Method for Determining the Spatial Distribution of Electrical Current Density in a Two-dimensional Material Device

Patent metadata

Field	Value
Publication number	US-2022011355-A1
Application number	US-202117363310-A
Country	US
Kind code	A1
Filing date	Jun 30, 2021
Priority date	Jul 8, 2020
Publication date	Jan 13, 2022
Grant date	—

Abstract

The current density distribution is determined in an electronic device including a first and a second electrode, and a layer of a 2-dimensional conductive material extending between the first and second electrode. The total current through the electrodes is measured, and then a first current measurement probe is placed at a plurality of positions near the interface between the 2D material and the first electrode. The probe is coupled to the same voltage as the first electrode. The same is done at the interface between the channel and the second electrode, by placing a second probe coupled to the same voltage as the second electrode. The boundary conditions are determined for the current, and assuming that the current density vector is normal to the interfaces, this yields the boundary conditions for the current density vector. Finally, the continuity equation is solved, taking into account the boundary conditions.

First claim

What is claimed is:

1 . A method comprising:
applying a voltage between a first electrode and a second electrode, thereby causing a first current to flow from the first electrode through a conductive material to the second electrode and back to the first electrode; while the voltage is also applied between a first probe and the second electrode, placing the first probe on first locations along a first interface between the first electrode and the conductive material, thereby causing second currents to flow from the first locations through the conductive material to the second electrode, through the first probe and back to the first locations; while the voltage is also applied between a second probe and the first electrode, placing the second probe on second locations along a second interface between the second electrode and the conductive material, thereby causing third currents to flow from the second probe to the first electrode, through the conductive material and back to the second locations; and determining a current density within the conductive material using the first current, the second currents, and the third currents.

2 . The method of claim 1 , wherein determining the current density comprises using the first current to derive a first set of current density values each representing a boundary condition of the current density at the first interface.

3 . The method of claim 1 , wherein determining the current density comprises using the second currents to derive a second set of current density values each representing a boundary condition of the current density at the second interface.

4 . The method of claim 1 , wherein determining the current density comprises determining the current density based on a divergence of the current density being zero throughout the conductive material.

5 . The method of claim 1 , wherein the first probe and the second probe are different probes.

6 . The method of claim 5 , wherein the first probe and the second probe comprise essentially the same materials.

7 . The method of claim 5 , wherein the first probe and the second probe comprise different materials.

8 . The method of claim 1 , wherein the first probe and the second probe are the same probe.

9 . The method of claim 1 , further comprising:
applying pressure to the first probe such that respective sums of the first current and the second currents are essentially equal to the first current when no probe is present on the conductive material; and applying pressure to the second probe such that respective sums of the first current and the third currents are essentially equal to the first current when no probe is present on the conductive material.

10 . The method of claim 1 , further comprising:
applying a first pressure to the first probe at each of the first locations; and applying a second pressure that is unequal to the first pressure to the second probe at each of the second locations.

11 . The method of claim 1 , wherein the first interface and the second interface form a closed boundary.

12 . The method of claim 1 , wherein the first electrode and the second electrode are both rectangular having a width and oriented parallel to each other, and spaced apart by a distance, wherein the distance is considerably smaller than the width.

13 . The method of claim 1 , wherein determining the current density comprises determining the current density numerically.

14 . The method of claim 13 , wherein determining the current density comprises:
determining a starting value for the current density; determining how closely the starting value conforms to the first current, the second currents, or the third currents; and updating the current density based on determining how closely the starting value conforms.

15 . The method of claim 1 , wherein determining the current density comprises solving ∇· J =0.

16 . The method of claim 15 , wherein solving ∇· J =0 comprises solving ∇σ(x m , y n )·∇E F (x m , y n )=−σ(x m ,y n )∇ 2 E F (x m , y n ), wherein σ(x m , y n ) is the effective value of the position-dependent conductivity in the channel, and E F the position-dependent quasi Fermi level in the channel, σ(x m , y n ) is used as a fitting parameter, for determining the current density based on the relation J (x m , y n )=σ(x m , y n )∇E F (x m , y n ), taking into account the boundary conditions.

17 . The method of claim 1 , further comprising performing a nanopotentiometry measurement at a plurality of points of the conductive material.

18 . The method of claim 17 , wherein performing the nanopotentiometry measurement yields ∇E F (x m , y n ) and ∇ 2 E F (x m , y n ).

Assignees

• Imec Vzw

Inventors

• Sutar Surajit Kumar

Classifications

• H10P74/207

  Electrical properties, e.g. testing or measuring of resistance, deep levels or capacitance-voltage characteristics · CPC title

• H10P74/23

  characterised by multiple measurements, corrections, marking or sorting processes · CPC title

• G01R31/2601

  Apparatus or methods therefor (G01R31/2607, G01R31/2642 take precedence) · CPC title

• G01R31/27

  Testing of devices without physical removal from the circuit of which they form part, e.g. compensating for effects surrounding elements {(testing printed circuit boards G01R31/2801)} · CPC title

• G01R19/08 Primary

  Measuring current density · CPC title