Optical and electronic properties in ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys

The optical and electronic properties in ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys with various compositions grown on InP substrates by using molecular-beam epitaxy were investigated through photoluminescence (PL) measurements and numerical calculations. The electronic subband energy states, the interband transition energies, and the exciton binding energies of ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys and corresponding ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}∕{\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ single quantum wells were calculated by using a finite difference method, taking into account two band Hamiltonian system. The numerical results for interband transitions of ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys were in reasonable agreement with the excitonic transitions obtained from the PL measurements.

Figure 1

(a) Schematic diagram of the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys structures and (b) electronic structures corresponding to the conduction bands of the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys structures with (i) $z=0.2$; ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ $\left(15\mathrm{\AA }\right)$ and ${\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ $\left(3.75\mathrm{\AA }\right)$, (ii) $z=0.4$; ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ $\left(9.8\mathrm{\AA }\right)$ and ${\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ $\left(6.6\mathrm{\AA }\right)$, (iii) $z=0.6$; ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ $\left(6.6\mathrm{\AA }\right)$ and ${\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ $\left(9.8\mathrm{\AA }\right)$, and (iv) $z=0.8$; ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ $\left(3.75\mathrm{\AA }\right)$ and ${\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ $\left(15\mathrm{\AA }\right)$.

Figure 2

Photoluminescence spectra for the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{0.6}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_{0.4}$ digital alloys measured at various excitation power intensities.

Figure 3

Photoluminescence spectra for the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys with $z$ values of 0.2, 0.4, 0.6, or 0.8.

Figure 4

The convergence of the theoretical interband transition energies with respect to the unit mesh size in a finite difference method. The solid line indicates the theoretical values for the $\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)∕\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)$ single quantum well $\left(10\mathrm{\AA }\right)$. The dashed line indicates the theoretical values for the $\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)∕\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)$ digital alloys $(10\mathrm{\AA }∕10\mathrm{\AA })$.

Figure 5

The interband transitions as a function of the $z$ composition at $9\mathrm{K}$ for the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys. The filled circles and the lines represent the experimental data and the theoretical values for the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys, respectively. Each line indicates the theoretical values obtained by using various band offset ratios, from 0.4 to 0.8.

Figure 6

The interband transitions as a function of the $z$ composition at (a) 9 and (b) $300\mathrm{K}$ for the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys. The filled circles and the dashed line represent the experimental data and the theoretical values for the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys, respectively. The solid line indicates the theoretical values for a ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}∕{\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ single quantum well.

Figure 7

Theoretical values of the exciton binding energies for the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys and the ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}∕{\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ single quantum well. The dashed line represent the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}∕{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys with $z$ values of 0.2, 0.4, 0.6, or 0.8. The solid line indicates for a ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}∕{\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ single quantum well.

Figure 8

Envelope functions as a function of the quantum-well width for the ${\left({\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}\right)}_{1-z}{\left({\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}\right)}_z$ digital alloys structures with a $z$ value of (a) 0.2 and (b) 0.8. The insets indicate the magnified envelope functions of the rectangular area.