Nano Science (Lec8 Bandgap Engineering)

Nano Science (Lec8 Bandgap Engineering) - MAE 287/EE 257 1...

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MAE 287/EE 257 1
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InSb InAs GaSb AlSb InP GaAs Ge Si SiC (6h) AlN (w) AlN (z) GaN (w) GaN (z) InN (w) InN (z) AlAs GaP AlP CdTe CdSe ZnTe CdS MgSe MgS ZnSe ZnS 10 20 30 0 10 -10 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.5 2.0 5.0 0 1 2 3 4 5 6 7 1.8 2 2.2 2.4 2.6 2.8 3 II-VI III-V (indir) III-V (dir) IV-IV Bandgap ( eV) Interatomic Distance ( A ) Wavelength ( m ) m Bandgap Engineering : By selecting the materials with appropriate bandgap and turning the bandgap by altering the sizes of quantum structures. 2
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3 The bandgap increases with decreasing quantum dot size. Because of this, smaller quantum dots are expected to emit light at higher energy (lower wavelength, a blue shift) and larger dots are expected to fluoresce (emit) at longer wavelengths (red shift). 22 , 2 * * 3 1 1 = + ( + ) 2L g g bulk eh h E E mm
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In natural materials, the electronic structures are defined by structures of atoms, molecules, and solids. However, we can modify the electronic structures further by controlling the sizes and dimensions to create 2D (quantum well), 1D (quantum wire) and 0D (quantum dot) structures. 4
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A quantum well is a potential well that confines electrons and holes to two dimensions. The effects of quantum confinement take place when the quantum well thickness becomes comparable at the de Broglie wavelength of the electrons and holes (usually smaller than ~100 nm). Quantum wells are formed in semiconductors by having a material, like gallium arsenide sandwiched between two layers of a material with a wider bandgap, like aluminum arsenide. The electronic and optical properties of such "quantum" semiconductor structures are profoundly altered from those of the bulk semiconductors. 5
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E c Conduction Band Edge E v Valence Band Edge This band structure is different for different materials. When two materials such as GaAs and AlGaAs joined together, the band offsets between the conduction and valance bands and acts as a potential barrier to confine the electrons. 6
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E 0 is the band edge of conduction or valance bands. Along x and y directions, the electrons and holes are moving like a free electron but with an effective mass m*, For a QW grown along z with a width L z . The Schrodinger’s equation can be written as 2 2 0 * ( ( ) ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 x y z V z x y z E E x y z m   ) ( ) ( * 2 2 2 2 x E x x m x ) ( ) ( * 2 2 2 2 y E y y m y * 2 2 2 m k E x x * 2 2 2 m k E y y 7
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22 0 2 () V(z) ( ) ( ) ( ) 2* xy z z E E E E z mz  Along z direction, the Schrodinger’s equation becomes, 0 2 * 2 * y x z k k E E E mm From the result of infinite potential well, with ) L n ( * 2 2 z 2 m E z With n=1,2,… 8
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The total energy E - k dispersion relation 22 2 2 0 z n E = E + ( ) 2 * 2 * 2 * L y x k k m m m  9
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This note was uploaded on 04/17/2011 for the course MAE 287 taught by Professor Yongchen during the Winter '11 term at UCLA.

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Nano Science (Lec8 Bandgap Engineering) - MAE 287/EE 257 1...

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