Calling Capacitor Experts

[WallWart]

I have seen several references in the forum to this article on severe temperature and voltage variation in multi-layer ceramic capacitors (MLCCs). 
https://www.analog.com/en/technical-articles/temperature-and-voltage-variation-ceramic-capacitor.html

For me, there were 3 big takeaways:

• The 3 character dielectric codes only specify temperature variation, not voltage or any other nonideality
• The 3 character dielectric codes do not denote a specific material.  Dielectric formulations and non-temperature performance vary from manufacturer to manufacturer. Beware of "identical" part substitutions
• For a fixed voltage and package size, choosing a part with a higher voltage rating may NOT improve the effective capacitance at all

The third point was particularly surprising so I have copied the graph here.  The author notes that conclusion is not an absolute rule and there is some variation from manufacturer to manufacturer.  Still, I spot checked a few parts and it seems to be roughly true.



For a parallel plate capacitor:
C = E₀*E_R*Length*Width/Separation

One cannot use arbitrarily thin dielectric layers to increase capacitance, because, at some field strength, the dielectric breaks down and the cap is destroyed.  So doubling the cap voltage rating  would require double the distance between layers to keep the electric field below that critical level.  Twice as many layers would be required to reach a given capacitance as compared to a low voltage cap. 

Picking the X5R 0805 curve for example, if the maximum field strength held roughly constant in different voltage caps by adjusting layer spacing:

• Holding the package size constant, why is capacitance vs voltage dependent on absolute volts instead of a percentage of rated volts?
• Holding the voltage rating constant, why is the capacitance vs voltage graph dependent on package size?

I must be missing something in the practical business of manufacturing MLCCs.  Are they adjusting the dialectic constant instead of number of layers to change capacitance?

[MarkT]

These are low voltage parts, and for them the metal layers may dominate the volume as the dielectric layers are very thin.  In this case the capacitor plate area is constant and the voltage and capacitance have a reciprocal dependence.  C * V will be approximately proportional to package volume for a given dielectric

For higher voltage devices where the dielectric thickness dominates then the volume is proportional to C * V^2, and the dependence is inverse-square.

The energy stored in a cap is 0.5 * C * V^2, and each dielectric has a maximum energy density it can sustain, hence the relationship above.

[WallWart]

Thanks for pointing out the metal thickness, MarkT.  I had to work through some unit-analysis examples to wrap my head around it.
 
Let me start from the second case which I find more familiar:
dielectric thickness >> metal_thickness (so we'll ignore the metal)
dielectric thickness increases proportionally to voltage to prevent breakdown
 
Ebreakdown [volts/meter] =  Vmax / dielectric_thickness
C = E0*Er*Area / dielectric_thickness
K is arbitrary constant
 
Volume = k *C*V^2
= (E0 * Er * Area / dielectric_thickness) * (Ebreakdown / dielectric_thickness)^2
= (E0 * Er * Ebreakdown^2) * Area * dielectric_thickness
Ok the units work out!
 
Maximum Stored Energy is 1/2*C*Vmax^2
Therefore max stored energy and volume are also proportional
 
 
If metal_thickness >> dielectric thickness:
Dielectric thickness is still proportional to Vmax
 
Volume = k * C * V * metal_thickness
= (Eo * Er * Area / dielectric_thickness) * (dielectric_thickness / Ebreakdown) * metal thickness
= (Eo * Er / Ebreakdown) *  Area * metal_thickness

[AnalogTodd]

I spent a lot of time talking to ceramic manufacturers over the years as MLCCs were commonly used as output capacitors for small regulators. As you can imagine, you run into a big problem with stability if you need a 4.7uF output capacitor for stability and what you actually get is less than 1uF at the operating voltage.

The three character code on capacitors specifies rated minimum and maximum temperatures and change of capacitance over the temperature range ONLY. It says nothing about voltage coefficient.

There are certain things you won't find out from manufacturer data sheets on capacitors, such as the fact that most capacitors have a higher dielectric breakdown compared to their specified voltage rating. The reason for this is the occasional variations in production that would create massive yield problems if they ran too close to the limit. Another item is exactly what the dielectric is in a given capacitor. This is the reason why each capacitor you tend to look at is different in terms of voltage coefficients. Quite often, manufacturers will adjust the chemistry of the slurry used to create the ceramic dielectric layers for given capacitor values and voltage ratings. This variation actually ends up effectively giving a change in the dielectric constant with applied electric field. If you chase down the physics of it (I know people who did this, I don't have the equations though) you find that the higher dielectric constant materials also end up giving higher variations as a function of field strength. Interestingly enough, this may also likely be related to why ceramic capacitors show piezoelectric effects.

So, there are some things that can come together from all of this information.

• Changing from a lower voltage rating to a higher voltage rating (in the same case size) will not get you higher capacitance at voltage. The manufacturer may simply be taking the same parts and checking a sample for higher voltage operation and then selling them for that rating instead of the lower voltage rating.
• Individual variation in chemistry of the ceramic dielectric causes variations in capacitor value versus applied voltage. This is why you get different results for capacitance versus voltage within the same manufacturer as you change to different values and why manufacturer to manufacturer is different as well.
• Case size is your best indicator for change in capacitance versus bias voltage. Why? Because in a larger case size you can use a material with a lower dielectric constant that has less change as a function of bias voltage.

MLCC capacitors are great for dropping a fair amount of capacitance into a small board area, and give low ESR and ESL characteristics. But there is a lot that can bite you if you aren't aware of their pitfalls.

[MarkT]

BTW if voltage coefficient is something you are worried about, try to get C0G capacitors (a.k.a. NP0), as they are highly linear and don't use ferroelectric dielectrics.
But they aren't as compact, since such dielectrics tend to have constants upto 20 or so, whereas ferroelectric materials have constants in the thousands - well not that constant in fact.

[Wolfram]

Ferroelectric is the keyword here. The capacitance formula you use only holds for conventional dielectrics. For ferroelectric dielectrics (Class II ceramics), the capacitance also depends on the field strength within the dielectric. The effect is similar to saturation in magnetic materials, where there are a fixed number of domains available to be polarized, with the number diminishing with applied field.

[berke]

Some manufactureres (e.g. Kyocera AVX) provide capacitor models, however these are linear RLC networks and do not model the voltage dependence.

I was looking for a realistic Spice model of an MLCC capacitor to get a feeling of the kind of non-linear effects one might encounter.
Of course I wasn't hoping to get a model for a specific capacitor, because as has been pointed out, they will vary widely, but I want something to get an idea of what happens.

I found this page which gives a simple model for a non-linear capacitor: https://www.analog.com/en/analog-dialogue/raqs/raq-issue-192.html



Turns out (LT)Spice allows you to specify the charge equation for a capacitor.

I don't know how good this model is, but it gives an idea.

EDIT: Attached some transients which show the theoretical difference between ideal caps and this model of non-linear caps.

[Berni]

This is the price you pay for using the very high dielectric coefficient ceramic materials.

All of the high capacitance ceramic caps must use these special ceramic materials in order to fit so much capacitance in such a small physical size capacitor. Then as you get to lower voltages they use thinner layers of the dielectric to make the capacitor even smaller, but this increases the field strength inside it, making the non linear problems even more pronounced.

The reason this happens is that these dielectric materials use a special trick to achieve such an absurdly high Er value. The atomic structure of these materials changes under a electric field (this is also what causes the piezzoelectric effects of capacitors making beeping/chirping sounds) this flex in the structure is what stores the extra energy and make it appear to have such a high Er. However you can only twist the atomic structure so far before all of it is in its most high energy state, at that point this effect disappears and starts acting like a regular low Er dielectric, causing capacitance to plummet.

You can buy NP0 dielectric capacitors that don't have this effect at all, but once you get to 100nF and above those capacitors are going to be pretty huge chonkers and also cost many times more.

[MarkT]

NP0 ceramic caps for low voltage can be pretty compact these days - 10uF is obtainable in 1206 package at reasonable cost.

[Wolfram]

NP0 ceramic caps for low voltage can be pretty compact these days - 10uF is obtainable in 1206 package at reasonable cost.

Do you have an example part number? NP0 starts to get impractical above some tens to low hundreds of nanofarads in my experience.

[Echo88]

Jep, please name the partnumber.
Mouser for example lists a lot of X7R 10µF MLCC as NP0 wrongly, Digikey is better in that regard.
I dont think its even possible to get to 10µF with NP0 in <=2512 package with current technology.

[berke]

Straight from the horse's mouth, if you select C0G/NP0 on Kyocera AVX's cap search it stops at 100 nF.

[TimFox]

Just a reminder of an important point raised above:
The non-linearity of the dielectric material is a function of the E field in the dielectric layer, which is the voltage gradient dV/dx,  where x is the thickness for parallel-plate construction.
Similarly, non-linearity in resistors depends on the voltage gradient along the length of the resistive material.
The direct result is that for a given material, non-linearity (voltage dependence of capacitance or resistance) will be worse for smaller packages, which will also have lower voltage capability.

[shapirus]

I've now been wondering for a while: does capacity always drop slower than voltage squared? In other words, for the same capacitor, is \$\frac{C_{2}U_{2}^{2}}{2} > \frac{C_{1}U_{1}^{2}}{2}\$ always true when \$U_{2} > U_{1}\$?

Or: does MLCC always have a higher stored energy at a higher charge potential?

[MarkT]

Straight from the horse's mouth, if you select C0G/NP0 on Kyocera AVX's cap search it stops at 100 nF.

Mouser has 22uF as the highest value.  There are many cap manufacturers and they will differ in the range of products they offer.

[MarkT]

I've now been wondering for a while: does capacity always drop slower than voltage squared? In other words, for the same capacitor, is \$\frac{C_{2}U_{2}^{2}}{2} > \frac{C_{1}U_{1}^{2}}{2}\$ always true when \$U_{2} > U_{1}\$?

Or: does MLCC always have a higher stored energy at a higher charge potential?

If you increase the voltage across a capacitor and current flows into it you've added to its stored energy - your question is the same as asking do capacitors ever show negative capacitance...

There is an effect called dielectric absorption (or soakage) where the voltage changes with no current flowing in or out, but that's not really what you're asking I think.

[Echo88]

"Mouser for example lists a lot of X7R 10µF MLCC as NP0 wrongly, Digikey is better in that regard."
There is no 22µF in NP0, theyre just wrongly listed as such when taking a look at the datasheet MarkT.

[T3sl4co1l]

Just a reminder of an important point raised above:
The non-linearity of the dielectric material is a function of the E field in the dielectric layer, which is the voltage gradient dV/dx,  where x is the thickness for parallel-plate construction.
Similarly, non-linearity in resistors depends on the voltage gradient along the length of the resistive material.
The direct result is that for a given material, non-linearity (voltage dependence of capacitance or resistance) will be worse for smaller packages, which will also have lower voltage capability.

At least as long as the above assumptions hold.  HV parts tend to be worse than LV parts, because they can be manufactured more consistently.  That is, consider a 47uF 6.3V chip with, lord knows, thousands of layers? Whatever it might be.  Those layers are extremely thin, 100s nm perhaps, at the limit of manufacturability; and not a single one can have a pinhole failure.  There is some practical minimum layer thickness with respect to manufacturing yield.  Which isn't to say denser, lower-voltage parts can't be made -- but it does mean you're going to pay through the tooth to use them.

Conversely, higher voltage parts, by the above reasoning, must use thicker dielectric to begin with, and can't fit so many layers into the package.  Even large chips don't get much thicker -- compare 2220 and 1210 for example.  So they're going for width more than height.

And yet, 470nF 250V X7R parts are available, for example; but the C(0)/C(Vmax) ratio is extraordinary, usually >10, maybe even 20 (i.e. 90-95% reduction at rating).  With the lower defect rate of the reduced dielectric area and increased thickness, they can simply run much higher E field before failure occurs.

A corollary: the maximum voltage handling at breakdown, of any random part, might actually be many times the nominal rating.  It's the lowest breakdown, for that series (dielectric thickness and area), for some tolerable manufacturing yield, that determines the ratio between nominal rating and best-case actual breakdown.

I don't know if it's what they actually do, or if there are indeed structural differences between parts -- I would guess a bit of both in practice -- but this might be one explanation for the existence of a range of voltage ratings in otherwise perfectly identical parts (same C(V) and temp curve, same package outline and height, same nominal value).  You should therefore prefer lower voltage parts for lower production cost -- at least in such quantities where the cost savings is justified, a reel change cost isn't incurred (or custom reeling can be done), etc.  Probably 10-100k's/yr?

Tim

[WallWart]

I think AnalogTodd and I are kindred spirits, except, I was looking at the recommended input filter for a switching regulator chip.  The MLCC value looked fine on the schematic but a tolerance analysis flagged the capacitance vs voltage droop.  The good news was I just needed bulk capacitance.   The bad news was the board was already being fabricated so I couldn’t change the package size.   I expected that capacitance droop vs voltage would scale with Vmax, I would drop in a higher voltage cap, and be home on time for dinner.  My expectations were soon corrected when I tried to actually identify a suitable part.  While I didn’t find an obvious replacement, I did find 3 manufacturer tools that can give droop specs, so I won’t get bit again.

https://spicat.kyocera-avx.com/home/index
https://ksim3.kemet.com/capacitor-simulation
https://ds.murata.co.jp/simsurfing/index.html

I would also like to link to this thread which suggests a simple way to measure the capacitance vs voltage by using some high value resistors to inject the DC bias, and large caps to isolate it from your meter
https://www.eevblog.com/forum/chat/how-to-test-the-capacitance-of-ceramic-capacitor-under-dc-bias/


I should probably link the relevant EEVblog videos too
https://www.eevblog.com/forum/blog/eevblog-626-ceramic-capacitor-voltage-dependency-download/

[WallWart]

Bernie, the point about dielectric constants being related to the atomic stricture twisting and stretching is fascinating explanation of piezoelectric and microphonic effects.  This link from Murata discusses it, but I think I’d need a stronger materials or physics background to really understand it.  There’s nothing more humbling than learning about someone else’s area of expertise.

https://www.murata.com/en-us/support/faqs/capacitor/ceramiccapacitor/char/0005


For a layman’s explanation of piezoelectricity, Steve Mould does a good job.

[Berni]

Yep he makes a great explanation of it.

The other interesting thing is just like they have the equivalent of "feromagnetisem" in electric fields, they also have equivalents in all the stuff that comes with it, like a 'curie temperature' where you can freeze the structure into a charged state, giving you the equivalent of a 'permanent magnet' called an electret that emits a permanent electric field around itself: https://en.wikipedia.org/wiki/Electret

The effect is not that widely known apart from electret microphones where the most common use is for these things (eliminates the need for a high voltage supply in condenser microphones by providing the electrostatic field using the electret material).