A Simple ZnO Nanocrystal Synthesis Illustrating Three-Dimensional

Laboratory Experiment pubs.acs.org/jchemeduc

A Simple ZnO Nanocrystal Synthesis Illustrating Three-Dimensional Quantum Confinement Philip J. Reid,* Bryant Fujimoto, and Daniel R. Gamelin Department of Chemistry, Box 351700, University of Washington, Seattle, Washington 98195-1700, United States S Supporting Information *

ABSTRACT: Semiconductor nanocrystals or “quantum dots” are attractive materials for exploring quantum confinement effects. For example, band-gap energies of these materials depend on particle size, and this dependence can be explained using simple, quantum mechanical models. We outline here an undergraduate physical chemistry laboratory involving the room-temperature synthesis and absorption spectroscopy of ZnO nanocrystals. The experimental results are compared with the predictions of a three-dimensional quantum confinement (or “particle-in-a-sphere”) model. The ease of synthesis and data collection, the common precursors employed, and the simple spectroscopic analysis allow facile incorporation of this experiment into essentially any undergraduate laboratory program.

KEYWORDS: Upper-Division Undergraduate, Inorganic Chemistry, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Interdisciplinary/Multidisciplinary, Nanotechnology, Quantum Chemistry, UV-Vis Spectroscopy

T

relative ease of preparation makes these particles an attractive target for study.10−13 The laboratory described here involves ZnO nanocrystal syntheses involving common precursors where the growth kinetics are sufficiently fast that particle growth can be studied within a three-hour lab period.14 Here, solutions of zinc acetate and tetramethyl ammonium hydroxide in ethanol are prepared and mixed, and particle growth at room temperature is monitored using UV−Vis absorption spectroscopy. The lowest-energy electronic transition provides a measure of the band-gap energy, which evolves as the particles grow in size. The change in band-gap energy with particle size is measured and compared to predictions of the “particle-in-a-sphere” model. All of the reagents used in this lab are easily acquired, and the entire experiment is performed at room temperature with the majority of particle growth evident in ∼30 min. This experiment provides a simple, robust way to incorporate modern materials chemistry and quantum mechanics into the undergraduate laboratory curriculum.

he remarkable growth in materials chemistry over the past two decades has increased the need to explore this area in undergraduate chemistry curricula. One class of materials that has received substantial interest is semiconductor nanocrystals, or “quantum dots”. These materials have a wide range of potential applications including single-particle imaging, particle tracking, and photovoltaics.1−4 Semiconductor nanocrystals are also fundamentally interesting materials in that their electronic properties depend on particle size.5,6 Specifically, the difference in energy between the valence and conduction band edges, or “band gap”, of the nanocrystal depends on its size, with a decrease in particle size increasing the band-gap energy. These so-called quantum confinement effects can be described using relatively simple “particle-in-a-box” quantum-mechanical models. Therefore, semiconductor nanocrystals are an excellent venue in which to explore foundational quantum-mechanical ideas in a modern context. A variety of laboratory experiments have been presented in which students synthesize the quantum dots and then analyze their properties.7,8 Early experiments focused on CdS and CdSe quantum dots, but these laboratories involved syntheses that employed relatively toxic compounds (in particular, Cd precursors) and high temperatures.8,9 CdS and CdSe quantum dots are now commercially available, so synthesis of these materials can be avoided altogether.9 However, the relative ease of nanoparticle synthesis is pedagogically attractive aspect of nanocrystal experiments. An alternative is to study materials where synthetic precursors are significantly less toxic than those employed for CdS or CdSe. In particular, ZnO quantum dots have emerged as an “experimentally friendly” material, and their © 2013 American Chemical Society and Division of Chemical Education, Inc.

■

THEORY

The simplest quantum-confinement model is the particle in a one-dimensional box.15 In this model, the particle is subjected to a constraining potential resulting in its confinement to the region of 0 ≤ x ≤ lx where lx is the “length of the box”.15 The available energy levels (En) are given by Published: December 9, 2013 280

dx.doi.org/10.1021/ed300693d | J. Chem. Educ. 2014, 91, 280−282

Journal of Chemical Education En =

n2ℏ2π 2 2lx2

Laboratory Experiment

dehydrate, Zn(C2H3O2)2·2H2O, with tetramethyl ammonium hydroxide pentahydrate, N(CH4)4OH·5H2O. Approximately 0.03 g of Zn(C2H3O2)2·2H2O (98% purity, Sigma-Aldrich) is dissolved in 7 mL of ethanol (200 proof, Decon Labs). A tetramethyl ammonium hydroxide solution is made by dissolving 0.07 g of N(CH4)4OH·5H2O (97%, Sigma-Aldrich) in 7 mL of ethanol. Formation of the ZnO nanoparticles is initiated by adding 0.10 mL of the tetramethyl ammonium hydroxide solution to a fused silica cuvette containing 0.25 mL of the zinc acetate solution and 1 mL of ethanol. The growth of ZnO nanoparticles is monitored by measuring the UV−vis absorption spectrum from 230 to 390 nm as a function of time. Absorption spectra are acquired 1, 2, 4, 8, 16, and 32 min after initiation of the reaction. The solution is transferred from the cuvette to a sealed vial where it was held for two days after which a final absorption spectrum is measured.

(1)

The energy levels are quantized, indexed by n where n = 1, 2, ..., ∞. The model also predicts that the energy levels depend on the length of the box as En ∝ 1/l2x. A long-standing experiment in physical chemistry laboratories is the application of this model to describe the absorption spectra of conjugated alkenes.16 The electrons residing in the π-conjugated orbitals are treated as residing in a box defined by the conjugation, and a study of conjugated molecules of varying length is performed to test the validity this model. For semiconductor nanocrystals, a three-dimensional (3D) version of the particle-in-a-box model is used to describe the change in energy levels with particle size. In semiconductors, absorption of a photon promotes an electron from the valence band to the conduction band, leaving a “hole” in the valence band. The electron−hole pair is referred to as an exciton. In the bulk, the electron and hole occupy a volume characterized by the exciton Bohr radius, which depends on the electronic structure and dielectric constant of the semiconductor. For example, this radius is 56 Å for CdSe9 and 24 Å for ZnO.12 When the nanocrystal radius is comparable to the Bohr radius, confinement effects are observed corresponding to an increase in the band gap energy. The confinement of an electron (or hole) in the nanocrystal can be modeled assuming spherical symmetry, or the “particle-in-a-sphere” model. In spherical polar coordinates, the time-independent Schrodinger equation is −

■

HAZARDS Safety goggles should be worn at all times during the experiment. Ethanol is flammable and should not be used around open flames. Tetramethyl ammonium hydroxide is highly toxic by ingestion, and somewhat toxic by skin absorption. Disposable gloves should be worn when handling this material. Zinc acetate is reactive with oxidizing agents.

■

RESULTS The absorption spectrum of the ZnO nanoparticle solution as a function of time is shown in Figure 1. After 1 min, a transition

ℏ2 ⎛ ∂ 2 2 ∂⎞ 1 ̂2 L ψ (r , θ , ϕ) ⎜ 2 + ⎟ψ (r , θ , ϕ) + 2m ⎝ ∂r r ∂r ⎠ 2mr + V (r )ψ (r , θ , ϕ) = Eψ (r , θ , ϕ)

(2)

The potential energy term is defined as V(r) = 0 when the particle is inside the sphere of radius a (0 ≤r ≤ a) and V(r) = ∞ everywhere else. The band gap energy derived from this model depends on the nanocrystal radius (R):8,13 bulk + E bg = E bg

ℏ2π 2 ⎛ 1 1 ⎞ ⎜ ⎟ + mh* ⎠ 2R2 ⎝ me*

(3)

Here, Ebg is band-gap energy of a nanocrystal with radius R, Ebulk eg is the band-gap energy of the bulk semiconductor, and m* e and m*h are the electron and hole effective masses. Due to dielectric screening, the electron and hole effective masses are smaller than that of a free electron. Because the photogenerated electron and hole have opposite charges, they attract one another via Coulomb interaction such that the band-gap energy of the semiconductor is less than expected from eq 3. This stabilization is referred to as the exciton binding energy, and a correction term is added to eq 4 to account for this effect: bulk E bg = E bg +

1 ⎞ 1.8e 2 ℏ2π 2 ⎛ 1 ⎟ ⎜ + − mh* ⎠ 4πεε0R 2R2 ⎝ me*

Figure 1. UV−vis absorption spectra collected during of ZnO nanocrystal growth. Spectra were taken at various times after initiation of the reaction as indicated. The lowest-energy absorption band provides a measure of the band-gap energy.

centered at ∼290 nm is observed corresponding to the band gap of the semiconductor. As the particles grow, this transition shifts to longer wavelengths (lower energy) ultimately reaching ∼340 nm in 48 h. Data analysis involves determining the band-gap energy from the electronic absorption spectrum by identifying the wavelength at which the rising edge of the absorption band edge is half of the bend maximum (λhalf) and converting this wavelength to energy. Next, the particle diameter is determined using the following empirical relationship:11

(4)

Here, ε is the dielectric constant of the semiconductor and ε0 is the vacuum permittivity. The central prediction of eq 5 is that the band-gap energy should scale as 1/R2.

■

EXPERIMENT Students typically perform this experiment individually. ZnO nanocrystals are formed through the reaction of zinc acetate 281

dx.doi.org/10.1021/ed300693d | J. Chem. Educ. 2014, 91, 280−282

Journal of Chemical Education ⎛ 1240 ⎞ − a⎟D2 + cD + b = 0 ⎜ ⎝ λhalf ⎠

■

AUTHOR INFORMATION

Corresponding Author

(5)

*E-mail: [email protected].

where D is the diameter of the particles in angstroms (Å). The empirical constants in eq 5 are taken from the literature: a = 3.301, b = −294.0, and c = −1.09.11 With the constants and λhalf values, the quadratic equation is solved to determine D. With particle diameters in hand, a plot of band-gap energy versus (radius)−2, or (D/2)−2, is constructed (Figure 2). The prediction of the particle-in-a-sphere model is that the band gap of the ZnO nanoparticle scale as R−2, and the data are in excellent agreement with this prediction.

Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This work was supported by the National Science Foundation (PJR: DMR 1005819, DRG: CHE 1151726). REFERENCES

(1) Debije, M. G.; Verbunt, P. P. C. Thirty Years of Luminescent Solar Concentrator Research: Solar Energy for the Built Environment. Adv. Energy Mater. 2012, 2, 12. (2) Jin, Z. W.; Hildebrandt, N. Semiconductor Quantum Dots for in Vitro Disgnostics and Cellular Imaging. Trends Biotechnol. 2012, 30, 394. (3) Kramer, I. J.; Sargent, E. H. Colloidal Quantum Dot Photovoltaics: A Path Forward. ACS Nano 2011, 5, 8506. (4) Singh, R.; Nalwa, H. S. Medical Applications of Nanoparticles in Biological Imaging, Cell Labeling, Antimicrobial Agents, and Anticancer Nanodrugs. J. Biomed. Nanotechnol. 2011, 7, 489. (5) Nirmal, M.; Brus, L. Luminescence Photophysics in Semiconductor Nanocrystals. Acc. Chem. Res. 1999, 32, 407. (6) Bawendi, M. G.; Steigerwald, M. L.; Brus, L. E. The Quantum Mechanics of Larger Semiconductor Clusters (Quantum Dots). Annu. Rev. Phys. Chem. 1990, 41, 477. (7) Winkelmann, K.; Noviello, T.; Brooks, S. J. Preparation of CdS nanoparticles by First-Year Undergraduates. J. Chem. Educ. 2007, 84, 709. (8) Nedeljkovic, J. M.; Patel, R. C.; Kaufman, P.; Joycepruden, C.; Oleary, N. Synthesis and Optical Properties of Quantum-Size Metal Sulfide Particles in Aqueous Solution. J. Chem. Educ. 1993, 70, 342. (9) Rice, C. V.; Giffin, G. A. Quantum Dots in a Polymer Composite: A Convenient Particle-in-a-Box Laboratory Experiment. J. Chem. Educ. 2008, 85, 842. (10) Wong, E. M.; Bonevich, J. E.; Searson, P. C. Growth Kinetics of Nanocrystalline ZnO Particles from Colloidal Suspensions. J. Phys. Chem. B 1998, 102, 7770. (11) Meulenkamp, E. A. Synthesis and Growth of ZnO Nanoparticles. J. Phys. Chem. B 1998, 102, 5566. (12) Wood, A.; Giersig, M.; Hilgendorff, M.; Vilas-Campos, A.; LizMarzan, L. M.; Mulvaney, P. Size Effects in ZnO: The Cluster to Quantum Dot Transition. Aust. J. Chem. 2003, 56, 1051. (13) Hale, P. S.; Maddox, L. M.; Shapter, J. G.; Voelcker, N. H.; Ford, M. J.; Waclawik, E. R. Growth Kinetics and Modeling of ZnO Nanoparticles. J. Chem. Educ. 2005, 82, 775. (14) Schwartz, D. A.; Norberg, N. S.; Nguyen, Q. P.; Parker, J. M.; Gamelin, D. R. Magnetic Quantum Dots: Synthesis, Spectroscopy and Magnetism of Co2+ and Ni2+ Doped ZnO Nanocrystals. J. Am. Chem. Soc. 2003, 125, 13205. (15) Engel, T.; Reid, P. J. Physical Chemistry; Pearson: Upper Saddle River, NJ, 2013; p 345−349. (16) Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical Chemistry, 8th ed.; McGraw Hill: Dubuque; 2008; pp 393− 397.

Figure 2. Experimental (eq 5; diamond) and theoretical (eq 4; square) ZnO band-gap energy versus particle size. Error bars for experimental values lie within the points. Both experiment and theory demonstrate the expected linear relationship between band-gap energy and R−2, where R is particle radius. The data presented in the figure were acquired by a student and represent the quality of data routinely acquired.

The experimental results can also compared to the theoretical predictions of eq 4 using values for the various constants for ZnO obtained from the literature:13 Ebulk bg = 3.4 eV, m*e = 0.25me = 0.25(9.1 × 10−31 kg), m*h = 0.45me = 0.45(9.1 × 10−31 kg), and ε = 3.7. With these values, the predicted dependence of Ebg on particle radius is calculated and plotted versus R−2 (Figure 2). The agreement between experiment and theory is modest for smaller particles, but improves with particle size. For the smallest particles (R = 10.4 Å), the predicted band gap is 4.6 eV versus the experimental value of 4.2 eV, a ∼10% difference in energy. Similar limitations of the theoretical model in describing the variation of the particle band-gap energy with particle size have been noted and attributed to modeling the nanocrystal environment as a spherical dielectric continuum.12

■

SUMMARY Over 200 students have successfully performed this experiment over the past 5 years. This laboratory is typically performed after coursework in quantum mechanics to reinforce concepts encountered in a more theoretical context.

■

Laboratory Experiment

ASSOCIATED CONTENT

S Supporting Information *

A complete description of the laboratory including instructions for students performing the lab. This material is available via the Internet at http://pubs.acs.org. 282

dx.doi.org/10.1021/ed300693d | J. Chem. Educ. 2014, 91, 280−282