Capacitance measurement for Spice model parameters

[chilternview]

I'm in the process of setting up hardware and software for spice model parameter extraction, in particular BJTs but in future JFETs and MOSFETs also.
For I/V  parameters I've an Agilent 4156C with 41501 for extending the range to 1A/200V, for capacitance measurements either a HP4280A or a E4980A with DC bias option.

In order to measure the (small) capacitances though, I'm wondering what sort of test fixture to use. AliExpress sell the blank boxes for standard capacitors, and Fischer make a 4 way TO-5 transistor socket in ptfe which would suit through hole devices. Has anyone else tried measuring transistor C/V parameters? In particular Cbe / Cbc or mos Cgs/Cgd measurements?

The more difficult parameters to measure are things like tf / tr (forward and reverse transit times) or noise, which I've not really looked into at all yet.

[jwet]

HP makes really good fixtures for all their analyzers.  They are designed to be mode free up to high frequencies as specified and generally use high quality materials. 

Now, I'm not suggesting you go out to Agilent dealer and shell out $5K for these things new (the prices are shocking).  I would look for them used and or copy some of their high points.  I've bought some where the plastic disintegrated over time and I 3d printed replacements.  3d printing is good for stuff like this by the way.

I use a 16092A Spring Clip Test fixture on top of an impedance test set on my 4195 and 4396 Network/Impedance Analyzers.  They're very flexible, one lives on my 4195.  These will come up on ebay for reasonable money and I can use them for thru hole or SMT stuff with good repeatability.

I got on a kick with S parameters for a while and wanted to characterize transistors.  The best solution that I evolved to was to make little PC boards with SMA's and a site for the DUT, I would just solder them down to pads.  I got 50 boards made in China for nothing and carved them up, make some calibration/de embedding fixtrures, etc. That I could use beforehand.

It all depends on your frequency needs- most of the stuff that I did was around 1 Ghz and below.  Its somewhat forgiving but gets less so higher.

NB- i went on Ebay for a browse and there are a lot of fixtures for good prices.  I just searched for "HP Test Fixtures".  By the way, some analyzers do equivalent circut analysis and can figure out a bunch of measurements and fit it to a model.  I've used the crystal model on the 4195 before- saves a lot of spreadsheeting.
Good topic.  If you come up with something clever- share.

[chilternview]

Thanks, I'm mainly interested in low frequency capacitance measurement for the Spice model cje / vje / mje etc which model the b-e and b-c junction capacitances. I do actually have a 4936B and 16092A for impedance measurements but the low freq modelling is likely to be easier too.

The main issue I see is the parasitic capacitance of the test fixture. Getreu's book has an iterative way of curve fitting to obtain the model parameters in the presence of parasitics but if they can be avoided by just open/short correction that would be a lot simpler.

[mawyatt]

These links might be helpful.

https://www.eevblog.com/forum/projects/bias-network-for-lcr-meter/
https://www.eevblog.com/forum/testgear/cheap-smd-lcr-fixture-the-good-bad-and-ugly!/
https://www.eevblog.com/forum/projects/different-type-lcr-smd-fixture/

Best

[chilternview]

So, I ordered a couple of the capacitance 'standard' boxes from AliExpress. These were empty ones, a bit cheaper than the ones with capacitors. Also ordered some Fischer ptfe transistor sockets, and drilled a hole in the box and fitted the socket.

Now the question is what do people think is the best way to wire to the socket? I only want to measure e-b and b-c of bipolar transistors at the moment. As the socket has 4 pins the idea is to use one  (e.g. the pin at the top in the picture), leave the one opposite open, and connect the other two together. So with a CBE pinout I can get either e-b or b-c connected by simply rotating the transistor 180 degrees.

To connect from the BNC sockets to the pins, is it really necessary to use coax or will I get away with plain wires, with the box metal case going to the BNC earth tags? And the wires should go from Hi Curr & Hi Pot to the e/c pin and from Lo Curr & Lo Pot to the b pins?

[chilternview]

Well I couldn't wait and wired it up using hookup wire. It would have been a real pain trying to use coax on such short lengths.

Looks good and measures well...

[chilternview]

And here's an example of capacitance vs voltage sweep for a BJT, with extraction of the SPICE model parameters CJE, VJE and MJE. The fit is pretty good.

I've attached the python code if anyone's interested, although it was run on a E4980A it should run on the Tonghui/BX precision LCR meters that have similar syntax, and using usb or rs232 instead of GPIB control.

[mawyatt]

Nice work!!!

One of the interesting areas of the classic Gummel-Poon Spice BJT model is the "effective" capacitance under "slight" forward bias. Vaguely recall the G-P Spice model switched over to another Capacitance vs Voltage (believe linear) model to better fit actual physical devices when the PN junction became forward biased. Later Spice BJT Models such as VBIC, MEXTRAM and HICUM addressed this differently.

Edit: Try some more available transistors like the 2N3904, 2N3906, TIP42 and TIP43 if you have any of those. BTW don't worry about the wires, the fixture is mechanically sturdy and the wires are in an effective Faraday Cage, so as long as they stay put your Open Cal will remove the parasitic capacitance they introduce in the fixture.

We've found the GIF socket we utilized in our Tek 577 with 177 Fixture quite useful for leaded components.

Best

[chilternview]

Yes, the classic equation holds for reverse bias, for forward bias there is a parameter FC, usually about 0.5, the voltage at which the diffusion capacitance takes over from the depletion capacitance equation. I've yet to try fitting that...

[mawyatt]

Recall the G-P Spice model usually doesn't give a good fit in the forward direction.

Best

[chilternview]

Here's a 2N3904. The model params after curve fit were:

 CJE  = 3.211p
 MJE  = 0.211
 VJE  = 0.380
 CJC  = 7.302p
 MJC  = 0.316
 VJC  = 0.674

I've used the test fixture for compensation with open = nothing connected and short = small loop of wire to short the pins of the socket. With slow mode and averaging=4 it's giving stable readings down to the 1fF digit.

Edit: the sharp eyed will notice I had the 2N3904 the wrong way round for those plots. CJE is normally higher than CJC!

[mawyatt]

In normal bias Cje is greater than Cjc because the doping density of the base-emitter junction is higher than the base-collector junction.

How does your results compare with the typical G-P Spice model for the 2N3904?

Best

[chilternview]

Good question, Mike. I found one online:

.MODEL 2N3904 NPN(IS=4.639E-15 NF=0.9995 ISE=2.091E-14 NE=1.6 BF=160.1 IKF=0.12
+                 VAF=98.69 NR=1.001 ISC=3.257E-12 NC=1.394 BR=5.944 IKR=0.06
+                 VAR=19.29 RB=1 IRB=1E-6 RBM=1 RE=0.3614 RC=1.755 XTB=0
+                 EG=1.11 XTI=3 CJE=5.631E-12 VJE=0.7002 MJE=0.3385
+                 TF=3.001E-10 XTF=27 VTF=1.461 ITF=0.2723 PTF=0 CJC=4.949E-12
+                 VJC=0.5969 MJC=0.1928 XCJC=0.864 TR=9.4E-8 CJS=0 VJS=0.75
+                 MJS=0.333 FC=0.5582)

If I compare just the cap values, with mine in brackets:

CJE=5.631E-12 (7.302p)
VJE=0.7002      (0.674)
MJE=0.3385      (0.316)
CJC=4.949E-12 (3.211p)
VJC=0.5969      (0.380)
MJC=0.1928      (0.211)

then what can you say, they are different, but not by a huge amount. Of course they are probably not from the same manufacturer, let alone the same batch or wafer.

Of the DC parameters, I'm getting there, but need to do the optimisation step to fit the measured data to the equations, with extracted parameter values as starting points. Then there's the tf / tr to do, which either needs frequency domain measurements of ft, or time domain pulse measurements. Lastly temperature and noise measurements - not having the means to do temperature measurement the theoretical values may have to do, the noise measurements - I notice they aren't present in the above model.