Modern Physics for Frommies IV The Universe - Small to Large Lecture 4

Transcription

1 Fromm Institute for Lifelong Learning University of San Francisco Modern Physics for Frommies IV The Universe - Small to Large Lecture 4 3 February 06 Modern Physics IV Lecture 4 Agenda Administrative matters Molecular Spectra Rotational Energy Levels Vibrational Energy Levels Solids -Band theory in solids -Bands and energy gaps -Conductors, insulators and semiconductors -Devices -Doping -Diodes -Transistors Lasers 3 February 06 Modern Physics IV Lecture 4 Administrative Matters UC Berkeley 06 Oppenheimer Lecture Monday 8 February 06 at 5:30 PM Chevron Auditorium at International House Free and open to the public Symmetry, Topology & Electronic Phases of Matter Charles Kane Professor of Physics, University of Pennsylvania 3 February 06 Modern Physics IV Lecture 4 3 Molecular spectra Atoms combine molecules ψ s of outer electrons overlap => energy levels altered. Additional degrees of freedom: rotation and vibration with quantized energy levels. Each atomic energy level becomes a set of closely spaced rotational and vibrational levels. Transitions appear as many very closely spaced lines. Lines are not always distinguishable. Spectra are called band spectra and fingerprint the molecule. 3 February 06 Modern Physics IV Lecture 4 4

2 Rotational energy levels: Consider a diatomic molecule (this analysis can be extended to polyatomic molecules). ( Iω) ( Iω) Erot = Iω = I where = ang. momentum L = 0,,, 3 February 06 Modern Physics IV Lecture 4 5 ( ) Q. M. Iω = L L + ħ L rotational angular momentum quantum number The rotational energy is then quantized Iω ħ Erot = = L( L + ) ; L = 0,,, I I Transitions between levels have the selection rule L = ± for the transition L L ħ ħ Erot = EL EL = L( L + ) ( L ) L I I ħ = L I 3 February 06 Modern Physics IV Lecture 4 6 µ-wave and far I. R. Frequencies, 3, 4, times higher than the lowest one. Reduced Mass Moment of inertia: I = mr + m r where mm µ = m + m = µr is called the reduced mass m m and r = r + r Note: m = m µ = = 3 February 06 Modern Physics IV Lecture 4 7 Attractive force, e.g. gravity or Coulomb. Replace the -body problem with a - body problem. mm µ = m + m Attractive force remains the same (not reduced q q e.g. F = 4πε 0 r 3 February 06 Modern Physics IV Lecture 4 8

3 Vibrational energy levels: Consider a diatomic molecule (this analysis can be extended to polyatomic molecules). Harmonic oscillator near r k ω SHO = m classical vibration frequency 0 Again, we must replace the mass m with the reduced mass mm µ = m + m If we solve the Schrodinger equation for SHO potential energy Evib = v + ωsho where ν = 0,,, ħ v is the vibrational quantum number Note: zero point energy: ħωsho for v = 0 Selection rule: v = ± 3 February /9/04 06 Modern USF Physi Physics IV Lecture February 06 Modern Physics IV Lecture 4 0 Rotational + Vibrational: Selection rules: v = ± L = ± Good for small v, then reality deviates from SHO approximation Transition energies 0. ev 0 00 times larger than rotational transitions infra-red 3 February 06 Modern Physics IV Lecture 4 3 February 06 Modern Physics IV Lecture 4 3

4 Consider a transition from a state with v and L to state with v+ and L ± A photon of energy E will be absorbed E = E + E vib vib rot = E + E rot ħ = ħωsho + ( L + ) L L + I ħ = ħωsho + L L L - I 3 February 06 Modern Physics IV Lecture 4 3 Expected spectrum for transitions between combined rotational and vibrational states Note that for L L+, L cannot be zero since L- = - is not an allowed state HCl Each line is split in because there are Cl isotopes of different m => different I 35 Cl and 37 Cl 3 February 06 Modern Physics IV Lecture 4 4 Solids Bonding in solids: Amorphous materials atoms and molecules show no long range order. e.g. glasses Crystalline materials atoms, ions, molecules in orderly 3-D array or lattice. e.g. NaCl Polymers show some or -D order, HHHHHHHHHH e.g. CH CCCCCCCCCCC HHHHHHHHHH Simple cubic Face-centered cubic Body-centered cubic 3 February 06 Modern Physics IV Lecture February 06 Modern Physics IV Lecture 4 6 4

5 NaCl Ionic bonding (There is also covalent bonding, e.g. C atoms in diamond, and bonds which are mixed) Each Na + feels attractive Coulomb potential due to 6 nearest Cl - neighbors and a repulsive potential from Na + farther away. Actually more complicated Na+ does not belong exclusively to Cl-. Do not treat ionic solids as composed of individual NaCl molecules 3 February 06 Modern Physics IV Lecture 4 7 Different in metals Outer electrons are free to roam amongst all the metal atoms. Atoms act like (+) ions. Attraction between metal ions and electron gas holds the solid together. Free electrons responsible for high electrical and thermal conductivity. Shininess of metals. Electrons reemit incident light. Electrons trapped in a metal are in potential well: Inside metal U = 0, high walls at surface. 3 February 06 Modern Physics IV Lecture 4 8 Band Theory of Solids 3 categories of solids: conductors free electrons at room temperature semiconductors not enough free electrons to explain relatively low conductivity insulators virtually no free electrons at room temperature Bring atoms close together so that their wave functions overlap. This results in different s and s levels corresponding to Ψ = ( ψ ± ψ ) S = 0, 3 February 06 Modern Physics IV Lecture February 06 Modern Physics IV Lecture 4 0 5

6 If 6 atoms are brought together And a large number of atoms Conductors: Highest energy band containing electrons is only partially filled or the bands overlap. If E is applied electrons can accelerate since empty higher energy states. Current flows readily. Highest energy band or bands overlap available unoccupied states. 3 February 06 Modern Physics IV Lecture 4 3 February 06 Modern Physics IV Lecture 4 Insulator: Highest (valence) band is completely filled. Next higher (conduction) energy band separated by a band gap of 5-0 ev. Room temperature, <K> /40 ev Almost no electrons can reach the conduction band 3 February 06 Modern Physics IV Lecture 4 3 Semiconductors: Like insulators except band gap is smaller, ~ ev. A few electrons may reach the conduction band => small current may flow with applied V. Number of conduction electrons increases with T. More than offsets more frequent collisions at higher T => ρ (resistivity) may decrease with T in a semiconductor. 3 February 06 Modern Physics IV Lecture 4 4 6

7 The above discussion of semiconductors refers to pure or intrinsic semiconductors. Current carriers: Apply potential difference to semiconductor The few electrons in the conduction band move toward the (+) Electrons in the valence band try to do the same and some succeed due to the empty states left by the e - that reached the conduction band. Each valence electron leaves behind a hole. The holes migrate towards the (-) 3 February 06 Modern Physics IV Lecture 4 5 Devices Doping: Addition of tiny amount of impurity into pure Si or Ge ( part in 0 6 or 0 7 ) Add As to pure Si As has 5 valence electrons, only 4 bind to lattice. Extra does not fit and acts like conduction electron Conductivity much higher than pure Si, controlled very precisely by concentration. (-) charges carry current => n-type 3 February 06 Modern Physics IV Lecture 4 6 Add Ga to pure Si Ga has 3 valence electrons, leaving hole in lattice. Electron moves to fill hole, hole moves in opposite direction Impurity additional states between bands n-type: donor states need only ~ 0.05 ev to reach conduction band. p-type: electrons can easily move from valence to acceptor states leaving holes behind. Again, conductivity much higher than for pure Si. (+) holes appear to carry current => p-type semiconductor Semiconductor electronic devices are made of combinations of p, n and i (intrinsic) materials 3 February 06 Modern Physics IV Lecture February 06 Modern Physics IV Lecture 4 8 7

8 Diodes: n-type joined to p-type. Separately the types are electrically neutral When joined a few electrons diffuse from n to p to fill holes. Forward bias Reverse bias + _ Equilibrium: Resulting potential difference prevents further diffusion. Now apply an external source of potential, e.g. a battery. 3 February 06 Modern Physics IV Lecture February 06 Modern Physics IV Lecture 4 30 Zener diode as voltage regulator: + Power supply - If power supply > breakdown diode maintains output voltage at breakdown value Full wave rectifier: ½ wave rectifier: 3 February 06 Modern Physics IV Lecture February 06 Modern Physics IV Lecture 4 3 8

9 Light emitting diodes (LED): Transistors: Forward bias npn V BE Photovoltaic or solar cells: pnp Reverse bias V BE Base bias voltage: V BE controls current flow thru device, emitter to collector or vice versa. 3 February 06 Modern Physics IV Lecture February 06 Modern Physics IV Lecture 4 34 npn V BE is (+) Electrons in emitter are attracted to base LASERs Light Amplification by Stimulated Emission of Radiation Produces a narrow intense beam of monochromatic coherent light monochromatic narrow frequency width coherent phase is constant across beam cross section Base is thin (~ µm) so electrons flow thru to collector which is (+) w.r.t. base. absorption Large current, I C, much smaller current, I B Small variation in V B large change in I C large voltage drop across R C. Small signal amplified into larger one. 3 February 06 Modern Physics IV Lecture 4 35 stimulated emission 3 February 06 Modern Physics IV Lecture

10 For lasing a population inversion must occur so that emission dominates over absorption. The excited state must be a metastable state (long lifetime) so that stimulated emission dominates over spontaneous, 3 February 06 Modern Physics IV Lecture February 06 Modern Physics IV Lecture 4 38 Ruby Laser Al O with small % of Al replaced with Cr 3 Cr does the lasing Flash lamp λ = 550 nm Holography Ordinary photography simply records the intensity as a function of position. This yields a -D image. A hologram produces 3-D images via interference, without lenses. He-Ne Laser 5% He + 85% Ne E ' is metastable 3 Decay to E ' triggered by collisions Gas discharge 3 February 06 Modern Physics IV Lecture 4 39 Illumination of the film with a laser beam produces a 3-D image. 3 February 06 Modern Physics IV Lecture

11 Reflected light from every point on the object reaches every point on the film. Interference between the two beams allows the film to record both the intensity and the relative phase of the light at each point. Note that information is stored in the pattern as a whole. Destruction of part of the hologram does not result in discrete destruction of part of the image but generates blurriness or loss of detail. 3 February 06 Modern Physics IV Lecture 4 4