6.2 Mobility calculations
6.2.3 Transit time for different film thicknesses
The transit time also depends on the He-film thickness and the roughness of the sub-strate. As we can see from Fig. 6.11) a) and b), for sample No.3, as expected the time needed for the electrons to pass through the channel is shorter when the film thickness
Figure 6.10: Schematically the transport mechanism of the electrons through the channel.
The red spot represents the electrons which will go back to the source because for pulse widths<400nsthe time is not enough for the electrons to cross at least more than L/2.
The green spot represents the electrons which will pass through the channel to the drain because for pulse widths≥400nsthe time is enough for the electrons to cross more than L/2.
is thicker. That is may be due to the roughness of the substrate which is become more important when we go to thinner helium films.
Figure 6.11: Forsample No.3: a) The number of passed electrons as a function of pulse width for a film thickness of 30nm. b) The number of passed electrons as a function of pulse width for a film thickness of 40nm. Here the channel is short (2µm) andVs−d= 1V.
Wigner crystal observations
In the experiments of the determination of saved electrons we obserevd different be-haviour in the pick-up current when we go to high numbers of saved electrons. From this different behaviour of the pick-up current we consider that the Wigner crystal regime is reached. Because when the gate was partially opened, a sharp peak was ex-pected but as we can see in Fig. 7.1. a) and b), the rate of passed electrons remain constant for some time and then decreases gradually until zero current again. There is an indication that, the Wigner crystal start melting after opening the gate partially.
After that, we see the peaks as expected because the crystal is already melted. So we have two regions in our graph the first one for Wigner crystal regime and the other for the classical gas regime. Furthermore the height of the pick-up current depends on the intial saved electrons at the source as expected from our electrons distribution model.
The time needed for the total saved electrons to go through the channel in this case is relatively long time compared to what observed before and depends on the intial saved electrons at the source namely when we go from low electron density (in classical regime) to relatively high electron density (in Wigner crystal regime), see Fig. 7.2. We interpret this behaviouras the localization of the electrons which forms in this case a Wigner crystal and so the mobility is very low.
Figure 7.1: Forsample No.5: Pick-up current (Ip) as a function of time during saving electrons measurements which shows the Wigner crystal and classical gas regimes. a) for 20 minutes charging time. b) for 60 minutes charging time.
Zusammenfassung
In dieser Arbeit wurden Untersuchungen zum Transport von Elektronen auf fl¨ussigen Heliumfilmen durch enge Kan¨ale gezeigt, die auf einem Siliziumwafer hergestellt wur-den und die Feldeffekt Transistoren (He-FET) darstellen. Die Probe hat ”source” und
”drain” Gebiete, die durch eine ”gate” Struktur getrennt sind, welche aus zwei Gold-elektroden mit einer engen L¨ucke besteht, durch die der Elektronentransport statt-findet. Die Elektronendichte auf ”source” und ”drain” werden mir einer elektronischen Methode direkt bestimmt. F¨ur zeitaufgel¨oste Messungen wird zuerst ein Puls von Elektronen von einem kleinen Filament im ”source” Gebiet gesammelt, und dann wird der Fluss dieses Pulses durch den Kanal des ”split gates” hin zum ”drain” betrachtet.
Das erlaubt die Be-stimmung des Elektronentransports von Oberfl¨achenelektronen in Kan¨alen verschiedener Gr¨osse und f¨ur einen breiten Bereich von Elektronendichten.
Die Untersuchung von m¨oglichen Potentialverl¨aufen auf den He-FET Proben resultiert in einem neuen Model f¨ur die Anzahl der verbleibenden Elektronen in Abh¨angigkeit der
”gate” Spannung. Deshalb hilft dieses Modell sehr um die gesamte zwei-dimensinale Elektronendichte mit Hilfe eines He-FET zu verstehen und erleichtert es, den Elek-tronentransport einer solchen Probe zu untersuchen. Diese Arbeit kann in folgenden Punkten zusammengefasst werden:
a) Einige Verbesserungen im experimentellen Aufbau wurden durchgef¨uhrt, so zum Beispiel der Schrittmotor, der zusammen mit dem Zylinderkondensator zur Be-stimmung des Heliumlevels benutzt wurde. Diese Arbeit wurde daher unter besser definierten Bedingungen durchgef¨uhrt als sie zuvor gegeben waren.
b) Wir haben die maximale Elektronendichte im ”source” Gebiet verbessert, indem neue und besser strukturierte Proben benutzt wurden.
c) Wir haben zeitaufgel¨oste Messungen durchgef¨uhrt, die Aufschluss ¨uber die Po-tentialverteilung in den Proben gegeben haben.
d) Wir haben die Potentialverteilung auf den Proben genauer untersucht, welche sowohl in unseren als auch in ¨alteren Experimenten Anwendung gefunden haben.
e) Diese Untersuchungen der Potentialverteilung nutzend, haben wir ein neues Mod-ell f¨ur die verbleibenden Elektronen entwickelt, das als Funktion der ”gate” Bar-riere als grundlegendes Modell verwendet werden kann um den Transport von SSE zu untersuchen.
f) Wir haben eine neue Methode zur Untersuchung des Elektronentransports auf fl¨ussigen Heliumfilmen genutzt indem wir das ”gate” pulsweise betrieben haben (das ”gate” wurde f¨ur eine kurze Zeit ge¨offnet).
Wir erhalten also einen tieferen Einblick in das System des Elektronentransports auf Heliumflimen in solch einer Geometrie.
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I herewith declare that I have produced this thesis without the prohibited assistance of third parties and without making use of aids other than those specified; notions taken over directly or indirectly from other sources have been identified as such. This thesis has not previously been presented in identical or similar form to any other German or foreign examination board.
The thesis work was conducted from January 2008 to September 2011 under the supervision of Paul Leiderer at University of Konstanz.
M Ashari,