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## Absorption Spectra of Nano-particles

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**CHEM 4396 (W237)**Physical Chemistry Laboratory Fall 2009 Absorption Spectra of Nano-particles Instructor: Dr. Aleksey I. Filin**-**Absorption Spectra of Nano-particles CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Introduction Electron energy band structure in semiconductor Conduction band Forbidden band Electron energy Energy gap Valence band Eph>Eg If the photon energy is higher than the energy gap the electron can be excited We work with CdSe nanostructures (quantum dots) Energy gap of bulk CdSe is Eg = 1.829 eV @ room temperature Instructor: Dr. Aleksey I. Filin**-**Absorption Spectra of Nano-particles CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Introduction Electron energy band structure in semiconductor Conduction band Forbidden band Electron energy Energy gap + Valence band Electron being excited left in the valence band positively charged quasi-particle known as the electronic hole, or the hole. Positively charged hole interacts with negatively charged electron by Coulomb interaction. Instructor: Dr. Aleksey I. Filin**-**Absorption Spectra of Nano-particles CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Introduction Electron energy band structure in semiconductor Conduction band Forbidden band Electron energy Energy gap + Valence band Exciton: Large and strongly interactive particles formed when an electron, excited by a photon into the conduction band of a semiconductor, binds with the positively charged hole it left behind in the valence band. Exciton Bohr radius is the smallest possible orbit for the electron, that with the lowest energy, is most likely to be found at a distance from the hole Instructor: Dr. Aleksey I. Filin**Lack of mass negative mass**Lack of charge negative charge Absorption Spectra of Nano-particles CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Introduction Electron energy band structure in semiconductor m is negative! Why the effective charge of the hole is positive? Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Introduction A Quantum Dot is: A crystal of semiconductor compound (eg. CdSe, PbS) with a diameter on the order of the compound's Exciton Bohr Radius Or: A nanostructure that confines the motion of Excitons in all three spatial directions Exciton is an atomic-like quasi-particle, so, its energy spectrum is similar to that for Hydrogen atom Instructor: Dr. Aleksey I. Filin**y**y y y z z z z x x x x Absorption Spectra of Nano-particles CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Introduction Low dimensional structures 2D 3D 1D 0D Quantum well: motion is not confined in 2 dimensions Quantum wire: motion is not confined in 1 dimensions Quantum Dot: motion is confined in all dimensions Bulk: motion is not confined at all Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Introduction Wavefunction of Electron in Quantum Well Energy WF of electron in QW can contain only integer number of half wavelength -> Energy spectrum of electron in QW is discrete Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Introduction Wavefunction of Electron in Quantum Well Energy Energy level shifts towards higher energy for smaller size Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Absorption Spectra (in diagram form) Bulk Absorbance Single QD in theory 0 Eg Photon energy Lowest exciton state Energy spectrum of exciton in QD is discrete (or quantized) (similar to spectrum of electron in QW) Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Absorption Spectra (in diagram form) Position of lowest exciton state (as well as other states) depends on particle size: energy level shifts towards higher energy for smaller size (similar to electron in quantum well) Each sample contains mostly the particles of certain average size. There is also some amount of particles of bigger and smaller sizes. Average size Smaller size Absorbance Bigger size 0 Eg Photon energy Absorption lines have near-Gaussian shape due to near-Gaussian particles size distribution Absorption lines are broadened due to particles size distribution: Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Absorption Spectra (in diagram form) Absorbance 0 Eg Photon energy Lowest exciton state For each sample, the lowest exciton state position is defined by average particle size Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Absorption Spectra (in diagram form) Absorbance 1hr 2hrs 4hrs 0.5hrs 0 Photon energy Samples were heat treated @7000C for different times (0.5, 1, 2 and 4 hrs). Average particle size increases with increasing of heat treatment time. Absorption peak position shifts towards lower energy with average particle size increasing. Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Typical absorption spectra of CdSe nanoparticles Real experimental lines are broadened due to particles size distribution Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 • Our goals: • investigate the absorption spectra of nanoparticles (QDs) embedded in glass; • define the lowest exciton absorption peak position for each sample; • analyze the data and calculate an average particle size for each sample. Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Measurements Spectrophotometer measures absorbance vs. wavelength Theory works with absorbance vs. photon energy Absorbance Absorbance 0 0 0 0 Wavelength Photon energy Lowest exciton state To transfer wavelength into energy, use the formula: Instructor: Dr. Aleksey I. Filin**y**y y x x x Absorption Spectra of Nano-particles CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Data Analysis Gaussian Parabola Gaussian + Parabola + = Maximum of (Gaussian + Parabola) curve is shifted in comparison with that for the Gaussian curve. To find the correct position of Gaussian we have to subtract the background from the summary curve Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Data Analysis Parabola (result of your fit) Gaussian + Parabola (your experimental curve) Absorbance Gaussian 0 0 Wavelength • Pick 2 points on the left and 2 points on the right shoulders of the peak • Fit this 4 points with parabola • Subtract the parabola from the experimental curve • You get the unshifted position of the lowest exciton absorption peak • Find the wavelength, corresponding to the maximum position • Calculate the energy, corresponding to this wavelength Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Data Analysis Energy can be calculated using formula E[eV]=1240/l[nm] In theory, dependence of the shift of lowest exciton absorption state Ex on nanoparticle radius r can be approximately expressed as: Ex = Eg + 0.038[eV]+ 2.4[eV*nm2]/r2 (After Ekimov et al, J. Opt. Soc. Am. B10, January 1993) Energy gap of bulk CdSe is Eg = 1.829 eV So, you know the Ex for the particle, you can calculate the particle size as: Instructor: Dr. Aleksey I. Filin**Absorption Spectra of Nano-particles**CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Summary We measure the absorption spectra of CdSe nanoparticles in glass We define the energy of lowest exciton absorption peak position We estimate the average size of the nanoparticles in each sample Instructor: Dr. Aleksey I. Filin