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by: Alexandria Bauch


Alexandria Bauch
GPA 3.94


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Class Notes
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This 9 page Class Notes was uploaded by Alexandria Bauch on Monday October 26, 2015. The Class Notes belongs to CHEM1410 at University of Pittsburgh taught by Staff in Fall. Since its upload, it has received 53 views. For similar materials see /class/229441/chem1410-university-of-pittsburgh in Chemistry at University of Pittsburgh.




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Date Created: 10/26/15
Chapter 5 Particle in finite box Vx 0 a2 lt x lt 32 V0 for x 3 32 X E 3932 a2 a2 d2 2mE inside box 2 2 dx h outside box V0 n5 I tzI B39ek exponentially decaying 111 gym 2 Ae k n4 2mE m II lHCsinkxDcoskx k hz dv require that V and Econtinuous match at the boundaries a2 x a2 W1a2 lHa2 VIIa2 lWm 072 tunneling w a2 maz vim2 w39m oz2 zero energy gap 2 metal empty leVeIS large energy gap 2 insulator lled levels smallgap gt semiconductor Na cores Apply electrical potential gt charge will flow for metal V0 Tunneling through barrier 34 v0 Can showtunneling is proportional to 2ay 2mV0 Eh2 e E E 14 v0 i tunneling most important when particle light energy near top of barrier barrier width is small Note if E gt V0 the particle can be reflected by the barrier resonances E particle can tunneHng bound gt Examples 0 radioactive decay o temporary anions Be39 N23 benzene electron falls off 39 N 14 n10 sec V How can one measure something with such a short lifetime Chapter 5 continued Scanning tunneling microscopy STM invented 20 years ago at IBM Research Labs ZiJrich lt tip lt adsorbate l D lt surface Apply voltage measure current often run so that as the tip is scanned over the surface the height is varied so as to keep the current constant the tip does not actually touch the surface electrons tunnel between tip and surface Atomic resolution tunneling dominated by single atom at the end of the tip VVhy Used to study defects and adsorbed molecules on surfaces Si100 surface rows of silicon dimers Si Si Si Si PP s Si a Si 3 7 V39eW Si Si Si Si Si Si 0 0 Si Si Si Si STM measurements John Yates Pitt show 3 binding sites of acetylene on the surface H H I39KCSi Si Si 6 si row H H 6 SI 63 b SI direction Si Si H H C C H Si Si ONO dimer bridging two acetylene l0 two dimers molecules on two dimers can also study tunneling through molecules CH CH S 2 2 tunnelln current CHZ CH3 9 falls off exponentially I STM tip with distance hydrocarbon bridge Reaction is 10152 times faster than expected at T 10 K HF It proceeds via tunneling ratherthan going over the barrier conduction quantum and GaAs has a wells I gap smaller band a W valence g p j band AlaGa1aAs Make a layered device AlaGa1As X I GaAs AlaGamAs Electron is free in y 2 directions and confined in the x direction Such systems can act as lasers quantum dots O O lt CdSe dots 2 nm 5 nm emits green red fluorescence used as tags to study processes in cells


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