Trapped-Dopant Model of Doping in Semiconductor Nanocrystals

NANO LETTERS

Trapped-Dopant Model of Doping in Semiconductor Nanocrystals

2008 Vol. 8, No. 9 2878-2882

Mao-Hua Du,† Steven C. Erwin,* and Al. L. Efros Center for Computational Materials Science, NaVal Research Laboratory, Washington, D.C. 20375 Received June 5, 2008

ABSTRACT We propose a framework for describing the impurity doping of semiconductor colloidal nanocrystals. The model is applicable when diffusion of impurities through the nanocrystal is sufficiently small that it can be neglected. In this regime, the incorporation of impurities requires that they stably adsorb on the nanocrystal surface before being overgrown. This adsorption may be preempted by surfactants in the growth solution. We analyze numerically this competition for the case of Mn doping of CdSe nanocrystals. Our model is consistent with recent experiments and offers a route to the rational optimization of doped colloidal nanocrystals.

Systematic efforts to introduce intentional impurities into semiconductor nanocrystals began in the early 1990s, when ZnS nanocrystals were first doped with Mn impurities.1 Two main research directions have since emerged: investigations into the physical properties and potential applications of doped nanocrystals, and strategies to gain better control and understanding of the doping process itself.2,3 Both activities are essential prerequisites for a variety of nanocrystal technologies including thermoelectrics,4 photovoltaics,5 bioimaging,6 lasers,7 and nanoscale magnetism.8 And yet despite considerable effort, and decades of experience with doping bulk semiconductors, progress in controlling and understanding doping in semiconductor nanocrystals has been slow. Dopant concentrations in colloidally grown nanocrystals are often much lower than in their bulk counterparts. For example, Mn concentrations in II-VI semiconductor nanocrystals such as ZnSe are 1-2 orders of magnitude lower than in their bulk counterparts.9 In other cases, nanocrystal doping can greatly exceed the bulk solubility limit: Mn concentrations in III-V semiconductor nanocrystals such as InAs and InP can be 3-4 orders of magnitude higher than those in bulk crystals.10,11 In still other cases, such as Mn in ZnO nanocrystals, dopant concentrations close to the bulk solubility limit have been attained.12 In this Letter we propose a theoretical framework for understanding such diverse results, including the important role played by the surfactants that are often used to control growth. * Author to whom correspondence should be addressed. Tel.: 202-4048630. Fax: 202-404-7546. E-mail: [email protected]. † Present address: Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831. 10.1021/nl8016169 CCC: $40.75 Published on Web 08/05/2008

 2008 American Chemical Society

Trapped Dopant Model. We propose that the above findings are the consequence of nonequilibrium kinetic effects that may, at the low temperatures commonly used in liquid-phase colloidal synthesis, be more important than the equilibrium impurity solubility.3,13 The basic idea is straightforward. At sufficiently low temperatures the diffusion of impurities within a crystal becomes negligible. The relevance of this fact for doping colloidal nanocrystals can be judged from simple estimates. Colloidal synthesis is typically performed below 350 °C, and in some cases as low as room temperature. At these temperatures an activation barrier of roughly 1.5 eV is sufficient to trap impurities on the time scale of the growth. Activation barriers for many substitutional impurities are much larger than this. For example, the measured barrier for Mn impurity diffusion in bulk CdTe is between 2.3 and 2.8 eV.14 Moreover, in bulk crystals this barrier is controlled by native defects, mainly interstitials and vacancies.15 In nanocrystals such native defects are likely to be less effective for mediating diffusion, and so diffusion barriers in nanocrystals are probably even larger than in bulk. For example, diffusion can occur without vacancies or interstitials by a “concerted exchange” mechanism;16 the barrier for this process is 4 eV for Pb diffusion in PbSe,17 and almost 6 eV for self-diffusion in Si.18 The implication of these estimates for doping is evident: In many nanocrystalline materials an impurity atom that occupies a substitutional site at some point during colloidal growth will remain there as a “trapped dopant”. Within this scenario an important question concerns how, or even whether, an impurity comes to occupy a substitutional site in the first place. Because diffusion through the nanocrystal is strongly suppressed, the only viable alternative is adsorption on the surface, at a location that corresponds

Figure 1. Schematic description of dissociative adsorption of impurity-surfactant complexes near the surface of a nanocrystal. (a) Mn-surfactant complex approaches the nanocrystal surface, where it may be first physisorbed in intact form (blue). Closer to the surface it may be energetically favorable for the complex to dissociate (black). The separated surfactant molecule and impurity atom (red) must then adsorb at available surface sites. (b) Schematic potential energy diagram describing dissociative adsorption. The thick blue curve is the potential energy of an intact Mn-surfactant complex as it approaches a surface, where it forms a weakly bound physisorbed state. The thick red curve is the combined potential energy of a Mn atom and surfactant molecule, widely separated from each other, as they simultaneously approach the surface, where they are strongly bound to the surface (chemisorbed) by forming chemical bonds. The crossover point of these curves represents the dissociation of the Mn-surfactant complex mediated by the surface. In this figure the dissociation requires climbing an activation barrier. The individual Mn-surface and surface-surfactant contributions to the chemisorption curve are shown as thin red curves. The labeled binding energies are referred to in the text.

to a bulk lattice site when overgrown by additional material. Therefore a necessary, but not sufficient, condition for successful doping is the stable adsorption by an impurity on the surface of the nanocrystal. As we have argued elsewhere, impurity adsorption depends strongly on three factors not previously considered important to doping: surface morphology, nanocrystal shape, and surfactants in the growth solution.13 We showed that the very different outcomes of doping experiments using zinc blende semiconductors such as ZnSe, compared to wurtzite semiconductors such as CdSe, can be understood as arising in part from differences in the first two of these factors. Here we propose a framework for understanding the role of the thirdsthe surfactants in the growth solution. Role of Surfactants. Surfactants are used during the colloidal growth of nanocrystals to moderate the growth rate by passivating dangling bonds on the nanocrystal surface. Experiments show that the choice of surfactant can also influence the incorporation of impurities into nanocrystals. For example, when the surfactant tetradecylphosphonic acid (TDPA) was used in the synthesis of CdSe nanocrystals, attempts to dope the nanocrystals with Mn impurities failed.19 When the surfactant hexadecylamine (HDA) was used instead, successful doping by Mn was demonstrated.13 In the discussion below we will use this example for concreteness and in the next section will present numerical results for it Nano Lett., Vol. 8, No. 9, 2008

to quantify the central ideas. But the model is general and should be understood as a framework for analyzing arbitrary combinations of nanocrystal, impurity, and surfactant. Surfactant molecules can form chemical bonds not only to the nanocrystal but also to impurity atoms in the solution. This is especially true if the impurity and host atoms have the same chemical valence. In the example of CdSe nanocrystals and Mn impurities, both Cd and Mn are divalent. Hence a surfactant that forms chemical bonds to surface Cd atoms will be likely also to bind Mn atoms. And if a surfactant molecule strongly binds impurity atoms, then doping will be hindered because the adsorption of impurities on the nanocrystal surface is preempted. Conversely, surfactants that weakly bind impurities promote doping. To model this adsorption process, we begin by assuming that the surfactant molecules in solution greatly outnumber the impurity atoms, so that every impurity atom is bound to a surfactant molecule. We focus on what happens when one such impurity-surfactant complex approaches the nanocrystal surface. We propose that dissociative adsorption, illustrated in Figure 1a, is the principal route by which impurity atoms are delivered to the nanocrystal surface. For doping to occur, the impurity-surfactant complex must dissociate as it nears the surface, allowing the separated surfactant molecule and impurity atom to find stable binding sites. 2879

The energetics governing dissociative adsorption is shown schematically in Figure 1b.20 This figure shows two potentialenergy curves. The thick blue curve is the potential energy of an intact impurity-surfactant complex as it approaches a surface, where it forms a weakly bound physisorbed state arising from the van der Waals interaction. The thick red curve is the combined potential energy of an impurity atom and surfactant molecule, widely separated from each other, as they simultaneously approach the surface, to which they are strongly bound (chemisorbed) when sufficiently close. The crossover point of these curves represents the dissociation of the complex. For the scenario depicted in Figure 1b dissociative adsorption is an activated process characterized by an activation barrier Ea. If the isolated impurity atom is assumed to be strongly bound, as shown, then its subsequent desorption can be neglected and the impurity sticking probability is simply exp(-Ea/kT). If Ea is large compared to kT, then this process will be rare and consequently doping will be negligible. For this reason, it is important to understand qualitatively the factors that influence Ea. It is clear that even within the simple picture of Figure 1, Ea has a complicated dependence on many details of the surface, impurity, and surfactant. Thus the various energies labeled in Figure 1b are by no means independent. Nevertheless, to make possible a qualitative discussion, we will treat them as separate quantities that can be individually varied. For example, an increased Mn-surfactant binding energy B EMn-surfactant can be represented by a rigid downward shift of the blue potential-energy curve. Such a shift also increases the activation energy Ea. This is consistent with our earlier qualitative claim that doping is hindered (in this case because the sticking probability is reduced) if the surfactant molecule strongly binds impurity atoms. Conversely, smaller values B of EMn-surfactant lead to smaller or even vanishing values of Ea. Of course, a small activation barrier is not a sufficient condition for efficient doping. After dissociation, the impurity must also bind stably to the surface. The thick red curve in Figure 1b represents the sum of the Mn-surface and surface-surfactant contributions, which are shown individually as thin red curves. We have chosen to illustrate a B scenario in which the Mn-surface binding energy EMn-surface is relatively large, and the surface-surfactant binding energy B Esurface-surfactant is relatively small. In this scenario, after dissociation the Mn will be stably bound to the surface with a low desorption rate, while the surfactant will desorb more readily. Such a situation promotes both efficient doping and continued growth. B In the reversed situation of small EMn-surface and large B Esurface-surfactant (imagine these labels interchanged in the figure), the adsorbed Mn impurity will only be metastable, because it can gain energy by leaving the surface and binding to another surfactant in solution. Hence in this scenario even a small or zero activation barrier will not necessarily result in doping. 2880

To summarize our conclusions based on a model of dissociative adsorption, successful impurity doping in the presence of surfactants requires the following criteria to be satisfied: B (1) EMn-surface is large compared to kT. B B (2) EMn-surface > EMn-surfactant . (3) Ea is small compared to kT. In the next section we apply these requirements to a comparative case study of CdSe nanocrystals doped with Mn in the presence of two commonly used surfactants, HDA and TDPA. Our results explain previous experimental results for this system showing that doping could be achieved when using HDA but not when using TDPA. Mn Doping in CdSe Nanocrystals. To investigate quantitatively the above description, we use first-principles totalenergy methods to study Mn doping in wurtzite CdSe nanocrystals. This system has received considerable experimental scrutiny and was long considered undopable. In our earlier work, we showed that CdSe nanocrystals could, in fact, be doped using two alternative strategies. The first was to force the nanocrystals, which are normally wurtzite, to grow in the zinc blende structure. This leads to dopant incorporation because the impurity adsorption energy B EMn-surface is much larger on the (001) surface of zinc blende CdSe than on any surface of wurtzite CdSe, and hence better satisfies criterion 1 above. The second strategy was to switch the surfactant from the strongly binding TDPA to the weakly binding HDA. As we demonstrate below, this switch leads B to dopant incorporation because EMn-surfactant is greatly reduced, which favorably affects the Mn sticking probability by reducing Ea. We begin by studying the adsorption of isolated Mn impurities on the surface of CdSe. We modeled adsorption using a supercell with eight atomic layers. The atoms in the bottom layer, which were passivated using pseudo-hydrogen atoms, were fixed in their bulk positions. All other atoms were relaxed until the force on each atom was less than 0.05 eV/Å. Total energies and forces were calculated using density-functional theory (DFT) within the projector augmented wave (PAW) method and the PBE generalizedgradient correction, as implemented in VASP.21,22 The valence wave functions were expanded in a plane-wave basis with cutoff energy 400 eV. We considered adsorption on two inequivalent surfaces of wurtzite CdSe, the Cd-terminated (0001) surface and the Se-terminated (0001j) surface, which we will denote as (0001)-Cd and (0001j)-Se, respectively. These are structurally similar to the (111) and (1j1j1j) surfaces of zinc blende semiconductors. For each orientation we calculated Mn adsorption energies EBMn-surface on clean reconstructed surfaces and, for comparison, on surfaces passivated by the surfactants HDA and trioctylphosphine (TOP). Further details are in the Supporting Information. Our DFT results are shown in Figure 2. On the clean reconstructed surfaces, Mn binds with large adsorption B energies, EMn-surface ) 2.50 and 1.75 eV on (0001)-Cd and (0001j)-Se, respectively. On the (0001)-Cd surface passivated with the surfactant HDA, Mn binds with similarly large Nano Lett., Vol. 8, No. 9, 2008

B Figure 2. Calculated Mn adsorption energies, EMn-surface , on the Cd-terminated (0001)-Cd and Se-terminated (0001j)-Se surfaces of wurtzite CdSe. Results are shown both for clean reconstructed surfaces and for surfaces partially covered by the passivating surfactants hexadecylamine B (HDA) or trioctylphosphine (TOP). These should be compared to the calculated Mn binding energies, EMn-surfactant , to the two surfactant molecules HDA and tetradecylphosphonic acid (TDPA). Details concerning the surface reconstructions and surfactant molecules can be found in Supporting Information.

B adsorption energies, EMn-surface ) 2.56 and 1.84 eV for surfactant coverages of 25% and 75%, respectively. Likewise, on the (0001j)-Se surface passivated by 25% coverage TOP (a surfactant that binds to Se), we find that Mn binds with adsorption energy 1.40 eV. Thus, for a wide range of different surfaces and surfactant coverages the Mn impurity adsorption energy generally falls in the range 1.4-2.6 eV. We now compare these adsorption energies to the binding energy EBMn-surfactant of Mn to the isolated surfactant molecules TDPA and HDA. TDPA is the more commonly used surfactant, for which earlier experimental results showed no Mn incorporation. For computational purposes we truncated the TDPA molecule to the chemically analogous phosphonic acid molecule, H3PO3, shown in Figure 3a.23 We find that B EMn-surfactant ) 5.91 eV. This binding energy is much larger B than the values of EMn-surface on any surface we considered, and hence badly violates criterion 2. This violation is consistent with the experimental results showing no Mn incorporation in CdSe nanocrystals when using TDPA. The situation is very different for the surfactant HDA, a long hydrocarbon chain with a NH2 headgroup. We truncated this chain to the chemically similar methylamine molecule, B CH3NH2, shown in Figure 3b. We find that EMn-surfactant ) 0.52 eV. This binding energy easily satisfies criterion 2 and is consistent with experimental results showing Mn incorporation, with concentration 0.14%, when using HDA.13 In this study we have only considered the (0001)-Cd and (0001j)-Se surfaces of CdSe. It is not feasible to investigate exhaustively all possible surface orientations and binding sites on which Mn could adsorb during growth. However, B in a previous study we used DFT to calculate EMn-surface on two other CdSe orientations, the clean cleavage surfaces (112j0) and (101j0).13 The computed Mn binding energies were 0.43 and 0.56 eV, respectively. These are even smaller

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Figure 3. Optimized structure of two Mn-surfactant complexes. (a) Mn bound to tetradecylphosphonic acid (TDPA) and (b) Mn bound to hexadecylamine (HDA). For computational reasons the long chain tails (light gray) were replaced by single hydrogen atoms.

than those on the surfaces studied here. Thus, for adsorption on the four commonly found planar surfaces of CdSe, our qualitative conclusions regarding HDA vs TDPA surfactants are likely to be robust. And while adsorption at step edges and kink sites might lead to larger binding energies, planar facets on colloidal nanocrystals are known to occur under a wide range of experimental conditions. Therefore it is plausible that they would dominate the overall adsorption characteristics of a nanocrystal. Influence of Surfactants on Impurity Solubility. In our trapped-dopant model, the resulting concentration of impurity atoms inside the nanocrystal is proportional to the concentration in the growth solution. For this reason, surfactants can in principle play another role in nanocrystal doping, by 2881

influencing the solubility of impurities in the growth solution. We stress that this role may not be relevant in practice, because other extrinsic factors may impose even lower limits on impurity solubility. For example, highly concentrated solutions of dimethyl manganese, a standard precursor for Mn, are unstable and thus limit the maximum concentration of Mn impurities available for doping to about 5%. Hence, the discussion below remains hypothetical unless extrinsic factors such as these can be circumvented. In experiments on Mn-doped ZnSe nanocrystals, the Mn concentration measured in the nanocrystals (0.023% and 0.045%) was indeed proportional to the Mn concentration in the growth solution (0.025% and 0.05%).13 When HDA is used as a surfactant, the low Mn-surfactant binding energy B (EMn-surfactant ) 0.52 eV) can, in principle, result in low B solubility of Mn in solution. This is because EMn-surfactant is small compared to the enthalpy gained by forming a solid precipitate, namely, the Mn cohesive energy, which we calculate to be 3.79 eV. This leads to low solubility of Mn because low concentrations increase entropy and hence lower the free energy of Mn in solution sufficiently to favor solvation over precipitation. We note that this outcome (which limits nanocrystal doping) is opposite to the beneficial role played by HDA of satisfying criterion 2 (which enhances nanocrystal doping). Conversely, the more strongly binding surfactant TDPA B (EMn-surfactant ) 5.91 eV) could, in the absence of extrinsic factors, lead to increased impurity solubility in solution, which enhances doping. This is in opposition to TDPA’s effect on impurity adsorption, which suppresses doping. Summary. We have described a model for impurity doping in semiconductor colloidal nanocrystals based on ideas of kinetically limited adsorption and desorption of impurities from the nanocrystal surface. The model shows that surfactants, which are used to control nanocrystal growth, play another important role by affecting doping in two ways. First, they compete with the nanocrystal surface by binding impurity atoms. If this binding is stronger than the adsorption energy, then doping will be suppressed or zero. Moreover, the impurity-surfactant binding affects the activation barrier for dissociative adsorption of the impurity-surfactant complex. In a simple picture of adsorption without subsequent desorption, this barrier directly determines the impurity sticking probability. Second, surfactants may affect the solubility of impurities in the growth solution, unless extrinsic factors preempt this effect. A surfactant that strongly binds impurity atoms leads to higher impurity solubility in solution, but it does so at the expense of reduced impurity adsorption

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on the nanocrystal. This finding indicates the importance of optimizing the choice of surfactant to balance these two competing requirements and permit efficient nanocrystal doping. Acknowledgment. We thank Ed Foos, Lijun Zu, and SuHuai Wei for valuable discussions. This work was supported by the Office of Naval Research and the National Research Council. Computations were performed at the DoD Major Shared Resource Centers at ASC and NAVO. Supporting Information Available: Additional details regarding the density-functional theory calculations. This material is available free of charge via the Internet at http:// pub.acs.org. References (1) Bhargava, R. N.; Gallagher, D.; Hong, X.; Nurmikko, A. Phys. ReV. Lett. 1994, 72, 416–419. (2) Bryan, J. D.; Gamelin, D. R. Prog. Inorg. Chem. 2005, 54, 47–126. (3) Norris, D. J.; Efros, Al. L.; Erwin, S. C. Science 2008, 319, 1776– 1779. (4) Huynh, W. U.; Dittmer, J. J.; Alivisatos, A. P. Science 2002, 295, 2425–2427. (5) Gur, I.; Fromer, N. A.; Geier, M. L.; Alivisatos, A. P. Science 2005, 310, 462–465. (6) Michalet, X.; Pinaud, F. F.; Bentolila, L. A.; Tsay, J. M.; Doose, S.; Li, J. J.; Sundaresan, G.; Wu, A. M.; Gambhir, S. S.; Weiss, S. Science 2005, 307, 538–544. (7) Klimov, V. I.; Ivanov, S. A.; Nanda, J.; Achermann, M.; Bezel, I.; McGuire, J. A.; Piryatinski, A. Nature 2007, 447, 441–446. (8) Archer, P. I.; Santangelo, S. A.; Gamelin, D. R. Nano Lett. 2007, 7, 1037–1043. (9) Norris, D. J.; Yao, N.; Charnock, F. T.; Kennedy, T. A. Nano Lett. 2001, 1, 3–7. (10) Stowell, C. A.; Wiacek, R. J.; Saunders, A. E.; Korgel, B. A. Nano Lett. 2003, 3, 1441–1447. (11) Somaskandan, K.; Tsoi, G. M.; Wenger, L. E.; Brock, S. L. Chem. Mater. 2005, 17, 1190–1198. (12) Norberg, N. S.; Kittilstved, K. R.; Amonette, J. E.; Kukkadapu, R. K.; Schwartz, D. A.; Gamelin, D. R. J. Am. Chem. Soc. 2004, 126, 9387– 9398. (13) Erwin, S. C.; Zu, L. J.; Haftel, M. I.; Efros, Al. L.; Kennedy, T. A.; Norris, D. J. Nature 2005, 436, 91–94. (14) Jamil, N. Y.; Shaw, D. Semicond. Sci. Technol. 1995, 10, 952–958. (15) Queisser, H. J.; Haller, E. E. Science 1998, 281, 945–950. (16) Pandey, K. C. Phys. ReV. Lett. 1986, 57, 2287–2290. (17) Erwin, S. C. Unpublished. (18) Foulkes, W. M. C.; Mitas, L.; Needs, R. J.; Rajagopal, G. ReV. Mod. Phys. 2001, 73, 33–83. (19) Mikulec, F. V.; Kuno, M.; Bennati, M.; Hall, D. A.; Griffin, R. G.; Bawendi, M. G. J. Am. Chem. Soc. 2000, 122, 2532–2540. (20) Lennard-Jones, J. E. Trans. Faraday Soc. 1932, 28, 333–359. (21) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558–561. (22) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169–11186. (23) We assumed the Mn-TDPA binding configuration to be the same as that of Cd-TDPA, which undergoes abstraction of two hydrogen atoms.

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Nano Lett., Vol. 8, No. 9, 2008