Long-Lived Photo-Response of Multi-Layer N-Doped Graphene-Based Films

New insights into the mechanism of the improved photo(electro)catalytic activity of graphene by heteroatom doping were explored by transient transmittance and reflectance spectroscopy of multi-layer N-doped graphene-based samples on a quartz substrate prepared by chitosan pyrolysis in the temperature range 900–1200 °C compared to an undoped graphene control. All samples had an expected photo-response: fast relaxation (within 1 ps) due to decreased plasmon damping and increased conductivity. However, the N-doped graphenes had an additional transient absorption signal of roughly 10 times lower intensity, with 10–50 ps formation time and the lifetime extending into the nanosecond domain. These photo-induced responses were recalculated as (complex) dielectric function changes and decomposed into Drude–Lorentz parameters to derive the origin of the opto(electronic) responses. Consequently, the long-lived responses were revealed to have different dielectric function spectra from those of the short-lived responses, which was ultimately attributed to electron trapping at doping centers. These trapped electrons are presumed to be responsible for the improved catalytic activity of multi-layer N-doped graphene-based films compared to that of multi-layer undoped graphene-based films.

sonicated in Miliq water and acetone for 15 minutes.Then, dried under N 2 flow and O 2plasma treated for 15 minutes before chitosan solution deposition.300 µL of filtered chitosan solution were spin coated at 6 000 r.p.m. during 1 minute.Samples pyrolysis was carried out under argon (Ar) atmosphere in a tubular furnace at 5 • C/min rate up to 900, 1000, 1100 and 1200 • C and the temperature held for 2 h.The multi-layer graphene-based films were then cooled down to room temperature under Ar flow.For comparison purposes, multi-layer undoped graphene-based samples were prepared by polystyrene sublimation at 900 • C under Ar atmosphere.
Raman Spectroscopy Raman spectrum was collected with a Horiba Jobin Yvon-Labram HR UV-Visible-NIR (200-1 600 nm) Raman Microscope Spectrometer, using a laser with the wavelength of 632 nm.The spectrum was collected from 10 scans at a resolution of 2 cm −1 .
XPS spectra were measured on a SPECS spectrometer equipped with a Phoibos 150 9MCD detector using a non-monochromatic X-ray source (Al and Mg) operating at 200 W.The samples were evacuated in the prechamber of the spectrometer at 1•10 −9 mbar.The measured intensity ratios of the components were obtained from the area of the corresponding peaks after nonlinear Shirley-type background subtraction and corrected by the transition function of the spectrometer.
X-Ray Photoelectron Spectroscopy All XPS spectra were recorded via a SPECS spectrometer (SPECS Surface Nano Analysis GmbH, Berlin, Germany) with a Phoibos 150 MCD-9 detector.The non-monochromatic X-Ray source (Al and Mg) was operated at 200 W. Before data acquisition, the XPS setup antechamber was evacuated at 10 −9 mbar.The work function was calibrated with Ag, Au, and Cu standards, hence a value of 4.2440 eV was obtained.The intensity ratios of all analyzed samples were obtained after nonlinear Shirleytype background subtraction and correction by the transition function of the spectrometer.
Atomic Force Microscopy (AFM) measurements were conducted in the contact mode in air to measure thickness and roughness at ambient temperature using a Veeco AFM apparatus.The films were scratched to determine the thickness.It should be noted that AFM were not measured in a clean room and, therefore, films on quartz substrates may contain dust that will be detectable by these techniques.
Steady State Spectroscopy.The steady state transmittance, T, of the samples were measured with a Shimadzu UV-3600 series spectrophotometer.The specular reflectance, R, of the samples were measured with a specular reflectance attachment (for 5 • incidence angle).The reflectance spectra are measured relative to ideal "100 %" reflecting mirror.We found that the supplied aluminium reference mirror has relatively high (more than 10 %) deviation from ideal reflectivity in the desired range of 200-1200 nm.Therefore, we used a quartz plate as the reference, for which the transmittance was measured in a standard way and we assumed that the reflectance is R = 1 − T .Thus corrected data were more reasonable, though the accuracy of reflectance measurements in the UV part (200-300 nm) was still poor.
The "real absorbance", A, was calculated from the specular reflectance, R, and transmittance, T , of the sample using equation Transient Absorption Spectroscopy.The transient absorption measurements of the samples were carried out using a laser pump-probe set-up.The fundamental laser pulses at repetition rate 1 kHz and pulse width 100 fs were generated at 800 nm by the Libra F system, Coherent Inc., which was coupled with an optical parametric amplifier (OPA) Topas C, Light Conversion Ltd.These laser pulses were used to produce the pump beam to excite the sample and the probe beam (white continuum) to monitor the spectra.The pump beam wavelength at 500 nm excitation was generated by channeling a portion of the fundamental laser to the OPA.The pump beam average power was set at 500 ± 50 µW (corresponding to the excitation density or roughly 0.1 mJ cm −2 ) for the multi-layer N-doped and undoped graphene-based film samples.
For the probe beam, a sapphire crystal was used to produce a continuum of white light The pump-probe instrument only had a single detection channel, hence, the TT and TR measurements were made consecutively.For these consecutive measurements, the TT and TR probe beams had to be realigned with the fibre optic cable connected to the detector.In addition, the measurements were carried in two wavelength ranges, with an accompanying change of the detector (Si or InGaAs for visible or NIR range, respectively).Despite this, similar experimental conditions (the excitation energy and the studied spot of the sample) were ensured for each measurement.
Independent of the measuring mode, TT or TR, the instrument recalculated the measured change in probe to the change of optical density △A, which are referred to as △A T or △A R , respectively.To analyse the data we used global exponential fit of both △A T (λ, t) and △A R (λ, t) simultaneously: where

S2 Sample Structure Characterization
The formation of multi-layer defective graphene-based films was confirmed by Raman spectroscopy as shown in Figure S2.
Further study of the chemical composition of the obtained films was carried out by X-ray Photoelectron Spectroscopy (XPS).The high resolution XPS C 1s, O 1s and N 1s spectra of the different samples is presented as Figure S3.All samples present similar components but the relative percentage of each one varies between them.
The C 1s peaks of all samples have been deconvoluted in well presented by a single Gaussian corresponding to sp 3 hybridization, and no sign of the sp 2 can be seen on the lower energy side of the band.It was reported that the ratio of sp 3 and sp 2 bands in graphite is roughly 1:9, 1 which could not be detected in our case.This  Finally, the N 1s peaks present three components assigned to pyridinic-N, quaternary-N and N-oxides.Table S1 summarises the percentage of each component in the different samples.
Alternatively, the C, N, and O content in each sample are also summarized in Table 1 (in the main text).The N content decreased with the pyrolysis temperature, while the C content increased.Conversely, the trend for the O content from the incomplete carbonization of the chitosan precursor did not show such a smooth transition, although there was an overall decrease from NGF900 to NGF1100.The C content in the different samples increases with the temperature from NGF900-NGF1100, while it remains approximately constant at 1200 • C. At the same time, the sp 2 component in the C 1s peaks of the samples also increases with the temperature.In contrast, the N content in the samples reduces with pyrolysis temperature.Pyridinic-N component decreases with temperature, whilst the N-oxides increases.The oxygen content fluctuates within a particular range in all samples.
The composition trend was reasonably smooth from NGF900-1100, but "broken" at NGF1200.Almost two times rise is observed for N-oxide peak, and essential drop for O − − C, from average 75% to 45% on the temperature increase from 1100 to 1200 • C. Also an increase Overall, the pyrolysis temperature promoted a decrease in the N content of the samples, increasing the graphitization degree, as reported before. 2 However, the O content fluctuated from lower to higher proportions with increased pyrolysis temperatures.
The as-prepared multi-layer graphene-based films roughness and thickness were investigated by Atomic Force Microscopy (AFM).Figure S4 shows AFM images of NGF900, NGF1000, NGF1100 and NGF1200 films which were scratched to determine their thicknesses.
Independent cross-section measurements (n = 6) on the acquired images of the NGF900, NGF1000, NGF1100 and NGF1200 samples reveal an average particle size of 29.3 ± 5.7, 20.5 ± 1.7, 30.3 ± 2.4 and 45.3 ± 3.5 nm, respectively.The measured roughness mean square (R q ) of all samples is approximately 1.5 nm, indicating very flat and homogeneous surface films.

S3.1 Steady State Spectra Modeling
For a multi-layer graphene-based film or any other semitransparent film, the transmittance in a single passage of light would be exp(−αd), where α is the absorption coefficient of the material and d is the film thickness.However, part of the light will be reflected from the film surface as the light enters the sample, and part of the light is reflected at the other side of the film, which is the substrate interface in most cases.Furthermore, the reflection will result in the light interference, which affects the measured intensities of the transmitted and reflected light.The reflectance from the surface or at the interface depends on refractive index, which need to be taken into account to model the transmittance and reflectance spectra.
Typically, the modeling is done using transfer matrix method (TMM). 3,4The method allows to calculate the transmittance and reflectance spectra for know film thickness d, and the material and k is the extinction coefficient related to the absorption coefficient as α = 2π λ k where λ is the wavelength.In our case the film is deposited on a quartz (fused silica) substrate for which the refractive index n s also must be known.We used Sellmeier dispersion equation with coefficients originally reported by Melitson, 5 but slightly adjusted to reproduce better the measured transmittance and reflectance spectra of our substrates.The transmittance, T , and reflectance, R, coefficient of a thin film with (complex) refractive index ñ deposited on a transparent substrate were calculated using Python library kindly provided by Steve Byrnes and called tmm. 4 We assumed a homogeneous photo-induced change of both n and k when modeling photo-responses of the samples.This assumption is reasonable as our film thickness (typically 20-60 nm, see Table S2 below) are much smaller than the wavelength.
Although the complex refractive index is used to calculate optical properties of media, the physical properties are better presented by complex dielectric function ε where ε 1 = ℜ(ε) and ε 2 = ℑ(ε).In particular, dielectric properties of graphene can be approximated reasonably well by the so-called Drude-Lorentz (D-L) model [6][7][8] ε where E = hν is the photon energy (for measurements in the wavelength domain, hν = hc/λ), ε ∞ is the high frequency dielectric constant, A, E L and Γ L are the strength, resonance The relation between the complex refractive index and dielectric function is ñ = √ ε.
Therefore, ñ is known if ε is known, and the measurable transmittance (T) and reflectance (R) spectra of the multi-layer graphene-based film samples can be calculated for given (complex) dielectric function using TMM approach.In other words, the model T and R spectra can be calculated for given film thickness, d, and six It can be noted that for each pair of T and R spectra, seven parameters are required to fit the measured spectra.However, at least some of the parameters can be expected to have the same values for different samples, and for a series of reasonably similar graphene compositions and low doping concentrations, the D-L parameters can be expected to be the same which leaves the thickness d to be the only parameter varying from the sample to sample.We measure T and R for each sample in the series and fit the data globally to obtain a set of D-L parameters common for all samples and thicknesses for each sample.
There were two samples for each of the four pyrolysis temperatures.The difference between the samples pyrolyzed at the same temperature was minor.
The measured T and R spectra were fitted to estimate the sample thicknesses and D-L parameters.The in-house developed fit program (in Python fit TR.py, see Section S5) uses tmm, numpy, scipy and lmfit libraries for calculations. 4,9,10The program works by calculating the few loaded spectra into dielectric function spectra ε(λ) for each sample, and subsequently converting them to complex refractive index spectra ñ(λ).Then the TMM method is utilized to calculate model T and R spectra for each sample, and calculates the standard deviation of the measured data from the model, which is used as internal parameter for the data fitting (in lmfit library).
Since the quality of the T and R spectra was different, a weight factor was introduced when summing up residuals from different type of spectra.The reported results were obtained with weight factors 1 and 0.1 applied to T and R spectra, which accounts for the fact that the T spectra were roughly 10 time more accurate.This discrepancy was attributed to the low accuracy of the reflectance measurements, at shorter wavelengths due to the reference mirror, as explained in Section S1.A so-called global fitting was utilized which means the spectra of the whole series of samples, NGF900, NGF1000, NGF1100 and NGF1200, were Presumably, pyrolysis results in larger variation of graphene sheets sizes and arrangements, which leads to some variation in the Lorentz band positions.
For the multi-layer graphene-based film reference used in this work (solid lines), the peak of the imaginary part of the dielectric function is at approx.4.3 eV at the lower limit (≈288 nm) which is within the range of previously reported values, 4-4.6 eV, [11][12][13] and also in agreement with the CVD graphene spectra shown in Figure S6.There is a report suggesting that the peak of real part of the dielectric function should be at approx. 3 eV (≈413 nm) 11 which is in agreement with the spectra shown in Figure S6.Dielectric Function (ε) Figure S6: Comparison of the real (blue) and imaginary (red) part of the dielectric function obtained for the sample series in this work (solid lines) and reported for 20 layer graphene prepared by chemical vapor deposition method (dashed lines). 6

S3.2 Film Thickness Modeling
The film thicknesses estimated, by AFM and optical measurements (T and R) in Table S2 are similar with minor differences due to the acquisition method; AFM revealed the "local" thickness of a scratch, while optical measurements deliver an average thickness from an area of a few squared millimeters.For example, the AFM thickness of NGF1000 was approx.
21 nm, while the optically estimated thickness was approx.31 nm.However, the trend in the sample thickness variation with the temperature is the same for both estimation methods.
The optically estimated thicknesses will be used for transient absorption data fittings since it relies on the same optical properties of the samples as used in the following analysis.
Table S2: Film thicknesses (in nm) obtained from the spectra global fit with D-L fit parameters listed in Table 2. Temperature, However, the obtained △T m and △R m are not so informative because any changes in the real or imaginary part of ñ (or ε, respectively), resulted in changes for both △T m and △R m .
Thus, it was more informative to instead monitor the changes in the real and imaginary part of the dielectric function.Assuming a small photo-induced change of dielectric function, one could rely on the linear approximation: where are the partial derivatives of T and R over ε 1 and ε 2 , respectively.The derivatives can be evaluated numerically for known Drude-Lorentz model parameters and film thickness (d) which are obtained from the steady state transmittance and reflectance spectra analysis.Eq. (S5) is a system of two linear equations and its solution is: At this step, the experimental data, △A T (λ, t) and △A R (λ, t), could be recalculated to △ε 1 (λ, t) and △ε 2 (λ, t) for known T (ε) and R(ε).There would be no fitting involved and from this point of view we could derive three equivalent presentations of the experimental results: (△A T , △A R ) ⇔ (△T, △R) ⇔ (△ε 1 , △ε 2 ).However, in practice, the spectra △A T (λ) and △A R (λ) at characteristic delay times, or their decay associated spectra (DAS) from primary fittings, were recalculated to the spectra of △ε 1 (λ) and △ε 2 (λ) (see the main text for details).
Finally, to better understand the phenomena behind the photo-induced change of the dielectric function, the spectra of △ε 1 (λ) and △ε 2 (λ) were fitted to the changes in D-L parameters: △ε ∞ , △A L , △E L , △Γ L , △E D and △Γ D using eq.(S3), namely where p is the set (vector , respectively, and ε() is calculated according to eq. ( S3).This was the final step of the TT and TR data treatment.
In conclusion, the key steps for the collection and analysis of the spectroscopy data and schematically outlined in Figure 4, are: 1. measure steady state transmittance, T , and reflectance, R, spectra of a series of samples; 2. fit the spectra to the D-L model, eq. ( S3) and using TMM approach to account for the sample thickness; this results in a set of D-L parameters (common to all the samples) and thickness evaluations (for each sample), ε ∞ , A, E L , Γ L , E D , Γ D and d, respectively; 3. conduct transient absorption measurements in transmittance and reflectance modes, which deliver 2D arrays of spectroscopy data, △A T (λ, t) and △A R (λ, t), respectively; 4. fit the data to determine characteristic time constants and characteristic spectra corresponding to specific intermediate state; this results in pairs of spectra, △A T (λ) and △A R (λ), to be analysed further; 5. recalculate the △A T (λ) and △A R (λ) spectra to △ε(λ) spectra using previously determined D-L parameters and thicknesses (step 2) to evaluate

Wavelength Dependence
The excitation density, excitation wavelength and monitoring wavelength dependencies of the undoped GTF and doped NGF1100 films were explored.The excitation density dependence measurements were made at 500 nm excitation to monitor the decays of the multi-layer graphene-based films at 700 nm in the reflectance mode.The reflectance mode was used to ensure clear measurement of the "second wave".From these decays, the intensities of the "first wave" (at approx.0.1 ps) and the "second wave" (at approx.40 ps) are plotted at three different excitation density dependencies of 0.05, 0.1 and 0.2 mJ/cm 2 .The resulting excitation density dependencies are shown in Figure S14.
The NGF1100 film has both the "first wave" and "second wave" with linear dependencies as a function of power.However, it should be noted that the GTF film has only the "first wave" with a linear dependence while the "second wave" was absent.The "second wave" represented for GTF was measured at the same time scale as the "second wave" of NGF1100, to highlight the presence of the "second wave" in the NGF series.The excitation wavelength dependence measurements were made at 0.1 mJ/cm 2 excitation density to monitor the decays of the multi-layer graphene-based films at 700 nm.From these decays, the intensities of the "first wave" (at approx.0.1 ps) and the "second wave" (at approx.40 ps) were plotted at three different wavelengths (energies) of 320 (3.875), 500 (2.48) and 640 (1.94) nm (eV).The resulting excitation wavelength dependencies are shown in Figure S15.
The excitation wavelength dependencies did not show any significant changes to the photophysics of the undoped GTF and the N-doped NGF1100 at different excitation wavelengths (energies).GTF without a "second wave" within noise levels while the NGF1000 has a prominent "second wave".The differences in the absorbance intensities were mainly due to the differences in amount of photons absorbed by carriers at different excitation wavelengths (energies).Therefore no essential excitation wavelength (energy) dependence was observed for all samples.

S4.4 Comparison of the Transient Absorption Response
All doped samples were measured in reasonably same conditions (same excitation densities) which allows "direct" comparison of the responses spectra and spectra amplitudes.The spectra of the "first wave" (fitted results) are presented in Figure S17.The responses of samples pyrolyzed at 900, 1000, and 1100 • C were rather similar to each other.However, the "first wave" response spectrum of the sample pyrolyzed at 1200 • C differs significantly from that of the samples pyrolyzed at lower temperatures.Also the "second wave" spectrum of the sample pyrolyzed at 1200 • C differs significantly from that of the samples pyrolyzed at lower temperature as will be discussed later.
Next, the △A T (λ) and △A R (λ) spectra were recalculated to △ε(λ) (complex) spectrum, as described above, eq.(S6) and step 5.The calculated changes in dielectric function corresponding to the "first wave" are presented in Figure 5 of the main text.
The "second wave" responses (△A T and △A R ) are presented in Figure S18.The responses are more complex but also show a trend.The calculated changes in the dielectric W a v e l e n g t h ( n m ) The TA spectra associated with the "second wave" and obtained in transmittance (whole symbol) and reflectance (split symbol) modes, △A T and △A T , respectively.The pyrolysis temperatures are 900 (blue square), 1000 (green diamond), 1100 (brown triangle) and 1200 • C (orange triangle).

S28
The decay time constant for the "first wave" (in the mono-exponential approximation) is 100-150 fs for all samples.The rise time constant for the "second wave" is 20-30 ps for all the samples (no temperature dependence).The lifetime of the "second wave" increases from 3 to roughly 30 ns as the pyrolysis temperature increases.With the exception of 1200 • C, there is a trend for the "second wave" with the real and imaginary parts of the dielectric function (Figure S19) which is reversed compared to the "first wave", a higher pyrolysis temperature leads to stronger response.
in the near-infrared (NIR) and visible ranges.The central detection wavelength in the NIR and visible ranges were 960 and 600 nm, respectively.The probe beam was passed through a delay line for the differential response in time.The transient absorption responses of the probe beam were measured using an ExciPro TA spectrometer (CDP, Inc.).The spectrometer was coupled with an InGaAs diode array to detect NIR wavelengths and a Si charge coupled device (CCD) array to detect visible range wavelengths.For the transient absorption measurements, both the transient transmittance (TT) and transient reflectance (TR) modes were explored, as schematically presented in FigureS1.All the beams (pump, probe transmitted and reflected) propagated to/from the sample surface at roughly normal incidence, with deviation from the normal α ≤ 5 degrees, therefore all the modeling and calculations were carried out assuming normal incidence.

Figure S1 :
Figure S1: Schematic presentation of the TT and TR measurements with the transient absorption spectroscopy setup.

4 different components attributed to sp 2 C
, C−O/C−N, C − − O and O−C − − O bonds.It can be noted that the C 1s band is

Figure S3 :
Figure S3: XPS peaks of the NGF900 (a-c), NGF1000 (d-f), NGF1100 (g-i) and NGF1200 (j-l) samples showing their experimental C 1s, O 1s and N 1s compositions and the best deconvolution to individual components.

Figure S4 :
Figure S4: AFM images of the NGF900 (a), NGF1000 (b), NGF1100 (c) and NGF1200 (d) films.Cross-section measurements of the different samples (e-f) are marked on blue, red and green lines with coincident colors.
energy and the width (damping) of the Lorentz band due to π → π * transition, and E D and Γ D are the energy and damping of the Drude component, which describes dielectric properties of the free electrons or electron plasma.This presents the optical properties of multi-layer graphene-based films as superposition of three factors, (i) the Drude component due to free carriers or plasmon-type effect, (ii) the Lorentz component due to electronic transitions (π → π * transition) with transition energy corresponding to the UV range, and (iii) a contribution of high frequency transitions (above the Lorentz band) which are presented by ε ∞ .
loaded and fitted using different combination of global (common to all samples) and local (individual to each sample) parameters.The fit with common set of D-L parameters delivered the most stable and consistent results with negligible loss of fit accuracy for individual spectra, and this result is reported in the steady state spectra section of the main text.The model spectra of the real and imaginary parts of the dielectric function, with their D-L components are shown in FigureS5.The dielectric function spectra of the samples in this paper compared to those reported for pyrolytic graphene deposited by chemical vapor deposition (CVD) method 6 are presented in FigureS6.The difference in the amplitudes may be attributed to a somewhat different density of the films, or an average distance between graphene sheets.Aslo, the CVD films has somewhat narrower Lorentz band (at 288 nm).

Figure S5 :
Figure S5: Dielectric function of the NGF900-1200 samples obtained from the global fit of the T and R spectra.The solid line represents the total real (blue) and imaginary (red) parts, while the dashed and dotted lines represent the Drude, ε D , (including ε ∞ ) and Lorentz, ε L , components, respectively.
Standard pump-probe measurements were carried out by detecting both transmitted and reflected light, which will be referred to as transient transmittance (TT) and transient reflectance (TR), respectively.In both cases, the relative change of the probe light intensity was measured and recalculated to "transient absorbance" signals, △A T and △A R , respec-tively.The transmittance and reflectance changes obtained from the measured data are:

2 Figure S8 :Figure S9 :Figure S10 :Figure 3 Figure S11 :Figure S12 :
Figure S8: TT and TR decay profiles of the sample pyrolyzed at 1000 • C monitored at 650 nm.The time scale is logarithmic.
Figure S13: DAS resulting from the global fit of the TT and TR spectra for the NGF1200 sample.The transmittance and reflectance DAS are indicated by filled symbols and open symbols respectively.Plots (a) and (b) represent the same data but in plot (b) the scale is magnified to highlight the second wave.

2 R s p e c t r a f i r s t w a v e R s p e c t r a s e c o n d w a v e A b s o r b a n cFigure S16 :
Figure S15: The excitation wavelength (energy) dependencies of (a) GTF (b) NGF1100 at 0.1 mJ/cm 2 excitation density, monitored at 700 nm.

Figure S19 :
Figure S19:The spectra of real (blue) and imaginary part (red) of the dielectric function corresponding to the "second wave".The pyrolysis temperatures are 900, 1000, 1100 and 1200 • C and the darker color corresponds to lower temperature.
t) are the transient absorption (in transmittance, △A T , or reflectance,

Table S1 :
Summary of the percentages of the components in C 1s, O 1s and N 1s peaks of the different samples.