9. Semiconductor Devices /Phonons

Transcription

1 Technische Universität Graz Institute of Solid State Physics 9. Semiconductor Devices /Phonons Oct 29, 2018

2 p and n profiles p n V bi ~ 1 V E c W ~ 1 m E F E max ~ 10 4 V/cm ev bi E v p Ev E F Nv exp kt B n EF E c Nc exp kt B The electric field pushes the electrons towards the n-region and the holes towards the p-region. Diffusion sends electrons towards the p-region and holes towards the n-region.

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4 Diode I I s ev exp 1 kt B

5 Zener tunneling Electrons tunnel from valence band to conduction band Occurs at high doping

6 Light emitting diodes Solid state lighting is efficient.

7 Light emitting diodes absorption reflection total internal reflection Electrons and holes are injected into the depletion region by forward biasing the junction. The electrons fall in the holes. For direct bandgap semiconductors, photons are emitted. For indirect bandgap semiconductors, phonons are emitted.

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9 Equivalent circuit Solar cell

10 Solar spectrum

11 JFETs Junction Field Effect Transistors low noise

12 Bipolar transistor collector base emitter n p n + lightly doped p substrate

13 MOSFETs Metal-oxide semiconductor field effect transistors oxide

14 Heterojunctions Quantum hall effect Quantized conductance HBTs HEMTs

15 HEMT High electron mobility transistor HBT Hetero junction bipolar transistor Modulation doped field effect transistor High electron mobility transistor

16 Phonons

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18 In a normal mode, all of the atoms oscillate at the same frequency. Natalia Bedoya

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20 Phonons N atom atoms in crystal 3N atom normal modes p atoms in the basis N atom /p unit cells N atom /p translational symmetries N atom /p k-vectors 3p modes for every k vector 3 acoustic branches and 3p-3 optical branches

21 Normal modes are eigenfunctions of T x x u u exp i lka mka nka t lmn These are eigenfunctions of T. k y y u u exp i lka mka nka t lmn k z z u u exp i lka mka nka t lmn k T u u i lk a pa mk a qa nk a ra t x exp x i lpk a1 qmk a2 rnk a3 u exp i lk a k 1 mk a2 nk a3 t x pqr lmn k exp x exp ilpka qmka rnka u lmn

22 fcc 2 x dulmn 2 C m u u u u u u u u dt 2 x x x x x x x x l1mn lmn l1mn lmn lm1n lmn lm1n lmn x x x x x x x x ul 1mn 1ulmn ul 1mn1ulmn ulm1n 1ulmn ulm 1n 1ulmn y y y y y y y y ul 1mn ulmn ul 1mn ulmn ulm1n 1ulmn ulm 1n 1ulmn u z z lm z z 1 1 z z 1 1 z z n ulmn ulm n ulmn ul mn ulmn ul 1mn 1ulmn and similar expressions for the y and z motion

23 fcc Substitute the eigenfunctions of T into Newton's laws. l nkya x x x l m kxa m n kza ulmn uexp i lka1mka2nka3 uexp i. k k

24 3N degrees of freedom fcc phonons

25 Phonon dispersion Au From Springer Materials: Landholt Boernstein Database

26 Materials with the same crystal structure will have similar phonon dispersion relations Cu Au

27 fcc phonons energy spectral density internal energy density specific heat

28 Table summarizing the thermodynamic properties of phonons

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30 Two atoms per primitive unit cell NaCl Si

31 GaAs Hannes Brandner

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33 Phonon quasiparticle lifetime Phonons are the eigenstates of the linearized equations, not the full equations. Phonons have a finite lifetime that can be calculated by Fermi's golden rule. 2 2 f H i E E i f ph ph f i Occupation is determined by a master equation (not the Bose-Einstein function). dp 0 0 i 1 0 N 0 dt i0 P0 dp i N1 P 1 i1 dt P N dp N 0N 1N Ni i N dt

34 Acoustic attenuation The amplitude of a monocromatic sound wave decreases as the wave propagates through the crystal as the phonon quasiparticles decay into phonons with other frequencies and directions.