amplifying a sub femtoamp of current

[Arch]

Hi
I have a high impedance source at 4 Kelvin generating sub femto-amp of
ac current (10Khz to 1MHz). I have to amplify it to few mVs before
feeding to a DAC.
I am planning to use a 1G ohm resistor to convert it to voltage and
using a simple amplifier for impedance transformation.
The noise of a 1G ohm resistor at 4 Kelvin is only 0.46 fA/rtHz - seems
i should be able to discern signal from the noise.
Now, here if i have my signal current into a voltage level high enough
(fA * 1G ~ mVs), i can use any sort of amplifier for impedance
conversion.
Does this seems right?

 

[Sven Wilhelmsson]

Hi
I have a high impedance source at 4 Kelvin generating sub femto-amp of
ac current (10Khz to 1MHz). I have to amplify it to few mVs before
feeding to a DAC.
I am planning to use a 1G ohm resistor to convert it to voltage and
using a simple amplifier for impedance transformation.
The noise of a 1G ohm resistor at 4 Kelvin is only 0.46 fA/rtHz - seems
i should be able to discern signal from the noise.
Now, here if i have my signal current into a voltage level high enough
(fA * 1G ~ mVs), i can use any sort of amplifier for impedance
conversion.
Does this seems right?

Just do not forget the capacitive loads.
At 10 kHz the impedance of 1 pF is ~0.0159 G ohm.
So try a (hf-) mosfet with low input capacitance.
4K is probably to low for a mosfet, but some cooling should lower
the noise.

 

[Phil Hobbs]

Hi
I have a high impedance source at 4 Kelvin generating sub femto-amp of
ac current (10Khz to 1MHz). I have to amplify it to few mVs before
feeding to a DAC.
I am planning to use a 1G ohm resistor to convert it to voltage and
using a simple amplifier for impedance transformation.
The noise of a 1G ohm resistor at 4 Kelvin is only 0.46 fA/rtHz - seems
i should be able to discern signal from the noise.
Now, here if i have my signal current into a voltage level high enough
(fA * 1G ~ mVs), i can use any sort of amplifier for impedance
conversion.
Does this seems right?

You can't usefully use a 1 MHz bandwidth with a femtoamp of current, at
least not if it has full shot noise, which I imagine it does. If your
current consists of N electrons per second, counting statistics predict
that your SNR will drop to 0 dB in a measurement bandwidth of N/2 Hz. A
femtoamp is only 6200 electrons/s, so assuming you want at least a 20 dB
SNR (because below that you haven't got a measurement really), your
bandwidth is going to be limited to 31 Hz.

Sorry about that.

Cheers,

Phil Hobbs

 

[Tim Wescott]

Hi
I have a high impedance source at 4 Kelvin generating sub femto-amp of
ac current (10Khz to 1MHz). I have to amplify it to few mVs before
feeding to a DAC.
I am planning to use a 1G ohm resistor to convert it to voltage and
using a simple amplifier for impedance transformation.
The noise of a 1G ohm resistor at 4 Kelvin is only 0.46 fA/rtHz - seems
i should be able to discern signal from the noise.
Now, here if i have my signal current into a voltage level high enough
(fA * 1G ~ mVs), i can use any sort of amplifier for impedance
conversion.
Does this seems right?

You have two problems with basic physics:

Problem One:

To get a 3dB corner frequency of 1MHz you need to keep your total
capacitance down to about 160 atto farads, assuming I got my prefixes
right. That implies a capacitor that's about 0.02mm on a side, with air
dielectric.

You _may_ be able to get there from here with some custom IC operating
at 4K, but I wouldn't know.

I would suggest that you need some other, more reliable, way of
amplifying small currents. Hopefully someone will jump in with
suggestions. All I can think of is that if you can get your voltages up
high enough you may be able to do something with ionization, like a
Geiger counter.

Problem Two:

One fA implies that you're flowing about 62400 electrons per second.
Even at 10kHz the shot noise is going to be enormous, and at a 1MHz
bandwidth you'll be seeing the electrons as individual events, not as
anything resembling a continuous current.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

[John Larkin]

Hi
I have a high impedance source at 4 Kelvin generating sub femto-amp of
ac current (10Khz to 1MHz). I have to amplify it to few mVs before
feeding to a DAC.
I am planning to use a 1G ohm resistor to convert it to voltage and
using a simple amplifier for impedance transformation.
The noise of a 1G ohm resistor at 4 Kelvin is only 0.46 fA/rtHz - seems
i should be able to discern signal from the noise.
Now, here if i have my signal current into a voltage level high enough
(fA * 1G ~ mVs), i can use any sort of amplifier for impedance
conversion.
Does this seems right?

Tricky. 1 fA integrated over 500 ns (1/2 cycle at 1 MHz) is 0.003
electrons. You're going to need some serious signal averaging.

And a charge amp with very low input current, probably a cold jfet.

What's the physics?


John

 

[Arch]

Great Comments,
Now i see the problems - and am not that happy when i started this
post
I was planning to use GaAs MESFETs with the 1G resistor at gate bias.
However, now it seems it won't work as i thought.
Here i am trying to detect a motion of a single ion in a penning trap -
people use tuned circuits to pick up this ~50 fA image current. But i
want to build something for broadband detection (upto 1 MHz).

 

[Tim Wescott]

You have two problems with basic physics:

Problem One:

To get a 3dB corner frequency of 1MHz you need to keep your total
capacitance down to about 160 atto farads, assuming I got my prefixes
right. That implies a capacitor that's about 0.02mm on a side, with air
dielectric.

You _may_ be able to get there from here with some custom IC operating
at 4K, but I wouldn't know.

I would suggest that you need some other, more reliable, way of
amplifying small currents. Hopefully someone will jump in with
suggestions. All I can think of is that if you can get your voltages up
high enough you may be able to do something with ionization, like a
Geiger counter.

Problem Two:

One fA implies that you're flowing about 62400 electrons per second.
Even at 10kHz the shot noise is going to be enormous, and at a 1MHz
bandwidth you'll be seeing the electrons as individual events, not as
anything resembling a continuous current.

Damn. 6240, per Phil Hobbs. Apparently I was visiting a universe where
6.24*10^3 = 62400, but I'm back now.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

[[email protected]]

Great Comments,
Now i see the problems - and am not that happy when i started this
post
I was planning to use GaAs MESFETs with the 1G resistor at gate bias.
However, now it seems it won't work as i thought.
Here i am trying to detect a motion of a single ion in a penning trap -
people use tuned circuits to pick up this ~50 fA image current. But i
want to build something for broadband detection (upto 1 MHz).

Heisenberg's uncertainty rules, at least in principle.

 

[John Larkin]

Great Comments,
Now i see the problems - and am not that happy when i started this
post
I was planning to use GaAs MESFETs with the 1G resistor at gate bias.

Mesfets are nasty, leaky, noisy, and have very strange changes of gain
at low (KHz) frequencies, some sort of trapping-state thing. Jfets are
often used cold, and work at liquid helium temps. The ultimate charge
amp uses pure capacitive feedback to eliminate resistor noise, but has
to be reset now and then to cancel offset drift buildup.

However, now it seems it won't work as i thought.
Here i am trying to detect a motion of a single ion in a penning trap -
people use tuned circuits to pick up this ~50 fA image current. But i
want to build something for broadband detection (upto 1 MHz).

That may not be possible... there's just not enough signal. Signal
averaging (lock-in technique, done in hardware or software) would
work, but that's just equivalent to reducing the bandwidth. At least
it's not fixed-tuned.

How do you get the signal out of the ion... tiny antennas? Optical?

Non-trivial, for sure.

John

 

[Ken Smith]

You can't usefully use a 1 MHz bandwidth with a femtoamp of current, at
least not if it has full shot noise, which I imagine it does.

My reading of the OPs comments doesn't rule out a narrow bandwidth around
some carrier in the range he suggested. If this is the case, this won't
be his biggest problem.

Figuring out how to amplify a signal that small accurately will be trouble
too.

 

[Ken Smith]

I would suggest that you need some other, more reliable, way of
amplifying small currents.

He's already cold so maybe a SQUID is the answer.

 

[Robert Baer]

Great Comments,
Now i see the problems - and am not that happy when i started this
post
I was planning to use GaAs MESFETs with the 1G resistor at gate bias.
However, now it seems it won't work as i thought.
Here i am trying to detect a motion of a single ion in a penning trap -
people use tuned circuits to pick up this ~50 fA image current. But i
want to build something for broadband detection (upto 1 MHz).

Remember that Millikan "measured" single electron "flow"; guesstimate
1 electronper ten seconds.
So for 1000 electrons, theoretically that could be done in 10mSec or
a rough bandwidth of 100Hz.
Following that to 1MHz, one would need (crudely now) a flow of 10,000
electrons.
But do not use a high value resistor, as displacement currents will
kill what it would "see"; if you insist, then look into measuring the
displacement current or the voltage it generates on a known capacitor.
Say, use a huge 1.00 pF capacitor....
Or, try to be more nasty and get them electrons to "jump" thru a
chamber with a view port, at one electron per oil drop (or other
insulating liquid) - and *count* those or determine when they pass by
(132 this time interval, 45 next one, etc...).

 

[Robert Baer]

Heisenberg's uncertainty rules, at least in principle.

I will have you know, that *he* was NOT the principal of my school!

 

[vasile]

Hi
I have a high impedance source at 4 Kelvin generating sub femto-amp of
ac current (10Khz to 1MHz).

What kind of source ?

greetings,
Vasile

 

[Ancient_Hacker]

Great Comments,
Now i see the problems - and am not that happy when i started this
post
I was planning to use GaAs MESFETs with the 1G resistor at gate bias.
However, now it seems it won't work as i thought.
Here i am trying to detect a motion of a single ion in a penning trap -
people use tuned circuits to pick up this ~50 fA image current. But i
want to build something for broadband detection (upto 1 MHz).

As others have noted, you're going to have a heck of a time with noise
if your signal is just 6200 electrons per second. Plus seeing a 1MHz
signal is going to require a whole lot of auto-correlation and
filtering.

Do you have a known frequency and bandwidth to look for? I suspect
seeing that weak a signal is going to require like many many seconds of
observation and a very narrow bandwidth, like 1Hz or so.

I'd suggest forgetting about measuring the voltage, and instead measure
the current directly with a transimpedance circuit. You're getting so
few electrons it's a shame wasting them heating up a 1Gohm resistor.

 

[Phil Hobbs]

Remember that Millikan "measured" single electron "flow"; guesstimate
1 electronper ten seconds.

Yeah, by watching oil drops in a microscope and changing the voltage
across two capacitor plates to levitate them. Doing that even 6200
times per second is a good trick, besides the fact that M. was wasting
almost all the oil drops while concentrating on one at a time.

So for 1000 electrons, theoretically that could be done in 10mSec or a
rough bandwidth of 100Hz.
Following that to 1MHz, one would need (crudely now) a flow of 10,000
electrons.
But do not use a high value resistor, as displacement currents will
kill what it would "see"; if you insist, then look into measuring the
displacement current or the voltage it generates on a known capacitor.
Say, use a huge 1.00 pF capacitor....
Or, try to be more nasty and get them electrons to "jump" thru a
chamber with a view port, at one electron per oil drop (or other
insulating liquid) - and *count* those or determine when they pass by
(132 this time interval, 45 next one, etc...).

If the current starts out in a wire, i.e. it comes from displacement
current due to ion motion, the OP going to have to use bandwidth
narrowing of some sort. Signal averaging is generally much better than
using a narrow bandwidth near DC, because you can get out of the 1/f
noise and the drift pretty well. Tuned circuits are not a stupid idea
at all, because you can set the fields in the trap up to get a
particular cyclotron resonance frequency--i.e. you can tune the signal
to the filter. (Superhets do the same thing.)

If the signal starts out as free electrons in a vacuum, then the
situation is much better--a Channeltron or other electron multiplier is
the way to go. It's trivially easy to put 140 dB of gain on those
pulses, at which point you can probably even detect them with a neon bulb.

Cheers,

Phil Hobbs

 

[Arch]

Guys thanks again for the suggestions - though my eyes are so dilated
from an eye exam that i am not able to read properly. But let me tell
more about the signal source, which might help.
Ions of range of mass to charge ratio are made to rotate in a cubic
electrode arrangement. The rotation of ions induces an image
charge/current on the plates/electrodes of the cubic cell. The
frequency of the induced current corresponds to the frequency of the
rotation of ions and proportional to their mass to charge ratio.
A typical Ion cyclotron resonance experiment. This current is in the
order of 100's pA if their are lot of ions (generally a million).
However i want to be able to detect single ion using some sort of
amplification. And i want to do this for ions with a range of mass to
charge ratio, hence a range of frequencies (10 KHz - 1MHz). The plates
of the cell (cubic electrode arrangement) has a capacitange of around
20 pF, thus we model our source as an ideal current source in parallel
with this 20 pF capacitor.
Here we have put the cubic cell at 4 kelvin and i hope to put the
preamplifier right on it - getting to cool the electronics and reduce
the thermal noise.

 

[Arch]

If the current starts out in a wire, i.e. it comes from displacement

current due to ion motion, the OP going to have to use bandwidth
narrowing of some sort. Signal averaging is generally much better than
using a narrow bandwidth near DC, because you can get out of the 1/f
noise and the drift pretty well. Tuned circuits are not a stupid idea
at all, because you can set the fields in the trap up to get a
particular cyclotron resonance frequency--i.e. you can tune the signal
to the filter. (Superhets do the same thing.)

I have to do a broadband detection, hence can't use tuned circuits.

If the signal starts out as free electrons in a vacuum, then the
situation is much better--a Channeltron or other electron multiplier is
the way to go. It's trivially easy to put 140 dB of gain on those
pulses, at which point you can probably even detect them with a neon bulb.

The ICR detection is non-destructive i.e. you don't loose the ions
which you are detecting. The signal starts as induced charge on the
plates of the detector where as the ions keep rotating (damped slightly
by the loss of energy during detection).

 

[Sven Wilhelmsson]

Guys thanks again for the suggestions - though my eyes are so dilated
from an eye exam that i am not able to read properly. But let me tell
more about the signal source, which might help.
Ions of range of mass to charge ratio are made to rotate in a cubic
electrode arrangement. The rotation of ions induces an image
charge/current on the plates/electrodes of the cubic cell. The
frequency of the induced current corresponds to the frequency of the
rotation of ions and proportional to their mass to charge ratio.
A typical Ion cyclotron resonance experiment. This current is in the
order of 100's pA if their are lot of ions (generally a million).
However i want to be able to detect single ion using some sort of
amplification. And i want to do this for ions with a range of mass to
charge ratio, hence a range of frequencies (10 KHz - 1MHz). The plates
of the cell (cubic electrode arrangement) has a capacitange of around
20 pF, thus we model our source as an ideal current source in parallel
with this 20 pF capacitor.
Here we have put the cubic cell at 4 kelvin and i hope to put the
preamplifier right on it - getting to cool the electronics and reduce
the thermal noise.

Thanks for the description. Interesting!

I understand we have 1 nV or less at 20 pF. I believe this is possible to
detect provided data acquisition time is longer than life time of the ion.
It is not a problem with Heisenberg, IMHO.

A capacitance of 20 pF is a lot. The signal would increase if C could be
reduced. If this is not possible maybe one could raise the impedance by
means of an inductor to form a tuned circuit at the amplifier input.

I hope someone can give advice on the best choice of 4 Kelvin charge
amplifier. John Larkin suggested a cold jfet. I guess that is a good
suggestion. Some semiconductors do not work at 4K as minority carriers are
not generated thermally as they are at room temp.

 

[Sven Wilhelmsson]

detect provided data acquisition time is longer than life time of the ion.

Sorry, I mean
"I believe this is possible to detect provided the NEEDED data acquisition
time is NOT longer than life time of the ion."


I saw Werner Heisenberg once. The closer he came, the more uncertain I was
whether it was really him.