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Adobestock 250253567

Miniaturized capacitors with carbon nanofibers

Smoltek has developed the world’s thinnest discrete capacitor. You have to stack ten of them on top of each other to reach the same height as today’s industry-standard when it comes to surface-mounted capacitors. The most amazing thing about this microscopic capacitor is its performance. One square millimeter has a capacitance of a whopping 650 nanofarads (650 nF/mm2). Read on for more details.

The world’s thin­nest dis­crete capa­cit­or has a total build­ing height is less than thirty micro­met­ers (30 µm). The capa­cit­or itself, without encap­su­la­tion, is a mere 0.5 to 10 µm. It can be built dir­ectly onto an integ­rated circuit’s die or built into its inter­poser. One square mil­li­meter has a capa­cit­ance of a whop­ping 650 nan­o­farads (650 nF/​mm2). Its intern­al res­ist­ance (ESR) is less than forty mil­liohms (40 mΩ), and its intern­al induct­ance (ESL) is below fif­teen pico­henry (15 pH).

Carbon nanofiber capacitors

We describe our capa­cit­or as a CNF-MIM capa­cit­or since it is a met­al-insu­lat­or-met­al (MIM) capa­cit­or where car­bon nan­ofibers (CNF) are used to cre­ate a much lar­ger sur­face area hence high­er capa­cit­ance than the form factor suggest.

Technical data

  • Sol­id-state construction
  • Capa­cit­ance dens­ity: > 650 nF/​mm2
  • Equi­val­ent series res­ist­ance (ESR): < 40 mΩ
  • Equi­val­ent series induct­ance (ESL): < 15 pH
  • Break­down voltage: Up to ~ 25 V
  • Leak­age cur­rent: ~ 4 mA/​F
  • Excel­lent capa­cit­ance sta­bil­ity up to 150 °C

Applications for discrete CNF-MIM capacitors

A dis­crete CNF-MIM capa­cit­or has a smal­ler foot­print (area) and much thin­ner pro­file (z‑dimension) than any oth­er capa­cit­or with the same capa­cit­ance. CNF-MIM capa­cit­ors up to more than 650 nF can be made less than 30 µm in height. The actu­al form factor can be var­ied accord­ing to the design and need.

As shown in the illus­tra­tions, a dis­crete CNF-MIM capa­cit­or can be

  • moun­ted on prin­ted cir­cuit board (PCB)
  • embed­ded in PCB
  • moun­ted on chip interposer
  • embed­ded in chip interposer
  • moun­ted on chip die

Dis­crete CNF-MIM capa­cit­ors are com­pat­ible with wafer to wafer (W2W) or die to wafer bond­ing (D2W).

Applications for integrated CNF-MIM capacitors

A CNF-MIM capa­cit­or can be integ­rated dir­ectly into chip die or chip inter­poser. The height of the integ­rated capa­cit­ors is a mere 0.5 to 10 µm. The bene­fits with integ­rated CNF-MIM are many:

  • CMOS-com­pat­ible man­u­fac­tur­ing process
  • Unpar­alleled design free­dom for cir­cuit designers
  • Pos­sible to man­u­fac­ture dir­ectly on-chip
  • Closer to the cir­cuit where it is needed
  • Extremely small 2D footprint
  • Very com­pact 3D volume
  • Elim­in­ates the need for integ­rated dis­crete capacitors

As shown in the illus­tra­tions, a CNF-MIM capa­cit­or can be

  • integ­rated with chip interposer
  • integ­rated with built on-chip die

Discrete CNF-MIM capacitor compared to alternatives

Mul­tilay­er Ceram­ic Capa­cit­ors (MLCC) form the industry stand­ard for sur­face-moun­ted device (SMD) capa­cit­ors. Every year, tril­lions of MLCCs are built into all kinds of elec­tron­ic devices. They are 300 µm high. CNF-MIM offers the same capa­cit­ance at a tenth of that height.

The mini­atur­iz­a­tion of elec­tron­ics is cre­at­ing a grow­ing need for ever smal­ler capa­cit­ors. And some cir­cuits (such as Apple’s) use capa­cit­ors that are state of the art. These use improve­ments of MLCC and Low Induct­ance Chip Capa­cit­ors (LICCs) and Trench Sil­ic­on Capa­cit­ors (TSCs), all of which have a height of 80–100 µm.

How­ever, MLCC, LICC, and TSC struggle to go down in height due to mater­i­als involved, pro­cessing schemes, and the cost of raw mater­i­als and pro­cessing. At the same time, SiP and SoC con­tin­ue to become more com­pact. There is less and less space between inter­con­nects (bumps), and they are get­ting short­er. To fit capa­cit­ors between the bumps, the capa­cit­ors must have a smal­ler foot­print and, above all, be shorter—preferably less than 20 µm.

This is the prob­lem that CNF-MIM capa­cit­ors solve. They have a much smal­ler foot­print and, above all, a much lower height.

How a MIM capacitor works

A met­al-insu­lat­or-met­al capa­cit­or, or MIM capa­cit­or for short, has par­al­lel met­al plates with a thin lay­er of an elec­tric insu­lat­or between them. The simplest form of a MIM-capa­cit­or is the par­al­lel plate capacitor.

Now, ima­gine we con­nect a bat­tery to a MIM-capa­cit­or. Since no cur­rent can pass through the isol­at­or, the elec­trons pushed into the plate on one side of the isol­at­or build up a pos­it­ive charge. The elec­trons pulled out from the plate on the oth­er side of the isol­at­or build a neg­at­ive charge. The charges increase respect­ively decrease the elec­tric­al poten­tial on the plates. The buildup con­tin­ues until the dif­fer­ence between the poten­tial is the same as the battery’s voltage. The dif­fer­ence in charge between the two plates cre­ates an elec­tric field between them.

When the bat­tery is removed, the elec­tric field remains since the charges have nowhere to go. Only when the capa­cit­or is con­nec­ted to a closed cir­cuit, the charges in the capa­cit­or can flow. The capa­cit­or thus stores energy in the form of an elec­tric field.

Any mater­i­al that does not con­duct cur­rent can be used as an elec­tric­al insu­lat­or. But gen­er­ally, dielec­tric mater­i­als are used.

Dielec­tric mater­i­al con­sists of atoms whose elec­trons can­not move freely enough to carry cur­rent like all insu­lat­ors. But unlike mater­i­als that are com­monly called insu­lat­ors, such as ceram­ics, dia­lectic mater­i­als become polar­ized in the pres­ence of an elec­tric field. They have elec­trons that are so free to move that the elec­tric field pulls them away from the nuc­le­us. Fig­ur­at­ively, the atom becomes elong­ated, with one end being neg­at­ively charged and the oth­er being pos­it­ively charged.

Dielec­tric in a MIM capa­cit­or becomes polar­ised when the elec­tric field is built up due to the plates’ dif­fer­ent charges. Because of the polar­iz­a­tion, the pos­it­ively charged plate comes into con­tact with the neg­at­ive ends of the atoms closest to it. That reduces its elec­tric­al poten­tial. The oppos­ite is hap­pen­ing at the neg­at­ively charged plate. The bat­tery responds by push­ing in even more charges to main­tain the elec­tric poten­tials. Since capa­cit­ance is a meas­ure of how much charge a capa­cit­or can store, the effect of using a dielec­tric is an increase in capacitance.

The ease with which a mater­i­al becomes polar­ized is pro­por­tion­al to its rel­at­ive per­mit­tiv­ity κ. The high­er the rel­at­ive per­mit­tiv­ity, the easi­er the mater­i­al becomes polar­ized. Thus, a dielec­tric with a high rel­at­ive per­mit­tiv­ity should be chosen to make a small capacitor.

How to make the worlds thinnest capacitor

To cre­ate a capa­cit­or with a min­im­al foot­print and height, we use car­bon nan­ofibers (CNFs) to mul­tiply the con­tact area between the two metals and the inter­me­di­ary dielectric.

Con­sider a single CNF with a dia­met­er of 10 nm and a length of 5 µm. Its mantle sur­face is 2,000 times lar­ger than the area it occu­pies.1 Thus, a forest of such CNFs would mul­tiply the sur­face, but not by as much as 2,000. We can’t cov­er the entire ori­gin­al sur­face with CNFs; there must be space between them to allow access to the con­tact sur­face. But if the forest of CNFs cov­ers about half the sur­face, then the sur­face mul­ti­plic­a­tion would be in the range of 1,000 times.

CNF has many metal­lic prop­er­ties, includ­ing being a good con­duct­or of cur­rent. There­fore a met­al plate covered to fifty per­cent by CNFs is a single elec­trode with a sur­face area about 1,000 times lar­ger than the area of the met­al plate itself. By coat­ing this elec­trode with a uni­formly thick lay­er of a dielec­tric and then coat­ing this in turn with a met­al, a MIM capa­cit­or is obtained. Of course, the dielec­tric should have a high rel­at­ive per­mit­tiv­ity to max­im­ize the capacitance.

Since the CNF has a length much lar­ger than the dia­met­er, we can neg­lect what hap­pens to the elec­tric field near the base and top of each CNF. Essen­tially it will be a uni­form field, just as in a par­al­lel plate capacitor.

Since the capa­cit­ance of a par­al­lel plate capa­cit­or is dir­ectly pro­por­tion­al to the sur­face area, we con­clude that CNFs have increased the capa­cit­ance dens­ity by 1,000 times.

But it doesn’t end there. If the second lay­er of met­al is made uni­formly thick, both sides of it will have the same shape as the first elec­trode. So by coat­ing it with anoth­er lay­er of dielec­tric and then coat­ing this in turn with a met­al, anoth­er MIM capa­cit­or is obtained. It will have the same capa­city as the first. And by elec­tric­ally con­nect­ing the first and the third met­al lay­er, we achieve a par­al­lel con­nec­tion, which doubles the capa­cit­ance. This can be repeated as long as desired and there is space between the car­bon nan­ofibers. The last lay­er of met­al does not need to be uni­formly thick but can fill in any remain­ing spaces between the car­bon nanofibers.

The fig­ure below shows a dis­crete CNF-MIM capa­cit­or with three CNF-shaped capa­cit­ors con­nec­ted in par­al­lel. Using the same assump­tions about dia­met­er, length, and dens­ity as above, this capa­cit­or has 3,000 times the capa­cit­ance pos­sible with a par­al­lel plate capa­cit­or in the same location.

A schem­at­ic cross-sec­tion of a dis­crete CNF-MIM capacitor.
  1. Let r be the radi­us of the car­bon nan­ofiber, and h be its height. Then the ori­gin­al area A1 = πr2 and the new area A2 = A1 + 2πrh. The increase in area is A2 /​ A1 = (A1 + 2πrh) /​ A1 = 1 + 2πrh /​ (πr2) = 1 + 2h /​ r. If r = 5 nm and h = 5,000 nm, A2 /​ A1 = 1 + 2 ⋅ 5,000 /​ 5 = 2,001. 

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