Yat Li Department of Chemistry & Biochemistry University of California, Santa Cruz CHEM 146_Experiment #6 A Visual Demonstration of “Particle in a Box” theory: Multicolor CdSe Quantum Dots

Objective In this laboratory experiment, we will learn: 1.The principle of interband transition and quantum confinement effect in zero dimensional quantum dots 2.Synthesis of CdSe nanocrystals 3.Absorption and Emission properties of CdSe nanocrystals

Semiconductor nanocrystals Nanocrystals are zero dimensional nanomaterials, which exhibit strong quantum confinement in all three dimensions, and thus they are also called “quantum dots”. Size dependent optical properties! UV light Ambient light

“Particle in a Box” theory Schrödinger equation: d2d2 dx 2 2m ħ2ħ2 + [E - V(x)]  (x) = 0 Free particle: the particle experience no potential energy  V(x) = 0 d2d2 dx 2 + 2mE ħ2ħ2 (x)(x) = 0 ħ = h/2  E = total energy of the particle; V(x) = potential energy of the particle; and  (x) = wavefunction of the particles a0x ∞∞  (0) =  (a) = 0 The particle is restricted to the region 0 ≤ x ≤ a; the probability that the particle is found outside the region is zero. Free particle in a one-dimensional box

“Particle in a Box” theory  (x) = A cos kx + B sin kx The general solution of Schrödinger equation: k = (2mE) 1/2 ħ 2  (2mE) 1/2 h = when  (0) = 0; cos (0) = 1; sin (0) = 0  A = 0 when  (a) = 0;  (a) = B sin ka = 0  B = 0 (rejected) or ka = n  n = 1, 2, 3…. Substitute k = n  /a back to equation for k; En =En = h2n2h2n2 8ma 2 n = 1, 2, 3….  E = h2h2 8ma 2 (n f – n i ) 2

Quantum dots CdSe has a Bohr exciton radius of ~56 Å, so for nanocrystals smaller than 112 Å in diameter the electron and hole cannot achieve their desired distance and become particles trapped in a box. A quantum dot is in analogy to the “particle in a box” model, where ΔE increases with decreasing a.  E = h2h2 8ma 2 (n f – n i ) 2 Free exciton

Synthesis of CdSe nanoparticles 30 mg of Se and 5 mL octadecene mL trioctylphosphine 3. completely dissolve the selenium Preparation of Se precursors: Preparation of Cd precursors: 1.2. a.Add 13 mg of CdO to a 25 mL round bottom flask b.add by pipet 0.6 mL oleic acid and 10 mL octadecene Heat the cadmium solution to 225 °C

Synthesis of CdSe nanoparticles Preparation of CdSe nanocrystals: 1. Transfer 1 mL of the room temperature Se solution to the 225 C Cd solution and start timing 2. Remove approximately 1 mL samples at 10s intervals (for the first five samples) 3. Ten samples should be removed within 3 minutes of the initial injection

Spectroscopy Spectroscopic techniques all work on the principle of that, under certain conditions, materials absorb or emit energy Quantized energy: photon E = h  E = h = hc/ X-axis: Frequency or wavelength

UV-vis Spectroscopy Transitions in the electronic energy levels of the bonds of a molecule and results in excitation of electrons from ground state to excited state Energy changes: 10 4 to 10 5 cm -1 or 100 to 1000 kJ mol -1 i)Within the same atom e.g. d-d or f-f transition ii)To adjacent atom (charge transfer) iii)To a delocalized energy band, conduction band (photoconductivity) iv)Promotion of an electron from valence band to conduction band (bandgap in semiconductors) Four types of transitions: A powerful technique to study the interband electronic transition in semiconductors!

Interband absorption Electrons are excited between the bands of a solid by making optical transition E f = E i + h Indirect bandgap: Relative position of conduction band and valence band is not matched The transition involve phonon to conserve momentum h < E g,  (h ) = 0 h ≥ E g,  (h ) = (h –E g ) ½ Direct bandgap:  indirect = (h –E g ± ħ  ) 2 E f = E i + h + ħ 

Beer-Lambert law log(I 0 /I) =  cl  = A/cl  : extinction coefficientI 0 : incident radiation c: concentrationI: transmitted radiation l: path lengthA: absorbance  value determine transition is allowed or forbidden

Spontaneous emission when electron in excited states drop down to a lower level by radiative emission Spontaneous emission rate:  R = A -1 Electron in excited states will relax rapidly to lowest level in the excited band Sharp emission peak Non-radiative emission: If  R <<  NR,  R  1 (maximum light will be emitted) Luminescence

Interband luminescence Direct bandgap materialsIndirect bandgap materials Allowed transition  short lifetime (ns) Narrow emission line close to bandgap e.g. GaN, CdS, ZnS Second order process involve phonon Low emission efficiency e.g. Si, Ge