Supporting Information: Determination of n-type doping level in single GaAs. nanowires by cathodoluminescence

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1 Supporting Information: Determination of n-type doping level in single GaAs nanowires by cathodoluminescence Hung-Ling Chen 1, Chalermchai Himwas 1, Andrea Scaccabarozzi 1,2, Pierre Rale 1, Fabrice Oehler 1, Aristide Lemaître 1, Laurent Lombez 2,3, Jean-François Guillemoles 2,3, Maria Tchernycheva 1, Jean-Christophe Harmand 1, Andrea Cattoni 1, Stéphane Collin 1,2 * 1 Centre for Nanoscience and Nanotechnology, CNRS, University Paris-Sud/Paris-Saclay, Marcoussis, France 2 Institut Photovoltaïque d'ile-de-france (IPVF), Antony, France 3 Institut de Recherche et Développement sur l Energie Photovoltaïque (IRDEP) EDF/CNRS/Chimie Paris Tech, Chatou, France * stephane.collin@c2n.upsaclay.fr Table of contents : 1) Scanning electron microscope images of GaAs nanowires ) Generation volume under electron beam excitation ) Comparison between CL and PL measurements ) Room temperature CL mapping of nanowires ) Low temperature CL mapping of nanowires ) Model for the surface depletion width in n-gaas ) Model for the absorption coefficient ) Model for the luminescence spectra and fitting procedure ) References

1) Scanning electron microscope images of GaAs nanowires SEM images of the nanowires on the growth substrate studied in this work are shown in Figure S1.

Larger diameter usually corresponds to a faster growth rate, leading to a longer wire.

2 1) Scanning electron microscope images of GaAs nanowires SEM images of the nanowires on the growth substrate studied in this work are shown in Figure S1. Due to random size distribution of the initial Ga droplets, intrinsic GaAs nanowire cores have different diameters. Larger diameter usually corresponds to a faster growth rate, leading to a longer wire. During the shell growth of n-type GaAs, shorter wire may suffer from slower shell growth rate due to shadowing from neighboring wires (especially at the bottom part of the wires). Because of severe surface states in GaAs, shell thickness smaller than 50 nm without passivation may significantly reduce the free electron concentration. Therefore, bottom of the wires always show less blueshift compared to middle-top of the wires (Figure S4 to Figure S13). Comparison of the electron Fermi levels between different wires (Table 1) also reveal a direct correlation of free electron densities with nanowire lengths. Figure S1. SEM micrographs of nanowires grown on Si substrate in tilt (a) and cross-sectional (b) view. 2) Generation volume under electron beam excitation Figure S2. Maps of the density of energy dissipated by an electron beam in GaAs, with an incident energy of (a) 4keV and (b) 6keV (white dashed line: 80% of the maximum). 2

3 3) Comparison between CL and PL measurements To verify the injection level in n-gaas samples, 4 kv and 6 kv electron beam as well as PL are performed at room temperature and luminescence spectra are shown in Figure S3 for (a)-(b) planar layers and (c)-(d) nanowires. We used 532 nm laser excitation (520 µw power with spot size of about 5 to 7 µm in diameter) for PL measurement. CL and PL spectra are very similar in linear scale (except for the highly-doped sample (C), probably due to inhomogeneity or different injection profile). In logarithmic scale, a slightly deeper tail at high-energy for the highest excitation power might be due to local heating of the carriers. Overall, CL with 4 kv or 6 kv electron beam (current 1 na) are considered representative for investigating n-type GaAs. Figure S3. Comparison of room-temperature luminescence spectra with different excitation conditions. CL/PL spectra of planar layers are shown in linear scale (a) and logarithmic scale (b). CL spectra of nanowires are independent of electron beam voltage from 4 kv to 6 kv (linear scale in (c) and logaritmic scale in (d)) and typical PL spectra are consistent with CL spectra. 3

4) Room temperature CL mapping of nanowires Figure S4.

The arrow in the SEM image indicates the growth direction of

the top of the nanowire are also plotted (right graph: dash

The low temperature CL measurement of the same nanowire is shown

4 4) Room temperature CL mapping of nanowires Figure S4. Room temperature CL measurement of NW-1. The arrow in the SEM image indicates the growth direction of nanowire core, and the CL spectra extracted from the bottom to the top of the nanowire are also plotted (right graph: dash vertical line indicates the bandgap). The low temperature CL measurement of the same nanowire is shown in Figure 1 and the fit of room temperature spectrum in Figure 9. Figure S5. Room temperature CL measurement of NW-5 and the fit. 4

5 Figure S6. Room temperature CL measurement of NW-6 and the fit. Figure S7. Room temperature CL measurement of NW-7 and the fit. Figure S8. Room temperature CL measurement of NW-8 and the fit. 5

6 Figure S9. Room temperature CL measurement of NW-9 and the fit. Figure S10. Room temperature CL measurement of NW-10 and the fit. 6

7 5) Low temperature CL mapping of nanowires Figure S11. Low temperature CL measurement of NW-2. Figure S12. Low temperature CL measurement of NW-3. 7

8 Figure S13. Low temperature CL measurement of NW-4. 8

9 6) Model for the surface depletion width in n-gaas Here, we give a quantitative estimation of the thickness of the depletion layer of n-type GaAs. GaAs surface is known for surface states that pin the Fermi level at near mid-gap. The surface potential φ! of (110)GaAs is about 0.7 V below the conduction band for n-type GaAs (density of interface states of ~10 13 cm -2 ev -1 ) 1. For n-type thin-film layers, theoretical values of surface depletion layer thickness are given by 2 : w = 2ε(φ! φ!! kt/e) e(n! N! ) Here ε = 12.9ε! is the dielectric constant for GaAs and ε! = !!" F/m is the vacuum permittivity, φ! denotes the surface potential, φ!! is the channel (neutral region) potential depending on the doping level. For the electron concentration N! N! 10!" cm!!, φ!! 0.04 V calculated using a Fermi integral. We obtain w 32 nm. In the core-shell configuration of the nanowires presented in this manuscript, the calculation of the depletion layer thickness should be modified. However, we expect a small impact of the exact geometry since the depletion depth is much smaller than the nanowire radius. This is confirmed by the analytical model of surface depletion in GaAs nanowires developed by Chia et al. for a cylindrical symmetry 3, which leads to similar values for w. The interface between nominally undoped core and n-type shell may also create internal field, but this effect should be negligible since the background doping of the core is significantly smaller than the shell doping. In conclusion, the depletion depth of 32 nm is significantly smaller than the nominal shell thickness of 55 nm, ensuring a ~20 nm quasi-neutral region where the free electron concentration can be probed by cathodoluminescence. This result is also consistent with our findings on nanowires with thinner shells (see NW-8 and NW-9 in Table 1 and discussion in the manuscript): fitting their CL spectrum with our model results in lower electron quasi-fermi levels that can be attributed to the increased impact of the depletion region. For this reason, we emphasize that the results obtained with these thinner NWs (NW-8 and NW-9) should be taken apart and analyzed carefully. 9

7) Model for the absorption coefficient In this work, only room temperature spectra are fitted using the theoretical model because low temperature absorption presents sharp excitonic features and are

Black dash curve presents the experimental measurement for high purity GaAs from Sturge 4. Colored dash lines are absorption models for n-gaas without electron filling (α! in Eq.

10 7) Model for the absorption coefficient In this work, only room temperature spectra are fitted using the theoretical model because low temperature absorption presents sharp excitonic features and are more difficult to model. Figure S14(a) shows the modeled absorption coefficients that give the best fit to the CL spectra of planar layers. Black dash curve presents the experimental measurement for high purity GaAs from Sturge 4. Colored dash lines are absorption models for n-gaas without electron filling (α! in Eq. (3) in the main article), and colored solid lines account for electron filling in the conduction band (α in Eq. (4)). For the highly-doped sample (C), the parabolic model is used for α!"#$% in Eq. (3). For lower doping levels (sample (A), (B) and nanowires), measurements from Sturge 4 are used for α!"#$% because a more rapid rise of the absorption close to the gap is required.! These values are slightly shifted in energy to account for the bandgap narrowing using the plot of α! for the determination of the bandgap (Figure S14(b)). Figure S14. Absorption coefficients of doped GaAs layers. (a) Modeled absorption coefficients, for each layer (A), (B) and (C), α 0 (without electron filling) and α (with electron filling) are plotted for comparison. They are also compared to data from ref 4! (black dots). (b) Plot of α! versus energy and linear fit to define the bandgap. 10

11 8) Model for the luminescence spectra and fitting procedure To complete the analytical form of modeled luminescence spectrum, Equation (4) concerning the occupation probability needs additional assumption. Since there is an infinite number of pairs of optical transitions that corresponds to the photon energy hν, a parameter p between 0 and 1 is introduced: E! = p hν E! E! = E! 1 p hν E! The optical absorption creates an electron at energy level E! in the conduction band and a hole at energy level E! in the valence band (zero level is placed at the conduction band minimum). The average value of p over many absorption events depends on the density of states in each band 5. p = 1/2 is applicable to lightly doped materials with equivalent electron and hole mass. p = 1 corresponds to usual assumption made for degenerated n-type GaAs 6,7 : excitation from the valence band minimum to an energy level hν E! higher than the conduction band minimum. We assume p = 0.9 for GaAs considering the ratio between the conduction and valence bands effective density of states, and the hole Fermi level is far above the valence band edge (E!" E! > 3kT) so that f! 1. Figure S15 shows the influence of the parameter p on the modeled luminescence spectra. High value of p is desired to emphasize the electron occupation in the CB and to give the correct estimation of the electron Fermi level. However, the absorption tail will be slightly underestimated in n-type GaAs if p is assumed close to 1, because the optical transition below bandgap should take place from the valence band tail to the conduction band. Figure S15. Modeled luminescence spectra with various values for the parameter p (Eq. (3), (4) and (5) in the main article). The model for α!"#$% is parabolic with fixed parameters: E! = 1.42 ev, E!" = 60 mev above the conduction band minimum, γ = 15 mev, T = 300 K and d = 2 µm. 11

12 Figure S16 shows the modeled luminescence spectra with different values for the parameter d which appears in the absorptivity term of Equation (5). We can observe the luminescence spectra redshift with increasing values of d, corresponding to a deeper injection profile or a longer diffusion length of minority carriers. The variation of d can lead to difference of several tens of mev in peak energy and FWHM, so need to be considered when deducing material properties from luminescence analysis. Figure S16. Modeled luminescence spectra with various values of the parameter d (Eq. (3), (4) and (5) in the main article). The model for α!"#$% is parabolic with fixed parameters: E! = 1.42 ev, E!" = 60 mev above the conduction band minimum, γ = 15 mev, T = 300 K and p = 0.9. The fitting parameters (bandgap E!, electron Fermi level E!", band tail γ, characteristic length d) are determined by minimizing the root-mean-square error between the measured and calculated luminescence spectra (linear scale). The temperature is fixed at T = 300 K. The fitting parameters are given in Table 1 of the main text. The reliability of the fitting procedure has been tested as follows: noise (1% of the maximum intensity) has been added to the modeled spectrum and the resulting luminescence intensity has been fitted once again. The fitted parameters are unchanged within less than 1 mev. 12

13 9) References 1. Spicer, W. E., Lindau, I., Skeath, P., Su, C. Y. & Chye, P. Unified Mechanism for Schottky-Barrier Formation and III-V Oxide Interface States. Phys. Rev. Lett. 44, (1980). 2. Look, D. C., Stutz, C. E. & Evans, K. R. Surface and interface free-carrier depletion in GaAs molecular beam epitaxial layers: Demonstration of high interface charge. Appl. Phys. Lett. 56, (1990). 3. Chia, A. C. E. & LaPierre, R. R. Analytical model of surface depletion in GaAs nanowires. J. Appl. Phys. 112, (2012). 4. Sturge, M. D. Optical Absorption of Gallium Arsenide between 0.6 and 2.75 ev. Phys. Rev. 127, (1962). 5. Katahara, J. K. & Hillhouse, H. W. Quasi-Fermi level splitting and sub-bandgap absorptivity from semiconductor photoluminescence. J. Appl. Phys. 116, (2014). 6. Szmyd, D. M., Porro, P., Majerfeld, A. & Lagomarsino, S. Heavily doped GaAs:Se. I. Photoluminescence determination of the electron effective mass. J. Appl. Phys. 68, (1990). 7. Lee, N.-Y. et al. Determination of conduction band tail and Fermi energy of heavily Si-doped GaAs by room-temperature photoluminescence. J. Appl. Phys. 78, (1995). 13

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