In the direction of defining and controlling the system we introduce here the response of different samples which were used to improve the low limit of the number of saved electrons. We are interested in high electron densities because the Wigner crystal regime and degenerate Fermi gas regime can only be reached at high electron densities (see Fig. 2.19). At the beginning of this study we assumed that there is a homogeneous electron distribution at the source area [Doi04b, Sch07] and the gate potential used to open the channel is 0V (i.e. does not depend on the source and drain potentials as we will see later in section 5). To determine the number of electrons in the source area, we used the following method:
• switch on the filament by pulsing it continuously and see wether we have a current at the pick-up,
• close the gate completely for some time (charging time) by applying a certain negative voltage to the gate electrode and switch off the filament,
• wait for some time (saving or delay time) and open the gate by applying 0V (here the gate barrier is supposed to vanish atVgate= 0).
The total number of saved electrons can be calculated by integrating the area under the pick-up current (Ip), see Fig. 4.5. The charging timetcis the time between closing the gate and switching off the filament, and the saving time ts is the delay between switching off the filament and opening the gate again. The saving time can be used to determine the stability of the electrons on the source. Because one can fix the intial number of stored electrons and increase the saving time and see the influence of this saving time on the remaining number of electrons on the source. In the following we discuss results for samples No. 1,2,3,5,8.
a) Samples from PSI:
Figure 4.5: Method of charging the source. tc is the charging time andts is the saving time. The total charge is calculated from the area under theIpcurve (area highlighted in blue)
Sample No.1: For this sample, the maximum number of saved electrons that could
be reached was relatively small ≈ 4.5×108, see Fig. 4.6 a). Also the stability of the electrons at the source is not good, see. Fig. 4.6 b). That means there is some loss on the saved electrons with time, which as mentioned before is due to the contacts between the silicon wafer and the gold electrodes (because the insulating layer between the silicon wafer and the gold electrodes is not thick enough).
At the beginning we tried to improve the electron density by varying the electrode po-tentials and see the response of every electrode[Sch07]. But then we had an impression that there is a problem in the samples itself. And so we started to use more samples to see the response of each sample on the maximum number of saved electron and the stability of these saved electrons at the source.
Figure 4.6: For sample No.1: a) The number of saved electrons at the source as a function of charging time. b) The stability of electrons at the source by measuring the remaining electrons with the saving time for two different intial number of saved electrons.
Sample No.2: Using this sample, the maximum saved electrons was improved by reaching≈3×1010 which was a considerable improvement, see Fig. 4.7 a). As we can see from Fig. 4.6 a) and Fig. 4.7 a), the number of saved electrons seems to increase linearly with the charging time until a certain value and then decreases. Until now we do not have a good explanation for this drop. The problem with this sample is that the stability of electrons was also not good due to the same reason in sample No.1, see Fig. 4.7 b).
As long as the charging time increases one would expect a saturation instead of this decreasing, because the maximum saved electrons which can be put on to any helium film surface is limited by the applied potential to the substrate underneath such a film.
Figure 4.7: For sample No.2: a) The number of saved electrons at the source as a function of charging time. b) The stability of electrons at the source by measuring the remaining electrons with the saving time.
sample No.3: The saturation which has been discussed above was observed by using sample No.3, see Fig. 4.8 a). This measurement was done for a short saving time (ts = 10sonly) because the stability of the electrons also was not good (see Fig. 4.8 b)).
Figure 4.8: For sample No.3: a) The number of saved electrons at the source as a function of charging time. The saturation happened at 3×109. b) The stability of electrons at the source by measuring the remaining electrons with the saving time.
After these results it was clear that with the samples made at PSI one could not mea-sure under well defined conditions. Since there is a collaboration work between our group and the group of Professor Kimitoshi Kono at RIKEN institute in Japan, we made some new samples there (see table 3.1).
b) Samples from RIKEN:
Sample No.5: With this sample the first measurements under well defined conditions were done. The maximum number of saved electrons could be reached with this sample is relatively high 4.2×1010 and the electrons are more stable than before, see Fig. 4.9 a) and b). We will see later in our new model that the gate potential needed for the gate barrier to vanish depends on Vsource and Vdrain and it is not always zero. So in all previous measurements we should take into account that the gate is not completely open becauseVsourceandVdrainalways have a positive values and so the actual number of saved electrons should be more than the presented ones.
Sample No.8: With these new samples from RIKEN, we improved not only the
Figure 4.9: For sample No.5: a) The number of saved electrons at the source as a function of charging time. The saturation happened at a number of saved electrons of 4.2×1010. b) The stability of electrons at the source by measuring the remaining electrons with the saving time.
maximum number of saved electrons, but also the problem of electrons loss, because these two facts are closely related. For example, using sample No.8, it becomes easier to reach a number of saved electrons above 1010 with electron life times of more than 10 minutes, see Fig. 4.10 a) and b).
As a conclusion, the stability of the saved electrons using RIKEN samples is better than the stability of the PSI samples.
Figure 4.10: For sample No.8: a) The number of saved electrons at the source as a function of charging time. The saturation happened at electron density of 1.4×1010. b) The stability of electrons at the source by measuring the remaining electrons with the saving time. The saved electrons is more stable until 10 minutes saving time.