Type-II GaSb/GaAs quantum-dot intermediate band with extended optical absorption range for efficient solar cells

Abstract

GaSb/GaAs type-II quantum-dot solar cells (QD SCs) have attracted attention as highly efficient intermediate band SCs due to their infrared absorption. Type-II QDs exhibited a staggered confinement potential, where only holes are strongly confined within the dots. Long wavelength light absorption of the QDSCs is enhanced through the improved carriers number in the IB. The absorption of dots depends on their shape, material quality, and composition. Therefore, the optical properties of the GaSbGaAs QDs before and after thermal treatment are studied. Our intraband studies have shown an extended absorption into the long wavelength region $1.77 \, \upmu \text {m}$. The annealed QDs have shown significantly more infrared response of $7.2 \, \upmu \text {m}$ compared to as-grown sample. The photon absorption and hole extraction depend strongly on the thermal annealing process. In this context, emission of holes from localized states in GaSb QDs has been studied using conductance–voltage (G–V ) characteristics.

Appendix conductance–voltage (G–V)characteristics of self-assembled quantum dots

Under the thermodynamic equilibrium state $\displaystyle \frac{ \text {d}{P_{\text {QD}}(t)} }{ \text {d }t }=0$ we have, [14]

$$\begin{aligned} \sigma ^{\text {p}} \nu _{\text {p}} p \left( 1-f_{\text {p}}^{\text {eq}}\right) =e_{\text {p}}f_{\text {p}}^{\text {eq}} \end{aligned}$$

we define the equilibrium occupation fraction by $f_{\text {h}}^{\text {eq}}$, which is given by $f_{\text {p}}^{\text {eq}}=\displaystyle \frac{P_{\text {QD}}}{N_{\text {QD}}}$

For a small perturbation at a given angular frequency $\omega =2{\varPi }f$, the variation of population is given to first order by

$$\begin{aligned} \displaystyle \frac{ \text {d}\delta {P_{\text {QD}}(t)} }{ \text {d }t }= & {} j \omega \delta P_{\text {QD}}(t) \\ \displaystyle \frac{ \text {d}\delta {P_{\text {QD}}(t)} }{ \text {d }t }= & {} - \left( e_{\text {p}}+ \sigma ^{\text {p}} \nu _{\text {p}} p \right) \delta P_{\text {QD}}(t) +\sigma ^{\text {p}} \nu _{\text {p}} N_{\text {QD}} \left( 1-f_{\text {p}}^{\text {eq}}\right) \delta p, \end{aligned}$$

where $j=\sqrt{-1}$, we obtain for $\delta p=p \displaystyle \frac{e\delta \varphi _{\text {con}}}{K_{\text {B}}T}$ and $\delta \varphi _{\text {con}}$ represents the potential difference at the GaSb QDs layer caused by the applied ac bias. Then, we can write the change of population as follows:

$$\begin{aligned} \delta {P_{\text {QD}}(t)}= N_{\text {QD}} \left( \displaystyle \frac{e\delta \varphi _{\text {con}}}{K_{\text {B}}T}\right) \displaystyle \frac{f_{\text {p}}^{\text {eq}}\left( 1-f_{\text {p}}^{\text {eq}}\right) }{1+j\omega \left( \displaystyle \frac{\left( 1-f_{\text {p}}^{\text {eq}}\right) }{e_{\text {p}}}\right) }. \end{aligned}$$

For a device with surface S the small applied voltage causes the modulation of the charge will fill and empty the GaSb QD levels, which will induce an ac current defined as $\delta I=S_{\text {p}} e \displaystyle \frac{ \text {d}\delta {P_{\text {QD}}(t)} }{ \text {d }t }$

By taking the real part of $(\displaystyle \frac{\delta I}{\delta V})$ we can determine the QD conductance G, which can be written by

$$\begin{aligned} G (\omega , T)=\alpha \displaystyle \frac{f_{\text {p}}^{\text {eq}}\left( 1-f_{\text {p}}^{\text {eq}}\right) }{K_{\text {B}}T}\displaystyle \frac{\omega ^{2} \tau }{1+ \omega ^{2} \tau ^{2}} \end{aligned}$$

where $\tau =\displaystyle \frac{(1-f_{\text {p}}^{\text {eq}})}{e_{\text {p}}^{\text {th}}}$, $\alpha =S_{\text {p}} q^{2}N_{\text {QD}}\beta$ and $\beta =\displaystyle \frac{\delta \varphi _{\text {conf}}}{\delta V}$. We can note from the last expression the function $f_{\text {p}}^{\text {eq}}(1-f_{\text {p}}^{\text {eq}})$ shows a peak when $f_{\text {p}}^{\text {eq}}= \displaystyle \frac{1}{2}$ and the term $\displaystyle \frac{\omega ^{2}\tau }{1+\omega ^{2}\tau ^{2}}$ has a maximum value when $\omega \tau =1=2e_{\text {p}}.$