SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION doi: 1.138/nphoton Efficient Photovoltage Multiplication in Carbon Nanotubes Leijing Yang 1,2,3+, Sheng Wang 1,2+, Qingsheng Zeng, 1,2, Zhiyong Zhang 1,2, Tian Pei 1,2, Yan Li 1,4, Lian-Mao Peng 1,2* 1 Key Laboratory for the Physics and Chemistry of Nanodevices, Peking University, Beijing 1871, China 2 Department of Electronics, Peking University, Beijing 1871, China 3 Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 1871, China 4 College of Chemistry and Molecular Engineering, Peking University, Beijing 1871, China + These authors contributed equally to this work. * lmpeng@pku.edu.cn Structure and electronic characterization The structural characterizations on CNT were made by AFM and Raman spectroscopy. Figure S1(a) shows the AFM image and height measurement on a CNT with d~ 3.1nm. Figure S1(c) shows the resonance Raman spectrum of a CNT (used in Figure 3 of the main text) under the excitation of a 633nm laser. The radial breathing mode (RBM) transition band gives Ω RBM = 164 cm -1. Based on d= 248/Ω RBM (valid for CNTs with diameters between 1nm < d < 2nm), the CNT diameter of this nanotube is estimated to be ~ 1.5nm. The G band associated with the transversal and longitudinal optical phonon modes exhibits 1565 cm -1 and 1588 cm -1 peaks which correspond to G - and G + respectively. Electronic characterization of the CNT was made by field-effect measurements. Transfer characteristics of the CNT with d=3.1nm (contacted using Sc) shows clearly n-type field-effect characteristics and verifies that the CNT is a semiconducting CNT with a small bandgap and a low ON/OFF ratio of about 1 3 at nature photonics 1

2 supplementary information doi: 1.138/nphoton V ds =.1V [Figure S1(b)]. For the CNT with smaller diameter d~1.5nm, the transfer characteristic show a much larger ON/OFF ratio of more than 1 6 [Figure S1(d)]. For a CNT with a suitable diameter (~1.8nm), both AFM and Raman experiments were made on the same sample [Figures S1(e) and S1(f)] showing excellent agreement between the two methods. Photocurrent Spectroscopy Photocurrent spectroscopy experiments were carried out with a tunable laser (AQ compact tunable laser source module, Yokogawa company) that is continuously tunable between 144 nm (.86eV) -164 nm (.76eV). The laser illuminates the device via a single model fibre and the power is ~ 3mW at the exit of the fibre with a diameter of ~ 3μm. The fibre was fixed on a probe which approached to the devices with high precision. Figure S2 gives photocurrent spectra obtained from two CNT diodes. In both photocurrent spectra the photocurrent is given as a function of the illuminating photon energy showing well-defined resonance at the excitation wave length 1595nm (.78eV) [Figure S2(a)] and 1565nm (.79eV) [Figure S2(b)], respectively. Height measurement by AFM shows that Figure S2(a) corresponds to a CNT with d ~ 1.8nm and Figure S2(b) to that with d ~1.3nm. For the CNT with d=1.8nm [see also Figures S1(e) and S1(f)], the corresponding E 11 and E 22 excitation energies are respectively ~.6eV and ~1eV from the Kataura plot [1]. The resonant peak energy is about.78ev in Figure S2(a) which is larger than E 11 ~.6eV, and the difference is ~.18eV which could be attribute to result from the exciton-phonon ( ~.18eV for optic phonon) interaction [2, 3]. For the CNT with d ~ 1.3nm [Figure S2(b)], the resonant peak energy is.79ev which is related directly to that from the Kataura plot. [1] Transport channels of CNT tandem diodes We designed an experiment to investigate the transport mechanism of the CNT tandem cell. The virtual Sc and Pd contact pads were initially separated and then 2 nature photonics

3 doi: 1.138/nphoton supplementary information connected, and electronic transport measurements were carried out. Results corresponding to three distinct device configurations are given in Figure S3. (1) When the two Sc and Pd contact pads are separated [Figure S3(a)], the overall I-V characteristic of the tandem double cell [Figure S3(b)] is not so different from that of a single diode, and the resulting open circuit voltage and short circuit current are respectively V oc ~.11V and I sc ~ 3.5nA. (2) When the two Sc and Pd contact pads are connected [Figure S3(c)], the two diodes are connected via two parallel channels, i.e. the CNT channel and the virtual contact channel. Both V oc and I sc become much larger than that of configuration (1) [Figure S3 (a)], with V oc ~.285V and I sc ~ 13.31nA [Figure S3 (d)], and in particular the open circuit voltage is more than doubled than that shown in Figure S3(b). (3) When the two Sc and Pd contact pads are connected, but with the CNT channel being removed [Figure S3(e)], the Sc and Pd contact pads provides the only channel for the transport. The CNT tandem double cell is seen to result in an open circuit voltage of V oc ~.27V [Figure S3 (f)], which is about the same as that shown in Figure S3(d), but with a much reduced short circuit current of about 6.16nA. Statistics on photovoltages While photovoltage is ultimately determined by the energy bandgap of the material, in a real device it is affected by a range of other factors including that due to the contact, substrate and coating. As a result, photovoltages measured from our 3 devices are different. Nevertheless Figure S4 shows that typically the deviation from the averaged photovoltage value is small and less than 25%. Long time stability of the devices While both Sc and Y are easily oxidized once exposed to air, the Sc (Y)/CNT interface is very stable leading to long time device stability. Shown in Figure S5 are I-V characteristics of a quadruple CNT tandem cell measured recently and more than six month ago, the two I-V curves are seen to be almost identical. In Table 1 we also nature photonics 3

4 supplementary information doi: 1.138/nphoton presented data on photovoltage for five other devices, showing excellent device stability over six months. The internal efficiency The internal efficiency η of a CNT device can be estimate from the absorption cross section of CNT [4]. α L N ( λ) = N ( λ) N( λ) = N ( λ)*(1 e ) forα = n* σ abs nσ L = N ( λ) * (1 e ) IM * VM * t IM * VM * t IM * VM * t IM * VM * t η = = = = nσl nσl N ( )* ( ) abs λ hv N( λ)*(1 e )* hv nσ L Etot λ (1 e ) * * hv (1 e )* Wtot ( λ)* t hv IM * VM 1 = = * η nσl nσl pre (1 e ) * W (1 e ) tot 1 define : M = (1 n L ) ρ n= m C * N A e σ m c kg, mass of atom carbon. ρ- 1.3g/cm 3 density of carbon nanotube. n - number of mole C per cm 3. n=.184 mole C /cm 3, σ=.6 *1 6 cm 2 /mole C; L=1.5*1-7 cm, N A = 6.2*1 23 -Avogadro's number. σ - absorption cross section (σ =.6*1 6 cm 2 /mole C from reference 4), N number of photons of light. η pre efficiency of device (single cell) with d ~ 1.5nm in Figure 3. With L=1.5nm (For CNT with d ~ 1.5nm in Figure 3), internal efficiency η is estimated to be ~ 57.4%. References 1. R. B. Weisman, S. M. Bachilo, Nano Lett., 3, 1235, (23) 2. X. Qui, M. Freitag, V. Perebeinos, Ph. Avouris, Nano Lett. 5, 749 (25) 3. J. U. Lee, Phys. Rev. B, 75, 7549(27) 4 nature photonics

5 doi: 1.138/nphoton supplementary information 4. M. F. Islam, D. E. Milkie, C. L. Kane, A. G. Yodh, and J. M. Kikkawa, Phys. Rev. Lett. 93, 3744(24). nature photonics 5

6 supplementary information doi: 1.138/nphoton a b V ds =.1V I ds (A) V gs (V) c Intensity(a.u.) e Intensity(a.u.) RBM G G Raman Shift(cm -1 ) d I ds (A) f V gs (V) V ds =.1V Raman Shift(cm -1 ) Figure S1. Geometric and electronic characterizations of CNTs used in this work. (a) AFM image of the CNT with d=3.1nm (used in Fig. 4 of the main text) and (b) transfer characteristics of a Sc contacted FET based on the same CNT. (c) Raman spectrum taken from a single walled CNT with a diameter of about 1.5nm, the used laser wavelength is 633nm, and (d) transfer characteristics of a Pd contacted FET based on the same CNT (used in Fig. 3 of the main text). Shown in (e) and (f) are Raman spectrum and AFM image of the same CNT, both methods give d ~ 1.8nm. 6 nature photonics

7 doi: 1.138/nphoton supplementary information a Photocurrent(nA) b Experiment Fitting Wavelength(nm) Experiment Fitting Photocurrent(nA) Wavelength(nm) Figure S2. Photocurrent spectra for diodes based on CNTs with different diameter. (a) Photocurrent spectrum for a diode based on a CNT with d ~ 1.8nm, the wavelength of the laser is from 148nm (.83eV) to 164nm (.76eV). Blue dots shows experimental data, and red line the fitting curve. The absorption peak is at about λ=1594nm (.78eV). (b) Photocurrent spectrum of a diode based on a CNT which a diameter of about 1.3nm. Blue dots and red lines are experimental and fitting data separately. At λ=156nm (.79eV), photocurrent reaches a maximum. nature photonics 7

8 supplementary information doi: 1.138/nphoton a b 1 tandem cell conneted only with CNT 5 I(nA) na.1v c d V(V) tandem cell conencted with CNT and virtual contacts I(nA) V e f na..2.4 V(V) tandem cell connected only with virtual contacts 5 I(nA) V g tandem cell connected only with CNT only with virtual contacts both with CNT and virtual contacts -6.16nA..2.4 V(V) I(nA) nA nA..2 V(V) Figure S3: The transport mechanism of the CNT based tandem diodes. All curves are measured by probing into Ti/Au electrode 1 and 4. Depicted structure models of the tandem cell (a) connected only with CNT (virtual contact are floating), (c) both CNT and virtual contact and (e) only with virtual contact. Shown in (b), (d), (f) are corresponding I V curves of the three types of tandem cells correspond to (a), (c), (e) respectively. (g) Comparison of the I V characteristics of these three types of double cells. 8 nature photonics

9 doi: 1.138/nphoton supplementary information a.72 triple cell double cell PV(V) single cell Device Number b PV(V) Device Numbers Figure S4: Open circuit photovoltages for 3 CNT devices. (a) Detailed photovoltage data for 14 single, 5 double and 8 triple cell devices, and (b) data for all 3 devices. nature photonics 9

10 supplementary information doi: 1.138/nphoton six months ago few days ago I(nA) V(V) Figure S5: Current voltage characteristics showing the Stability of a quadruple cell device of Figure 3(c). Table 1:Open circuit photovoltages for 5 CNT diodes measured six months ago and recently. Device No. PHOTOVOLTAGE (V) (Six Months Ago) PHOTOVOLTAGE (V) (Now) nature photonics