Optimizing write current and power dissipation in MRAMs by using an astroid curve

Analytical expressions of minimum electric current and power dissipation, and bit line and word line currents that produce them, for writing data into magnetic tunnel junction (MTJ) magnetoresistive random access memory (MRAM) cells are derived with the assumption that an asteroid curve can be applied to all MTJs in a memory cell array. The expressions contain word length, that is, the number of bits per word, and parasitic resistances of the write word line and bit line (which are important design parameters of memory cell arrays) and distances between the write currents and the free magnetic layer for data storage (which are important structural parameters of MTJ cells). They provide quantitative MRAM design guidelines and help to understand current and power behavior. For example: 1) the current along the bit lines should be decreased and the current along the write word line should be increased as the word length increases; 2) the word line currents for the minimum total current and power dissipation have maximum values at certain word line distances from the free layer; and 3) the minimum current and power have tendencies to saturate as the word length increases. Plots of the expressions exemplify the current and power dissipation behavior and dependence on the parameters related to the design of MRAM and MTJ cells.