Picoammeter Design

[Kleinstein]

The slow part could DA in the tiny 0.04 pF capacitor. The model would be something like a parallel  even smaller capacitor (ca. 0.1-1%) and a huge (Pohm range to get the right time constant) resistor in series.
I am not so sure where the slow part comes from, but loss in that parasitic capacitance is a candidate.
There are a few other effects to cause the recovery. There could be surfaces that are partially isolated and add extra parasitic capacitance to the input. These surfaces can slowly charge / discharge.
There is also the possiblity to have some thermal effects, e.g. from the relay cooling after turned off. The temperature may effect the FET - though the effect looks quite strong for this.

[iMo]

Ok, finally below 3 pictures:
1. a long run with relay contacts shorted, noise around 20-25uV stddev in quiet periods, it continued straight into the
2. overnight run with relay contacts opened - you may see the switching the relay at the very beginning
3. the same overnight run with relay contacts opened - but the detailed view after the voltage settled (at aprox -0.9mV)

After the 3. the DC voltage with relay shorted is -0.27mV aver. Thus the difference is aprox -0.27-(-0.9)=0.63mV.

PS: HDIG1030 source resistor 68k+5k6, Vds=2.108V, Ids=0.180mA

PPS: The slow part after the relay opening contacts is aprox 2 hours long..

[iMo]

Perhaps did it somebody here - a TIA calibration with ramp input voltage and capacitor generating pA level currents (see below the sim).
Not sure whether it is even feasible..

[ch_scr]

Shodan from ampnuts.com has built multiple revisions of this idea. Here is a demonstration video of his latest finished revision. More information can be found searching for GLIN on his blog. Reading the site with Chrome auto translate works well.
I have tried the idea with the Yokogawa 7651 as ramp generator, but at least my unit is not linear enough so there were periodic jumps in the current. Not sure if my unit is broken or out of cal.
Edit: Here is the github for GLIN v.2

[Kleinstein]

The calibration with ramp and capacitor is defintely possible. A point to observe is that the TIA may need some series resistance at the input. Not all TIA circuit are happy with a low impedance or capacitive source.

[bsw_m]

calibration with ramp input voltage and capacitor generating pA level currents

This technique of generation of ultra-low currents was used in at least two calibrators developed by MNIPI, these are ЕК1-6 (in mass production since 1979) and НК4-1 (in production since 1989, until about 2014).
The minimum current that these calibrators could reproduce is 1E-17A.
I began to describe the calibrator NK4-1, but as I did not meet much interest in this device - a branch stalled: https://www.eevblog.com/forum/metrology/nk4-1-low-current-and-high-resistance-calibrator-(made-in-belarus)/

[bsw_m]

Shodan from ampnuts.com has built multiple revisions of this idea.

Making a ramp generator is not such a big problem. The main problem is differentiating the ramp signal (ramp-to-current conversion). And this is primarily the design, not the circuitry, or the software. .

[iMo]

Ok, while reading above documents I get the method with the ramp voltage and capacitors works fine in the LTspice only
In the real life you would need special capacitors made of sapphire, etc.

[bsw_m]

All in all, it's not as complicated as it seems. But there are nuances, of course.
Here are pictures of the 100pF and 10pF air capacitors used in the EK1-6 and NK4-1 calibrators to get the 1E-12A and 1E-13A direct current ranges.
Lowest capacitor, that used in these calibrators is a 0.1pF. Highest capacitors that used in these calibrators is 11200pF teflon dielectric (2x parallel K72P-6) capacitors.

In general, to form the 1E-12A range, you can try to use PP type capacitor, of course with the leakage current selection and the minimum DA.

[David Hess]

Bob Pease mentioned that the problem with larger air dielectric capacitors is that they get charged from cosmic ray hits, so a dielectric like Teflon is required to reduce the volume.

[bsw_m]

The large air capacitor can to some extent be considered an ionization chamber. Therefore, indeed, the condensers should have the smallest possible dimensions. But with proper air capacitor design, up to 100pF air capacitors are the best choice.

[zrq]

I tested my 1 TOhm Victoreen glass sealed resistor more carefully today with a Keithley 617. It's marked with 2% tolerance, but the linear fit of the IV curve gives 885 GOhm, way out of tolerance. Per the fit residual, the voltage coefficient is up to 300ppm/V, which is also quite poor.

[ch_scr]

You've inspired me to try my hand at this, since I've had all the parts for it in the drawer already.
I've used GDR-made SMY60 (dual P-FET without gate protection zeners) as a input stage into an OP07, 1G KVM in the feedback.
The 3pF feedback capacitor is made of three 0805 NP0 10pF in series (is that a good idea?).
I've just now made and set it up:
- shorting the input (wondering why the output pegs  )
- measuring at the two inputs of the opamp
- then set the balance potentiometer of the input stage to get zero across -IN +IN.
To try it out:
- remove short, put 100Meg towards the bias voltage source on the outside
- feed in 1V, expect -10V out.
But out come only -7.42V. With -1V in, the output is 7.42V. With no input, output is pretty much zero
Possible conclusion to me:
- Feedback cap is leaky, shunting the 1G
- 1G is lower or dirty
- 100M is higher (metal film, this much drift up seems less likely?)
Is the feedback cap the likely culprit, or is it dirt on the 1G? Or something else entirely?

Edit: nevermind, just realised it's oscillating, 3pF seems too little.
Edit#2: with 100pF PS foil capacitor, after waiting a loooong time (for the capacitor to fully dry in circuit), it settles at 7.41V. So not the capacitor leakage?
Edit#3: These 100M all read high  The one used measures 120.8Meg. With 1.208V Bias, -8.96V comes out. (-1.208V -> 8.97V) Still "a little" short, but closer to reasonable.
Edit#4: At the same time / from the same ebay seller, I got other 1G, an 100M, etc. among other values. After quick rinse with IPA, the 100Meg reads low at about 90M, and the other 1G reads ~905M (even though I have less confidence in the latter measurement). Coincidence, or did these KVM all drift low with age? I should have measured the one I put in beforehand 
Edit#5: With 120.8Meg & -12.08mV Bias the output is 94.5mV, at +12.08mV the output is 85mV. Is that explaineable as ~5pA leakage?
Edit#6: With 0.57mV Bias on the 120.8Meg, the output is zero, so ~5pA input leakage confirmed?

[bsw_m]

Coincidence, or did these KVM all drift low with age?

High value (>1GOhm) KVM resistors most often drift in the direction of decreasing resistance.

[magic]

IME they drift down with age, but I only recall the 100G being more than 10% off.

I tested them by applying 100V DC in series with a 10MΩ multimeter.

[ch_scr]

Coincidence, or did these KVM all drift low with age?

High value (>1GOhm) KVM resistors most often drift in the direction of decreasing resistance.

IME they drift down with age, but I only recall the 100G being more than 10% off.

I tested them by applying 100V DC in series with a 10MΩ multimeter.

Even the 100MΩ is definitely down to 90.7MΩ. (Cleaned it more thoroughly and tried again) I have a lot more confidence in that measurement than the 905MΩ one. Did test them with up to 120V. Even going from 10V to 100V the voltage coefficient was noticeable. Not that it would matter in this usecase though.

[TizianoHV]

100Mohm shouldn't be that hard to measure. You can find much better (1% 100pm/°C) 100M resistors at affordable prices.
I dont like the look of these binding posts in the last photo, these could leak. A easy and accurate way to measure resistor up to a few Gohm's is to use a 100kOHM resistor as shunt and a 6dig multimeter to measure the current across the DUT while being careful to shield sensitive conductors.

Would be interesting to see if adding guard rings could help reducing voltage coefficient/leakage of these glass resistors

[bsw_m]

Would be interesting to see if adding guard rings could help reducing voltage coefficient/leakage of these glass resistors

My tests show that it will not help

I dont like the look of these binding posts in the last photo, these could leak.

If you mean the glass beads in the shielding box, they should not be a problem, the amplifier input has a potential of almost zero. No potential, no leakage. The box should be connected to the measurement ground.

[David Hess]

100Mohm shouldn't be that hard to measure. You can find much better (1% 100pm/°C) 100M resistors at affordable prices.

I have measured up to 1 gigaohm using a common 10 megohm input multimeter.  Use the most sensitive DC range with a 10 megohm input resistance as a current input and apply a fixed voltage to the resistor.  With a resolution of 1 millivolt, 1 millivolt across 10 megohms is 100 picoamps.  10 volts across 100 megohms is 100 nanoamps, so the measurement can be made to 1 part in 1000.

[ch_scr]

I dont like the look of these binding posts in the last photo, these could leak.

I've checked just now and the instrument reads 0.3nA while sourcing 202V into the open binding posts.

If you mean the glass beads in the shielding box, they should not be a problem, the amplifier input has a potential of almost zero. No potential, no leakage. The box should be connected to the measurement ground.

Box is not connected yet, good catch.
I've realised it's not particulary clear from the picture (the installed shorting link doesn't help either), but the DUT (resistor, low leakage diode or the like)
will be in the box together with the amplifier, and the beads only carry supply and bias voltages in and measured voltage out.

[magic]

Even the 100MΩ is definitely down to 90.7MΩ. (Cleaned it more thoroughly and tried again) I have a lot more confidence in that measurement than the 905MΩ one. Did test them with up to 120V. Even going from 10V to 100V the voltage coefficient was noticeable. Not that it would matter in this usecase though.

Similar experience to mine. I tested several specimens of different values, it was a few years ago, but I'm fairly sure all were found to be 5~10% off, always on the low side. Except for 100G, which was 72G. I felt like something may be wrong with my 100G measurement, but the fact that it came within 30% gave me confidence that at least the lower ones are likely right. No amount of cleaning the surface changed anything appreciably. I then obtained another batch of 100G and found them to be ~90G, kinda in line with the lower values, while my first 100G was still 72G. I also bought other 1G resistors, from Ohmite and a different Soviet type (not glass) and these tested in spec following my procedure.

Conclusion seems inescapable that KVM resistors just aren't that great. They may still be used if no other choice (e.g. 100G or 1000G - fairly exotic) but individual calibration is necessary. In the TIA picoammeter, one could insert a corrective voltage divider between the opamp and the feedback resistor. SNR will be somewhat higher than with a true 100G, but still better than with 10G or 1G.

Note that KVM are only rated for 100V.

edit
What I haven't done was to re-test at 10V to check voltage coefficient. Back then I didn't even know that I was already running them at their maximum rating, I assumed they would be good for at least a few hundred volts. So I don't know how much VC they have - could it be on the order of 5% at 100V and responsible for my results?

edit edit
Point 9 of the datasheet does specify "change in resistance as a function of change in voltage, no more than ±5%". So maybe it's partly responsible?

I'm attaching the datasheet. I have a scan of the original, a transcript found somewhere, and a machine translation of the transcript. Can't vouch for the accuracy of the latter two, but they seem about right at first glance.

Values up to 10G have specified TCR: ±2000ppm/K.

[iMo]

I've found 2 none-glass resistors - 300Meg and 500Meg in my junkbox, as well as an LMC6062 in smd (I previously wrongly reported as the 662). While being used in a T configuration - what could be actually achieved (noise regardless) in such a setup? Any formula known for the T gain calculation with such an asymmetric resistor setup?
Also - I have found couple of n-channel mosfets KF521 - I wonder how to replace that p-mosfet with them easily..

[magic]

Put them in series for 800MΩ, feed them from an 80% divider. Sensitivity will be 1mV/1pA as with 1GΩ. Not sure what else you need to know?

Unlike μA776, LMC6062 has low enough bias (10fA) that you could try it without external FETs.

[iMo]

So far I've made a sim with the T in the FB..
Aprox 10pA/V output..

PS: and with the 80% div in the FB

[ch_scr]

The "T" is often misunderstood. I know, because I did too when playing around with it in spice, trying to make sense of it.
R8 / R9 form a voltage divier, before going into the R2 feedback resistor. That's why there is no need to waste 300Meg on R8.
magic suggests to form an 80% divider with more regular values for R8 / R9, because it's just a voltage divider anyway!
Then have R2 as 300M+500M and take only a slight performance hit from dividing to 80% - but gain a convenient way to trim the output to 1mV/pA excactly.
I guess the 1G in my case beeing low is a blessing in disguise, having such a convenient way trim the output.
Compare that to the hassle of trimming a high one down with an excact parallel resistor