Impurity Sub-Band in Heavily Cu-Doped InAs Nanocrystal Quantum

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Impurity Sub-Band in Heavily Cu Doped InAs Nanocrystal Quantum Dots Detected by Ultrafast Transient Absorption Chunfan Yang, Adam Faust, Yorai Amit, Itay Gdor, Uri Banin, and Sanford Ruhman J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b10682 • Publication Date (Web): 31 Dec 2015 Downloaded from http://pubs.acs.org on January 2, 2016

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The Journal of Physical Chemistry

Impurity Sub-Band in Heavily Cu Doped InAs Nanocrystal Quantum Dots Detected by Ultrafast Transient Absorption Chunfan Yang1, Adam Faust2, Yorai Amit2, Itay Gdor1, Uri Banin*,2, and Sanford Ruhman*,1 1. The Institute of chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel 2. The institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

ABSTRACT

The effect of Cu impurities on the absorption cross section, the rate of hot exction thermalization, and on exciton recombination processes in InAs quantum dots was studied by femtosecond transient absorption. Our findings reveal dynamic spectral effects of an emergent impurity sub-band near the bottom of the conduction band. Previously hypothesized to explain static photo-physical properties of this system, its presence is shown to shorten hot carrier relaxation. Partial redistribution of inter-band oscillator strength to sub-band levels reduces the band edge bleach per exciton progressively with the degree of doping, even though the total linear absorption cross section at the band edge remains unchanged. In contrast, no doping effects were detected on absorption cross sections high in the conduction band, as expected due to the relatively high density of sates of the undoped QDs. KEYWORDS: quantum dots, doping, ultrafast spectroscopy, density of states

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ACS Paragon Plus Environment


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Introduction Electronic impurity doping by aliovalent impurities is the fundamental approach for modifying bulk semiconductor properties, which has enabled their widespread application in micro- and opto-electronic devices.1 However, in quantum confined semiconductor nanocrystals the use of aliovalent doping to control electrical properties is still in its early stage of development. 2-10 This is due to difficulties in synthesis, where the challenge is to incorporate a moderate and controlled number of impurity atoms in defined locations in the nanocrystals without their being expelled to the surface. Further challenges lay in determining the number of dopant atoms and their spatial distribution in such impurity doped nanocrystals. Successful incorporation of such aliovalent impurities inside semiconductor nanocrystals allows us to address interesting fundamental questions concerning the doping effects in strongly quantum confined systems. It also promises to provide further control of nanocrystals properties towards their application in diverse optoelectronic and solar energy harvesting scenarios. For studying how doping may affect the electronic properties of semiconductor QDs we study herein heavily Cu doped InAs quantum dots (QDs),2,11 by ultrafast transient absorption (TA). The doped QDs are prepared in a room-temperature diffusion-based reaction, which involves adding of the impurities to a solution of pre-synthesized QDs. Using this method, both the crystal structure and the size of the QDs are maintained, which eliminates any size dependent effects on the electronic structure of the doped-QDs. A direct meaningful comparison of the electronic properties as a function of the impurity concentration is thus made possible. InAs QDs were also previously doped by Cd impurities during the synthesis step itself, and studied in terms of their transport characteristics.7 Post-synthesis doping, similar to the approach used here, was also 2


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reported for CdSe nanocrystals doped by Ag,12,13 where an interesting transition between n to ptype behavior was observed for varying dopant concentrations. Importantly, doping by impurity atoms differs from “surface doping” performed via attaching electron donating species that donate excess charge to the QD.14,15 This latter approach usually does not significantly modify the electronic structure of the QD itself, while it adds free carriers as can be seen by photobleaching of the band-gap transition accompanied by conductance enhancement related to presence of excess electrons. Similar effects of charging of the QDs were also achieved elegantly via electrochemical means16 or by optical irradiation.17 Introduction of aliovalent impurities into InAs QDs led to the formation of heavily doped nanocrystals.2 Heavy doping is loosely defined in bulk semiconductors as the regime where impurities interact with each other. This occurs typically for doping levels exceeding 10-19 cm-3, a nominal impurity concentration easily achieved already for several different impurities in strongly confined semiconductor nanocrystals only a few nanometers in diameter. At this level of impurities, the average distance between them is on the order of the respective carrier Bohr radius, leading to interactions between them. Accordingly, in heavily doped bulk semiconductors,18 an impurity band emerges close to the respective band edge (conduction band for n-type doping, Valence band for p-type doping), typically situated asymmetrically into the band. Through the occupation of the levels by excess carriers, blue shift of the absorption may result due to the Moss-Burstein shift. An additional effect of heavy doping in bulk is band tailing, associated with disorder that is induced in the crystal, and typically leads to red shift of the band gap.

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The heavy doping of InAs QDs with Cu atoms was previously reported to yield n-type QDs.2,11 Thorough chemical and structural characterization using transmission electron microscopy (TEM) methods, analytical study, powder Xray diffraction, X-ray absorption spectroscopy (XAS) methods and DFT calculations were performed on this system. These revealed the location of the Cu impurities within the InAs QDs. It was found that for a wide range of concentrations, including all the doping levels studied in this work, the relatively smaller Cu atoms reside in hexagonal interstitial sites and have a partially positive charge state, in agreement with n-type donors in semiconductors. The hexagonal interstitial sites were energitcally favoured over other possible positions including surface sites, indium substitution, and tetrahedral interstitial sites. Even at the high concentrations of Cu, the InAs lattice remained essentially intact, indicating that effectively the crystal serves as a “sponge” able to host large numbers of Cu interstitial atoms. The heavy doping regime in QDs was found to affect the density of states (DOS), the optical properties, and the Fermi energy. This was observed through shifts in the optical absorption spectra and via scanning-tunneling microscopy measurements. This was also supported by theoretical calculations showing the changes in the electronic band structure and the formation of an impurity sub-band for Cu doped InAs QDs, emerging near the location of the lowest confined conduction band level in analogy to the behavior of heavily doped bulk semiconductors. However, there is still a gap of understanding concerning the interactions between the charge carriers of the impurity with those of the host NC under strong quantum confinement, as well as the electronic structure and the impurity sub-band as exerted by heavily doped semiconductor QDs. 4


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Here femtosecond pump hyperspectral probe methods are employed to investigate the electronic structure and dynamics of Cu-doped InAs QDs. Ultrafast pump-probe has been extensively applied to measure absorption cross sections and carrier dynamics in colloidal quantum dots.19-28 Hence it is a powerful method to address the photophysics of doped QDs, and in particular to study how the doping affects QD absorption, hot exciton cooling, and carrier recombination. The results demonstrate that doping does not significantly affect the total linear absorption spectra of the crystals, but strongly enhances the rate of hot carrier cooling to the band edge, and reduces the resulting state filling induced 1S(e)1S(h) bleach (abbreviated as 1S hereafter) per exciton. The findings are discussed in terms of doping induced redistribution of the band gap transition dipole strength to states arising from an impurity sub-band which was previously introduced to rationalize other doping effects in similar samples. Over the doping range where it was quantifiable, doping does not change the rate of Auger recombination, consistent with the lack of excess carriers in a neutral doped system. Experimental Methods InAs QDs synthesis. Colloidal InAs QDs were synthesized following a well-established method.2,29 Precursor solutions containing mixtures of (TMS)3As (tris(trimethylsilyl)arsine) and InCl3 (indium(III) chloride) in TOP (trioctylphosphine) were prepared and kept under inert conditions throughout. Distilled TOP was evacuated for ∼30 min and heated to 300 °C. The nucleation solution (molar ratio 2:1 In:As) was rapidly injected in to the distilled TOP and the temperature was decreased to 260 °C. To allow particle growth, controlled volumes of a growth solution (1.2:1 In:As) were gradually introduced to the reaction vessel, until the desired size was 5



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reached. Narrow size distributions were achieved through size selective precipitation performed under inert conditions by adding methanol to the QDs dispersion and filtering the solution through a 0.2 µm polyamide membrane filter (Whatman). The precipitant was subsequently dissolved in anhydrous-toluene (Sigma) and kept under constant inert conditions throughout. Cu doping of InAs QDs. The doping of pre-synthesized InAs QDs was achieved by a room temperature diffusion based reaction as reported previously2. The impurity solution contained copper chloride (CuCl2), didodecyldimethylammonium bromide (DDAB), and dodecylamine (DDA) dissolved in anhydrous-toluene (Sigma). Calculated amounts of the impurity solution were added to InAs QDs suspensions. To terminate the doping process, methanol was added to the reaction solution and the doped QDs were precipitated, separating them form any Cu ions left in the solution. For the spectroscopic study, the doped QDs were dissolved in anhydrous-toluene. To estimate the number of Cu atoms/QD ICP-MS measurements were performed on 5 nm InAs QDs doped with various levels of Cu atoms. The Cu atoms/QD values reported above are extracted based on the resulting calibration curve (see S1). The nominal doping yield was found to be approximately 25% of the reported solution ratio. Experiment setup. All samples were handled in oxygen-free environment and irradiated in air tight 1 mm path length optical glass cuvettes at room temperature. The 30 fs amplified output from a homemade multipass titanium sapphire system served to generate a white light continuum probe by focusing in 3 mm of sapphire. The continuum pulses were collimated and refocused into the sample using reflective optics. Another portion of the amplified fundamental was used to generate pump pulses, either directly at ∼800 nm or by pumping a TOPAS (Light Conversion) to 6


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produce ∼40 fs pump pulses centered at 640 nm. After the sample, the probe pulses were collected into an InGaAs PD array spectrometer (BTC262E, BWTek) alternating with and without sample pumping. Subtraction of these produced the time-dependent difference spectra displayed below, which have been corrected for the measured probe group delay. The experiments were run on static samples after test runs on translating cells were shown to be identical to stationary ones. Signal decay kinetics, particularly at low pump fluences, provide additional indications that no photo-charging effects were present.

Results Cu doping of InAs quantum dots. InAs QDs with a diameter of 5 nm were synthesized via a well-established wet chemical synthesis. 29 The pre-synthesized QDs were then doped with Cu atoms in solution, at room temperature, following the previously reported diffusion based reaction. Breifely, the QDs were reacted with calculated volumes of a solution containing the appropriate surface ligands and the CuCl2 metal salt (see methods for further details). The control, undoped sample (0 Cu atoms/QD) underwent the same chemical treatment by reacting the pre-synthesized QDs with a solution containing only the surface ligands. Figure 1a presents the linear absorption spectra for InAs QDs with various Cu doping levels, ranging between 0 and 2000 Cu atoms/QD as calculated in the reaction solution. As can be seen, neither the shape nor the overall oscillator strength changes significantly. Inductively coupled 7



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plasma (ICP) measurements were used to correlate between the above solution values and the number of Cu atoms within the QD (Figure S1 in the SIO).2,11 Close investigation reveals a slight red-shift of the first exciton (~5meV) for Cu doping levels up to 125 Cu atoms/QD; this is related to the initial appearance of doped states situated slightly below the QD conduction band. As the doping level increases, the red shift changes over to an increasing blue-shift, reaching values of ~30meV for 500 Cu atoms/QD. This behavior was ascribed to an evolution of an impurity band that is partially filled by electrons donated by the impurity Cu atoms through the Moss-Burstin shift,

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and theoretical analysis was able to show such behavior for heavily Cu

doped InAs NCs.2 TEM images and size histograms (Figure 1c,d) of undoped and Cu doped InAs QDs reveal that no change in size or morphology is induced by doping. The mean diameter before and after doping was found to be 4.9 nm with a similar standard deviation of about 0.5 nm. This stands to show that the observed optical shifts result from doping and not size dependent effect, as already established in previous works.2 In the entire regime of Cu levels up to the highest values studied herein, Cu atoms reside in hexagonal interstitial sites whie maintaining the InAs lattice intact as established in our earlier reports. As Cu atoms populate interstitial sites, they act as n-type donors in the InAs QD. Further insight on the effects of such heavy doping, was gained via the ultrafast transient absorption study.

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Figure 1. (a) Absorption spectra for 5 nm InAs QDs with various Cu doping levels. The Cu values indicated in the graph correspond to the calculated number of Cu atoms/QD in the reaction solution. Spectra are vertically shifted for clarity of presentation. (b) Energy shift of the first exciton peak upon doping, as a function of the actual number of Cu atoms/QD based on ICP measurements (see S1). A gradual change from red to blue shift is revealed, consistent with previous studies;2,11 color coding matches that in (a). (c) and (d) TEM images of InAs QD, udoped and ~500 Cu atoms/QD respectively, revealing no significant change in size or morphology of the QDs upon doping. Scale bars are 50 nm. Insets present normalized size distribution histograms for each sample.

Ultrafast transient absorption spectra. Transient difference absorption spectra (TA) at a series of probe delays are shown in Figure 2 for samples of varying degrees of doping. The central pump pulse wavelength is 640 nm. Transient signals at short delays in the upper panels consist of a rapidly rising broad negative feature centered at 1080 nm which is assigned predominantly to 1S bleach. As in TA data from 9



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QD of other materials, excitation above the band gap also induces a concomitantly rising absorption to the red of this bleach,30,31 which decays on a picosecond time-scale due to exciton cooling, leaving the strong 1S bleach as the main residual spectral change. Pump photon flux is controlled in these experiments to deposit an average number of excitons /QD at the front surface of the sample (η0) of ~1.5. Accordingly the lower panels which follow spectral evolution at extended delays show a gradual decay of the band edge bleach by ~30% over tens of picoseconds assigned to Auger recombination of multi-excitons generated by multi-photon absorption due to the non-negligible η0. After about 50 ps, there is still a slow rate of bleach recovery which reflects radiative and non-radiative single exction decay. When pumped at 640 nm, the excitons formed in the QDs have more than a band gap of excess energy, generating electrons and holes high up within the first conduction and valence bands respectively. During the descent of these hot carriers to the band edge the amplitude of the 1S bleach rapidly increases, with kinetics reflecting the cooling rate. At about 2 ps, the bleach amplitudes reach their maximum values. The most noticeable doping effect on the TA spectra pertains to the 1S bleach amplitude which is systematically reduced with increasing Cu doping. As shown in Figure 2 the maximum bleach of undoped QDs is about 4 times stronger than that for 500 Cu atoms /QD though the number of photons absorbed is similar. It is note-worthy that this reduction in amplitude cannot be assigned to doping induced band broadening as the 1S bleach signals after exciton cooling display similar bandwidths (Figure S2 in the supporting information on-line).

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Figure 2. Transient spectra at different time delays after excitation at 640 nm in different doped InAs QDs. Different time delays ranges ,0-2 ps , 1.5-200 ps are presented above and below respectively, with a column for each QDs. Pump photon fluxes are controlled to deposit similar average excitons /QDs at the front surface for all samples (η0~1.5).

In order to test for doping effects on exciton cooling rates, the delayed rise at the 1S bleach peak (1080 nm) is fit to an exponential build up followed by a slow exponential recovery. The related data and the fits, along with the associated cooling rates, are presented in Figure 3(a) and 3(b), respectively. The apparent time constant of hot exciton cooling is found to depend on the doping level, changing monotonically by a factor of nearly three going from the un-doped sample (~0.78ps) to that doped with 500 Cu atoms /QD (~0.3ps). This shortening of the cooling rates is the second strong effect of doping observed by the TA measurements. Note that at all doping levels the rise in the BE bleach is temporally separable from the ensuing decay. The

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possibility that processes other than phonon scattering contributes to the rates presented in Figure 3 will be addressed in the section on doping effect on the hot exciton cooling.

b) 0.8

0.0 undoped 25 Cu/QD 60 Cu/QD 125 Cu/QD 250 Cu/QD 500 Cu/QD

-0.2 -0.4

Time constant / ps

a)

Normalized ∆OD

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-0.6

0.6

0.4

-0.8 -1.0 0.2

0

1

2

3

4

time / ps

0

250

500

Cu atoms /QD

Figure 3. (a) Buildup dynamics of the 1S bleach signal. The solid lines are exponential fits. (b) The cooling time constants of hot excitons extracted from (a). A clear shortening of the cooling time upon increased doping level is associated to increased density of states near the bottom of the conduction band.

To further investigate doping effects on exciton dynamics in InAs QDs, recombination kinetics of single and multiple excitons were also examined by analyzing data in the range of delays shown in the lower panels of Figure 2 for different pump photon densities. For this purpose pumping was conducted at 800 nm, closer to the band gap, where reasonable signal to noise ratio in the 1S bleach is obtainable with a sample of lower OD at λPUMP. This allows more 12


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uniform pump intensities along the optical path, and generation of a significant fraction of multiple excitons without prohibitive front surface pump intensities which can lead to sample degradation. Furthermore the recovery of the excitons at the band edge is easier to analyze when free of convolution with the effects of extensive and therefore prolonged exciton cooling.

125 Cu / QD

undoped

500 Cu / QD

∆OD [a.u.]

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η= 0.2 η= 0.4 η= 0.8 0

60

120

0

60

120

0

60

120

Time (ps) Figure 4. Normalized decay of the exciton bleach for un-doped, 125, and 500 Cu atoms/QD following 800 nm pumping at various photon fluxes. The curves presented are the result of averaging the signal around the central wavelength of the 1S bleach.

Results of these experiments are depicted in Figure 4. Presented are integrated bleach intensities over a wavelength range of 60 nm around the peak at 1080 nm for various pump

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fluences which are designated in units of for three doping levels. For un-doped and lightlydoped samples at low photon flux, decay of the 1S band bleach consists almost exclusively of a slow decay which extends far beyond the 180 ps delay shown. As the photon flux increases and approaches unity, multiexcitons are generated by consecutive multiple photon absorption with significant probability. Under these excitation conditions the bi-excitons in undoped or mildly doped QDs decay exponentially with a ~15 ps decay time to single excitons, and then decay onward with similar dynamics to those observed at low fluence. This time scale is typical for Auger recombination of bi-excitons in these QD.19,32 At doping levels above 125 Cu atoms /QD a very rapid additional decay component emerges which is not related to multi-excitons, and is present even at very low pump fluence. As shown in Figure 4, the amplitude of this rapid decay in the band edge bleach rises significantly with the degree of doping. Using a fitting procedure including a third decay constant, this fast component can be reasonably characterized by a ~3 ps exponential process. The presence of this component limits the precision with which we can determine the timescale of Auger recombination, and the error associated with this estimate rises steeply with the degree of doping. Only in the case of lightly doped samples is this timescale reliably extractable, and found to be identical within error to that in the untreated QDs. Discussion A) Doping effects on the absorption cross section. The absorption cross section (σ(λ)) is a very important optical parameter which connects sample optical density (OD) with QD concentration. It in turn determines the average number of 14


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photons absorbed per QD at a given flux which is crucial for conducting quantitative photophysical experiments.33 A related parameter from which the degeneracy of band edge electron and hole states can be deduced is the band edge bleach per exciton ∆σbg; 1 ∕ = 1⁄ where represents the gain threshold or the integer number of band edge excitons which induces full transparency of the 1S transition. The gain threshold of undoped InAs QDs like those of CdSe is reported to be two.34 In PbSe QDs it has been reported to be four,35 however, recent three pulse ultrafast experiments on PbSe QDs questions the latter assertion,30 but to date no significant deviations have been reported for in InAs nanocrystals. Aided with these definitions, the effects of doping on σ(λ) and can be quantified. Absorption spectra collected in situ during doping provide a first indication concerning doping effects on σ(λ). Aside from the mild spectral shifts reported in Figure 1, and the induction of slight tailing of absorption to the red of the band edge, copper doping does little to change the steady state optical density or observed spectrum of the sample either near the band edge or higher up in photon energy. Since the particle concentartion is unchanged, it follows that doping does not significantly alter the particle absorption cross sections in either regime. Surprisingly, however, doping progressively reduces 1S bleach signals following photoexcitation both at the band edge and significantly above it. An alternative method is thus required for verifying conservation of in the doped samples which does not rely upon equation 1. This can be achieved by measuring saturation curves36,37 of 15



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the band edge bleach after carrier cooling and Auger recombination as a function of pump intensity high above the band edge (λpump = 640 nm). At low pump intensities multi-photon absorption is negligible, and the pump fluence and ∆ODbg are related through the equation: 2 2.303 ∗ Δ = − = 1 − 10

!"#!

where J0 is the pump photon density at the front surface of the sample, as defined above, and $%&$ is the OD of the sample at the pump wavelength, 640 nm in our case. This equation assumes that all excitations result in band edge excitons following the brief stage of carrier cooling. As intensity increases, the number density of absorbed photons continues to rise linearly with fluence since '()& is effectively impervious to existing excitations. The occurrence of multi-photon absorption however becomes more and more probable with higher pump fluence. Since Auger recombination rapidly reduces multi- to mono-excitons, the 1S bleach for t ≥ 50 ps is sub-linear in pump fluence, and saturates asymptotically once all crystals have absorbed at least one photon. The profile of this saturation with pump fluence is an independent measure of $%&$ . Modeling the residual 1S bleach after multi-exciton recombination, ignoring other exciton decay processes, requires integration in optically thick samples such as those employed here. Using Poisson statistics for multiple photon absorption and considering the exponential decay of pump fluence along the excitation path, the residual bleach is given by: 38

3 =

1

,-

$%&$

1 − + , * / ; = $%&$

,.

16


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where and ∞ are the average number of absorbed photons per QD in the front and back faces of the sample respectively. Since appears as a constant pre-factor, the normalized saturation curve 1 / ∞4 is only a function of $%&$ . Normalized saturation curves for doped and un-doped samples (Figure S3) demonstrates nearly identical saturation behavior with pump intensity in all the samples. This corroborates that doping does not significant alter the absorption cross section well above the band edge. This is in accord with the constant absorption spectra during doping. Since the $%&$ / ratio is also nearly the same for all samples, must also be unchanged by doping. Iterative application of eq 2 leads to the presented in Figure 5 for all doping levels, all within the associated error bounds. These significant margins reflect the confidence range related to matching $%&$ to the saturation curves.

1.0

0.6

-15

cm

2

0.8

σ/10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


σbg

0.4

∆σbg

0.2

0.0 0

125

250

375

Cu atoms/ QD

17


500


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Figure 5. and ∆ obtained from the saturation curves and from the 1S bleach measurements at low fluence following photo-excitation at 640 nm, demonstrating the change in the ratio between and ∆ (nT) upon doping. See text for details.

Reviewing the dopant concentration dependence of , extracted from the saturation curves (Figure S3), vs that of the obtained from the bleach amplitudes at low fluence questions the applicability of eq 1. These values for the un-doped sample do, within experimental error, exhibit the expected ratio of two. With the introduction of more and more copper atoms this ratio rises to nearly four above 125 Cu/QD. Clearly the effective nT in eq 1 varies with the degree of doping. To appreciate what this means requires a review of the assumptions embodied in eq 1. The value of nT reflects the degeneracy of the band edge quantized states, and the selection rules for transitions between them. It also assumes linearity of band edge bleach with the number of relaxed excitons. In the case of lead chalcogenides the band edge states have been assigned a degeneracy of eight including spin, and both holes and electrons are proposed to participate in the 1S transition, resulting in an nT value of four. For InAs, as in CdSe, the degeneracy is two, but since hole-states at the band edge are suggested to be "dark", this still leads to nT of two.34 Gain threshold is somewhat of a misnomer in this case since in this scenario gain is never achieved at the band edge regardless of the amount of excitations. Variations in the apparent nT are fully consistent with a redistribution of band edge transition moment strength over more transitions related to the doping. This is cast as a change in degeneracy of the transition, implying that all of the resulting optical transitions remain identical. Another possibility is that states related to the dopant sub-band, which are vacant due to only 18


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partial filling from the donor impurities, are mixed with valence band states to redistribute the dipole strength over additional mixed states which although unequal are still optically active and contribute to . A third possibility is that contrary to our assumption, following hot carrier excitation, a dopant concentration dependent fraction of electrons are scavenged during relaxation to the band minimum. While no evidence for such behavior is seen in the TA data, we have further addressed this possibility. To do this the value of was measured by photoexcitation directly into the band gap 1S transition. This populates the target states without the possible scavenging during relaxation to the band edge. This can be understood if we consider that the excitons generated with very high energy (pump at 640 nm), can cool to doping related states laying above and below the band gap. However, when pumping near the band-gap energy (1160 nm), only the doping states with the same energy as the band gap and below are accessible. This agrees with calculations showing an asymmetric band evolving near the QD band edge increasing the density of states (DOS) both above and below the band gap.2 Whether one describes this as an increased degeneracy, or a state dilution, the meaning is the same. The results of this experiment are presented in Table 1, for undoped and 125 Cu atoms/QD samples. While the ratio ⁄ is slightly smaller than that obtained at λpump = 640 nm, it is more than twice the expected value of two, proving that the doping effect on the bleach per exciton cannot be the result of electron scavenging during cooling. Even when pumping directly at the band edge and instantaneously blocking the 1S absorption (see figure S4 which demonstrates ~60 fs rise of bleach amplitude), the maximal bleach signals attainable are significantly reduced with doping, corroborating that copper doping does indeed reduce . 19



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This result is particularly significant for it demonstrates that no dynamic process discernable with ~30 fs resolution gives rise to this reduction. This result is fully consistent with the previous work which suggested that doping in QDs, due to the small size, easily reaches the formal limit of heavily doped semiconductors.2 In this heavily doped limit, the energy levels of the conduction band (in the n-type case) are modified by the presence of dopants. The impurities interact with each other and an impurity sub-band emerges near the edge of the conduction band.18 The situation in heavily doped QDs is depicted schematically in Figure 6. In the limit of a single hydrogenic impurity, its level is red shifted below the 1S(e) state. At high doping levels an impurity sub band develops with increased weight of levels expected above the 1S(e) state. Evidence to this was presented in our previous work by combination of optical study, STM measurements, and theoretical modelling. The red shift turning into a blue shift in the absorption (Figure 1b) is consistent with the emergence of the impurity sub-band. The blue shift is a signature of a Moss-Burstein like effect related to partial filling of the sub-band as also corroborated by the theoretical analysis in the previous work. STM study also showed an increased DOS near the lowest conduction band state, consistent with the emergence of the sub-band.2

20


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Figure 6. Schematic representation Cu doping effects in InAs QDs. The red solid lines represent the electronic states in both conduction and valence bands of InAs QDs, while the blue shades indicate the impurity levels as they develop into an impurity sub-band interacting with the host states. As a result, in heavily doped QDs, the density of electronic states near the conduction band edge is increased. Additionally, after excitation, the initial hot excitons cool down to the 1P(e) state by fast relaxation processes (dashed green arrows), followed by a transition to the 1S(e). The final part of the hot exciton relaxation (solid green arrows) was found to hasten as the Cu doping level increases.

The observation of the reduced band edge bleach per exciton with increased doping is consistent with the appearance of such impurity sub-band states and is the most significant finding of this study. Due to appearance of the impurity sub-band there are more electronic states which can accommodate electrons, akin to increasing “the degeneracy” near the band edge. The overall oscillator strength of the band edge transition is distributed over a large number of states of the impurity sub-band. Therefore, the observed near band edge bleach decreases systematically upon doping. Meanwhile, at high photon energies, excitation is into a bulk-like manifold of states and the absorption cross section is neither affected by the impurities, nor by other excitons present in the QDs. Since the change in the absorption coefficient of the 1S transition is relative to the degeneracy of the lowest conduction band, the increased DOS reduces the absorption coefficient of the 1S transition. This additional DOS, distributed over both the original 1S states in undoped InAs QDs, into the impurity sub-band levels, also explains the difference between the mechanism described above, and that active in bleaching of the 1S(e)1S(h) transition by electron injection doping in QDs.14 In this latter case, electrons are injected into the QDs 21



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electrochemically by bias change, or by charge transfer from ligands on the QD surface. This type of “charge doping” does not alter or re-distribute the density of band edge states but only changes the charging state of the QD. Therefore, in this latter case, the injected electrons occupy the electronic states of the QDs and lead to decreasing the absorption upon charge injection.14 In contrast, for the Cu impurity doped InAs QDs, the presence of the impurities leads to the creation of the impurity sub-band, and alteration of the distribution of the DOS among the 1S states and the impurity sub-band levels near the band edge. The TA bleach signal does not exhibit notable broadening even at the highest Cu levels since its width is dominated by inhomogeneous broadening (~150meV), while the impurity sub-band width is expected to be lower (~50100meV). Experimentally measurable consequences of an increased effective degeneracy of the 1S band are predicted to be: 1) The saturation fluence of this transition should increase with the degeneracy. 2) The band edge absorption feature should ultimately be totally bleachable, albeit at a higher pump fluence than in undoped samples. In a further test for our understanding of the doping effects at the band edge, saturation curves were obtained by following the maximum 1S bleach, pumping at differing intensities with pulses centered at 1160 nm. The results of these tests are depicted in Figure 7. In complete agreement with the predicted behavior the asymptotic bleach in doped and un-doped samples is nearly the same, yet the 50% bleach intensity is almost two times higher in the case of the doped sample. The difference in the ultimate bleach which is obtained is probably due to imperfect separation 22


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of timescales between hot carrier relaxation and Auger recombination of high multi-excitons, which will limit this bleach more for the doped samples as observed. We note in passing that the similarity in the ultimate bleaching level which is within a factor of 0.8 between the two samples is in stark contrast to the bleach per exciton ratio of 2-3.5.

1.0

0.8

0.6

∆OD/OD

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0.4

0.2

undoped

125 Cu/QD

0.0 0

1

2

3

4

5

6

7

η

Figure 7. Saturation curve of the 1S transition while pumping near the band edge (1160 nm). The normalized maximum bleach, at various pumping intensities, reveals a rapid saturation of the undoped QDs compared to that of the 500 Cu atoms/QD, indicating the doping related states near the bottom of the conduction band are optically active.

Table 1. calculated by using the saturation method and by the bleach method

λpump σbg/10-15cm2

640nm

Undoped 0.90±0.11

23


125 Cu atoms/QD 0.76±0.04


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∆σbg/1015

cm2

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640nm

0.54±0.06

0.15±0.01

1160 nm

0.42±0.02

0.20±0.02

B) Doping effects on hot exction cooling. The 1S bleach exhibits a fast build up process in the initial

Impurity Sub-Band in Heavily Cu-Doped InAs Nanocrystal Quantum

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