Supplementary Figure 1. Supplementary Figure 1 Characterization of another locally gated PN junction based on boron

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1 Supplementary Figure 1 Supplementary Figure 1 Characterization of another locally gated PN junction based on boron nitride and few-layer black phosphorus (device S1). (a) Optical micrograph of device S1. (b) Transfer characteristic at V ds = 100 mv. The local gates are linked and act as a global back gate. The resulting field-effect modulates the current from ~ 6 μa (hole enhancement) to ~ 500 na for electron enhacement. The inset shows the data in a linear scale. The hole field-effect mobility of the device is 17 cm 2 V -1 s -1. (c) Output characteristics of the device in different gate configurations (PP: V lg = V rg = -15 V, NN: V lg = V rg = 15 V, NP: V lg = 15 V, V rg = -15 V, PN: V lg = -15 V, V rg = 15 V) PP and NN gate configurations display linear transfer characteristic while PN and NP show strong rectifying behavior. 1

2 Supplementary Figure 2 Supplementary Figure 2 Characterization of locally gated PN junction based on boron nitride and few-layer black phosphorus (device S2). (a) Optical micrograph of device S2. (b) Transfer characteristic at V ds = 100 mv. The local gates are linked and act as a global back gate. The inset shows the data in a linear scale. The hole field-effect mobility is about 0.27 cm 2 V -1 s -1 (c) Output characteristics of the device in different gate configurations (PP: V lg = V rg = -10 V, NN: V lg = V rg = 10 V, NP: V lg = 10 V, V rg = -10 V, PN: V lg = -10 V, V rg = 10 V). 2

3 Supplementary Figure 3 Supplementary Figure 3 AFM and optical images of three devices. (a) AFM of the device described in the main text. b-p thickness ~ 6 nm, h-bn thickness ~ 20 nm. (b) AFM of the device S1. b-p thickness ~ 14.5 nm, h-bn thickness ~ 15 nm. (c) AFM of the device S2. b-p thickness ~ 5 nm, h-bn thickness ~ 25.8 nm. (d) Optical image of the device described in the main text. (e) Optical image of the device S1. (f) Optical image of the S2. In panels (d) to (f) the black box indicate the region where the AFM image is measured. 3

4 Supplementary Figure 4 Supplementary Figure 4 Comparison of consecutive G-V g curves for few-layer b-p FETs on SiO 2 and on h-bn We compare two consecutive G-V g curves measured for a few-layer b-p FET on SiO 2 (black lines) and for the device presented in the main text (with the local gates used as a single back gate, red lines). The measured shift in gate voltage is evaluated at G = 30 ns and is equal to 1.18 V for the SiO 2 dielectric and 0.14 V for the h-bn dielectric. The smaller shift for few-layer b-p on h-bn indicates a reduced effect of gate bias stress most likely caused by a lower density of surface states at the b-p/h-bn interface 4

5 Supplementary Figure 5 Supplementary Figure 5 Finite-element simulation (COMSOL Multiphysics) of the formation of an electrostatically defined PN junction. (a) Simulation geometry indicating the different materials. The gap between the gates is 300 nm wide and the plot is centered around zero. The different components are indicated: the local gates (ε r gold, yellow) with hexagonal boron nitride ( ε r = 4, blue) and black phosphorus (ε r b-p, gray), on top. The surrounding regions are vacuum (ε r = 1). The left gate is set to +10 V and the right gate is set to 10 V. (b) Calculated electric field lines across the device. (c) Linecut of the electric potential along the junction region. Above the left gate the potential is + 10 V, smoothly decreases across the junction region and reaches -10 V above the right gate. (d) Magnitude of the horizontal electric field E x along the junction. The electric field is positive in the junction region indicating that it is oriented to the right. The horizontal electric field makes electrons drift to the left and holes to the right, contributing to charge accumulation above the gates and sustains depletion of charges in the junction region 5

6 Supplementary Figure 6 Supplementary Figure 6 Shockley fits of the IV-characteristics in PN and NP configuration for the measured devices. (a- c) I ds -V ds curves in PN configuration (red dots) and model (black solid line). The inset of (a) shows the circuit model schematics. (d-f) I ds -V ds curves in the NP configuration (blue dots) and model (black solid line) 1. 6

7 Supplementary Figure 7 Supplementary Figure 7 V oc and I sc aas function of incident optical power for the main text device. V oc (left axis, blue dots) and I sc (right axis, red dots) against illumination power. Both the open circuit voltage and the short circuit current show a linear relationship with the illumination power. The deviation from the ideal behaviour can be attributed to parasitic resistive losses in our device (see Supplementary Figure 6). I sc is linear with the excitation power for the whole range of incident optical power, indicating that the recombination rate of photogenerated carrier is independent from the rate of incoming photons. This is usually associated with monomolecular recombination: the recombination rate is linearly proportional to the density of photogenerated carriers, even in the presence of trap states. 2,3 7

8 Supplementary Figure 8 Supplementary Figure 8 Comparison of output characteristics with and without illumination (λ = 640 nm) in PN configuration. (a) I ds vs I ds for device S1. The gates are biased in different polarities (V lg = -4 V, V rg = 9 V). The inset shows the data in a smaller bias range. The shape of the IV under illumination may be due to a combination of processes: photovoltaic (causing an open-circuit voltage and short-circuit current) and photoconductive (changing the resistance in reverse and forward bias). The photoconductive component might be caused by conduction in the top region of the flake, which is not affected by the gates due to screening. (b) Device presented in Supplementary Figure 2. The gates are biased in different polarities (V lg = - 10 V, V rg = 10 V). The inset shows the data in a smaller bias range. The IV under illumination preserves the diode-like character, indicating that the photovoltaic process is dominant. 8

9 Supplementary Figure 9 Supplementary Figure 9 Photovoltaic behavior of Device S2 in PN configuration. (a) I ds -V ds characteristics for different illumination powers (λ = 640 nm) near zero bias. The generated electrical power reaches a maximum of ~ 2.7 pw for illumination power 2.82 μw. (b) Generated electrical P el = V ds I ds power for different illumination powers. (c) V oc (left axis, blue dots) and I sc (right axis, red dots) against illumination power. Both the open circuit voltage and the short circuit current show a linear relationship with the illumination power, confirming the behaviour found for the device presented in the main text 9

10 Supplementary Figure 10 Supplementary Figure10 Wavelength dependence in PN configuration of the device presented in the main text. (a) Output characteristics for wavelengths ranging from 532 to 940 nm. (b) Output characteristics near zero bias, showing photovoltaic behavior. (c) The magnitude of the generated electrical power as a function of V ds, obtained by multiplying the voltage values in Supplementary Figure 10b by the current values. The generated electrical power reaches a maximum of about 0.78 pw for illumination with P = 0.32 μw and λ= 640 nm. 10

11 Supplementary Figure 11 Supplementary Figure 11 Wavelength dependence of S1device in PN configuration. (a) Output characteristics for wavelengths ranging from 532 to 940 nm. Qualitatively, the presented IVs show similar behavior, showing an increase in current in forward and reverse bias. (b) Responsivity as a function of wavelength extracted from Supplementary Figure7a at V ds = -500 mv. The responsivity R can be calculated by R = I ph / P, where I ph is the photocurrent and P is the illumination power. The responsivity increases up to 28 ma/w as the wavelength decreases. This value is higher than previously reported for photodetectors on SiO

12 Supplementary Figure 12 Supplementary Figure 12 Time response of the devices S1 and S2 (PN configuration, V ds = 0V, λ = 640 nm, P = 2.7 μw). (a) I sc vs time t for one period of light illumination for device S1. The dashed vertical lines indicate the 90/10 rise and fall times. (b) I sc vs time t for one period of light illumination for device S2. The dashed vertical lines indicate the 90/10 rise and fall times. (c) I sc vs time t for several periods of light illumination for device S1. (d) I sc vs time t for several periods of light illumination for device S2. Note that, for both devices, I sc rises in phase with the light excitation with rise and fall times in the order of 2 ms The rise and fall times are comparable with few-layer b-p based photodetectors 4 and at least an order of magnitude shorter than photodetectors based on other layered materials (for a comparison of various photodetectors see ref 4 and 5 ). Moreover, the value of I sc is constant over several illumination cycles. The high signal to noise ratio provided by the extremely small dark current (~ 100 pa) makes few-layer b- P PN junctions promising as fast and sensitive photodetectors. 12

13 Supplementary Figure 13 Supplementary Figure 13 EQE as a function of excitation wavelength for the main text device (red dots). The EQE values measured in this work are in the same order of magnitude and even larger for λ > 532 nm than the EQE for a PN junction based on 1L WSe

14 Supplementary Table 1 Shockley fit parameters of the IV-characteristics in PN and NP configuration for the measured devices (see Supplementary Figure 6). Main text S1 S2 PN NP PN NP PN NP I s (na) n R s (MΩ) R p (MΩ) > Supplementary Table 2 Solar cell figures-of-merit or the three studied devices. Note that the excitation powers are different than those used in Supplementary Table 3. λ = 640 nm Main Text (PN) S1 (PN) S2 (PN) Thickness (nm) P opt (μw) I sc (na) V oc (mv) P el (pw) FF EQE 0.050% 0.053% 0.048% Supplemetary Table 3 Open circuit voltage (V oc ), short-circuit current (I sc ), maximum generated electrical power (P el, max ), fill factor FF = P el,max / (V oc I sc ) and the external quantum efficiency EQE = I sc /P hc/eλ for the device in the main text as a function of wavelength (P = 0.32 μw for all wavelengths). λ (nm) V oc (mv) I sc (na) P el,max (pw) FF (-) EQE (%)

15 Supplementary Note 1 Determination of diode parameters by modeling with Shockley equation In this section, we model the I ds -V ds characteristics in the PN and NP configuration of all the measured devices with a modified form of the Shockley equation. In an ideal case, the relationship between the current (I ds ) and the voltage bias (V ds ) across a PN diode is described by the Shockley model: I ds V, ds Is exp 1 nvt (1) where I s is the saturation current, n is the ideality factor, V kt(k B is the Boltzmann constant T B in ev/k and T is the temperature in K) is the themal voltage. The ideality factor is related to the carrier recombination mechanisms at the PN junction; n = 1 indicates that there is only band-toband recombination of minority carriers, which is the ideal case. A more realistic model should include current losses due to parasitic resistances in parallel (R p ) and in series (R s ) with the junction. A schematic of the model circuit is presented in Supplementary Figure 6a. The series resistance R s models the voltage losses due to e.g. contact resistance and the resistance of the degenerately doped regions of the b-p flake. The parallel resistance R p models additional carrier recombination mechanisms that drain current from the junction. The slope of the measured I ds -V ds curves at V ds = 0 V indicates a non-infinite R p (Figure 3d in main text and Supplementary Figure 6 in Supp. Info.). To include these effects, we can rewrite Supplementary Equation (1) as 15

16 I ds I s V I R V I R nvt Rp ds ds s ds ds s exp 1. (2) An analytical expression can be obtained in the following form: 1 I ds nv I R R R ( V I R ) V I R Rs nvt ( Rs Rp ) nvt ( Rs Rp ) Rs Rp T s s p p ds s s ds s p W exp, (3) where W is the Lambert W-function. The measured IV curves and the model described in Supplementary Equation (3) are in good agreement (Supplementary Figure 6). We summarized the extracted model parameters in Supplementary Table1. Supplementary References deal diode equation with series and shunt parasitic resistances. Solid-State Electronics 44, (2000). 2 Bube, R. H. Photoelectronic Properties of Semiconductors. (Cambridge University Press, 1992). 3 Pospischil, A., Furchi, M. M. & Mueller, T. Solar-energy conversion and light emission in an atomic monolayer p-n diode. Nature Nanotechnol. 9, (2014). 4 Buscema, M. et al. Fast and Broadband Photoresponse of Few-Layer Black Phosphorus Field- Effect Transistors. Nano Lett., 14, (2014). 5 Island, J. O. et al. Ultrahigh Photoresponse of Few-Layer TiS3 Nanoribbon Transistors. Advanced Optical Materials, doi: /adom (2014). 6 Baugher, B. W. H., Churchill, H. O. H., Yang, Y. & Jarillo-Herrero, P. Optoelectronic devices based on electrically tunable p-n diodes in a monolayer dichalcogenide. Nat Nanotechnol. 9, , (2014). 16