Transport experiments on InAs self-assembled quantum dots in the microwave regime

We report an experimental study on microwave (MW) transport through InAs self-assembled quantum dots (SAQDs) embedded in a $\mathrm{Au}∕\mathrm{Ga}\mathrm{As}$ Schottky diode. In the dc measurement, we observed isolated conductance peaks resulting from the resonant tunneling through the quantum states of the SAQDs. A single peak split into two peaks when MW signals were added. The relative strengths of these split conductance peaks changed with frequency, and it was explained by a simple convolution model including nonadiabatic electron tunneling. The inverse tunneling rate was obtained from the degree of this nonadiabacity at high frequencies.

Figure 1

Simple schematic of the measurement system and the sample structure.

Figure 2

(a) dc $dI∕dV\text{−}V$ characteristics. (b) Splitting of the differential conductance peak due to MW. dc $I\text{−}V$ (solid line), $dI∕dV\text{−}V$ without MW (solid line), measured $dI∕dV\text{−}V$ with MW (dotted line, $\mathrm{f}=50\mathrm{MHz}$), and calculated $dI∕dV\text{−}V$ with MW (dashed line).

Figure 3

(a) Peak splitting as a function of $V_{\mathit{MW}}$ at various frequencies. (b) Ratio of peak splitting to $V_{\mathit{MW}}$ as a function of $1∕f$.

Figure 4

Evolution of the split conductance peaks as the frequency changes from $40\mathrm{MHz}\text{to}2\mathrm{GHz}$. The listed value of $V_{\mathit{MW}}$ was adjusted to maintain the same value of $V_{\mathit{eff}}$ (the same amount of splitting).

Figure 5

(a) Segmentation of the MW signal. (b) Schematic $I\text{−}V$ for adiabatic (left) and the nonadiabatic (right) case.

Figure 6

Calculated $dI∕dV\text{−}V$ at several different $\delta$ values.

Figure 7

Extracted $\delta$ as a function of $1∕f$.

Figure 8

(a) Equivalent circuit of our diode structure. (b) Measured and calculated real admittance of the diode. (c) Measured and calculated imaginary admittance of the diode.

Figure 9

Output current shape as a function of the input voltage (either sinusoidal or pulse) when the current through QD shows staircases.

Figure 10

Schematic of electron tunneling for the two-terminal QD system with a double barrier.