Semiconductor Quantum Structures And nergy Conversion April 011, TTI&NCHU Graduate, Special Lectures Itaru Kamiya kamiya@toyota-ti.ac.jp Toyota Technological Institute
Outline 1. Introduction. Principle of Quantum Mechanics 3. Preparation of Quantum Structures pitaial Growth Colloidal Synthesis 4. nergy Conversion in Quantum Structures
nergy Conversion: Particle-Material Interaction Absorption (lectronic Transition), Luminescence, Scattering, Transmission, Imaging, etc. Size/Shape, lectronic States of Material Wavelength of light, nergy
CdSe Nanoparticles (Quantum Dots) Dispersed in Solvent ~.5nm ----> ~4.5nm f O =P ~1.nm CdSe PL Quantum fficiency 0~30% @RT in solvent!
What are we observing with colors? White light citation Green! Light yellow Supply of nergy (UV light) Why do we observe Green?
Colors by Metallic Nanoparticles Lucurgus cup: Greece, BC4C Gold nanoparticles dispersed in glass matri Observed by light a) transmission b) reflection Paul Maulvaney, MRS Bulletin, 6 (001) 1009.
Colors by Metallic Nanoparticles Transmission: Only RD passes (Blue, Green are absorbed or scattered) Reflection: Green Red are reflected (Blue is absorbed) Observed by a) Transmission or b) Reflection
Color Conversion and White Light 1.B R, G.UV R, G, B 3.Phosphor R,G,B (Display) Rare arth doped oides Semiconductor NPs White Application of InGaP
lectronic nergy Conversion in Semiconductors In Out amples lectron lectron lectronic devices (general) lectron Photon L, LD, Laser, lectron Heat Heaters lectron Chemical Reaction lectrochemical devices Photon lectron Photodetectors, Solar Cells, Photon Photon PL, Color conversion, Laser, Photon Heat Filters Photon Chemical Reaction Photochemical devics
citation and Relaation in Semiconductor Conduction Band Conduction Band Minimum Conduction Band g Forbidden Band (Bandgap) g Valence Band Maimum Valence Band Valence Band
citation and Relaation in Quantum Well Barrier Well V n=3 ml 3 9 0.3 ev 1 Conduction Band Minimum n= ml 4 AlGaAs 1.5 ev 0.06 ev H 1 GaAs AlGaAs Valence Band Maimum 0 n=1 0 L 1 ml y ( ) sin L n n ml n L
Quantum Confinement in Nanostructures e Barrier Well CBM Quantized States g,b g,w gn gw VBM Narrow Wide
Color Selection by Quantum Structures Narrow Wide
citation and Relaation in Semiconductors Under Bias CBM CBM g g VBM VBM Photoconductunce Photoluminescence in Q-Structure
Charge Injection in Semiconductor under Bias CBM CBM g g VBM VBM Conduction lectroluminescence
Photoecitation of Quantum Structures CBM CBM g g VBM VBM Photoluminescence Photoconduction
Two Possible Mechanisms for jecting Carriers from Q-Structures CBM D CB CBM g g VBM VBM D VB Quantum Tunneling Thermal Activation
Transmission through Potential Barrier I V m Calculate the tunneling probability and reflectance of a particle with mass m when it travels from region I with potential V 1 through region II with potential V into region III with potential V 3 (= V 1 ). V 1 I II III 0 d Solutions to the Schrödinger eq. in each region Boundary conditions, Since V 1 = V 3 = 0, k 1 = k 3,
T Transmission through Potential Barrier II T k k 3 1 c c 3 1 c c 3 1 V 1 sin 4 m V V d 1 For > V, T = 1 when For < V, 1.0 0.8 0.6 0.4 0. 0 Tunneling 1 3 4 5 6 7 8 9 10 /V By choosing the right thickness for a combination of / V, transmittance can be maimized or reflectance can be suppressed completely. Let b m V Then, for < V and bd >> 1, For AlGaAs-GaAs, m e = 0.067 m 0, V - ~ 1 ev
Tunneling through Potential Barrier: GaAs V V 1 m I II III 0 d 0.4eV Calculating the tunneling probability for V = 0.4 ev, V 1 = 6 mev, V 1 = V 3 = 0 T k k 3 1 c c 3 1 c c 3 1 V 1 sinh 4 V m V 31 19 For AlGaAs-GaAs, m e = 0.067 m 0, 0.067 9.110 0.41.610 8 b 8.4110 34 1.054 10 d 1 Ref: Thermal Current V ep kt
Current Resonant Tunneling Diode Metal n-gaas AlGaAs GaAs QW AlGaAs n-gaas 0.3 ev n-gaas 1.5 ev 1 CBM AlGaAs AlGaAs GaAs n-gaas Metal 0.06 ev H 1 VBM u.d.gaas n + -GaAs n + -GaAs Bias lectron F C AlGaAs AlGaAs qv b Resonant Voltage Bias Voltage
Boundary Conditions for Probability Current Density 1/ Schrodinger eq. is In quantum mechanics, the probability density r is given by Therefore, the time derivative is given by r t t * 1 i m H m Time dependent Schrodinger eq. is * t V The probability current density Hence, 1 i V * * r * * * i * * r V r S r i t H H is defined by m and its comple conjugate is H r S 0 t * * * Im i S m m m i t * H * The probability current density continuous at boundaries. S actually represents the flow of material, and needs to be
Boundary Conditions for Probability Current Density / Therefore, the boundary conditions are V m 1 m m 3 V 1 I II III 0 d The above need to be considered for dealing with heterostructures!
citation & Relaation in Quantum Structures e, hn, citation e - Relaation e - h + Luminescence (recombination) h + e - Conduction Band h + Non-radiative recombination (IR/heat dissipation) Valence Band e - h + Charge separation (Generation, chemical reaction)
Quantum Dots: lectronic States and Preparation Threshold current (normalized by 0 ) of semiconductor lasers (calculation) (a) Bulk T 0 = 104 (b) QW T 0 = 85 (c) QWR T 0 = 481 (d) QD T 0 = Fabrication process for QDs Y. Arakawa and H. Sakaki, Appl. Phys. Lett. 40 (198) 939 Y. Miyamoto, M. Cao, Y. Shingai, K. Furuya, Y. Suematsu, K. G. Ravikumar, and S. Arai, Jpn. J. Appl. Phys. 6 (1987) L5
Quantum Well Structures and lectronic States k z dk k 3D The volume between k & k+dk is 4k dk N() 1/ N() 1/ Bulk k ~nm Quantum Well (planar) ~nm ~nm ~nm Quantum Wire ~nm k y k y dk k dk dk -k 0 +k k D The area between k & k+dk is k dk N() = const. 1D The length between k & k+dk is dk N() -1/ 0D Discrete N() = d(-e) N() N() N() 0-1/ d(-e) ~nm Quantum Dot
),, (,, z y z y n n n z y z y n n n,, In a 3D system, with potential barrier V, dk k N ) ( where d D ) ( The number of DOS in volume L 3 is DOS for Low Dimensional Systems where Here, there is an electron in every L 3 in real space, or (/L) 3 in reciprocal space. Therefore, the number of states N(k) between k and k+dk is ),, ( ),, ( ) ( ) ( ) ( ),, ( z y L n z L n y L n z y z y z y z y Then, for each ais, The corresponding energy is ) ( d d m dk d,,
Summary Principle of Quantum Mechanics Solid State Physics, Statistical Mechanics Preparation of Quantum Structures pitaial Growth Colloidal Synthesis nergy Conversion in Quantum Structures Conversion of lectronic nergies Control of nergy Conversion