping; Fermi level; Schottky contact; built-in electric field 1 ACS Paragon Plus Environment
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ABSTRACT:
Metal-semiconductor-metal
(MSM)-structured
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GaAs-based
nanowire photodetectors have been widely reported due to their promises as an alternative for high-performance devices. Owing to the Schottky built-in electric fields in the MSM structure photodetectors, enhancements in photoresponsivity can be realized. Thus, strengthen the built-in electric field is an efficacious way to make the detection capability better. In this study, we fabricate a single GaAs nanowire MSM photodetector with superior performance by doping-adjusting the Fermi level to strengthen the built-in electric field. An outstanding responsivity of 1175 A/W is obtained. This is two orders of magnitude better than the responsivity of the undoped sample. Scanning photocurrent mappings and simulations are performed to confirm that the enhancement in responsivity is because of the increase in the hole Schottky built-in electric field, which can separate and collect the photogenerated carriers more effectively. The eloquent evidences clearly prove that doping-adjusting the Fermi level has great potential applications in high-performance GaAs nanowire photodetectors and other functional photodetectors.
1. INTRODUCTION GaAs nanowires (NWs) metal-semiconductor-metal (MSM)-structured photodetectors have been frequently reported due to their being a promising 2 ACS Paragon Plus Environment
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alternative
for
high-performance
devices.1-4
An
enhancement
in
photoresponsivity can be realized with a MSM-structured photodetector and is due to the Schottky barrier at contact area.5-8 The Schottky barrier can limit the transport of dark current. Meanwhile, the Schottky built-in electric field can separate the photogenerated carriers more efficiently. Thus, strengthen the built-in electric field is an efficacious way to make the detection capability better, which improves the separation efficiency of photogenerated carriers, and promotes the enhancement in photocurrent. High-work-function metal electrodes have been fabricated to provide larger built-in electric fields and improve the device responsivity.2,
3, 9, 10
However, the improvements for the
built-in electric fields are limited owing to the small adjusting range of metal work functions. Additionally, changes in the electrode materials increase the risks of instability and complexity during the preparation processes. Thus, a method to improve the built-in electric field strength in a stable electrode material should be implemented. Doping-adjusting the Fermi level is an efficacious way to strength the built-in electric field.11, 12 Unintentionally doped GaAs NWs usually express a p-type features because of the intrinsic acceptor defects relevant to gallium vacancies.4 By introducing proper dopants, such as Si atoms, which can be incorporated as p-type dopants in GaAs nanowire13, the Fermi level will be dragged downwards towards the valence band after Si doping, thus, the Schottky barrier region will be narrowed and will lead to a decrease in the 3 ACS Paragon Plus Environment
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contact resistance of hole transportation in the GaAs NWs. Therefore, photogenerated holes will across the barrier more easily and will be collected more effectively. As a result, an enhancement in photoresponsivity can be realized for doped GaAs NW devices. In this paper, a remarkable enhancement in the optoelectronic properties of a GaAs NW photodetector is observed by doping-adjusting the Fermi level. Particularly, the Si-doped GaAs NW photodetector exhibits a distinct responsivity of 1175 A/W. This is two orders of magnitude better than the responsivity of the undoped sample (~2.7 A/W). This phenomenon is principally because of the more efficient separation and collection process for photogenerated carriers, which is origin from the increased hole Schottky built-in electric field strength. This observation is further confirmed by scanning
photocurrent
mapping
and
Silvaco
TCAD
simulations.
Doping-adjusting the Fermi level will have great potential applications in high-performance
GaAs
NW
photodetectors
and
other
functional
photodetectors. 2. EXPERIMENTAL SECTION Growth of the NWs: The GaAs nanowires were grown in a DCA P600 molecular beam epitaxy system by self-catalyzed growth mechanism. The Si substrate was first ultrasonicated in ethanol for 5 min and subsequently transferred to the preparation chamber to degas at 400 °C. Next, the
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substrate was shifted to the growth chamber to deposit Ga droplets at 620 °C, followed by 80 s of growth interruption. Then, the NWs began to grow. During the growth process, the Ga beam equivalent pressure (BEP) was set as 6.2×10-8 Torr, and the Si BEP was set as 0 (sample 1), 1.4×10-9 (sample 2), and 1.9×10-9 (sample 3) Torr. The temperature and V/III ratio were kept at 620 °C and 25. After 1 h, the growth process is stopped. Switching off the Ga source and Si source, and supplying the As source until the substrate cools down to 300 °C. Finally, bring down the substrate temperature to room temperature in natural. Fabrication of the Photodetectors: To fabricate the NW photodetectors, the GaAs NWs were shifted to a silicon substrate with 300 nm oxide layer. After patterning the electrodes by electron beam lithography (EBL), Cr/Au (15/50 nm) were evaporation on the substrate. Ultimately, acetone is performed to remove the excess metal. To get rid of the intrinsic oxide layer of GaAs NWs, the hydrogen fluoride liquor with two percent concentration was performed for 20 s. Furthermore, a back-gate device is realized by using the substrate as gate pole. Characterization: A 4156 semiconductor parameter analyzer is applied to research the electrical and optoelectronic properties of single GaAs NW devices. A 532 nm laser was applied with a series of luminous powers within
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the purview of 0.38 mW/cm2 to 822.64 mW/cm2 to observe the photoresponse of the NW photodetectors. 3. RESULTS AND DISCUSSION The SEM images of undoped GaAs NWs (sample 1) and Si-doped GaAs NWs (sample 2 and sample 3) with different doping concentrations are displayed
in
Figure
1(a)-(c).
And
the
low-temperature
(10
K)
photoluminescence (PL) spectra for all samples are shown in Figure 1(d). For sample 1, the free exciton recombination of wurtzite GaAs NWs is appeared at 818 nm14. Besides, another peak at 831 nm also can be seen and it is concerned as the donor-acceptor recombination which is related to silicon acceptors15. It is derived from the inadvertent doping through the Si substrate diffusion. For Si-doped GaAs NWs, except for the peak near 831 nm, they also show a quite obvious PL peak at lower energy, which is attributed to the defect-related emission induced by the Si impurity.16 With the increase in doping concentration, the PL peak become significantly broaden. The deviation of PL peaks between the samples is due to the change in the Si doping concentrations. A higher Si doping concentration will result in more defects associated with Si, which can lead to a significantly broader PL peak. To observe the changes of the nanowire composition, the TEM images and EDS maps of gallium, arsenic and silicon are shown in Figure S1. The changes in Si content are evident from Figure S1 (d), (h) and (l), and the 6 ACS Paragon Plus Environment
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effectiveness of doping is determined. Si content can also be seen in the undoped GaAs nanowire (sample 1), and this result can exclude the unintentional doping by Si via the Si substrate diffusion. The result agrees with the low-temperature PL spectra in Figure 1(d). Back-gate NW FETs with the MSM structure are fabricated with the same 2 µm channels, and the electrical properties of the GaAs NWs with different Si doping concentrations are investigated. The device schematic diagram is shown in Figure 2(a) and the output characteristics with different Vgs are displayed in Figure 2(b)-(d). The Ids drops with the raise of Vgs. It means that all the devices exhibit representative p-type semiconducting behaviors. The equation qφB=kTln(A*T2/JS)/q can be used to calculate the Schottky barrier height (qφB), where A* is the effective Richardson constant (74 AK-2cm-2 for p-type GaAs), k is the Boltzmann constant, T is the temperature, and q is the electron charge.17 The calculated Schottky barrier heights for GaAs NW FETs without gate voltage are 0.644 eV (sample 1), 0.502 eV (sample 2), and 0.494 eV (sample 3). The formula n=CgVth/Lqπr2 can be applied to estimate the carrier concentration of GaAs NW FETs, where Cg is the back-gate capacitance and is gotten from Cg=2πɛ0ɛrL/(ln4h/r) (where h is the thickness of the SiO2 layer, ε0 is the vacuum dielectric constant, and εr is the relative dielectric constant of SiO2); Vth is the threshold voltage (which is obtained in the Ids-Vgs curves in Figure S2); L is the channel length.18 The carrier
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concentrations of sample 1, 2 and 3 are 1.47×1017 cm-3, 4.74×1017 cm-3, and 6.25×1017 cm-3. The optoelectronic properties of the devices are specifically investigated in Figure 3. The Ids-Vds curves of the devices illuminated with a 532 nm laser (0.38 mW/cm2) and in the dark are shown in Figure 3(a) and 3(b). The results show that the light current has a visible enhancement as does the dark current. The responsivity (R), external quantum efficiency (EQE), and specific detectivity (D*) are three essential parameters for measuring the performance of a photodetector. The responsivity is used for evaluating the sensitivity of a photodetector and is defined as R=(Ilight-Idark)/(A×P), where P is the illumination density, and A is the photosensitive region.19,
20
The external
quantum efficiency is defined as EQE=hcR/eλ, where h is the Planck constant,
c is the velocity of light, and λ is the wavelength of light.21, 22 In addition, the specific detectivity is important for distinguishing the ability of a photodetector to discern a weak signal and is defined as D*=RA1/2/(2eIdark)1/2.23, 24 The R of all the devices with different illumination densities at -1 V are shown in Figure 3(c) and the detailed Ids-Vds can be obtained from Figure S3. We find the responsivity of the devices showed a significant enhancement after doping. With the illumination density of 0.38 mW/cm2, the R of sample 1, 2, and 3 are 2.7 A/W, 129.4 A/W and 1175 A/W, respectively. This result represents an improvement for about two orders of magnitude after doping, 8 ACS Paragon Plus Environment
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and particularly, the responsivity after doping is higher than that of most GaAs nanowire photodetectors2,
4, 17, 25-27
(consult to the extracted comparison of
significant parameters of GaAs-based nanowire photodetectors in Table 1) and some other functional nanowire-based photodetectors28-32. Considering the reproducibility of the experiment, a total of 12 devices are studied for every sample of devices.30-32 Figure 3(d), (e) and (f) display the statistical studies on responsivity, the average and standard deviation of the responsivity are 5.3±3.3 A/W (sample 1), 163±88 A/W (sample 2) and 1028 ± 288 A/W (sample 3). The increase in average responsivity is about two orders of magnitude after doping, the results indicate that doping-adjusting Fermi level to improve the device responsivity is repeatable and convincing. Furthermore, the EQE and D* of all the devices with different incident light intensities at -1 V are shown in Figure 3(g) and 3(h). The EQEs of sample 1, 2, and 3 are 6.34×102 %, 3.02×103 %, and 2.74×105 %, respectively, and the D* values of samples 1, 2, and 3 are 1.35×1011 cmHz0.5W-1, 9.52×1011 cmHz0.5W-1, and 3.02×1012 cmHz0.5W-1, respectively. In addition, we also analyze the device performance at 1 V, they are displayed in Figure S4, which also effectively improves the performance of the devices after doping. We consider that the improvement in performance is mainly due to the enhancement in light currents, which are increased by approximately two orders of magnitude.
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There are two origins to understand the enhancement in light current. One is the increase in the conductivity, which means the photocurrent can be transported better than that in the undoped GaAs NWs, and the other one is the increase in the Schottky built-in electric field, which promotes the separation of photogenerated carriers. A comparison picture of the current under illumination and in the dark at ±1 V for undoped and doped GaAs NWs photodetectors is shown in Figure 3(i). The light current presents a clear improvement compared with that of the dark current, which means the enhanced photocurrent is derived from not only the increase in conductivity but also the variation in the Schottky built-in electric field strength. To verify the major photocurrent origin, the devices FESEM images and the corresponding scanning photocurrent mappings are performed on the devices at -1 V, which are displayed in Figure 4(a)-(f) with a scale bar of 2 μm. All the devices exhibit significant photocurrents at the area of the Schottky contact, which means the photocurrents are mainly derived from the contact area. A mechanism behind the doping-enhanced photoresponsivity of the GaAs NW photodetectors is confirmed as the adjustment of the Schottky barrier located at the contact regions between the NW and electrodes, as shown in Figure 4(g)-(i). Upon illumination of the GaAs NW photodetectors, the carriers in the GaAs NW will drive by a bias and pass through the hole Schottky barrier to be collected at the metal electrodes and devote to the
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channel current. Simultaneously, with the drive of contact built-in electric field, the photogenerated electron-hole pairs are separated, thus contribute to the channel current as well (Figure 4(d)). After the effective Si doping of the GaAs NW, the Fermi level of the doped GaAs NW is dragged downwards towards the valence band, this will reduce the depletion width of the hole Schottky barrier, and thus increases the built-in electric field strength, as displayed in Figure 4(h). This action significantly accelerates the separation and collection of photogenerated electron-hole pairs and results in an increase in photocurrent. As the concentration of the dopant increases, the shift in the Fermi level becomes more apparent, it is displayed in Figure 4(i). At the same time, the hole Schottky barrier built-in electric field becomes stronger. Therefore, the photogenerated carriers can be separated and collected more effectively. To further confirm our above analysis, simulations of the electric field distributions for all the devices are performed by Silvaco TCAD to determine the depletion widths and the hole Schottky barrier built-in electric field strengths, the results are shown in Figure 5. The parameters are set up corresponding to our measurement results. Figure 5(a), (b) and (c) presents the simulated electric field distribution schematic images of samples 1, 2 and 3. The evidently wide electric fields under the electrodes determined the depletion widths. An increase in the electric field strength and a decrease in
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the depletion width can be seen after doping. To further determine the variations in the electric field strength and the depletion region width, the distributions of horizontal electric field strengths, the HR-electric field strengths near the drain electrodes, and the vertical electric field strengths are displayed in Figure 5(d)-(f). The insets reveal the positions of the electric fields. Distinctly, the depletion widths are narrowed and the electric field strengths are enhanced after doping with Si. The depletion widths decrease from 0.140 μm to 0.090 μm and 0.075 μm, while the electric field strengths are approximately 1.168×106 V/cm, 1.681×106 V/cm and 1.811×106 V/cm for samples 1, 2 and 3. Combined with Figure 4 and Figure 5, the origin of the enhanced light current is confirmed as the increase in the Schottky barrier built-in electric field strength, which is in line with our expectations from the above analysis. 4. CONCLUSION
In this paper, a remarkable enhancement in the optoelectronic properties of GaAs NWs is demonstrated via doping-adjusting the Fermi level. The photoresponsivity is found to be significantly enhanced up to 1175 A/W. This is two orders of magnitude better than the responsivity of the undoped sample. Additionally, the external quantum efficiency is increased to 2.74×105 %, and the specific detectivity is enhanced to 3.02×1012 cmHz0.5W-1. Based on the scanning photocurrent mappings and the simulations of the built-in electric 12 ACS Paragon Plus Environment
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field strengths and depletion widths, the majority of the photocurrents are generated from the contact regions between the NW and electrodes, and the eminently enhanced photoresponsivity is precisely because of the increase in the built-in electric field strength of the hole Schottky barrier. Our research promises that doping-adjusting the Fermi level has great potential applications in high-performance GaAs nanowire photodetectors and other functional photodetectors.
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FIGURES
Figure 1. The typical characterization of the as-grown GaAs NWs. (a) SEM images of undoped GaAs NWs (sample 1). (b), (c) SEM images of Si-doped GaAs NWs (sample 2, 3). (d) Low-temperature (10 K) PL spectra of all the GaAs NWs.
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Figure 2. (a) Schematic image of a single GaAs nanowire FET. (b), (c), and (d) The series of Ids-Vds curves for samples 1, 2, and 3 at different Vgs from bottom to top.
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Figure 3. The optoelectronic properties of single GaAs NW photodetectors. (a) The Ids-Vds curves of the devices illuminated with a 532 nm laser (0.38 mW/cm2) and (b) in the dark. (c) The dependence of R for the GaAs NW photodetectors with various light power intensities. The responsivity is significantly up to 1175 A/W. Statistical studies on responsivity for the (d) undoped (sample 1) and (e-f) doped (sample 2; sample 3) GaAs NW photodetectors. The average and standard deviation of the responsivity (a total of 12 devices for each sample) are 5.3±3.3 A/W (sample 1), 163±88 A/W (sample 2) and 1028±288 A/W (sample 3). The dependence of (g) EQE and (h) D* for the GaAs NW photodetectors with various light power intensities. The external quantum efficiency and specific detectivity are significantly increased to 2.74×105 % and 3.02×1012 cmHz0.5W-1. (i) A comparison picture of the current under illumination and in the dark at ±1 V for undoped and 16 ACS Paragon Plus Environment
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doped GaAs NWs photodetectors. The light current presents a clear improvement compared with that of the dark current.
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Figure 4. FESEM images and scanning photocurrent mappings of single GaAs NW photodetectors for (a), (d) sample 1, (b), (e) sample 2, and (c), (f) sample 3. (Scale bar: 2 μm.). The energy band diagrams for (g) sample 1, (h) sample 2, and (i) sample 3 upon illumination and drive by a bias. After the effective Si doping of the GaAs NW, the Fermi level of the doped GaAs NW is dragged downwards towards the valence band, this will reduce the depletion width of the hole Schottky barrier, and thus increases the built-in electric field strength. Consequently, increases in photocurrent and responsivity can be realized.
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Figure 5. Simulations of the electric field distributions diagrams for all the devices. The full views of the electric field distributions for (a) sample 1, (b) sample 2 and (c) sample 3. The obviously wide electric fields under the electrodes determine the depletion widths. (d) The distributions of electric field strengths along the horizontal. (e) The distributions of HR-electric field strengths near the drain electrodes. (f) The normalized distributions of electric field strengths along the vertical to observe the depletion widths. The insets reveal the positions of the electric fields.
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TABLES Table 1. The comparison of significant parameters of GaAs-based nanowire photodetectors.
λ
R
Material
D (cmHz0.5W-1
Reference
(nm)
(A/W)
855
0.57
532
0.00154
532
0.231
1.60×109
17
GaAs nanowire
532
25
9.04×1012
26
GaAs nanowire
500
87.67
GaAsSb nanowire
1300
2.37
1.08×109
27
GaAs nanowire
532
1175
9.52×1011
This work
GaAs/AlGaAs nanowire Graphene/GaAs nanowire Graphene/GaAs nanowire
) 7.2×1010
2
24
4
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ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. The TEM images and the corresponding EDS maps of gallium, arsenic and silicon. The Ids-Vgs cuvers for all the devices. The detailed Ids-Vds with series of illumination densities. The dependence of R, EQE, and D* of the GaAs NW photodetectors with series of illumination densities at 1 V. AUTHOR INFORMATION Corresponding Author *Email:
[email protected] *Email:
[email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT
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This work is supported by the National Natural Science Foundation of China (61574022, 61674021, 11674038, 61704011), the Foundation of State Key Laboratory of High Power Semiconductor Lasers, the Innovation Foundation of Changchun University of Science and Technology (XQNJJ-2018-18), Royal Society-Newton Advanced Fellowship (Grant No. NA170214). REFERENCES (1) Ali, H.; Zhang, Y.; Tang, J.; Peng, K.; Sun, S.; Sun, Y.; Song, F.; Falak, A.; Wu, S.; Qian, C. High-Responsivity Photodetection by a Self-Catalyzed Phase-Pure p-GaAs Nanowire. Small 2018, 14, 1704429. (2) Dai, X.; Zhang, S.; Wang, Z.; Adamo, G.; Liu, H.; Huang, Y.; Couteau, C.; Soci, C. GaAs/AlGaAs Nanowire Photodetector. Nano Lett. 2014, 14, 2688-2693. (3) Huh, J.; Yun, H.; Kim, D.-C.; Munshi, A. M.; Dheeraj, D. L.; Kauko, H.; Van Helvoort, A. T.; Lee, S.; Fimland, B.-O.; Weman, H. Rectifying Single GaAsSb Nanowire Devices Based on Self-induced Compositional Gradients. Nano Lett. 2015, 15, 3709-3715. (4) Zhang, L.; Geng, X.; Zha, G.; Xu, J.; Wei, S.; Ma, B.; Chen, Z.; Shang, X.; Ni, H.; Niu, Z. Self-catalyzed Molecular Beam Epitaxy Growth and Their Optoelectronic Properties of Vertical GaAs Nanowires on Si (111). Mat. Sci.
Semicon. Proc. 2016, 52, 68-74. 22 ACS Paragon Plus Environment
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(5) Fan, Y.; Zhou, Y.; Wang, X.; Tan, H.; Rong, Y.; Warner, J. H. J. A. O. M. Photoinduced
Schottky
Barrier
Lowering
in
2D
Monolayer
WS2
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SYNOPSIS
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Figure 1. The typical characterization of the as-grown GaAs NWs. (a) SEM images of undoped GaAs NWs (sample 1). (b), (c) SEM images of Si-doped GaAs NWs (sample 2, 3). (d) Low-temperature (10 K) PL spectra of all the GaAs NWs. 129x57mm (300 x 300 DPI)
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Figure 2. (a) Schematic image of a single GaAs nanowire FET. (b), (c), and (d) The series of Ids-Vds curves for samples 1, 2, and 3 at different Vgs from bottom to top. 129x99mm (300 x 300 DPI)
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Figure 3. The optoelectronic properties of single GaAs NW photodetectors. (a) The Ids-Vds curves of the
devices illuminated with a 532 nm laser (0.38 mW/cm2) and (b) in the dark. (c) The dependence of R for the GaAs NW photodetectors with various light power intensities. The responsivity is significantly up to 1175 A/W. Statistical studies on responsivity for the (d) undoped (sample 1) and (e-f) doped (sample 2; sample 3) GaAs NW photodetectors. The average and standard deviation of the responsivity (a total of 12 devices for each sample) are 5.3±3.3 A/W (sample 1), 163±88 A/W (sample 2) and 1028±288 A/W (sample 3). The dependence of (g) EQE and (h) D* for the GaAs NW photodetectors with various light power intensities. The external quantum efficiency and specific detectivity are significantly increased to 2.74×105 % and 3.02×1012 cmHz0.5W-1. (i) A comparison picture of the current under illumination and in the dark at ±1 V for undoped and doped GaAs NWs photodetectors. The light current presents a clear improvement compared with that of the dark current. 160x122mm (300 x 300 DPI)
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Figure 4. FESEM images and scanning photocurrent mappings of single GaAs NW photodetectors for (a), (d) sample 1, (b), (e) sample 2, and (c), (f) sample 3. (Scale bar: 2 μm.). The energy band diagrams for (g) sample 1, (h) sample 2, and (i) sample 3 upon illumination and drive by a bias. After the effective Si doping of the GaAs NW, the Fermi level of the doped GaAs NW is dragged downwards towards the valence band, this will reduce the depletion width of the hole Schottky barrier, and thus increases the built-in electric field strength. Consequently, increases in photocurrent and responsivity can be realized. 160x104mm (300 x 300 DPI)
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Figure 5. Simulations of the electric field distributions diagrams for all the devices. The full views of the electric field distributions for (a) sample 1, (b) sample 2 and (c) sample 3. The obviously wide electric fields under the electrodes determine the depletion widths. (d) The distributions of electric field strengths along the horizontal. (e) The distributions of HR-electric field strengths near the drain electrodes. (f) The normalized distributions of electric field strengths along the vertical to observe the depletion widths. The insets reveal the positions of the electric fields. 159x73mm (300 x 300 DPI)
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