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AlGaAs superlattices
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999 Article No. spmi.1998.0612 Available online at http://www.idealibrary.com on
Mean free path of ballistic electrons in GaAs/AlGaAs superlattices C. R AUCH , G. S TRASSER , M. K AST, E. G ORNIK Solid State Electronics, University of Technology Vienna, Floragasse 7, A-1040 Wien, Austria
(Received 26 October 1998) The mean free path of ballistic electrons in GaAs/AlGaAs superlattices was measured using the technique of hot electron spectroscopy in magnetic fields perpendicular to the growth direction. We utilize the fact that the total effective path of an injected hot electron is a function of the applied magnetic field. For a superlattice with 6.5 nm GaAs wells and 2.5 nm GaAlAs barriers we measure a mean free path of 80 nm. The experimental results of a ten-period SL sample are compared to a fully three-dimensional calculation of the transmission including interface roughness with island sizes of 10 nm. We demonstrate that the observed mfp is limited due to interface roughness scattering for temperatures up to 50 K. c 1999 Academic Press
Key words: superlattice, hot electron spectroscopy, mean free path, transport.
Stimulated by a need to understand the physics of electron transport in small device structures much interest is centered on the problem of nonequilibrium electron transport in semiconductor superlattices (SLs). The unique properties of such artificial quantum structures have attracted extensive research. Electrical measurements [1, 2] of diodes with a SL in the active region, as well as optical spectroscopy [3, 4], and magnetotransport techniques [5] have been used to study the formation of SL minibands. However, one of the main problems hindering the experimental study of electron transport in SLs has been the interdependence of the intensity of the current injected and the field present in the SL which is unavoidable in the two terminal structures studied so far. At higher fields the large current densities injected make the field in the SL nonuniform and cause the formation of field domains [6]. In this paper we use the technique of hot electron spectroscopy [7], which enables us to obtain spectroscopic information about the hot electron transport in undoped SLs. The measurements are performed utilizing a modified hot electron transistor [8] shown in Fig. 1. An energy tunable electron beam is generated by a tunneling barrier and passes the SL after traversing a thin highly doped n-GaAs base layer and an undoped drift region. The measured collector current reflects the probability of an injected electron to be transmitted through the SL. The transmittance of the SL can be measured directly at given SL bias conditions by varying the energy of the injected hot electrons independently from the SL bias voltage. The structures which are described in Fig. 1 were grown by molecular beam epitaxy on a semi-insulating GaAs substrate. The growth started with a highly doped n+ -GaAs collector contact layer (n = 1×1018 cm−3 ) followed by a SL and the drift region that is slightly n-doped (n ∼ 5 × 1014 cm−3 ) in order to avoid undesired band bending. This is followed by a highly doped (n = 2 × 1018 cm−3 ) n+ -GaAs layer (base) of 13 nm 0749–6036/99/010047 + 05
$30.00/0
c 1999 Academic Press
48
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
0.3
0.1
Injection electron distribution
1st MB
Collector
0.2 Emitter
Energy (eV)
2nd MB
0 Base 1000
2000
3000
4000
5000
6000
Distance (Å) Fig. 1. Schematic band diagram of a three terminal device with negative bias applied to the SL.
width. On top of the base layer a 13 nm undoped Ga0.7 Al0.3 As barrier is grown followed by a GaAs spacer and an n+ -GaAs layer, nominally doped to n = 3 × 1017 cm−3 , in order to achieve an narrow normal energy distribution of the injected electrons of about 17 meV.† The width of the injected electron beam limits the energy resolution of the experiment. Finally, an n+ -GaAs contact layer (n = 1 × 1018 cm−3 ) is grown on top of the heterostructure to form the emitter. Two SL structures were investigated consisting of five and ten periods of 2.5 nm Ga0.7 Al0.3 As barriers and 6.5 nm GaAs wells. The layer structure was verified by transmission electron microscopy (TEM). For these parameters a simple Kronig–Penny calculation gives the lowest miniband lying between 46 and 68 meV, and a second one between 182 and 276 meV. The fabrication of a three terminal device includes the following steps: (a) selective etching of 20 × 20 µm2 mesas to reach the base layer, (b) unselective etching to the collector layer, (c) evaporation of standard AuGeNi ohmic contacts, (d) deposition of a Si3 N4 isolation layer and (e) evaporation of extended bonding pads. The static transfer ratio α = IC /I E is measured as a function of negative emitter bias (= injected electron energy) at 4.2 K in a common base configuration. Typical static transfer ratios α of the five-period SL is shown in Fig. 2 for different collector biases. No collector current is observed up to the lower edge of the first miniband, indicating that there is no significant leakage current between base and collector. The bold full line represents the transfer ratio at flat band condition (UBC = 0). The sharp increase of the transfer ratio at about 43 meV coincides very well with the lower edge of the first miniband which is calculated to be 46 meV. The peak due to transport through the first miniband is broader than the expected miniband width (1 = 22 meV) due to the finite width of the injected electron distribution. The second observed peak is shifted 36 meV to higher injection energies and is ascribed to the first longitudinal optical (LO) phonon emission replica (h¯ ωLO = 36 meV). Superposition of the transfer ratio of the replicas and the nonscattered electrons lead to a nonvanishing transfer ratio as evident in the experiment (Fig. 2). A clear shift of the maximum (due to the voltage drop in the drift region) and a reduction of the amplitude of the transfer ratio is observed for increasing collector voltages. We have taken the total miniband transmission (Tα ), which is defined as twice the area of the lower energy side of the first transfer ratio peak, as a measure for the average current through the first miniband at given bias conditions. The current above the first maximum is influenced by the first LO phonon replica and, thus, not used for the determination of Tα . The miniband transmission versus electric field for the five-period SL † The FWHM of the injected hot electron distribution is measured using a resonant tunneling diode as an energy analyser grown in the drift region instead of the SL.
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
49
0.025 Phonon replica Transfer ratio IC/IE
0.02
UBC= 0 mV
0.015 20 mV 0.01 0.005
–20 mV 40 mV –40 mV
0 0.02
0.04
0.06 0.08 0.1 Injection energy (eV)
0.12
Miniband transmission, Tα(a.u.)
Fig. 2. Transfer ratio versus injection energy (= UEB ) at different collector base voltages of the five-period sample. The bold full line represents the transfer ratio under flat band condition (UBC = 0).
–8
5 periods
Calculation Experiment 0T
5 periods 0.4 T –6
0.8 T
2 4 –4 –2 0 Electric field (kV cm )
6
8
Fig. 3. The miniband transmission versus electric field for different magnetic fields. The magnetic field is applied perpendicular to the growth direction. The dashed line shows the result of a one-dimensional calculation for B = 0 using the transfer matrix method.
at different magnetic fields is shown in Fig. 3. The measured miniband transmission at zero magnetic field is symmetric with respect to the applied electric field and quenches at about 12 kV cm−1 due to the increasing localization of the Wannier–Stark states. We observe an excellent agreement to a calculation based on a transfer matrix method, considering a onedimensional ideal structure with nominal sample parameters. This demonstrates that the transport is dominated by coherent transmission through the SL. However, for nonzero magnetic fields we observe a clear asymmetric behavior of the measured miniband transmission and an overall decreasing transmission with increasing magnetic fields. While the electric field leads to the localization of the electron wavefunction, the magnetic field increases the total effective electron
50
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
10 periods
Miniband transmission, Tα(a.u.)
Calculation Experiment
–4
2 –2 0 Electric field (kV cm–1)
4
Fig. 4. Miniband transmission versus electric field of the ten-period sample (dots) compared to a calculation including interface roughness (full line).
path in the SL. This leads to a decrease of the measured transfer ratio and an increase of the asymmetric behavior due to an additional electric field induced incoherent current for positive (accelerating) electric fields. For magnetic fields above 1 T, which corresponds to a total effective length of the electron path of about 80 nm, no coherent transport is observed. A detailed analysis of the miniband transmission gives us a coherence length of 80 nm and a scattering time of 0.8 ps. In order to identify the limiting scattering mechanism we have grown an additional ten-period SL. The measured miniband transmission (dots, Fig. 4) shows again an asymmetric behavior with respect to the applied electric field direction, since the total length of the SL (90 nm) is longer than the coherence length of the ballistically injected electrons. We observe a good agreement of our experimental results to a fully threedimensional calculation [9] (full line) including interface roughness scattering using typical island sizes of 10 nm. Thus we claim that the measured coherence length is limited by interface roughness scattering for temperatures up to 50 K. In summary we have measured the miniband transmission of ballistic electrons in biased undoped SLs at different magnetic fields using the technique of hot electron spectroscopy. We have determined a coherence length of 80 nm and a scattering time of 0.8 ps. Furthermore, we have shown that the coherent transport in the investigated SL at 4.2 K is limited by interface roughness scattering. Acknowledgements—This work has been partly supported by the Austrian Federal Ministry of Science, the Society for Microelectronics (GMe, Austria), and the U.S. Army Research Office.
References [1] [2] [3] [4] [5] [6] [7]
}L. Esaki and L. L. Chang, Phys. Rev. Lett. 33, 495 (1974). }A. Sibille, J. F. Palmier, H. Wang, and F. Mollot, Phys. Rev. Lett. 64, 52 (1990). }R. Dingle, A. C. Gossard, and W. Wiegmann, Phys. Rev. Lett. 34, 1327 (1975). }E. E. Mendez, F. Agull´o-Ruada, and J. M. Hong, Phys. Rev. Lett. 60, 2426 (1988). }T. Duffield, R. Bhat, M. Koza, F. DeRosa, K. M. Rusch, and S. J. Allen, Phys. Rev. Lett. 59, 2693 (1987). }K. K. Choi, B. F. Levine, R. J. Malik, J. Walker, C. G. Bethea, Phys. Rev. B35, 4172 (1987). }C. Rauch, G. Strasser, K. Unterrainer, B. Brill, and E. Gornik, Appl. Phys. Lett. 70, 649 (1997).
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
[8] }B. Brill, M. Heiblum and H. Shtrikman, Solid-State Electron. 37, 543 (1994). [9] }A. Wacker, S. Bose, C. Rauch, G. Strasser, and E. Gornik, Superlatt. Microstruct. 25, 43 (1999).
51
Mean free path of ballistic electrons in GaAs/AlGaAs superlattices C. R AUCH , G. S TRASSER , M. K AST, E. G ORNIK Solid State Electronics, University of Technology Vienna, Floragasse 7, A-1040 Wien, Austria
(Received 26 October 1998) The mean free path of ballistic electrons in GaAs/AlGaAs superlattices was measured using the technique of hot electron spectroscopy in magnetic fields perpendicular to the growth direction. We utilize the fact that the total effective path of an injected hot electron is a function of the applied magnetic field. For a superlattice with 6.5 nm GaAs wells and 2.5 nm GaAlAs barriers we measure a mean free path of 80 nm. The experimental results of a ten-period SL sample are compared to a fully three-dimensional calculation of the transmission including interface roughness with island sizes of 10 nm. We demonstrate that the observed mfp is limited due to interface roughness scattering for temperatures up to 50 K. c 1999 Academic Press
Key words: superlattice, hot electron spectroscopy, mean free path, transport.
Stimulated by a need to understand the physics of electron transport in small device structures much interest is centered on the problem of nonequilibrium electron transport in semiconductor superlattices (SLs). The unique properties of such artificial quantum structures have attracted extensive research. Electrical measurements [1, 2] of diodes with a SL in the active region, as well as optical spectroscopy [3, 4], and magnetotransport techniques [5] have been used to study the formation of SL minibands. However, one of the main problems hindering the experimental study of electron transport in SLs has been the interdependence of the intensity of the current injected and the field present in the SL which is unavoidable in the two terminal structures studied so far. At higher fields the large current densities injected make the field in the SL nonuniform and cause the formation of field domains [6]. In this paper we use the technique of hot electron spectroscopy [7], which enables us to obtain spectroscopic information about the hot electron transport in undoped SLs. The measurements are performed utilizing a modified hot electron transistor [8] shown in Fig. 1. An energy tunable electron beam is generated by a tunneling barrier and passes the SL after traversing a thin highly doped n-GaAs base layer and an undoped drift region. The measured collector current reflects the probability of an injected electron to be transmitted through the SL. The transmittance of the SL can be measured directly at given SL bias conditions by varying the energy of the injected hot electrons independently from the SL bias voltage. The structures which are described in Fig. 1 were grown by molecular beam epitaxy on a semi-insulating GaAs substrate. The growth started with a highly doped n+ -GaAs collector contact layer (n = 1×1018 cm−3 ) followed by a SL and the drift region that is slightly n-doped (n ∼ 5 × 1014 cm−3 ) in order to avoid undesired band bending. This is followed by a highly doped (n = 2 × 1018 cm−3 ) n+ -GaAs layer (base) of 13 nm 0749–6036/99/010047 + 05
$30.00/0
c 1999 Academic Press
48
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
0.3
0.1
Injection electron distribution
1st MB
Collector
0.2 Emitter
Energy (eV)
2nd MB
0 Base 1000
2000
3000
4000
5000
6000
Distance (Å) Fig. 1. Schematic band diagram of a three terminal device with negative bias applied to the SL.
width. On top of the base layer a 13 nm undoped Ga0.7 Al0.3 As barrier is grown followed by a GaAs spacer and an n+ -GaAs layer, nominally doped to n = 3 × 1017 cm−3 , in order to achieve an narrow normal energy distribution of the injected electrons of about 17 meV.† The width of the injected electron beam limits the energy resolution of the experiment. Finally, an n+ -GaAs contact layer (n = 1 × 1018 cm−3 ) is grown on top of the heterostructure to form the emitter. Two SL structures were investigated consisting of five and ten periods of 2.5 nm Ga0.7 Al0.3 As barriers and 6.5 nm GaAs wells. The layer structure was verified by transmission electron microscopy (TEM). For these parameters a simple Kronig–Penny calculation gives the lowest miniband lying between 46 and 68 meV, and a second one between 182 and 276 meV. The fabrication of a three terminal device includes the following steps: (a) selective etching of 20 × 20 µm2 mesas to reach the base layer, (b) unselective etching to the collector layer, (c) evaporation of standard AuGeNi ohmic contacts, (d) deposition of a Si3 N4 isolation layer and (e) evaporation of extended bonding pads. The static transfer ratio α = IC /I E is measured as a function of negative emitter bias (= injected electron energy) at 4.2 K in a common base configuration. Typical static transfer ratios α of the five-period SL is shown in Fig. 2 for different collector biases. No collector current is observed up to the lower edge of the first miniband, indicating that there is no significant leakage current between base and collector. The bold full line represents the transfer ratio at flat band condition (UBC = 0). The sharp increase of the transfer ratio at about 43 meV coincides very well with the lower edge of the first miniband which is calculated to be 46 meV. The peak due to transport through the first miniband is broader than the expected miniband width (1 = 22 meV) due to the finite width of the injected electron distribution. The second observed peak is shifted 36 meV to higher injection energies and is ascribed to the first longitudinal optical (LO) phonon emission replica (h¯ ωLO = 36 meV). Superposition of the transfer ratio of the replicas and the nonscattered electrons lead to a nonvanishing transfer ratio as evident in the experiment (Fig. 2). A clear shift of the maximum (due to the voltage drop in the drift region) and a reduction of the amplitude of the transfer ratio is observed for increasing collector voltages. We have taken the total miniband transmission (Tα ), which is defined as twice the area of the lower energy side of the first transfer ratio peak, as a measure for the average current through the first miniband at given bias conditions. The current above the first maximum is influenced by the first LO phonon replica and, thus, not used for the determination of Tα . The miniband transmission versus electric field for the five-period SL † The FWHM of the injected hot electron distribution is measured using a resonant tunneling diode as an energy analyser grown in the drift region instead of the SL.
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
49
0.025 Phonon replica Transfer ratio IC/IE
0.02
UBC= 0 mV
0.015 20 mV 0.01 0.005
–20 mV 40 mV –40 mV
0 0.02
0.04
0.06 0.08 0.1 Injection energy (eV)
0.12
Miniband transmission, Tα(a.u.)
Fig. 2. Transfer ratio versus injection energy (= UEB ) at different collector base voltages of the five-period sample. The bold full line represents the transfer ratio under flat band condition (UBC = 0).
–8
5 periods
Calculation Experiment 0T
5 periods 0.4 T –6
0.8 T
2 4 –4 –2 0 Electric field (kV cm )
6
8
Fig. 3. The miniband transmission versus electric field for different magnetic fields. The magnetic field is applied perpendicular to the growth direction. The dashed line shows the result of a one-dimensional calculation for B = 0 using the transfer matrix method.
at different magnetic fields is shown in Fig. 3. The measured miniband transmission at zero magnetic field is symmetric with respect to the applied electric field and quenches at about 12 kV cm−1 due to the increasing localization of the Wannier–Stark states. We observe an excellent agreement to a calculation based on a transfer matrix method, considering a onedimensional ideal structure with nominal sample parameters. This demonstrates that the transport is dominated by coherent transmission through the SL. However, for nonzero magnetic fields we observe a clear asymmetric behavior of the measured miniband transmission and an overall decreasing transmission with increasing magnetic fields. While the electric field leads to the localization of the electron wavefunction, the magnetic field increases the total effective electron
50
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
10 periods
Miniband transmission, Tα(a.u.)
Calculation Experiment
–4
2 –2 0 Electric field (kV cm–1)
4
Fig. 4. Miniband transmission versus electric field of the ten-period sample (dots) compared to a calculation including interface roughness (full line).
path in the SL. This leads to a decrease of the measured transfer ratio and an increase of the asymmetric behavior due to an additional electric field induced incoherent current for positive (accelerating) electric fields. For magnetic fields above 1 T, which corresponds to a total effective length of the electron path of about 80 nm, no coherent transport is observed. A detailed analysis of the miniband transmission gives us a coherence length of 80 nm and a scattering time of 0.8 ps. In order to identify the limiting scattering mechanism we have grown an additional ten-period SL. The measured miniband transmission (dots, Fig. 4) shows again an asymmetric behavior with respect to the applied electric field direction, since the total length of the SL (90 nm) is longer than the coherence length of the ballistically injected electrons. We observe a good agreement of our experimental results to a fully threedimensional calculation [9] (full line) including interface roughness scattering using typical island sizes of 10 nm. Thus we claim that the measured coherence length is limited by interface roughness scattering for temperatures up to 50 K. In summary we have measured the miniband transmission of ballistic electrons in biased undoped SLs at different magnetic fields using the technique of hot electron spectroscopy. We have determined a coherence length of 80 nm and a scattering time of 0.8 ps. Furthermore, we have shown that the coherent transport in the investigated SL at 4.2 K is limited by interface roughness scattering. Acknowledgements—This work has been partly supported by the Austrian Federal Ministry of Science, the Society for Microelectronics (GMe, Austria), and the U.S. Army Research Office.
References [1] [2] [3] [4] [5] [6] [7]
}L. Esaki and L. L. Chang, Phys. Rev. Lett. 33, 495 (1974). }A. Sibille, J. F. Palmier, H. Wang, and F. Mollot, Phys. Rev. Lett. 64, 52 (1990). }R. Dingle, A. C. Gossard, and W. Wiegmann, Phys. Rev. Lett. 34, 1327 (1975). }E. E. Mendez, F. Agull´o-Ruada, and J. M. Hong, Phys. Rev. Lett. 60, 2426 (1988). }T. Duffield, R. Bhat, M. Koza, F. DeRosa, K. M. Rusch, and S. J. Allen, Phys. Rev. Lett. 59, 2693 (1987). }K. K. Choi, B. F. Levine, R. J. Malik, J. Walker, C. G. Bethea, Phys. Rev. B35, 4172 (1987). }C. Rauch, G. Strasser, K. Unterrainer, B. Brill, and E. Gornik, Appl. Phys. Lett. 70, 649 (1997).
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
[8] }B. Brill, M. Heiblum and H. Shtrikman, Solid-State Electron. 37, 543 (1994). [9] }A. Wacker, S. Bose, C. Rauch, G. Strasser, and E. Gornik, Superlatt. Microstruct. 25, 43 (1999).
51