Minibands and Wannier-Stark ladders in semiconductor superlattices studied by infrared spectroscopy

We review the basic features of interminiband absorption in superlattices, focussing on the joint density of states, the oscillator strength and the associated sum rule. Then we will discuss infrared spectroscopic studies under application of an electric field. With a field in the plane of the layers, a hot-electron distribution can be generated. Using the temperature dependence of the interminiband absorption, energy loss and relaxation rates can be determined. A vertical electric field leads to negative differential resistance, domain formation and the break-up of the minibands into Wannier- Stark ladders. We will present experiments showing the formation of interpenetrating Wannier- Stark ladders in the continuum, which are strongly coupled by Zener resonances. This is the first time to correlate transport and infrared absorption in a biased superlattice.

Authorship

M. Helm

Universität Linz, Institut für Halbleiter- und Festkörperphysik , Linz, AustriaUniversität LinzAustriaLinz, AustriaUniversität Linz, Institut für Halbleiter- und Festkörperphysik , Linz, Austria

W. Hilber

G. Strasser

Institut für Festkörperelektronik, Wien, AustriaInstitut für FestkörperelektronikAustriaWien, AustriaInstitut für Festkörperelektronik, Wien, Austria

R. DeMeester

University of Antwerp, Department of Physics , Wilrijk, BelgiumUniversity of AntwerpBelgiumWilrijk, BelgiumUniversity of Antwerp, Department of Physics , Wilrijk, Belgium

F. M. Peeters

University of Antwerp, Department of Physics , Wilrijk, BelgiumUniversity of AntwerpBelgiumWilrijk, BelgiumUniversity of Antwerp, Department of Physics , Wilrijk, Belgium

SCIMAGO INSTITUTIONS RANKINGS

Institut für Festkörperelektronik, Wien, AustriaInstitut für FestkörperelektronikAustriaWien, AustriaInstitut für Festkörperelektronik, Wien, Austria

University of Antwerp, Department of Physics , Wilrijk, BelgiumUniversity of AntwerpBelgiumWilrijk, BelgiumUniversity of Antwerp, Department of Physics , Wilrijk, Belgium

Figures

Figures (12)

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Figure 1.
The calculated miniband structure of the GaAs/AlGaAs superlattice under investigation (well width 75 Å, barrier width 25 Å ). The horizontal dashed line indicates the top of the barriers. The 1s and 2p_z impurity states are also included schematically [4]. The interminiband transitions at the center and the edge of the mini-Brillouin zone are indicated as well as the impurity transition.

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Figure 2.
Calculated joint density of states (JDOS, dotted) and theoretical absorption coefficient for the above SL with n = 6×10¹⁷ cm^-3 at T=5 K.

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Figure 3.
Measured absorption spectrum of the higher doped SL at T=20 K and T=300 K (absorbance = -log₁₀ (transmission)). This should be compared with the theoretical curve in Fig. 2.

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Figure 4.
Measured absorption spectrum of the lower doped SL superlattice at different temperatures as indicated. For an explanation, see text.

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Figure 5.
Electric-field dependence of the transmission change: The transmission spectrum at the time of the voltage pulse is divided by the transmission after the pulse. The respective electric- field values are indicated.

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Figure 6.
Ratio of the transmission at the lattice temperature T_L (as indicated) to the transmission at T_L = 10K.

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Figure 7.
Energy relaxation time as a function of electron temperature.

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Figure 8.
Interminiband transmission spectrum for zero electric field. The insets show the absorption process in k-space and real-space, respectively. The main absorption and the high-energy shoulder, due to the singularities in the joint-density of states, are indicated by arrows.

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Figure 9.
Current-voltage characteristic of the superlattice. The inset shows the conduction-band edge near the boundary of the low- and high-field domain together with a schematic of the transport process.

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Figure 10.
Differential transmission spectrum (T(F)/T₀) of the superlattice for a series of bias voltages between 8 and 30 V. Minima essentially correspond to electric-field-induced absorption lines (marked by arrows).

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Figure 11.
Absorption coefficient calculated for electric fields from 0 to 70 kV/cm. In addition, the transmission change is shown for 50, 60, and 70kV/cm in the upper panel to facilitate comparison with the experiment (see text). The experimentally relevant 60kV/cm spectra are plotted with thicker lines (compare with Fig. 10).

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Figure 12.
Conduction-band profile, energy levels and squared wavefunctions drawn for four superlattice periods with an electric field of 60kV/cm. The calculation was performed for a 19 period SL. The experimentally observed transitions are indicated by arrows and the main parts of the respective wavefunctions are emphasized by thicker lines. The numbers on the right represent an (approximate) assignment in terms of WS states (see text). In addition, the calculated absorption coefficient is shown on the left for comparison, including the peak photon energies.

Figure 1. The calculated miniband structure of the GaAs/AlGaAs superlattice under investigation (well width 75 Å, barrier width 25 Å ). The horizontal dashed line indicates the top of the barriers. The 1s and 2p_z impurity states are also included schematically [4]. The interminiband transitions at the center and the edge of the mini-Brillouin zone are indicated as well as the impurity transition.

Figure 2. Calculated joint density of states (JDOS, dotted) and theoretical absorption coefficient for the above SL with n = 6×10¹⁷ cm^-3 at T=5 K.

Figure 3. Measured absorption spectrum of the higher doped SL at T=20 K and T=300 K (absorbance = -log₁₀ (transmission)). This should be compared with the theoretical curve in Fig. 2.

Figure 4. Measured absorption spectrum of the lower doped SL superlattice at different temperatures as indicated. For an explanation, see text.

Figure 5. Electric-field dependence of the transmission change: The transmission spectrum at the time of the voltage pulse is divided by the transmission after the pulse. The respective electric- field values are indicated.

Figure 6. Ratio of the transmission at the lattice temperature T_L (as indicated) to the transmission at T_L = 10K.

Figure 7. Energy relaxation time as a function of electron temperature.

Figure 8. Interminiband transmission spectrum for zero electric field. The insets show the absorption process in k-space and real-space, respectively. The main absorption and the high-energy shoulder, due to the singularities in the joint-density of states, are indicated by arrows.

Figure 9. Current-voltage characteristic of the superlattice. The inset shows the conduction-band edge near the boundary of the low- and high-field domain together with a schematic of the transport process.

Figure 10. Differential transmission spectrum (T(F)/T₀) of the superlattice for a series of bias voltages between 8 and 30 V. Minima essentially correspond to electric-field-induced absorption lines (marked by arrows).

Figure 11. Absorption coefficient calculated for electric fields from 0 to 70 kV/cm. In addition, the transmission change is shown for 50, 60, and 70kV/cm in the upper panel to facilitate comparison with the experiment (see text). The experimentally relevant 60kV/cm spectra are plotted with thicker lines (compare with Fig. 10).

Figure 12. Conduction-band profile, energy levels and squared wavefunctions drawn for four superlattice periods with an electric field of 60kV/cm. The calculation was performed for a 19 period SL. The experimentally observed transitions are indicated by arrows and the main parts of the respective wavefunctions are emphasized by thicker lines. The numbers on the right represent an (approximate) assignment in terms of WS states (see text). In addition, the calculated absorption coefficient is shown on the left for comparison, including the peak photon energies.

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Minibands and Wannier-Stark ladders in semiconductor superlattices studied by infrared spectroscopy

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