Photon Assisted Tunneling in Single and Coupled Quantum Dot Systems

T. Fujisawa and S. Tarucha

  We describe photon assisted tunneling (PAT) in single and coupled 
quantum dot systems which have  a relatively large zero-dimensional 
(0D) level  separation.  A microwave electric  field applied across 
the  tunneling  barrier  leads  to  the  formation  of  a  sideband 
structure. For a  single quantum  dot system, a PAT current peak is 
clearly observed in addition to the Coulomb oscillation peak. For a 
weakly-coupled  double-dot  system, we  observe resonant  0D-0D PAT. 
The resonant  PAT current  appears  only when two discrete  quantum 
levels  in  the  neighboring  dots are  exactly  separated  by  the 
microwave photon energy. The PAT current shows a narrower peak than 
the main  resonant  tunneling  current  in  accordance  with  time-
dependent   tunneling   theory.   The photon  stimulated   emission 
associated  with PAT from a higher-lying occupied level to a lower-
lying empty level  is obtained at  a drain voltage  sufficient that 
population inversion takes place. 

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Fig 1. Schematic diagram of the double gate single electron transistor. A single and a coupled quantum dot are formed by applying relevant voltages to the Schottky gates.

Fig. 2. Energy diagram of the PAT through a dot in the classical Coulomb blockade regime (a), and in the quantum dot regime (b).

Fig. 3. A Coulomb oscillation peak and PAT current peaks through a quantum dot. Each curve is offset by 0.2 pA for clarity.

Fig. 4. (a) Schematic charging diagram of the coupled dot system. (n, m) corresponds to the number of electrons in the left dot and in the right dot, respectively. The resonant 0D-0D tunneling peaks are observed at the vertices, V and V'. The thick lines, PLR, PRL, etc., indicate the conditions for the resonant 0D-0D PAT. (b) Energy diagram of the PAT for the condition on the line PLR, at the point V, and (d) on the line PRL.

Fig. 5. (a) The drain current profile near the condition V' with and without applying microwave radiation. (b) The contour plot of the current profile. A part of the charging diagram is also attached on the top of the plot. The arrows indicate that E = (E_R + E_L)/2 and e = E_R - E_L are changed.

Fig. 6. (a)The drain current profile with a main resonance peak at V' and satellite PAT peaks on P'LR and P'RL. (b) Schematic diagram for the photon absorption and stimulated emission processes