Chemistry 2302 Nanocrystals Winter 2012 Spectroscopic Properties of Cadmium-­‐
Selenium Nanocrystals Recommended Preparatory Reading http://www.mrsec.wisc.edu/Edetc/nanolab/CdSe/index.html shows the synthesis procedure with videos that show each step being performed. Experiment 45 in Shoemaker, 8th ed., entitled “Spectroscopic Properties of CdSe Nanocrystals” Introduction This experiment is essentially Shoemaker’s Experiment 45, “Spectroscopic Properties of CdSe Nanocrystals”. CdSe nanocrystals (NCs) of different sizes will be synthesized. The visible absorption spectra of the NCs will be measured and their radii and various spectroscopic parameters will be determined. CdSe NCs are among the most widely studied semiconductor NCs. These have a hexagonal wurtzite crystal structure, which can be seen in Shoemaker’s Figure 1a (page 493 of 8th edition). A model of a NC is pictured in Figure 1b. The size of such NCs can be controlled by reaction kinetics. Once formed, the NC surface can be passivated (capped) by attaching organic ligands to prevent agglomeration. We will prepare nanocrystals with radii ranging from 1 to 2 nm. These NCs will have well defined spectral peaks with wavelengths, 𝜆𝜆, of 450 – 585 nm. If you have already done the particle-­‐in-­‐a-­‐box experiment you will know that a free electron in a one-­‐dimensional box of length 𝐿𝐿 can have energy levels, 𝐸𝐸 , given by the expression 𝐸𝐸 =
ℎ 𝑛𝑛
8𝑚𝑚 𝐿𝐿
Equation 1 where ℎ is Plank’s constant, 𝑛𝑛 is the principal quantum number and 𝑚𝑚 is the mass of the electron. This model can be extended to apply to an electron confined to a three-­‐dimensional rectangular box to yield similar expressions for each of the 𝑥𝑥 , 𝑦𝑦 and 𝑧𝑧 coordinates. The total energy is given by the sum of the three energies. If the electron is confined inside a sphere, the two lowest energy levels, 𝐸𝐸 and 𝐸𝐸 , are given as 𝐸𝐸 =
and 𝐸𝐸 = 2.04
Equation 2 With 𝑎𝑎 the radius of the sphere. Note that this model predicts that the energy level spacing increases proportional to 1 𝑎𝑎 as the radius increases. Chemistry 2302 Nanocrystals Winter 2012 All semiconductors have a band gap, 𝐸𝐸 , between the valence band and the conduction band. The band structure of CdSe NCs is shown in Shoemaker’s Figure 2 (page 494 of 8th edition). Here, 𝑘𝑘 is the wave vector. The kinetic energy of the electron is proportional to 𝑘𝑘 and the energy minimum of the conduction band and the maximum of the valence band occur at 𝑘𝑘 = 0 (corresponding to 𝑎𝑎 = ∞ in the bulk sample). The valence bands have sixfold degeneracy and contain, at 0 K, the six Se valence electrons. Spin-­‐orbit coupling causes the degeneracy to split into a fourfold degenerate 𝐽𝐽 = 3/2 band and a twofold degenerate 𝐽𝐽 = 1/2 valence band (𝑉𝑉 ) at 𝑘𝑘 = 0. For 𝑘𝑘 ≠ 0 the fourfold degenerate 𝐽𝐽 = 3/2 band splits into two doubly degenerate bands: the heavy hole valence band 𝑉𝑉 and the light hold valence band 𝑉𝑉 . If one sets zero energy at the top of the 𝑉𝑉 band, then, according to band theory, the 𝐸𝐸 − 𝑘𝑘 relations for the conduction band 𝐸𝐸 (𝑘𝑘) and valence band 𝐸𝐸 (𝑘𝑘) are 𝐸𝐸 𝑘𝑘 = 𝐸𝐸 +
ℎ
𝑘𝑘 8𝜋𝜋 𝑚𝑚∗
Equation 3 𝐸𝐸 𝑘𝑘 = −
ℎ
𝑘𝑘 8𝜋𝜋 𝑚𝑚∗
Equation 4 Here 𝑚𝑚∗ and 𝑚𝑚∗ are the effective masses of the electron and the positive hole created with a electron is excited from the valence band to the conduction band. We can see that the form of these equations is similar to that for a free electron in a sphere (Equation 2) but with a negative sign for the energies of the hole. The electronic structure of a CdSe NC can be semiquantitatively represented by a simple effective mass parabolic-­‐band model, in which the finite NC size quantizes the allowed 𝑘𝑘 values to 𝑘𝑘 = 𝑛𝑛 with 𝑛𝑛 = 1, 2, … . A smaller NC radius will increase the value of 𝑘𝑘 and the energy separation between the valence and conduction bands increases, as indicated in Figure 2. Thus the fundamental (𝑛𝑛 = 1) frequency of a photon that excites an electron into the conduction band from the valence band, as given by this model, is ℎ𝜈𝜈 = Δ𝐸𝐸 = 𝐸𝐸 − 𝐸𝐸 = 𝐸𝐸 +
ℎ
ℎ
ℎ
+
=
𝐸𝐸
+
8𝑚𝑚∗ 𝑎𝑎 8𝑚𝑚∗ 𝑎𝑎 8𝜇𝜇𝑎𝑎 Equation 5 where 𝐸𝐸 and 𝐸𝐸ℎ are the energies of the electron and hole respectively and 𝜇𝜇 is the reduced mass given by 𝜇𝜇 =
∗
∗ ∗
∗ = 0.097𝑚𝑚 . The use of this quantum confinement model ignores the fact that when an electron is excited into the conduction band and a positive hole is left behind in the valence Chemistry 2302 Nanocrystals Winter 2012 band, the hole and electron are coulombically attracted (opposite charges attract one another). The electron and hold can be treated as a quasiparticle called an exciton. For a NC, the basic model for an electron-­‐hole exciton, first proposed by Brus in 1983, involves a number of simplifying assumptions. Firstly, the NC is assumed to be a sphere having a radius 𝑎𝑎 . Secondly, the interior of the NC is assumed to be a uniform dielectric medium with a dielectric constant 𝜅𝜅 (𝜅𝜅 = 10.2 for CdSe). In other words, the excited electron and the hole are assumed to be the only charged particles in the sphere. Finally, the potential energy is assumed to jump from zero inside the NC to infinity outside. The Schrödinger equation for the Brus strong confinement model can be solved analytically to yield hydrogen-­‐like wavefunctions and the energy needed to create the exciton in its ground state (𝑛𝑛 = 1). The resulting energy is 𝜈𝜈 =
Where 𝜈𝜈 ≡
(cm)
≡
(nm)
Δ𝐸𝐸
1.8𝑒𝑒 ℎ
= Δ𝐸𝐸 = 𝐸𝐸 + 𝐸𝐸 −
+
4𝜋𝜋ℎ𝑐𝑐𝜀𝜀 𝜅𝜅𝜅𝜅 8𝑐𝑐𝑐𝑐𝑎𝑎 ℎ𝑐𝑐
Equation 6 is the wavenumber (cm-­‐1) of the transition frequency for the absorption or luminescence fundamental (i.e. 𝑛𝑛 = 1) band of a NC. The term is an approximate coulombic interaction term and the term 𝐸𝐸 is a small polarization energy whose size dependence can be ignored. In the case of this experiment, one could also ignore the size variation of the coulombic interaction term. Equation 6 would then reduce to the approximate form 𝜈𝜈 ≈ 𝐸𝐸 +
ℎ
8𝑐𝑐𝑐𝑐𝑎𝑎 Equation 7 with 𝐸𝐸 = 𝐸𝐸 + 𝐸𝐸 −
. , where is an average over the range of NC radii studied. 𝐸𝐸 can be treated as a constant since is value is mostly due to 𝐸𝐸 and the weak variation of the coulombic term has been suppressed over a short range of a values. Note that Equation 7 has the same dependence as the parabolic-­‐band model (Equation 5) but the constant terms differ. This experiment will be concerned with the two simple electronic state models presented above. A more exact treatment of the electronic states of CdSe NCs requires nonparabolic bands that can be coupled to each other, a treatment of the energy dependence of the effective masses, consideration of both the nonshpericity of the NCs and the leakage of the wavefunction out of the confines of the NC, and inclusion of electron-­‐hole exchange. These refinements are beyond the scope of this experiment; however, it is remarkable that many essential features of NC spectroscopy can be captured by the very simple models presented above. Chemistry 2302 Nanocrystals Winter 2012 Experimental Synthesis Prior to the lab period, your instructor has prepared a Se stock solution by adding 60 mg of powered Se metal and 10 mL of octadecene to a 50 mL round-­‐bottom flask in a fume hood over a stirring hot plate. 0.8 mL of trioctylphosphine (a coordinating ligand to enable dissolution of the Se and to coat the surface of the final NCs) was added to the flask, along with a magnetic stir bar. The mixture was heated and stirred until the Se was completely dissolved. The solution was then transferred to the stoppered 50 mL Erlenmeyer flask now containing it. Your work will begin with the preparation of a fresh sample of Cd precursor solution. NCs will be formed when the Se stock solution is added to the hot Cd precursor solution. You will withdraw samples of this mixture at predetermined times yielding CdSe NC samples with crystals having radii ranging in from 1 to 2 nm. Warning: Selenium metal and compounds containing cadmium are toxic. Also, cadmium compounds are labeled as potential carcinogens. All synthesis operations with Se and CdO (except for weighing) are to be done in a fume hood. Disposable gloves MUST be worn for the duration of the experiment. Be extremely careful not to spill any of the chemicals. If a spill does occur, inform your instructor immediately. 1. In the fume hood in C-­‐3041B, remove the 50 mL round bottom flask from the heating mantle. Using a cork ring for support, tare (zero) the flask on an analytical balance and add to it 26 mg of CdO. Please try not to spill any CdO. Back in the hood, clamp the flask in the heating mantle as it was when you found it. 2. Add 20 mL of octadecene to the flask with a graduated cylinder. 3. Add 1.2 mL of oleic acid (a coordinating ligand) to the flask using an Eppendorf pipette. If your instructor has not already done so, as him/her to demonstrate the proper use of this pipette. 4. Place the mercury thermometer found in the hood into the flask and turn the on the variable transformer to which the heating mantle is connected (90 setting). Occasionally, gently stir the mixture. Warning: The contents of the round bottom flask will be heated to a high temperature (225 oC). Before heating, ensure that the flask is tightly and securely clamped in the heating mantle. Also, the heated flask MUST NOT be moved, under any circumstances, until the solution contained within has cooled to room temperature. Spilling the hot solution on your skin will result in severe burns! 5. Obtain 10 large test tubes in a rack and number them 1 -­‐ 10. Place the tubes in order in the rack. 6. OPTIONAL: Place a small amount of dry ice in the bottom of each tube shortly before performing the next step. When the samples are removed cooling them quickly will result in NCs having a small range of radii and well-­‐defined spectroscopic peaks. Chemistry 2302 Nanocrystals Winter 2012 7. As the temperature of the Cd precursor solution nears 225 oC one partner should fill a 2 mL pipette with Se solution. As soon as the temperature reaches 225 oC he/she should quickly add the Se solution to the flask and then stir the mixture quickly with the thermometer and remove it. The other partner should be ready to start the timer when the pipette is half drained. 8. As the NCs grow in size, the partner that added the Se solution will use a 9” Pasteur pipette to remove approximately 2 mL samples and quickly place each sample into an appropriately labeled test tube. The suggested removal times are listed below: VIAL: 1 2 3 4 5 6 7 8 9 10 -­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐ REMOVAL TIME (s): 10, 20, 30, 40, 50, 65, 85, 110, 140 , 180 It is difficult to remove the samples exactly at the times listed above; therefore, as each sample is removed the second partner should record the time of removal to the nearest second. As you can see, the partner working at the fume hood must be work quickly (yet carefully!) when removing the first 5 samples, as there is not much time in between samples. Also, try to remove as much sample as possible with the 9” pipette (squeeze the bulb fully when aspirating samples into the pipette). Warning: The solution that is being sampled is very hot (~225 oC). Be very careful when performing this part of the procedure. Use only one hand to hold the pipette and withdraw the samples. The other hand should be kept out of the hood, thus avoiding the risk of hot solution dripping or spilling on it. 9. When all samples have been collected turn of the variable transformer. Wait for the samples to reach room temperature before proceeding. Do not attempt to unclamp the 50 mL round bottom flask for cleaning until it has cooled completely. Spectroscopy For absorption spectra, the concentration of the NC solutions should be such that the solutions in a 1 cm path length cuvette show a well defined maximum at the n=1 exiciton peak. Obtain spectra over the 350 nm – 700 nm range using the HP 8452A UV/visible diode array spectrophotometer. The cuvettes used are made of quartz and hold a volume of 4 mL. They need to be at least half full or the spectrometer’s light beam will not go through the solution. If you do not have enough sample to half fill the cuvette you may need to raise the cuvette in the sample holder slightly (~ 1 cm) so that the light beam will go through the sample. The spectra shown on the monitor are low resolution, therefore, it will be difficult to determine the wavelength of maximum absorption of the exciton peak for this reason and because the peaks lie on a sloping baseline; however, plotting the spectra in Excel will allow you to determine the wavelengths of the peak maxima more easily. After all measurements have been made. Save the spectra data files from the instrument registers onto a floppy disk. Take the disk to another computer with a floppy drive and transfer the files Chemistry 2302 Nanocrystals Winter 2012 to your flash drive (if you do not have a flash drive you may e-­‐mail them to yourself. Your instructor will explain the format of the data files and how to copy the data into Excel. Results In Excel, Label a column “Wavelength (nm)” and generate a list of wavelengths from 350 – 700 nm (or whatever wavelength range that was used) in 2 nm intervals. In subsequent columns paste the absorption intensity data from the data files you saved. For each sample plot absorption vs. wavelength on the same graph. Have a different color curve for each sample and a legend. Determine the wavelength, 𝜆𝜆, of the 𝑛𝑛 = 1 exciton peak of each sample. Tabulate these wavelengths in Excel. Yu et al. have determined the following empirical relation between the radius, 𝑎𝑎 (in nm), of CdSe NCs and the wavelength, 𝜆𝜆 (in nm), of the first (reddest) absorption maximum: 𝑎𝑎 = 0.8061 ×10 𝜆𝜆 − 1.3288 ×10 𝜆𝜆 + 0.8121×10 𝜆𝜆 − 0.2139𝜆𝜆 + 20.79 Equation 8 Use this relationship to determine the size of your synthesized NC samples. The values of 𝑎𝑎 calculated in this way are not based on the quantum models we wish to test. Plot a graph of the translational energy, 𝜈𝜈 cm ≡
regression analysis. Report the values of =
vs. . Fit the data with a and 𝐸𝐸 . To test the importance of retaining the explicit dependence of the coulombic term shown in equation 6 one can calculate this term for each 𝑎𝑎 value and subtract it from 𝜈𝜈 , yielding 𝜈𝜈 +
1.8𝑒𝑒 ℎ
= 𝐸𝐸 + 𝐸𝐸 +
4𝜋𝜋ℎ𝑐𝑐𝜀𝜀 𝜅𝜅𝜅𝜅
8𝑐𝑐𝑐𝑐𝑎𝑎 Equation 9 Plot a graph of the left hand side of equation 9 vs. and perform a regression analysis to yield the equation of the best-­‐fit line. Again, report the values of use of one equation over the other? and 𝐸𝐸 + 𝐸𝐸 . Do the fits clearly favor the Chemistry 2302 Nanocrystals Winter 2012 Discussion For the range of sizes studied, compare the contribution of the coulombic term with that from the quantum confinement term (see Equation 6). From the values obtained by fitting with equations 7 and 9, calculate 𝜇𝜇 /𝑚𝑚 and compare these values with the value 0.097 for an exciton in bulk CdSe. According to equation 9, the intercept value is 𝐸𝐸 + 𝐸𝐸 . Estimate 𝐸𝐸 using the bulk CdSe band gap value of 1.75 eV (14,110 cm-­‐1). From the two parameter fit with equation 7, the intercept can be taken to be 𝐸𝐸 = 𝐸𝐸 + 𝐸𝐸 −
. studied. Using a suitable average value for , where is an average over the range of NC radii , calculate 𝐸𝐸 and compare it with the value obtained from equation 9. Is the assumption that the polarization energy is small compared to 𝐸𝐸 justified?