Fig. 1. (Color online) Illustration of RRAM device at (a) switched on state and (b) switched off state.

Fig. 2. (Color online) The overall lithography physical verification methodology for RRAM devices.

Fig. 3. (Color online) The definition of RRAM device length and RRAM device spacing in an RRAM array layout. The number of rows and number of columns are M and N, respectively.

Fig. 4. (Color online) Waveforms for evaluation. (a) The concept of apply voltage across TE and BE and (b) the change of read resistance during SET and RESET processes. (c) An example of simulated I−V curve of RRAM device during SET and RESET processes.

Fig. 5. (Color online) Post lithography simulation layout. (a) Simulation result of 32 × 32 array and (b) the zoomed in view of lower left 3 × 3 corner.

Fig. 6. (Color online) Device area under different doses and focuses.

Fig. 7. (Color online) Statistics of RRAM device area.

Fig. 8. (Color online) Statistics of R_on of RRAM device.

Fig. 9. (Color online) Statistics of R_off of RRAM device.

Fig. 10. (Color online) Statistics of V_rst of RRAM device.

Fig. 11. (Color online) Statistics of V_set of RRAM device.

Fig. 12. (Color online) Effect of RRAM device length on (a)−(c) R_on, (d)−(f) R_off, (g)−(i) V_rst and V_set. The device spacing is 95 nm.

Fig. 13. (Color online) Effect of RRAM device spacing on (a)−(c) R_on, (d)−(f) R_off, (g)−(i) V_rst and V_set. The device length is 115 nm.

Fig. 14. (Color online) Effect of array's size on (a)−(c) R_on, (d)−(f) R_off, (g)−(i) V_rst and V_set. The device length and device spacing are 110 and 95 nm, respectively. From left to right: typical corner, max. corner, and min. corner.

Fig. 15. (Color online) The relationship between RRAM device spacing and (a) average device area and (b) variation with and without the OPC technique applied.

Fig. 16. (Color online) (a) RRAM patterns on the mask before and after the OPC technique is applied. (b) The printed RRAM patterns when the short circuit forms.

Fig. 17. (Color online) Comparison of (a)−(c) R_on and (d)−(f) R_off with and without the OPC technique applied.