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I'm currently reading Frank Wilczek's new book Fundamentals: Ten Keys to Reality and I've come across the following passage:

Inside modern computers, information is stored and processed in arrangements and rearrangements of electrons, as opposed to entire atoms or molecules. The energies involved can be much smaller, and the processing can be much faster. To represent information, we have either a high concentration of electrons (leading to a low voltage, interpreted as "0"), or a low concentration (leading to a high voltage, represented as "1") in each of billions or trillions of tiny buckets.

I find the last sentence puzzling. How is it that a higher concentration of electrons can lead to a lower voltage and vice versa? How can electrons become concentrated in a circuit in the first place? Does it have to do with the various states of semiconductors?

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“Voltage” and “concentration of charge” are two names for the same thing — or at least, two ways of talking about the same phenomenon.

Physicists love to talk about energy (it’s even in your quote already). When we say that there is an “electrical potential difference” between two points, what we mean is that an electric charge would have to gain or lose energy to travel from one point to another. A positive potential difference means that a positive charge would have to be given some energy (“pushed”) to go from one point to another; a negative potential difference means that a positive charge would make some journey on its own if there were a pathway, and have energy left over when it got to the destination. How do you create a region of high electrical potential, which positive charges would flee if they had the opportunity? You fill it up with positive charges, because same-sign charges repel each other.

Electrical potential differences are measured in volts, so many people will use “voltage” as a two-syllable shorthand. If a unit charge, like an electron or a proton, travels across a potential difference of one volt, its energy changes by one “electron-volt,” abbreviated “eV” and equal to about $10^{-19}$ joules.

Annoyingly for people who like positive numbers, the two signs of electrical charge were fixed before we discovered that the majority charge carriers in most materials are electrons. So if you want to know where an electron will go in a circuit, you have to figure out what a positive test charge would do, and then send your electron in the opposite direction. When Wilczek writes “a high concentration of electrons [leads] to a low voltage,” he means that if you pile up electrons somewhere, a positive charge would gain energy by traveling to that point — because it’s attracted by all the extra electrons.

You have another answer which talks about charge storage on capacitors, which is in fact how “dynamic RAM” works. But the idea that “a bit” on some wire is related to whether a charge would or wouldn’t change energy traveling between that wire and “the ground”: that idea is much more general. In some sense it helps to remember that every current-carrying wire in a circuit is secretly part of a capacitor.

How can electrons become concentrated in a circuit in the first place?

A device which does this by chemical means is called a “battery”; a device which does this by mechanical means is called a “generator.”

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He may be referring to the fact that information can be stored as accumulation of charge, e.g. on a capacitor's plates. In this case, a digital '1' is represented by a positive voltage across the capacitor, which gets positively charged by injecting current on its "top" plate (generally speaking, the one where the voltage is read), i.e. by removing electrons (which are negatively charged) from one of its plates and accumulating them on the other one, usually the bottom one connected to ground. If the capacitor is well isolated, such a charge can be maintained and it effectively becomes a 1 bit memory cell.

Such a capability of accumulating charge is not related to the "various states of semiconductors" (although I'm not sure of what you mean with that), but to the structure and components of the circuits that drive electrons around and can isolate certain nodes of the circuits so that the accumulated charge is not lost (not entirely true, there will always be some leakage).

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    $\begingroup$ Information in all modern computing devices is stored in semiconductors. Just like info can be stored as charge across capacitor. It can also be stored in semiconductors which have "on " and "off" states according to the charge on various parts of logic gates. $\endgroup$ Mar 20 at 14:16
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    $\begingroup$ @silverrahul Capacitors are indeed the storage mechanism for “dynamic RAM,” though charge leakage means that each bit must be refreshed (i.e. read and re-written) about a dozen times per second. In “static RAM” the information is stored in a transistor-based “flip-flop”; that hardware is faster, but more expensive, and is used for CPU caching. See e.g. $\endgroup$
    – rob
    Mar 20 at 14:28
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    $\begingroup$ @silverrahul,rob you are both right: as you mentioned, capacitors are used in dynamic RAMs, while floating-gate MOS transistors can be found in flash memories. My answer referred to a capacitor for the sake of simplicity and generality, since I don't think the question was about specific memory technologies (moreover, resistive RAMs store information as resistance value instead of charge...). silverrahul, I don't think those on and off states that you mention can be considered "states" of semiconductors per se, those are properties of components or circuits made of semicondutors. $\endgroup$
    – DavideM
    Mar 20 at 14:53
  • $\begingroup$ Davidem Yes, on-off state are more accurately described as on off state of circuit made of semiconductor. But your statement 'Such a capability of accumulating charge is not related to the "various states of semiconductors" needs to be edited. Semiconductors do not have on-off states per se, but they do have different states of accumulated charges , dont they? I think u can edit the answer to incorporate the semiconductor technology and what Rob said. Also, @rob , is dram really refreshed only a dozen times per second ? That seems way too slow for the speed at which modern devices operate. $\endgroup$ Mar 20 at 18:50
  • $\begingroup$ @silverrahul I'm sorry but I don't fully get what the "state of a semiconductor" is supposed to mean in the first place. When talking about the "state" of materials or matter the amount of accumulated charge in them doesn't come to mind. How would you even define such a thing, how would you discern one state from the other? $\endgroup$
    – DavideM
    Mar 20 at 20:14
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The vault measure how much we can allocate of potential energy to the charges in mouvement inside a potential differencial ,why? because more good is the differential more potential energy is disponible to the movement of charges , when a lot of charges, say électrons negatively charged, accumulate in a certain point of space they are modifying the potential differential so the potential energy disponible for the charge movement ,in a more imaged way the electron are blocking the way behind ,cutting the flux a situation that can lead to a lower voltage.

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