1. Hysteresis – Bias Switching Sweep Method Edward Cazalas 11/30/12

2. Method Description Perform sweep by alternating bias between positive and negative voltage while also incrementing absolute voltage toward (Inward, shown above) or away from (Outward) 0 V center. Bias switching (BS). Hope is to “pulse” voltage and obtain quick reading of Dirac curve. and so on …

3. A series of startup sweeps are first performed to determine position of Dirac peaks. Forward peak @ 5 V, Backward peak @ 9 V. Blue = Forward Sweep Red = Backward Sweep

4. Outward sweep For 3 s, Dirac peak settles +7.5V (BS-FW) Previously (startup) +5 V (FW) and +9 V (BW) Artifact peaks derive from the short time of acquisition. Artifact PeaksReal Dirac Peaks

5. Inward sweep Dirac peak settles at +7V (BS-BW) Previously (startup) +5 V (FW), +9 V (BW), and +7.5V (BS-FW) Little change in Dirac peak voltage from outward to inward sweep

6. Outward sweep with various acquisition times Dirac peak settles at +8.5V (BS-FW) Previously (startup) +5 V (FW), +9 V (BW), +7.5V (BS-FW), and +7V (BS-BW) Longer acquisition times eliminate artifact peak

7. Artifact peaks come from the graphene resistance reading occurring before resistance has reached a reasonably stable state. For 1s acquisition time, Dirac peak @ +10.5/11.5V. Artifact peak @ -16V Measured value is taken as last resistance point in acquisition feed. Voltage increases with time +0.5V -1V + 1.5V -2V ect… 0V -16V +10.5V +11.5V

8. Artifact peaks come from the graphene resistance reading occurring before resistance has reached a reasonably stable state. For 1s acquisition time, Dirac peak @ +10.5/11.5V. Artifact peak @ -16V Measured value is taken as last resistance point in acquisition feed. Voltage increases with time +0.5V -1V + 1.5V -2V ect… 0V

9. Artifact peaks come from the graphene resistance reading occurring before resistance has reached a reasonably stable state. For 10s acquisition time, Dirac peak @ +6.5. Artifact peak @ -20V Measured value is taken as last resistance point in acquisition feed. Voltage increases with time -20V +6V Negative voltage stabilization takes longer time for larger voltages After Dirac peak is reached, positive backgate voltage elicits peculiar graphene resistance behavior

10. What causes this longer stabilization? Perhaps due to applied voltage being farther away from Dirac point, and takes longer time for charge carrier density to increase to value reflected by applied bias. Does change of carrier density or carrier density saturation really take this long? -20V Negative voltage stabilization takes longer time for larger voltages

11. Artifact peaks removed with longer acquisition time. For 30s acquisition time, Dirac peak @ +8.5. Measured value is taken as last resistance point in acquisition feed. Voltage increases with time. +8.5V

12. Same graphene resistance behavior when crossing Dirac peak from other direction (BS-BW). Dirac peak @ +9 (BS-BW) nearly same in other direction (+8.5V BS-FW). Voltage increases with time. Behavior of graphene resistance after crossing Dirac peak may be due to change of graphene charge carrier (from h+ to e-). +9V

13. With longer acquisition times, sweep direction does not significantly affect Dirac curve. Solid black line does not use bias switching method.

14. General Observations of Bias Switching Method Artifact peak appears at negative voltage. Artifact peak results from longer stabilization time of negative backgate voltages. Artifact peak reduced and removed with longer acquisition times. Bias switching method not usable to obtain Dirac curve while backgate under detection voltage due to long time required by method and the subsequent shift of Dirac peak during this long time. Different method of obtaining Dirac curve needed (under testing).

15. Theory of Graphene Resistance Response to Backgate Bias Change Large change in bias leads to initial peaking of resistance for both positive and negative voltages. Peaks located at Dirac peak resistance (minimum conductivity and minimum charge carriers on graphene).

16. Theory of Graphene Resistance Response to Backgate Large Bias Change Cutout from Bias Switching 30s acquisitions A) Switching bias causes resistance peaking as charge carriers in graphene change type (from h+ to e-) and a minimum is charge carrier density is encountered just as carrier type switches. B) Quick decay of peak due to rapid increase of e- charge carriers on graphene. A) B) D) E) C) C) Resistance gradually increases as Dirac peak shifts into direction of applied voltage. D) Carriers on graphene minimized by application of opposite bias on backgate (switching from e- to h+ carriers). E) Decay of peak due to rapid increase of h+ charge carriers on graphene. What causes C) ?

17. Theory of Graphene Resistance Response to Backgate Large Bias Change What slow change in graphene resistance after application of backgate bias?

18. Why is there no peaking at theses voltages? The charge carrier is not being switched and is still in the h+ regime of the Dirac curve. Note that once Dirac peak is reached, charge carrier switching is expected and is observed in peaking. +8.5V Explaining Trends

19. Why increasing resistance for positive voltage? Resistance increases as the Dirac peak is approached and the number of charge carries are reduced. The Dirac peak is supposed to be at zero volts bias, but is shifted due to nearby electrochemical doping (p-doping). +8.5V Explaining Trends

20. Larger graphene conductance likely corresponds to larger number of charge carriers as bias is increased. It appears the change in conductance (and hence, change in number of charge carriers) is linear with voltage change until a saturation effect takes over at larger voltages. +8.5V Explaining Trends

21. Dirac peak should occur where graphene carrier switching just switching? Perhaps, if the resistance reading is taken at a time when resistance is at a “turning point”, i.e. when effects of hysteresis have just begun to dominate response, then perhaps a more accurate Dirac curve can be taken. +8.5V Explaining Trends +6.5V

22. General Conclusions Role of electrochemical doping still under investigation. Dirac curve measurements should be taken at resistance “turning points”. Analysis is qualitative. Quantitative assessment required. Mechanisms driving response to changing bias may be useful in considering response from radiation and is under review.