I haven't worked through your numbers, but to calculate the energy stored in a battery you need to multiply the current by the voltage by the time (actually you need to integrate the product over time as the current and voltage will both vary, especially on a capacitor). That voltage element is missing from your calculations.
In fact it ought to be possible to work out the theoretical maximum energy available in this "quantum" storage system by just working out the number of electron volts or eV (which is a unit of energy) of the "excited" electrons compared to the ground state and multiply that by the number of electrons.
If we consider a 1 Litre volume block of silicon then that gives a theoretical maximum of 10^21 of these notional 10nm "nanocapacitors". If the excited state is around the 1eV level off the ground state, then one electron per "nanocapacitor" would give 10^21 eV. That 1 Litre of Silixon would have a mass of about 2.3Kg (about 3 times the mass of diesel of the same volume).
One Joule is about 6.24^18 eV, so that notional 1Litre of silicon with one excited electron per 10nm cube would be worth just 159 joules. That is none too impressive. To increase this to the energy density of Li-Ion batteries (say about 1200Kj per Litre for a state-of-the-art battery, or a factor approaching 10,000), then there will have to be many more electrons per nanocapacitor. Each of those 10nm "nanocapacitors" will have around 5 x 10^4 silicon atoms, so with 4 electrons in the outer shell of a silicon atom, there are about 2 x 10^5 electrons available per 10nm "nanocapacitor".
So, if we could somehow, magically get all the available electrons in a 1L cube of silicon into excited states 1eV above ground then we might beat current energy densities of Li-Ion batteries (by volume) by a factor of 20. However, that's a tall order (and I'm not sure what the excited energy state would be - I vaguely remember that the forward bias on a silicon rectifier is 0.6V so it might be 0.6eV per electron for the jump to the conduction band. It's been a long, long time since I did any of this stuff...
Register
@Terry H
I haven't worked through your numbers, but to calculate the energy stored in a battery you need to multiply the current by the voltage by the time (actually you need to integrate the product over time as the current and voltage will both vary, especially on a capacitor). That voltage element is missing from your calculations.
In fact it ought to be possible to work out the theoretical maximum energy available in this "quantum" storage system by just working out the number of electron volts or eV (which is a unit of energy) of the "excited" electrons compared to the ground state and multiply that by the number of electrons.
If we consider a 1 Litre volume block of silicon then that gives a theoretical maximum of 10^21 of these notional 10nm "nanocapacitors". If the excited state is around the 1eV level off the ground state, then one electron per "nanocapacitor" would give 10^21 eV. That 1 Litre of Silixon would have a mass of about 2.3Kg (about 3 times the mass of diesel of the same volume).
One Joule is about 6.24^18 eV, so that notional 1Litre of silicon with one excited electron per 10nm cube would be worth just 159 joules. That is none too impressive. To increase this to the energy density of Li-Ion batteries (say about 1200Kj per Litre for a state-of-the-art battery, or a factor approaching 10,000), then there will have to be many more electrons per nanocapacitor. Each of those 10nm "nanocapacitors" will have around 5 x 10^4 silicon atoms, so with 4 electrons in the outer shell of a silicon atom, there are about 2 x 10^5 electrons available per 10nm "nanocapacitor".
So, if we could somehow, magically get all the available electrons in a 1L cube of silicon into excited states 1eV above ground then we might beat current energy densities of Li-Ion batteries (by volume) by a factor of 20. However, that's a tall order (and I'm not sure what the excited energy state would be - I vaguely remember that the forward bias on a silicon rectifier is 0.6V so it might be 0.6eV per electron for the jump to the conduction band. It's been a long, long time since I did any of this stuff...