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Long-wavelength (λ∼10.5 μm) quantum cascade lasers based on a photon-assisted tunneling transition in strong magnetic field
Physica E 7 (2000) 33–36
www.elsevier.nl/locate/physe
Long-wavelength ( ∼ 10:5 m) quantum cascade lasers based on a photon-assisted tunneling transition in strong magnetic eld Stephane Blaser ∗ , Laurent Diehl, Mattias Beck, Jerˆome Faist Institut de Physique, Universite de Neuchatel, ˆ Rue A.-L. Breguet 1, CH-2000 Neuchatel, ˆ Switzerland
Abstract Magnetic eld studies on photon-assisted tunneling transition-based quantum cascade lasers are reported. Laser action at a wavelength of ∼ 10:5 m is achieved by oscillator strength tuning. The characteristics of these lasers are a small threshold current at low temperature (1.1 kA=cm2 ), an optical power up to 160 mW at 80 K and a maximal operation temperature of 200 K. A strong magnetic eld applied perpendicularly to the layers results in a threshold current of the laser which shows several minima and maxima under increasing magnetic eld. In a parallel magnetic eld, electroluminescence measurements show a strong decrease, a broadening and a blue-shift of the luminescence peak. ? 2000 Elsevier Science B.V. All rights reserved. Keywords: Magnetic eld; Quantum cascade lasers; Mid-infrared; Photon-assisted tunneling
Quasi-two-dimensional electron systems in magnetic eld have been the subject of many experimental and theoritical studies. If the magnetic eld is perpendicular to the layers, i.e. parallel to the electric eld, the Hamiltonian can be separated in perpendicular and in-plane motion. The in-plane states are then localized into Landau levels. This additional localization o ers the possibility of simulating a quantum box structure: the intersubband emission should occur between Landau levels instead of subbands. Quantum cascade (QC) lasers [1] based on such quantum boxes have already been proposed ∗ Corresponding author. Fax: +41-32-7182901. E-mail addresses: [email protected] (S. Blaser), [email protected] (J. Faist)
[2,3]. The situation becomes more complicated if a magnetic eld is applied parallel to the layers: thus we end up with a crossed electric and magnetic eld system. Numerous studies have been done for such conditions: theoretically [4,5] as well as experimentally (see for example Refs. [6 –8]). Here, we report measurements on a QC laser [1] based on a diagonal transition in presence of a strong magnetic eld perpendicular and parallel to the layers. The laser designed for these measurements is based on a photon-assisted tunneling transition [9] by oscillator strength tuning [10]. In contrast to QC lasers based on diagonal transitions where the threshold condition is achieved by increasing population inversion, here the lasing threshold is achieved by keeping the population inversion constant and increasing
1386-9477/00/$ - see front matter ? 2000 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 9 9 ) 0 0 3 0 6 - 9
34
S. Blaser et al. / Physica E 7 (2000) 33–36
Fig. 1. Self-consistent computation of the energy band diagram of two periods of the structure under an average applied electric eld of 55 kV=cm. Shown are the moduli squared of the relevant wave functions. The wavy line indicates the transition responsible for laser action. The thickness of the di erent layers is indicated in nanometers.
both matrix element and energy of the designed photon-assisted transition. Fig. 1 shows one period of the structure, grown by molecular beam epitaxy (MBE) lattice-matched to an InP substrate. It consists of an Al0:48 In0:52 As=Ga0:47 In0:53 As superlattice and a Ga0:47 In0:53 As quantum well of 7.4 nm between two Al0:48 In0:52 As tunneling barriers. Under suitable applied bias, photon-assisted tunneling emission occurs across the injection barrier upstream from this quantum well. The downstream barrier allows fast electron escape into the next well by tunneling. Electroluminescence spectra without magnetic eld on a structure processed in squared mesas to avoid optical feedback and gain showed a strong rst-order Stark shift due to the interwell n = 1 to n = 10 designed transition (see Fig. 1). This is due to the large spatial di erence between the center of the electron probability distribution of the states 1 and 10 . A second peak attributed to the vertical interwell transition 20 –10 in the 7.4 nm-wide well was also observed. The main characteristics of the laser (processed into ridge waveguides of 28 m width by wet chemical etching) are a low threshold current of 1.1 kA=cm2 and a maximum output power of 160 mW at 80 K in pulsed mode. The laser operates up to 200 K with up to 20 mW at 190 K, with an emission wavelength of about 10:5 m depending on electric eld and temperature. In continuous wave it
Fig. 2. L–I curves of a 28-m-wide and 1.4-mm-long QC laser measured at di erent temperature. Also shown is a V –I curve measured at 80 K.
operates up to 40 K with a mono-mode emission just above the threshold current. Typical light (L–I ) and voltage (V –I ) versus current curves are displayed in Fig. 2 for a 1.4-mm-long device in pulsed mode. The intensity of light was measured with a calibrated 500 × 500 m2 room temperature HgCdTe detector. The curvature of the L–I curves at threshold is due to the fact that laser action takes place at a smaller voltage than expected. In such a case, the losses are still too high to yield a good di erential eciency. Details on electroluminescence spectra and laser characteristics will be presented in Ref. [11]. To performed magneto-optical measurements, the samples were mounted on special holders which allowed to characterize them in a magnetic eld either perpendicular or parallel to the layers. The magnetic eld with a maximum strength of 14 T was produced by a superconducting magnet located in a helium cryostat. The sample temperature could be varied between 2 and 300 K using a needle ow control valve between helium bath and sample tube. Light collection was then accomplished by lenses and mirrors and the resulting beam was sent in a Fourier-transform infrared spectrometer (FTIR) Nicolet 860 to perform spectra or in a HgCdTe detector to perform L–I curves. In perpendicular magnetic eld, we simulate, as mentioned in the introduction, a quantum box laser. Since the intersubband emission of the laser should occurs between Landau levels, the optical phonon emission is, in general, forbidden. Then, with applied
S. Blaser et al. / Physica E 7 (2000) 33–36
Fig. 3. Threshold current versus applied perpendicular magnetic eld.
magnetic eld, the threshold current should show maxima and minima when there is a resonance with the optical phonon. Fig. 3 shows experimental results of laser threshold current versus magnetic eld done at T = 30 K. Minima and maxima are observed but the separation between them is less than the expected one. Moreover, the size of the maxima should increase at high eld and this is not the case. In parallel magnetic eld, the Hamiltonian is H =−
˜2 ˜2 @2 + Vconf (z) + ? 2 2m @z 2m? 2 2 2 2eBkx z e B z ˜2 2 2 + × kx − k ; + ˜ ˜2 2m? y
(1)
where Vconf (z) is the periodic potential due to the conduction-band discontinuity, e the elementary charge and m? the e ective mass. Two terms are due to the magnetic eld: the rst one, 2eBkx z=˜, acting as an electric eld and the second one, e2 B2 z 2 =˜2 , being quadratic in B. To solve the Schroedinger equation with plane waves in the x- and y-directions, the magnetic eld can be treated as a perturbation. The rst-order correction in energy results in [4] ˜2 2 k + E = Econf (z) + 2m? y 2 eBz × kx − + ˜
˜2 2m? e 2 B2 2 (hz i − hzi2 ); 2m?
(2)
where hzi and hz 2 i are expectation values of the respective operators for the unperturbed wave functions
35
and Econf (z) corresponds to the energy quanti cation due to the potential Vconf (z). In fact, hzi represents the position of the gravity center of the wave function with respect to the origin of the z-axis. The third term on the left-hand side of Eq. (2) changes the usual dispersion in kx to a parabola shifted in k-space by a value called kshift = −eBhzi=˜. The fourth term is called diamagnetic shift and slightly changes the energy independently of the choice of the origin. It is clear that this e ect should be observed only for diagonal transitions where hzi is di erent for the two states involved in the transition. We investigated our structure in a parallel magnetic eld to study the behaviour of the intersubband electroluminescence spectra in presence of such a eld. The structure was processed in mesas like for the electroluminescence measurements without magnetic eld. The spectra were measured using the FTIR in step-scan mode and a lock-in ampli er. Luminescence spectra at 30 K obtained at a constant voltage of 13 V for di erent applied magnetic elds are displayed in Fig. 4a). The main peak due to the interwell 1–10 transition at about 130 meV presents three important different behaviours in function of the applied magnetic eld. First, the peak has a strong quenching of his intensity. The inset of Fig. 4a shows the decrease of the peak integral in function of the magnetic eld. The light intensity is proportional to the oscillator strength and then to the squared transition matrix element. Then this latter seems to strongly decrease in a parallel magnetic eld. We made computation of the energy band diagram and matrix elements of the transition taking into account the e ects of the parallel magnetic eld by inserting Hamiltonian 1 in our model. The inset of Fig. 4a shows the values of the transition matrix elements calculated by this model, which decrease signi cantly less than the experimental results. The peak exhibits also a broadening and a blue shift of the transition energy. In contrast, besides the broadening, our model predicts a red shift of the emission, as shown in Fig. 4b. Here we made the assumption that the matrix element of the transition is constant. This explains why the peak intensity does not change in the simulation. Measurements performed at 10 V and at 200 and 300 K at 13 V have shown the same decrease of the peak integral of the luminescence peaks. This e ect seems then to depend neither on the bias nor on the temperature. Although the model does not
36
S. Blaser et al. / Physica E 7 (2000) 33–36
and the k-space electronic distribution should re ne enough the model to become predictive. Acknowledgements We would like to thank Daniel Hofstetter and Antoine Muller for their careful reading of the manuscript. This work was supported by the Swiss National Science Foundation. References
Fig. 4. (a) Luminescence spectra at di erent applied parallel magnetic elds at a voltage of 13 V. The inset shows the peak integral decrease versus applied magnetic eld. (b) Simulated luminescence spectra predicting a broadening and a red shift of the peak.
correctly predict the observed comportment, we can see that it is in good agreement with the broadening of the luminescence peak. The blue shift and the strong decrease of the luminescence emission are still to be explained. We expect that introducing the Hall e ect
[1] J. Faist, F. Capasso, D.L. Sivco, C. Sirtori, A.L. Hutchinson, A.Y. Cho, Science 264 (1994) 553. [2] C.F. Hsu, J.S. O, P.S. Zory, D. Botez, Intersubband laser design using a quantum box array, Proceedings of SPIE, Vol. 3001, 1997. [3] S.J. Lee, J.B. Khurgin, Appl. Phys. Lett. 69 (1996) 1038. [4] F. Stern, Phys. Rev. Lett. 21 (1968) 1687. [5] W. Zawadzki, Semicond. Sci. Technol. 2 (1987) 550. [6] G. Belle, J.C. Maan, G. Weimann, Solid State Commun. 56 (1985) 65. [7] A.P. Heberle, M. Oestreich, S. Haacke, W.W. Ruhle, J.C. Maan, K. Kohler, Phys. Rev. Lett. 72 (1994) 1522. [8] C. Gauer, A. Wixforth, J.P. Kotthaus, M. Kubisa, W. Zawadzki, B. Brar, H. Kroemer, Phys. Rev. Lett. 74 (1995) 2772. [9] R.F. Kazarinov, R.A. Suris, Sov. Phys. Semicond. 5 (1971) 707. [10] J. Faist, F. Capasso, C. Sirtori, D.L. Sivco, A.L. Hutchinson, A.Y. Cho, Nature 387 (1997) 777. [11] S. Blaser, L. Diehl, M. Beck, J. Faist, U. Oesterle, J.H. Xu, S. Barbieri, F. Beltman, Long-wavelength ( ∼ 10 m) quantum cascade laser based on a photon-assisted tunneling transition, unpublished.
www.elsevier.nl/locate/physe
Long-wavelength ( ∼ 10:5 m) quantum cascade lasers based on a photon-assisted tunneling transition in strong magnetic eld Stephane Blaser ∗ , Laurent Diehl, Mattias Beck, Jerˆome Faist Institut de Physique, Universite de Neuchatel, ˆ Rue A.-L. Breguet 1, CH-2000 Neuchatel, ˆ Switzerland
Abstract Magnetic eld studies on photon-assisted tunneling transition-based quantum cascade lasers are reported. Laser action at a wavelength of ∼ 10:5 m is achieved by oscillator strength tuning. The characteristics of these lasers are a small threshold current at low temperature (1.1 kA=cm2 ), an optical power up to 160 mW at 80 K and a maximal operation temperature of 200 K. A strong magnetic eld applied perpendicularly to the layers results in a threshold current of the laser which shows several minima and maxima under increasing magnetic eld. In a parallel magnetic eld, electroluminescence measurements show a strong decrease, a broadening and a blue-shift of the luminescence peak. ? 2000 Elsevier Science B.V. All rights reserved. Keywords: Magnetic eld; Quantum cascade lasers; Mid-infrared; Photon-assisted tunneling
Quasi-two-dimensional electron systems in magnetic eld have been the subject of many experimental and theoritical studies. If the magnetic eld is perpendicular to the layers, i.e. parallel to the electric eld, the Hamiltonian can be separated in perpendicular and in-plane motion. The in-plane states are then localized into Landau levels. This additional localization o ers the possibility of simulating a quantum box structure: the intersubband emission should occur between Landau levels instead of subbands. Quantum cascade (QC) lasers [1] based on such quantum boxes have already been proposed ∗ Corresponding author. Fax: +41-32-7182901. E-mail addresses: [email protected] (S. Blaser), [email protected] (J. Faist)
[2,3]. The situation becomes more complicated if a magnetic eld is applied parallel to the layers: thus we end up with a crossed electric and magnetic eld system. Numerous studies have been done for such conditions: theoretically [4,5] as well as experimentally (see for example Refs. [6 –8]). Here, we report measurements on a QC laser [1] based on a diagonal transition in presence of a strong magnetic eld perpendicular and parallel to the layers. The laser designed for these measurements is based on a photon-assisted tunneling transition [9] by oscillator strength tuning [10]. In contrast to QC lasers based on diagonal transitions where the threshold condition is achieved by increasing population inversion, here the lasing threshold is achieved by keeping the population inversion constant and increasing
1386-9477/00/$ - see front matter ? 2000 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 9 9 ) 0 0 3 0 6 - 9
34
S. Blaser et al. / Physica E 7 (2000) 33–36
Fig. 1. Self-consistent computation of the energy band diagram of two periods of the structure under an average applied electric eld of 55 kV=cm. Shown are the moduli squared of the relevant wave functions. The wavy line indicates the transition responsible for laser action. The thickness of the di erent layers is indicated in nanometers.
both matrix element and energy of the designed photon-assisted transition. Fig. 1 shows one period of the structure, grown by molecular beam epitaxy (MBE) lattice-matched to an InP substrate. It consists of an Al0:48 In0:52 As=Ga0:47 In0:53 As superlattice and a Ga0:47 In0:53 As quantum well of 7.4 nm between two Al0:48 In0:52 As tunneling barriers. Under suitable applied bias, photon-assisted tunneling emission occurs across the injection barrier upstream from this quantum well. The downstream barrier allows fast electron escape into the next well by tunneling. Electroluminescence spectra without magnetic eld on a structure processed in squared mesas to avoid optical feedback and gain showed a strong rst-order Stark shift due to the interwell n = 1 to n = 10 designed transition (see Fig. 1). This is due to the large spatial di erence between the center of the electron probability distribution of the states 1 and 10 . A second peak attributed to the vertical interwell transition 20 –10 in the 7.4 nm-wide well was also observed. The main characteristics of the laser (processed into ridge waveguides of 28 m width by wet chemical etching) are a low threshold current of 1.1 kA=cm2 and a maximum output power of 160 mW at 80 K in pulsed mode. The laser operates up to 200 K with up to 20 mW at 190 K, with an emission wavelength of about 10:5 m depending on electric eld and temperature. In continuous wave it
Fig. 2. L–I curves of a 28-m-wide and 1.4-mm-long QC laser measured at di erent temperature. Also shown is a V –I curve measured at 80 K.
operates up to 40 K with a mono-mode emission just above the threshold current. Typical light (L–I ) and voltage (V –I ) versus current curves are displayed in Fig. 2 for a 1.4-mm-long device in pulsed mode. The intensity of light was measured with a calibrated 500 × 500 m2 room temperature HgCdTe detector. The curvature of the L–I curves at threshold is due to the fact that laser action takes place at a smaller voltage than expected. In such a case, the losses are still too high to yield a good di erential eciency. Details on electroluminescence spectra and laser characteristics will be presented in Ref. [11]. To performed magneto-optical measurements, the samples were mounted on special holders which allowed to characterize them in a magnetic eld either perpendicular or parallel to the layers. The magnetic eld with a maximum strength of 14 T was produced by a superconducting magnet located in a helium cryostat. The sample temperature could be varied between 2 and 300 K using a needle ow control valve between helium bath and sample tube. Light collection was then accomplished by lenses and mirrors and the resulting beam was sent in a Fourier-transform infrared spectrometer (FTIR) Nicolet 860 to perform spectra or in a HgCdTe detector to perform L–I curves. In perpendicular magnetic eld, we simulate, as mentioned in the introduction, a quantum box laser. Since the intersubband emission of the laser should occurs between Landau levels, the optical phonon emission is, in general, forbidden. Then, with applied
S. Blaser et al. / Physica E 7 (2000) 33–36
Fig. 3. Threshold current versus applied perpendicular magnetic eld.
magnetic eld, the threshold current should show maxima and minima when there is a resonance with the optical phonon. Fig. 3 shows experimental results of laser threshold current versus magnetic eld done at T = 30 K. Minima and maxima are observed but the separation between them is less than the expected one. Moreover, the size of the maxima should increase at high eld and this is not the case. In parallel magnetic eld, the Hamiltonian is H =−
˜2 ˜2 @2 + Vconf (z) + ? 2 2m @z 2m? 2 2 2 2eBkx z e B z ˜2 2 2 + × kx − k ; + ˜ ˜2 2m? y
(1)
where Vconf (z) is the periodic potential due to the conduction-band discontinuity, e the elementary charge and m? the e ective mass. Two terms are due to the magnetic eld: the rst one, 2eBkx z=˜, acting as an electric eld and the second one, e2 B2 z 2 =˜2 , being quadratic in B. To solve the Schroedinger equation with plane waves in the x- and y-directions, the magnetic eld can be treated as a perturbation. The rst-order correction in energy results in [4] ˜2 2 k + E = Econf (z) + 2m? y 2 eBz × kx − + ˜
˜2 2m? e 2 B2 2 (hz i − hzi2 ); 2m?
(2)
where hzi and hz 2 i are expectation values of the respective operators for the unperturbed wave functions
35
and Econf (z) corresponds to the energy quanti cation due to the potential Vconf (z). In fact, hzi represents the position of the gravity center of the wave function with respect to the origin of the z-axis. The third term on the left-hand side of Eq. (2) changes the usual dispersion in kx to a parabola shifted in k-space by a value called kshift = −eBhzi=˜. The fourth term is called diamagnetic shift and slightly changes the energy independently of the choice of the origin. It is clear that this e ect should be observed only for diagonal transitions where hzi is di erent for the two states involved in the transition. We investigated our structure in a parallel magnetic eld to study the behaviour of the intersubband electroluminescence spectra in presence of such a eld. The structure was processed in mesas like for the electroluminescence measurements without magnetic eld. The spectra were measured using the FTIR in step-scan mode and a lock-in ampli er. Luminescence spectra at 30 K obtained at a constant voltage of 13 V for di erent applied magnetic elds are displayed in Fig. 4a). The main peak due to the interwell 1–10 transition at about 130 meV presents three important different behaviours in function of the applied magnetic eld. First, the peak has a strong quenching of his intensity. The inset of Fig. 4a shows the decrease of the peak integral in function of the magnetic eld. The light intensity is proportional to the oscillator strength and then to the squared transition matrix element. Then this latter seems to strongly decrease in a parallel magnetic eld. We made computation of the energy band diagram and matrix elements of the transition taking into account the e ects of the parallel magnetic eld by inserting Hamiltonian 1 in our model. The inset of Fig. 4a shows the values of the transition matrix elements calculated by this model, which decrease signi cantly less than the experimental results. The peak exhibits also a broadening and a blue shift of the transition energy. In contrast, besides the broadening, our model predicts a red shift of the emission, as shown in Fig. 4b. Here we made the assumption that the matrix element of the transition is constant. This explains why the peak intensity does not change in the simulation. Measurements performed at 10 V and at 200 and 300 K at 13 V have shown the same decrease of the peak integral of the luminescence peaks. This e ect seems then to depend neither on the bias nor on the temperature. Although the model does not
36
S. Blaser et al. / Physica E 7 (2000) 33–36
and the k-space electronic distribution should re ne enough the model to become predictive. Acknowledgements We would like to thank Daniel Hofstetter and Antoine Muller for their careful reading of the manuscript. This work was supported by the Swiss National Science Foundation. References
Fig. 4. (a) Luminescence spectra at di erent applied parallel magnetic elds at a voltage of 13 V. The inset shows the peak integral decrease versus applied magnetic eld. (b) Simulated luminescence spectra predicting a broadening and a red shift of the peak.
correctly predict the observed comportment, we can see that it is in good agreement with the broadening of the luminescence peak. The blue shift and the strong decrease of the luminescence emission are still to be explained. We expect that introducing the Hall e ect
[1] J. Faist, F. Capasso, D.L. Sivco, C. Sirtori, A.L. Hutchinson, A.Y. Cho, Science 264 (1994) 553. [2] C.F. Hsu, J.S. O, P.S. Zory, D. Botez, Intersubband laser design using a quantum box array, Proceedings of SPIE, Vol. 3001, 1997. [3] S.J. Lee, J.B. Khurgin, Appl. Phys. Lett. 69 (1996) 1038. [4] F. Stern, Phys. Rev. Lett. 21 (1968) 1687. [5] W. Zawadzki, Semicond. Sci. Technol. 2 (1987) 550. [6] G. Belle, J.C. Maan, G. Weimann, Solid State Commun. 56 (1985) 65. [7] A.P. Heberle, M. Oestreich, S. Haacke, W.W. Ruhle, J.C. Maan, K. Kohler, Phys. Rev. Lett. 72 (1994) 1522. [8] C. Gauer, A. Wixforth, J.P. Kotthaus, M. Kubisa, W. Zawadzki, B. Brar, H. Kroemer, Phys. Rev. Lett. 74 (1995) 2772. [9] R.F. Kazarinov, R.A. Suris, Sov. Phys. Semicond. 5 (1971) 707. [10] J. Faist, F. Capasso, C. Sirtori, D.L. Sivco, A.L. Hutchinson, A.Y. Cho, Nature 387 (1997) 777. [11] S. Blaser, L. Diehl, M. Beck, J. Faist, U. Oesterle, J.H. Xu, S. Barbieri, F. Beltman, Long-wavelength ( ∼ 10 m) quantum cascade laser based on a photon-assisted tunneling transition, unpublished.