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quantum dots

Discussion in 'Electronic Design' started by Jamie M, Nov 18, 2011.

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  1. Jamie M

    Jamie M Guest

    Hi,

    What does it mean to say a "quantum dot" is restricted in 3 spatial
    dimensions:

    http://en.wikipedia.org/wiki/Quantum_dot

    "A quantum dot is a portion of matter (e.g. semiconductor) whose
    excitons are confined in all three spatial dimensions"

    Does this just refer to the direction that light is emitted from the
    "quantum dot"? Are all quantum dots typically spheres in order to
    fulfill the 3 spatial dimension requirement? Basically it is just a 3d
    diode or LED?

    I don't understand why people think they can use them for single photon
    sources either, but I guess it is because there is only one way for the
    electrons to switch from the conduction band to the valence band?

    cheers,
    Jamie
     
  2. : What does it mean to say a "quantum dot" is restricted in 3 spatial
    : dimensions:

    It means that the width, length and thickness of the conductor are
    all small. 'Small' means small-enough so that the electron energy can
    only take discrete values (energy level separation becomes larger than
    thermal energy). In macroscopic conductors the energy levels are so
    close to each other that they form a (thermally smeared) continuum.
    The reason why energy level spacing is related with the conductor size
    is that the de Brogile wave of the electron must make an integer number
    of nodes between the conductor edges.

    A typical way to make a Qdot is to start with a GaAs-AlGaAs wafer with a
    buried heterojunction layer - electrons are confined in the thickness
    direction by the potential wall within the heterojunction, and they
    form so called 2DEG, or 2-dimensional electron gas. Then one can etch
    a mesa on the wafer, confining them in width and length directions, too.
    Alternatively one can use gates to deplete the 2DEG evereywhere else
    except at the Qdot location.

    Note that the dot size which qualifies as 'quantum' is larger at
    cryogenic temperatures - even smallish energy level separations
    resolve as discrete, when thermal smearing is less.

    Regards,
    Mikko
     
  3. Tim Williams

    Tim Williams Guest

    QM in solids works like this:

    You take an atom of stuff. It has discrete energy levels according to the
    electron shell structure, all that stuff of which is reasonably well
    described with atomic spectral theory and whatnot. The energy level
    spacings on the order of a few eV, which is convieniently near the visible
    spectrum, which means a lot of atoms glow visibly when you put them in a
    hot flame (strontium, barium and copper being very important examples), or
    a discharge tube (neon, etc.), etc.

    When you rub two atoms together, two things can happen: either nothing
    happens (noble gasses, pretty much) and they go on their merry way, or
    their energy levels start distorting because their electrons 'feel' each
    other. When this happens, the energy bands skew, split and squash; total
    energy drops and the atoms stick together. Now you have a diatomic
    molecule, which has different energy levels, usually lower (fractional to
    several eV). But the important part to remember: there are more energy
    levels now.

    Suppose you keep introducing still more atoms. Sometimes they will
    stick -- carbon likes to stick to itself, but only in some ways. Like
    nanotubes. Those are produced in great quantity, along with other
    carbonaceous bric-a-brak, in a sooty flame (which is rich in diatomic C2,
    and various radicals like CH2 and CH, which glow blue, incidentially).
    Some won't stick together, like nitrogen and oxygen, which form diatomic
    molecules and that's that. But a lot of them (most of the periodic table)
    will keep glomming on.

    Each additional atom brings more energy levels, and pretty soon you get
    big gloms of energy bands -- there are so many atoms and so many energy
    levels that they look continuous, even though they are, in principle,
    discrete.

    Incidentially, as atoms come together, they form wads of levels for some
    reason. These are the valence and conduction bands familiar from
    semiconductor physics. The conduction bands are comparable to the higher
    energy levels of hydrogen (n > 1), they aren't used normally (in "cold"
    matter), they're just open, available. These are the conduction and
    valence bands.

    In reality, the levels are spaced maybe a few neV apart, which is utterly
    destroyed by all but the coldest conditions. In principle, you should be
    able to do some RF resonance (what's a 1neV photon, the AM radio band? --
    oh hey, good guess, it's actually an octave below:
    https://www.google.com/search?q=1e-9+elementary+charge+*+volt+/+planck+constant )
    with any superultrahypermegacold matter, at least if you can spontaneously
    polarize it (e.g., kick an electron into a conduction band in a
    semiconductor, I suppose). But at room temperature, those levels are
    completely scattered (like having 5 LSBs worth of noise on a 24 bit ADC),
    so you can't measure them and they are, in fact, continuous bands at
    nonzero temperatures.

    Anyways, the thing about QDs is, okay so we started with a quantized
    material, and it's still made of the same stuff, but now just by sheer
    virtue of it's being huge, it's magically unquantized now. Well, in that
    intermediate stage, when you've got gloms of just a few thousand atoms, so
    the bands aren't really continuous, at least not at room temperature. And
    the bandgap likewise isn't as well defined. In fact, nanoparticles of
    familiar things, like copper and gold (which have such a low conduction
    band that pretty much every atom contributes a charge carrier!) may have
    such unusual band structures that they, too, can glow like molecules and
    semiconductors! Well, I don't know if that's true of metal particles, but
    it is true of low-bandgap semiconductors, like CdTe. Or they might have
    weird chemistry -- it's one thing to form a chemical complex with a single
    atom, or a couple, but you get different surface chemistry when you have a
    very "round" particle (dozens of atoms across), versus a fairly flat
    crystalline surface (typical of bulk solids).

    You can pretty easily synthesize a colloidial suspension of CdSe, CdTe,
    etc. by precipitation from the salts, and by controlling the particle size
    precisely (concentration, temperature, additives), achieve a whole rainbow
    of fluorescent colors, because the QD bandgap is much wider. You also get
    to do middle-range things with the intra-band levels on the really small
    particles, like I suppose, microwave to THz resonances, maybe IR.

    Okay, so we can't "do" anything with QDs yet besides shine lasers on them
    and make glowy things, but the obvious potential is there -- if we could
    organize quantum wires up to them, we could carry electrons with about the
    right energy levels to this that and the other thing, and do who knows
    what.

    Tim
     
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