Negative Resistance with a Single Atom
sciencebulletin.org
sciencebulletin.org
Here is the original report of the effect: https://journals.aps.org/pr/abstract/10.1103/PhysRev.109.603
> The Petkau effect is an early counterexample to linear-effect assumptions usually made about radiation exposure.
> Petkau had been measuring, in the usual way, the radiation dose that would rupture a simulated artificial cell membrane. He found that 3500 rads delivered in 2 1⁄4 hours (26 rad/min = 15.5 Sv/h) would do it. Then, almost by chance, Petkau repeated the experiment with much weaker radiation and found that 0.7 rad delivered in 11 1⁄2 hours (1 millirad/min = 0.61 mSv/h) also ruptured the membrane. This was counter to the prevailing assumption of a linear relationship between total dose or dose rate and the consequences.
Fun note - the pulses it produced were so narrow that one of the visiting oscilloscope dealers (I forget if it was LeCroy or Tektronix) was using it to test out timing resolution of their top model oscilloscopes! (Normally we had to use a sampling scope to see the pulses).
It was a "quantum well", and IIRC grown as using layers of doped GaAs. (I might be way off here, I didn't work on the fabrication).
If you plot current vs voltage across a device : an ideal textbook resistor has a straight line. Normal resistors will have some curvature but generally be monotonically increasing.
Out RTD showed a current that went up, then down a bit, then back up again. We biased it with a chosen current and load that put the current smack in the negative differential region. If you draw a horizontal line through this current, it intersects the graph at three voltage points. The middle voltage point has a negative slope, and is an unstable state. At this bias level, the device would flip back and forth between the two same-current points on either side where the slope was positive.
The cool part of this thing was that each 'bounce' sent an EM wave through a waveguide we attached, like an antenna, and the returning wave would trigger the next flip. So the length of the waveguide set the period of the oscillation. It had horrible timing jitter on its own, but we could make it very stable by driving it with a sinusoid oscillator.
As wise people have known for millenia, it's very important to keep one's word, but I submit it's even more important that the useless internet points be correctly awarded. I'm sure the millenia will bear me out on that.
I put these on GitHub, if anyone wants to play with it, this applet is from the top screenshot : https://github.com/jeffwass/Physics_Simulations/blob/master/...
Basically, in one dimension, we represented an atom as an infinitely-thin 'spike' in potential, a Dirac Delta function.
For a single 'atom', regardless of how much energy an incoming electron wave function has, some energy is always reflected back and a smaller amount goes through. (Here, energy and frequency are basically synonymous, where E = h * nu, h is Planck constant and nu is the frequency.)
For two atoms (a double barrier), certain input frequencies cause destructive interference of the reflected quantum wave function at the first atom (ie - the reflections bouncing off the first and second atom cancel out), and exactly 100% of the incoming energy transfers through! At certain other frequencies, the output waves cancel and the wave is entirely reflected. The plot of transmission vs input frequency looks sinusoidal, between 0% and 100%. The applet shows the impact of adjusting the spacing and relative 'height' of the barrier atoms.
This interference is the quantum mechanical basis of resonant tunnelling.
In the applet, you can control how many atoms are in the crystal. As you add more atoms to the system, the output transfer function starts forming notable regions of high transmission and regions of low transmission.
This is for a perfectly ordered crystal (same potential and spacing). The applet also shows what happens if you randomise the spacing or the potential heights.
Question for the HN community : as Java web applets are seemingly obsolete these days, any recommendations on current front-end tech for making these types of simulations?
A typical transistor doesn't have the red part of the curve where resistance goes up with increased current. This effect might be useful for multi-level logic or for self current limiting (similar to a lamp)?
- For analog type devices, negative resistance gives you a way to easily make oscillators, and negative feedback loops. Practical applications could be things like smaller or lower power wireless chips, or more accurate filters / oscillators in those chips. Useful for everything from wireless chipsets to things like google's project soli.
- For digital type devices, the big draw is that you can make a memory cell (aka flip-flop) from one active component instead of 2. This could potentially halve the size of some of the digital logic in your microprocessor (at least the registers and all the temporary storage used in your processing pipelines!)
- Talking more pie-in-the-sky, some models of neurons include negative resistance areas...analog neural nets on a chip using these will probably support a grad student or two as a research project!
Start reading here: https://en.m.wikipedia.org/wiki/Negative_resistance
Looking around the web the most common way that is taken advantage of is in small oscillators; transistor turns on as the input voltage rises above a gate threshold but then turns off again once you get enough gate current to be in a different part of the resistance curve. There were some EE times articles suggesting multi-level memory (non-binary) as another application.
The weird thing is "negative resistance" isn't something that makes sense electrically, and what they are really talking about is plotting the value of current with respect to voltage, a resistor is a simple line, diodes are a discontinuous at their forward avalanche voltage, and these things have lower current passing through them at some higher voltage. So the slope of the line is 'negative' at that point. (and the differential part comes in because it is between two specific voltages).
That's not correct. An ordinary resistor will have a (weakly) non-linear V-I relationship as well. The key here is that in some small region, the V-I graph is "going down", whereas for normal components it's always "going up".
That said, where have you seen non-linearity in ordinary resistors? Just for grins a I pulled one out my parts drawer and threw it on the sweep generator on my bench. I could not identify any non-linearity in the sweep, it was simply a straight line between 0 to 10mA. Where are you seeing nonlinearity in your resistors?
An extreme example of this is the incandescent light-bulb filament.
I think we all agree though that a negative differential resistance is most simply defined as a negative slope on an I(V) plot for a specified range of V.
The original article is about an I-V curve from a structure involving a single-atom + a scanning-tunneling microscope (STM). That such a system would also exhibit NDR is not particularly surprising. Tunneling to a structure with discrete energy levels will have current flow when energies line up, and less current flow when energies don't line up. So even the "mystery" isn't much of a mystery.
The interesting results imho are:
1. The team got reproducible single-atom tunneling with an STM tip, and
2. They measured the time-response of about 10 microseconds.
fwiw.
Edit: Resonant tunneling diodes used to be a hobby of mine: https://dspace.mit.edu/handle/1721.1/38419
> measuring current vs voltage in a new way, by applying brief voltage pulses to the STM tip.
When the pulses lasted 10 microseconds or longer,
they saw NDR.
But when they reduced the pulse length to 10
nanoseconds, the effect disappeared.
...
Combining this information with other data,
the team determined the timescale for electrons
refilling the empty lower level.