Memristor with a non-planar substrate

A memristor comprising:

• a first electrode;
• a switching material having a first surface and a second surface opposite the first surface, said first surface contacting the first electrode, said second surface comprising a cavity extending in a first direction toward the first electrode;
• a second electrode positioned upon the second surface of the switching material such that a portion of the second electrode is substantially in line with a section of the first electrode along the first direction, wherein the portion of the second electrode that is substantially in line with the section of the first electrode conforms to the shape of the cavity, such that the second electrode has a trough having a substantially rounded bottom, and wherein an active region in the switching material is to be formed between the section of the first electrode and the trough of the second electrode;
• and
• a plurality of field concentration elements positioned between the first electrode and the second electrode, each of said plurality of field concentration elements having a tip that faces a direction that is substantially perpendicular to the first direction and toward each other.

A crossbar array composed of a plurality of memristors, said crossbar array comprising:

• a substrate having a plurality of protrusions, wherein each of the plurality of protrusions extend in a first direction;
• a plurality of first electrodes approximately parallel with respect to each other, each of the plurality of first electrodes positioned over at least one of the plurality of protrusions and conforming to the shape of the at least one protrusion such that each of the plurality of first electrodes has a crest, wherein the crest has a substantially rounded peak;
• a switching material positioned upon the crests of the plurality of first electrodes;
• and
• a plurality of second electrodes positioned approximately parallel with respect to each other and approximately perpendicularly with respect to the plurality of first electrodes upon said switching material such that a portion of each of the second electrodes is substantially in line with the crests of the plurality of the first electrodes along the first direction, wherein respective active regions in the switching material are to be formed between the crests of the first electrodes and the portions of the second electrodes that are substantially in line with respective ones of the crests of the first electrodes;
• and
• a plurality of field concentration elements positioned between the plurality of first electrodes and the plurality of second electrodes, each of said plurality of field concentration elements having a tip that faces a direction that is substantially perpendicular to the first direction and toward each other.

A method for fabricating a memristor, said method comprising:

• providing a substrate having a plurality of protrusions, wherein each of the plurality of protrusions extends in a first direction;
• providing a first electrode on at least one of the plurality of protrusions, wherein the first electrode conforms to the shape of the at least one protrusion such that the first electrode has a crest, wherein the crest has a substantially rounded peak;
• providing a switching material upon the first electrode;
• providing a second electrode upon said switching material such that a portion of the second electrode is substantially in line with the crest of the first electrode along the first direction, wherein an active region in the switching material is to be formed between the crest of the first electrode and the portion of the second electrode that is substantially in line with the crest of the first electrode;
• and
• providing a plurality of field concentration elements between the plurality of first electrodes and the plurality of second electrodes, each of said plurality of field concentration elements having a tip that faces a direction that is substantially perpendicular to the first direction and toward each other.