Article pubs.acs.org/JPCC
Solvent-Based Atomistic Theory for Doping Colloidal-Synthesized Quantum Dots via Cation Exchange Zhaoyang Zheng,†,§ Yi-Yang Sun,*,‡ Weiyu Xie,‡ Jijun Zhao,*,† and Shengbai Zhang*,‡ †
Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Dalian University of Technology, Ministry of Education, Dalian 116024, China ‡ Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, United States S Supporting Information *
ABSTRACT: Electronic applications require the ability to dope a material with a controllable amount of impurities. However, current understanding of the doping mechanism in colloidal−synthesized quantum dots (QDs) is still limited. This is in contrast with bulk semiconductors for which first-principles-based theories have been well established. Using prototype CdSe as an example, here we propose an atomistic theory for the doping of colloidal-synthesized QDs. The key in our theory is the evaluation of atomic chemical potential inside the solution, whose range can deviate considerably from the bulk value due to the presence of solvent. This theory, coupled to first-principles calculations and ab initio molecular dynamics, is able to explain the difference of doping limit in Mn (or Co)-doped CdSe QDs and their bulk counterparts. It also explains the doping behavior of a number of other 3d transition-metal impurities in CdSe QDs in contrast with the solid case.
■
On the contrary, in the self-purification model,20 it is suggested that dopant atoms are thermodynamically unstable inside the QDs, indicating an intrinsic difficulty of doping QDs. The colloidal QDs are synthesized in liquid solvents. The impurities are introduced through metal−salt or metal−organic precursors dissolved in the solvents.1,25,26 Doping bulk semiconductors, however, are usually under significantly different conditions. For example, the dopants can be driven into the semiconductor through a pure solid-state reaction at a temperature much higher than that used in QD synthesis (typically 25 to 310 °C).12−14,18,27,28 It is thus important to take such differences into account when comparing the doping limits in QDs and bulk semiconductors because the doping thermodynamics, in particular, the defect formation energy, is determined by the chemical potentials of the dopant atoms, which is, in turn, critically affected by the solvents. Such solvent effect, however, has not been explicitly considered in previous theoretical models. We propose a solvent-based theory for the QD doping via a cation exchange process. We explicitly include the solvent in our atomistic model and ab initio molecular dynamics (AIMD) simulations. Using 3d TM doping in CdSe QDs as an example, our results reveal that the chemical potential difference of dopants in the colloidal synthesis and solid-state reaction could account for the experimentally achieved doping concentrations of Mn and Co in bulk CdSe and CdSe QDs when the hexadecylamine solvent (HDA, C16H33NH2) is used. We also
INTRODUCTION Impurity doping is a highly pursued approach to tuning the properties of semiconductor quantum dots (QDs).1−3 Transition-metal (TM) impurities enhance this technique by introducing rich physical phenomena with the partially occupied d and f electronic states in the band gaps of the QDs. For example, the magnetism of the TM-doped QDs could be controlled by the charge state of the dopants4 and by light irradiation.5 Recently, multiphoton upconversion by TM-doped QDs has attracted significant attention because of the important applications in bioimaging.6−9 These applications rely on the ability of controlled doping of TM impurities into QDs. While some of such efforts have been successful,10,11 others still appear challenging because doping QDs are often governed by distinctly different physics from those of doping corresponding bulk semiconductors.12 TM doping in colloidal QDs of II−VI semiconductors, for example, CdSe and ZnSe, has been extensively studied. The doping limit in these QDs significantly differs from that in their bulk counterparts. For example, Mn concentration in CdSe and ZnSe QDs was significantly lower than that in bulk;13,14 until recently such doping limit has been overcome by delicately designed experiments.15,16 In contrast, however, Co concentration in CdSe QDs can greatly exceed its solubility limit in bulk CdSe.17,18 The mechanism of the doping limit in II−VI QDs has been discussed on the basis of both kinetic12,19 and thermodynamic arguments.20−22 In the surface kinetics model,12 it is suggested that doping QDs are controlled by adsorption of dopants on the QD surface during growth. Thus the difficulty of doping Mn in II−VI QDs is not intrinsic and can be overcome by controlling the kinetics of the QDs.23,24 © XXXX American Chemical Society
Received: November 6, 2016 Published: November 7, 2016 A
DOI: 10.1021/acs.jpcc.6b11150 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
ΔHfSS = Ebulk (CdSe:TM) − Ebulk (CdSe) − (μTM − μCd )
make predictions on the doping limits of other 3d TM elements in CdSe QDs.
■
(2) bulk
MODEL AND METHODS Cation exchange has been widely used in colloidal synthesis of QDs25,26,29−35 as well as in dopant incorporation into QDs.11,36,37 To model the effect of solvent, we consider the reaction as a colloidal process (CP) shown in Figure 1. Before
bulk
(1)
Here E (CdSe:TM)and E (CdSe) are the total energies of bulk CdSe with and without a TM impurity, respectively. Bulk CdSe with an impurity is typically simulated by a supercell approach. μTM and μCd are the chemical potentials of a TM and Cd atom, respectively. The allowed ranges for the chemical potentials are determined by the standard theory.38 To apply this model for the cation exchange reaction through the colloidal process, we have made two assumptions: (1) The effect of the interface between QD and solvent is ignored considering the experimental observation that TM impurities are usually located in the core of CdSe QDs.39 This allows us to only simulate the precursor TMCl2 and the product CdCl2 in solution. (2) The HDA solvent with a long alkyl chain is replaced with methylamine (CH3NH2) to reduce the computational cost.19,40,41 We have checked the interaction energy between an isolated solvent molecule and a dopant precursor in vacuum: the energy difference for MnCl2 and CdCl2 interacting with solvent molecule, that is, the term ETMCl2 − ECdCl2 in eq 1, changes by only
