Method and system of reconstructing electric current from magnetic field maps of 3d integrated circuits

A system, comprising:

• a memory storing instructions;
• one or more Input/Output (I/O) interfaces;
• one or more sensors;
• and
• one or more hardware processors coupled to the memory and the one or more sensors via the one or more communication interfaces (106), wherein the one or more hardware processors are configured by the instructions to:
• obtain a plurality of magnetic field maps along x-direction (bx) and y-direction (by) of a 3-Dimensional Integrated Circuit (IC), measured using the one or more sensors, wherein volume of the 3D IC is discretized into a plurality of layers of equal width (Δz);
• detect one or more layers, from among the plurality of layers, comprising a current flow, by:
• calculating a plurality of current density maps along x-direction and y-direction based on the plurality of magnetic field maps, associated with each of the plurality of layers using an iterative optimization technique;
• and
• computing one or more quality measures associated with each of the plurality of layers based on the associated plurality of current density maps, wherein one or more of the plurality of layers having the associated one or more quality measures greater than a first threshold value are determined as comprising the current flow;
• and
• estimate a current map for each of the one or more layers using the iterative optimization technique to obtain a 3D current map of the IC.

One or more non-transitory machine-readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors cause:

• obtaining a plurality of magnetic field maps along x-direction (bx) and y-direction (by) of a 3-Dimensional Integrated Circuit (IC), measured using the one or more sensors, wherein volume of the 3D IC is discretized into a plurality of layers of equal width (Δz);
• detecting one or more layers, from among the plurality of layers, comprising a current flow, by:
• calculating a plurality of current density maps along x-direction and y-direction based on the plurality of magnetic field maps, associated with each of the plurality of layers using an iterative optimization technique;
• and
• computing one or more quality measures associated with each of the plurality of layers based on the associated plurality of current density maps, wherein one or more of the plurality of layers having the associated one or more quality measures greater than a first threshold value are determined as comprising the current flow;
• and
• estimating a current map for each of the one or more layers using the iterative optimization technique to obtain a 3D current map of the IC.