Miniaturized capacitors with carbon nanofibers

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.

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. ↩︎