lecture1casgs-納米科學(xué)概論-wenkub
2023-05-21 18:20:40 本頁(yè)面
【正文】 and bound states 1D potential well of infinite depth: ?????? ??? ot h e r w i s e , ax0 if 0,)( xV V(x) 0 a x ?n ?n ????? ??? o t h er w i s e ,0ax0f o r x ) ,s i n ()( n an πAxn? )(22 222222nn kmanmkn ??? ??? ??Confined, discrete energy levels, with n = 1, 2, 3… Groundstate (n =1) energy = h2/(8ma2), zeropoint or confinement energy Potential wells of finite depth: ????? ??? o t h er w i s e ,0axa if ,0V)( xVFor negative E, only a certain number of E values are allowed. The particle remains confined, but not pletely within the well. For E above zero, any values are allowed, the probability of finding particle does not approach zero away from the well: The particle is free Quantum well: particle confined by a 1D potential well, but free in other 2D, quantum states labeled by n, kx and ky: )(2),( 222 222 yxyx kka nmkkn ??? ?? ?Each n represents a branch or subband Quantum wire: particle confined by 2D potential wells, free only in 1D (1D free particle), quantum states labeled by n1, n2 and kz: )(2),( 22 2222 212221 zz kb na nmknn ??? ??? ?Quantum dot: particle confined by potential wells in 3D, quantum states labeled n1, n2 and n3: )(2),( 22322222122321 bnanmnnn ??? ?? ?All discrete levels, like in atom Density of states (DOS): N(E) ? N(E)?E = number of states with energies of E to E + ?E ? Plays a important role in many physical processes: conductivity, light emission, magism, chemical reactivity… ? A measurable quantity to characterize a physical system, . to determine the dimensionality 1D: plane wave [?(x) = A exp(ikx)], with periodic boundary conditions: ?(L) = ?(0) and Lxxxx ??????? ?? 0 (L ? ? later) k and ? only take values: ,2Lnkn ?? mkk nn 2)(22??? , n = 0, ?1, ?2,… k L6π? L4π? L2π?0 L2π L4π L6π1D kspace amp。 MOS EF 反相層 低維電子系統(tǒng)制備與輸運(yùn)實(shí)驗(yàn) Further confinement to 2DEG ? 1DEG (Qwire) ? 0D (QD) Quantum pointcontact 量子觸點(diǎn) Conductance through a short wire or constriction (quantum point contact) between two leads of 2DEG Quantized conductance as a function of gate voltage Vg Ntrans can be changed by varying splitgate bias Vg Classical effect in transport through nanoparticles: Coulomb blockade Coup
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