Potential well

A generic potential energy well.

A potential well is the region surrounding a local mini-mum of potential energy. Energy captured in a potentialwell is unable to convert to another type of energy (kineticenergy in the case of a gravitational potential well) be-cause it is captured in the local minimum of a potentialwell. Therefore, a body may not proceed to the globalminimum of potential energy, as it would naturally tendto due to entropy.

1 Overview

Energy may be released from a potential well if sucientenergy is added to the system such that the local maxi-mum is surmounted. In quantum physics, potential en-ergy may escape a potential well without added energydue to the probabilistic characteristics of quantum parti-cles; in these cases a particle may be imagined to tunnelthrough the walls of a potential well.The graph of a 2D potential energy function is a potentialenergy surface that can be imagined as the Earths sur-face in a landscape of hills and valleys. Then a potentialwell would be a valley surrounded on all sides with higherterrain, which thus could be lled with water (e.g., bea lake) without any water owing away toward another,lower minimum (e.g. sea level).In the case of gravity, the region around a mass is a grav-itational potential well, unless the density of the mass isso low that tidal forces from other masses are greater thanthe gravity of the body itself.A potential hill is the opposite of a potential well, and isthe region surrounding a local maximum.

2 Quantum connement

Quantum connement is responsible for the increase of energydierence between energy states and band gap. A phenomenontightly related with the optical and electronic properties of thematerials.

Quantum connement can be observed once the di-ameter of a material is of the same magnitude as thede Broglie wavelength of the electron wave function.[1]When materials are this small, their electronic and op-tical properties deviate substantially from those of bulkmaterials.[2]

A particle behaves as if it were free when the conningdimension is large compared to the wavelength of the par-ticle. During this state, the bandgap remains at its orig-inal energy due to a continuous energy state. However,as the conning dimension decreases and reaches a cer-tain limit, typically in nanoscale, the energy spectrum be-comes discrete. As a result, the bandgap becomes size-dependent. This ultimately results in a blueshift in lightemission as the size of the particles decreases.Specically, the eect describes the phenomenon result-ing from electrons and electron holes being squeezed intoa dimension that approaches a critical quantum measure-ment, called the exciton Bohr radius. In current appli-cation, a quantum dot such as a small sphere connes inthree dimensions, a quantum wire connes in two dimen-sions, and a quantumwell connes only in one dimension.These are also known as zero-, one- and two-dimensionalpotential wells, respectively. In these cases they refer tothe number of dimensions in which a conned particlecan act as a free carrier. See external links, below, for ap-

1

2 4 REFERENCES

plication examples in biotechnology and solar cell tech-nology.

2.1 Quantum mechanics view

See also: Particle in a box

he electronic and optical properties of materials areaected by size and shape. Well-established technicalachievements including quantum dots were derived fromsize manipulation and investigation for their theoreticalcorroboration on quantum connement eect.[3] The ma-jor part of the theory is the behaviour of the exciton re-sembles that of an atom as its surrounding space shortens.A rather good approximation of an excitons behaviour isthe 3-D model of a particle in a box.[4] The solution ofthis problem provides a sole mathematical connection be-tween energy states and the dimension of space. It is ob-vious that decreasing the volume or the dimensions of theavailable space, the energy of the states increase. Shownin the diagram is the change in electron energy level andbandgap between nanomaterial and its bulk state.The following equation shows the relationship betweenenergy level and dimension spacing: nx;ny;nz =

q8

LxLyLzsinnxxLx

sinnyyLy

sinnzzLz

Enx;ny;nz =

~222m

nxLx

2+nyLy

2+nzLz

2Research results[5] provide an alternative explanation ofthe shift of properties at nanoscale. In the bulk phase,the surfaces appear to control some of the macroscopi-cally observed properties. However in nanoparticles, sur-face molecules do not obey the expected conguration inspace. As a result, surface tension changes tremendously.

2.2 Classical mechanics view

The classical mechanic explanation employs Young-Laplace lawto provide evidence on how Pressure drop advances from scaleto scale.

The Young-Laplace equation can give a background onthe investigation of the scale of forces applied to the sur-face molecules:

p = r n^= 2H

=

1

R1+

1

R2

Under the assumption of spherical shape R1=R2=R andresolving Young Laplace equation for the new radiiR(nm) we estimate the new P(GPa). The smaller theR, the greater the pressure it is. The increase in pressureat the nanoscale results in strong forces toward the inte-rior of the particle. Consequently, the molecular struc-ture of the particle appears to be dierent from the bulkmode, especially at the surface. These abnormalities atthe surface are responsible for changes of inter-atomicinteractions and bandgap.[6][7]

3 See also Quantum well

Finite potential well

Quantum dot

4 References[1] M. Cahay (2001). Quantum Connement VI: Nanostruc-

tured Materials and Devices : Proceedings of the Interna-tional Symposium. The Electrochemical Society. ISBN978-1-56677-352-2. Retrieved 19 June 2012.

[2] Hartmut Haug; Stephan W. Koch (1994). Quantum The-ory of the Optical and Electronic Properties of Semiconduc-tors. World Scientic. ISBN 978-981-02-2002-0. Re-trieved 19 June 2012.

[3] Norris, DJ; Bawendi, MG (1996). Measurementand assignment of the size-dependent optical spec-trum in CdSe quantum dots. Physical Review B 53(24): 1633816346. Bibcode:1996PhRvB..5316338N.doi:10.1103/PhysRevB.53.16338. PMID 9983472.

[4] Brus, L. E. (1983). A simple model for the ion-ization potential, electron anity, and aqueous re-dox potentials of small semiconductor crystallites.The Journal of Chemical Physics 79 (11): 5566.Bibcode:1983JChPh..79.5566B. doi:10.1063/1.445676.

[5] Kunz, A B; Weidman, R S; Collins, T C (1981).Pressure-inducedmodications of the energy band struc-ture of crystalline CdS. Journal of Physics C: Solid StatePhysics 14 (20): L581. Bibcode:1981JPhC...14L.581K.doi:10.1088/0022-3719/14/20/004.

[6] H. Kurisu, T. Tanaka, T. Karasawa and T. Komatsu(1993). Pressure induced quantum conned exci-tons in layered metal triiodide crystals. Jpn. J.Appl. Phys. 32 (Supplement 321): 285287.doi:10.7567/jjaps.32s1.285.

3[7] Lee, Chieh-Ju; Mizel, Ari; Banin, Uri; Cohen, Mar-vin L.; Alivisatos, A. Paul (2000). Observationof pressure-induced direct-to-indirect band gap transi-tion in InP nanocrystals. The Journal of ChemicalPhysics 113 (5): 2016. Bibcode:2000JChPh.113.2016L.doi:10.1063/1.482008.

5 External links Buhro WE, Colvin VL (2003). Semiconduc-tor nanocrystals: Shape matters. Nat Mater2 (3): 1389. Bibcode:2003NatMa...2..138B.doi:10.1038/nmat844. PMID 12612665.

Semiconductor Fundamental Band Theory of Solid Quantum dots synthesis Biological application

4 6 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

6 Text and image sources, contributors, and licenses6.1 Text

Potential well Source: http://en.wikipedia.org/wiki/Potential%20well?oldid=645545720 Contributors: Bdesham, Patrick, Fuelbottle, Jr-dioko, LucasVB, RetiredUser2, Rgrg, D6, Goochelaar, Laurascudder, KronicDeth, Grick, Bantman, Fasten, Linas, Rjwilmsi, Mgrueter,Chobot, YurikBot, Bob Stromberg, Jryden, SmackBot, Bill3000, RDBrown, DroEsperanto, Sadi Carnot, Spiritia, Euchiasmus, Nitro-master101, Pavithran, CmdrObot, Manuelkuhs, Unmitigated Success, Cydebot, Ohgrebo, Headbomb, Father Goose, TheNoise, Alek-sander.adamowski, R'n'B, Tdadamemd, Inteloutside2, SieBot, SchreiberBike, Rswarbrick, JiminyX, XLinkBot, MystBot, Pozdneev,Addbot, Luckas-bot, Yobot, Adi, Kulmalukko, Crystal whacker, Materialscientist, Yshen8, LucienBOT, Ysyoon, Pvkwiki, Alph Bot,Newty23125, ZroBot, JoeSperrazza, Donner60, ClueBot NG, Mudarahmed, Helpful Pixie Bot, Bibcode Bot, Rob Hurt, Kenanwang,Anrnusna and Anonymous: 39

6.2 Images File:Potential_energy_well.svg Source: http://upload.wikimedia.org/wikipedia/commons/c/c5/Potential_energy_well.svg License: Pub-

lic domain Contributors: Based upon Image:Potential well.png, created by User:Koantum. This version created by bdesham in Inkscape.Original artist: Benjamin D. Esham (bdesham)

File:Quantum_confinement_1.png Source: http://upload.wikimedia.org/wikipedia/commons/5/5e/Quantum_confinement_1.png Li-cense: CC BY-SA 3.0 Contributors: Own work Original artist: Yshen8

File:Quantum_confinement_2.png Source: http://upload.wikimedia.org/wikipedia/commons/7/70/Quantum_confinement_2.png Li-cense: CC BY-SA 3.0 Contributors: Own work Original artist: Yshen8

6.3 Content license Creative Commons Attribution-Share Alike 3.0

OverviewQuantum confinementQuantum mechanics viewClassical mechanics view

See alsoReferencesExternal linksText and image sources, contributors, and licensesTextImagesContent license