Illumination-induced nonequilibrium charge states in self-assembled quantum dots

We report on capacitance-voltage spectroscopy of self-assembled InAs quantum dots under constant illumination. Besides the electronic and excitonic charging peaks in the spectrum reported earlier, we find additional resonances associated with nonequilibrium state tunneling unseen in C(V) measurements before. We derive a master-equation-based model to assign the corresponding quantum state tunneling to the observed peaks. C(V) spectroscopy in a magnetic field is used to verify the model-assigned nonequilibrium peaks. The model is able to quantitatively address various experimental findings in C(V) spectroscopy of quantum dots such as the frequency- and illumination-dependent peak height, a thermal shift of the tunneling resonances and the occurrence of the additional nonequilibrium peaks.

Figure 1

(a) Band structure sketch of the sample. (b) Electron tunneling into excited states. The quantum dot energy for resonant tunneling is ascending from top to bottom.

Figure 2

(a) Reference C(V) curve without illumination (violet) followed by C(V) curves under illumination at a wavelength of approximately $920\mathrm{nm}$ using different LED currents ranging from $0.5\mathrm{mA}$ up to $20\mathrm{mA}$. The C(V) spectra are offset by $0.25\mathrm{pF}$ for better visibility. (b) To reveal the illumination-induced additional capacitances we subtracted the unilluminated reference curve from the illuminated ones. For a better allocation of the illumination-induced peaks within the quantum dot spectrum, we inserted the unilluminated reference curve (dashed line) subtracted by an alleged background capacitance of the diode, using the almost linear part before the $s$ peaks for fitting. The gate voltage is converted to energy by applying the simple lever-arm approach [19].

Figure 3

(a) C(V) spectrum with an LED illumination using a current of $I_{\mathrm{LED}}=20\mathrm{mA}$ and magnetic fields of up to $5.5\mathrm{T}$. The graphs are offset proportional to the magnetic field strength for clarity. Dashed lines are vertical; the solid lines are a guide to the eye for the Zeeman shift. The dip labeled $LL$ corresponds to capacitive charging of Landau levels in the wetting layer [20]. (b) Energetic position of the peaks for a magnetic field strength between 0 T and 5.5 T and linear fits. The dashed lines correspond to the dashed vertical lines in (a). For better visibility of the shifts, the peaks are offset. A clear shift of addition peak C is visible.

Figure 4

Theoretical C(V) spectrum of a quantum dot with up to two electrons and one hole for (a) different values of the hole creation rate at $\omega =0.1{\mathrm{\Gamma }}_e, T=0.1U$, (b) different driving frequencies at ${\mathrm{\Gamma }}_h=0.1{\mathrm{\Gamma }}_e, T=0.1U$, and (c) different temperatures at $\omega =0.001{\mathrm{\Gamma }}_e, {\mathrm{\Gamma }}_h=0.1{\mathrm{\Gamma }}_e$. Other parameters are $U_{eh}=0.7U$.

Figure 5

(a) Modeled C(V) spectrum as function of the gate voltage for different values of ${\mathrm{\Gamma }}_h$. Curves are offset and shifted for clarity. Dashed lines mark the peak positions. (b) Comparison of experimentally measured peak height as a function of the LED current (left and lower axis, data points with dashed lines as a guide to the eye) with the modeled peak height as a function of the hole creation rate ${\mathrm{\Gamma }}_h$ (right and upper axis, solid lines). Used model parameters are as follows: frequency $\omega =0.1{\mathrm{\Gamma }}_s, \hslash {\omega }_e=46\mathrm{meV}, \hslash {\omega }_h=25\mathrm{meV}, E_{ss}^C=21\mathrm{meV}, k_{\text{B}}T=0.5\mathrm{meV}, {\mathrm{\Gamma }}_p=10{\mathrm{\Gamma }}_s$.