第五讲半导体量子阱

1、第六讲 Semiconductors quantum wellsQuantum confined structuresGrowth and structure of semiconductor quantum wellsElectric levelsOptical absorption and excitonsOptical emissionQuantum wires and dots1Quantum confined structuresThe optical properties of solids do not usually depend on their size. Ruby! Fo

2、r very small crystals, then the optical properties do in fact depend on the size. Semiconductor doped glasses. The size dependence of the optical properties in very small crystals is a consequence of the quantum confinement effect. Quantum confinement effect (量子限制效应或量子尺寸效应）:The Heisenberg uncertaint

3、y principle tells us that if we confine a particle to a length x, then we introduce an uncertainty in its momentum given by: If the particle is free and has a mass m, the confinement in the x direction gives it an additional kinetic energy of magnitude ：This confinement energy will be significant on

4、ly if it is comparable to or greater than the kinetic energy of the particle (kBT)2Quantum effects criterion It means quantum size effects will be important if: x must be of the same order of magnitude as the de Broglie wavelength deB for the thermal motion in order to obtain obvious quantum effects

5、. For an electron in a typical semiconductor with me* = 0.1m0 at room temperature, x must be 5nm in order to observe quantum confinement effects. Very thin layers.3Quantum WellQuantum WireQuantum Dot1D confinement2D confinement3D confinementThree basic types of quantum confined structures Bulk: 3-D

6、crystals; Quantum wells: 2-D crystals; Quantum wires: 1-D crystals; Quantum dots: 0-D crystals.Preparation techniques:Quantum Wells: advanced epitaxial crystal growthQuantum Wires: lithographic techinique or by epitaxial growthQuantum Dots: lithographic patterning or by spontaneous growth techniques

7、4第六讲 Semiconductors quantum wellsQuantum confined structuresGrowth and structure of semiconductor quantum wellsElectric levelsOptical absorption and excitonsOptical emissionQuantum wires and dots5Growth and structure of semiconductor quantum wellsEpitaxial crystal growth techniques: molecular beam e

8、pitaxy (MBE, 分子束外延) and metal-organic chemical vapour deposition (MOCVD，金属有机物化学气相沉积)d is chosen to be close to: quantized motion in the z direction, and free motion in the x, y plane. Energy band structure: electrons and holes are trapped in GaAs layer due to the discontinuity of energy band.multipl

9、e quantum wells (MQWs): Have larger b values; isolatedSuperlattices: Have much thinner barbers; coupled and new extended states are formed in the z direction; additional properties. 6第六讲 Semiconductors quantum wellsQuantum confined structuresGrowth and structure of semiconductor quantum wellsElectri

10、c levelsOptical absorption and excitonsOptical emissionQuantum wires and dots7Separation of the variables The electrons and holes in a quantum well layer are free to move in the x, y plane but are confined in the z direction. This allows us to write the wave functions in the form: Free motion in the

11、 x, y plane, the states can by described by the wave vector k:Quantized energy in the z direction described by the quantum number n:The total energy for an electron or hole in the nth quantum level is therefore given by: 8Infinite potential wellsThe Schrodinger equation: The boundary condition: The

12、wave function:This form of wave function describes a standing wave inside the well: The energy that corresponds to the nth level is given by: 9The energy of the levels is inversely proportional to the effective mass and the square of the well width. the electrons, heavy holes and light holes will al

13、l have different quantization energies. In the valence band, the heavy holes are dominant in most situations because they form the ground state level.The wave functions can be identified by their number of nodes, the nth level has (n - 1) nodes. States of odd n have even parity, and vice versa. (-z)

14、 = + (z) (even parity) or (-z) = - (z) (odd parity). 10Finite potential wellsGaAs/Al0.3Ga0.7As quantum well In real quantum wells with finite barriers, the particles are able to tunnel into the barriers to some extent, and this allows the wave function to spread out further and thus reduces the conf

15、inement energy. The infinite well model overestimates the quantization energy.The quantization energies of holes are smaller than those of electrons (smaller mass)(meV)11第六讲 Semiconductors quantum wellsQuantum confined structuresGrowth and structure of semiconductor quantum wellsElectric levelsOptic

16、al absorption and excitonsOptical emissionQuantum wires and dots12Selection rules The selection rule for an infinite quantum well: n=0; (Fermis golden rule)13In finite quantum wells, there are small departures from the above selection rule.n 0 transitions are usually weak, and transitions are strict

17、ly forbidden if n is an odd number, because the overlap of states with opposite parities is zero. 14Two-dimentional absorptionThe threshold corresponds to the transition from the ground state of the valence band (the n=1 heavy hole level) to the lowest conduction band state (the n=1 electron level):

18、Ee1Ehh1Eg is the band gap of the quantum well material. The optical absorption edge of the quantum well has a blue shift by (Ehh1+Ee1) compared to the bulk semiconductor. The frequency of absorption edge can be tuned by the choice of well width.15Considering the free motion in x, y plane, the total

19、energy of electron and holes related to the conduction band bottom or the valence band to should be:The energy of the transition shown by the vertical arrow in E-kxy diagram: is the electron-hole reduced effective mass 16The joint density of states for a 2-D material is independent of energy and is

20、given by: The absorption coefficient of quantum well will have a step-like structure! The threshold energy for the nth transition:The blue-shift of the absorption edge by the confinement energy is evident.Step-like sturcture of QW absorption spectra17The measured absorption spectrumHeavy holeLight h

21、olen=1n=2Step like behavior.Strong peak at the edge of each step: excitonic effects.Weak peaks indentified by arrows are caused by n 0 transitions. 18Excitons in quantum wellsEnhancement of the excitonic binding energy in the quantum well due to quantum confinement effects. (10 meV vs. 4.2 meV for G

22、aAs).Excitons in quantum wells are still stable at RT.19第六讲 Semiconductors quantum wellsQuantum confined structuresGrowth and structure of semiconductor quantum wellsElectric levelsOptical absorption and excitonsOptical emissionQuantum wires and dots20Optical emissionThe electrons and holes injected

23、 electrically or optically rapidly relax to the bottom of their bandsThe lowest levels available to the electrons and hole correspond to the n = 1 confined states. The luminescence spectrum consists of a peak of spectral width kBT at energy:The emission peak is shifted to higher energy compared to t

24、he bulk semiconductor. 21Zn0.8Cd0.2Se: Eg=2.55eV 22Quantum wells offer three main advantages over the equivalent bulk materials: The blue-shift of the luminescence peak by the confinement energy can be controlled by the choice of the well width. The increased overlap between the electron and hole wave functions in the quantum well means that the emission probability is higher. Short radiative lifetime and higher energy efficiency.The thickness of the quantum wells is well below the critical thickness for dislocation formation in non