- Email: [email protected]
InAs quantum well
Applied Surface Science 254 (2008) 7889–7892
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Spatial imaging of valence band electronic structures in a GaSb/InAs quantum well K. Suzuki a,*, K. Kanisawa a, S. Perraud a,b, T. Fujisawa a a b
NTT Basic Research Laboratories, NTT Corporation, Atsugi-shi, Kanagawa 243-0198, Japan Laboratoire de Photonique et de Nanostructures, CNRS, 91460 Marcoussis, France
A R T I C L E I N F O
A B S T R A C T
Article history: Received 7 November 2007 Received in revised form 7 March 2008 Accepted 8 March 2008 Available online 16 March 2008
We measure local density of states (LDOS) for GaSb/InAs heterostructures with quantum wells in the valence band by scanning tunneling spectroscopy (STS) on the cleaved surface. Clear standingwave patterns of LDOS corresponding to the holes confined in the quantum wells are observed. ß 2008 Elsevier B.V. All rights reserved.
PACS: 73.21.Cd 68.37.Ef 81.05.Ea 81.15.Hi Keywords: Valence band Quantum well Scanning tunneling spectroscopy Local density of states Semiconductor heterostructures
1. Introduction As semiconductor devices become highly integrated with ultrafine structures, the wave properties of electrons in the devices become more and more dominant. The local analysis of the wavefunctions has been strongly desired for realizing high device performance. Scanning tunneling spectroscopy (STS) is one of the most powerful tools, which can image the spatial distribution of the electron local density of states (LDOS), corresponding to the squared wavefunction, as a function of the energy with nano-scale resolution [1–6]. Up to now, using STS, spatial distribution of LDOS showing the wave features of electrons has been observed [2–5]. However, most STS measurements have been performed focusing on electrons in the conduction band, few in the valence band [6]. Obtainable information by STS in the valence band has not been well understood. Provided LDOS imaging of holes is established, it becomes much powerful technique for investigating the complicated valence band structures, which are important feedback for
* Corresponding author. Tel.: +81 46 240 3473; fax: +81 46 240 4727. E-mail address: [email protected] (K. Suzuki). 0169-4332/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2008.03.036
device production. Furthermore, using this technique, behavior of holes and electron–hole interaction/correlation will be clarified precisely in view of nano-scale. Recently, we succeeded in observing the standingwave patterns of LDOS for the subbands formed in the quantum well (QW) in the conduction band by STS on the cleaved semiconductor heterostructure surfaces [4,5]. Here, to clarify obtainable information from the valence band by STS, we applied STS measurement to the QW in the valence band. As a result, clear standingwave patterns similar to those of the electrons confined in the QW in the conduction band were observed, showing the quantum confinement of the holes. 2. Experiments For the sample, 4 nm- and 12 nm-GaSb layers sandwiched between thick InAs layers were grown by molecular beam epitaxy on a (0 0 1) InAs substrate. In GaSb/InAs heterostructures, the conduction band bottom of InAs is lower in energy than the valence band top of GaSb, shown in Fig. 1. The band overlap of 0.15 eV is expected without consideration of the quantum confinement [7]. The GaSb layers work as a QW for holes. For
7890
K. Suzuki et al. / Applied Surface Science 254 (2008) 7889–7892
Fig. 2. Typical STM topographic image (empty state, V = +1.0 V) for the cleaved sample at 12 nm-QW.
Fig. 1. Schematic energy band profile of InAs/GaSb heterostructures.
the structure with thick layers, the Fermi level lies just below the valence band top of the GaSb [8]. For simplicity, we assume the above condition still applicable to the sample with thin layers and do not consider the effect of the band overlap in this paper.
The sample was loaded into an ultrahigh vacuum (UHV) chamber (<2 10 10 Torr) and cleaved to obtain a clean flat (1 1 0) surface. Then, the sample was transferred to the stage of the lowtemperature scanning tunneling microscope (STM) at 4.8 K cooled by liquid helium without breaking UHV. It is known that no surface Fermi level pinning states within the energy band gap are formed on the clean (1 1 0) surface of III–V compound semiconductors when cleaving is successful [9]. Scanning was performed in UHV of the order of 10 11 Torr. A bias voltage (V) was applied between the sample and the grounded tungsten STM tip, which was cleaned in situ by applying pulsed high bias voltages before measurements. A typical STM topo-
Fig. 3. (a) Spatial variation of STS spectra for 4 nm-QW; (b) and (c) cross-section at arrows in (a), V = plotted as dashed lines.
0.25 V and
0.4 V, respectively. Calculated LDOS for heavy holes are
K. Suzuki et al. / Applied Surface Science 254 (2008) 7889–7892
Fig. 4. (a) Spatial variation of STS spectra for 12 nm-QW; (b) and (c) cross-section at arrows in (a), V = plotted as dashed lines.
graphic image for the cleaved sample at 12 nm-QW is shown in Fig. 2. Clear atomic resolution was obtained. Steep interfaces can be seen. For STS measurements, differential conductance signal (dI/dV) as a function of V between the sample and the grounded tip was measured using a lock-in amplifier with a small modulation of V (5 mVpp, 700 Hz), where I is the tunneling current. Here, STS spectra represent the normalized differential conductance [(dI/ dV)/(I/V)] as a function of V(V) corresponding to the energy (eV) from the Fermi level in the sample. [(dI/dV)/(I/V)] is known to be proportional to the LDOS [1]. 3. Results and discussion Fig. 3(a–c) shows STS spectra for 4 nm-QW. The data is averaged along parallel to the layers. The gray-scale plot of LDOS [(dI/dV)/(I/V)] is shown in Fig. 3(a) as functions of the position along the growth direction and V. Contours are overlaid in an easy-to-understand manner. Bright regions correspond to high LDOS. White regions around 0 V are unavoidable divergence of LDOS due to the extremely low I for normalization. Dark regions on both sides correspond to the InAs band gap. V = 0 V is assumed to be the top of the GaSb valence band as mentioned before. LDOS are accumulated in the GaSb QW. In the lower (negative) voltage region up to 0.3 V, the LDOS curve as a
0.34 V and
7891
0.45 V, respectively. Calculated LDOS for heavy holes are
function of the position along the growth direction has a single peak at the center of the QW. In contrast, in the higher voltage region, the peak splits into two, corresponding to the shorter wavelength of the LDOS standingwaves. Observed numbers of peaks are indicated on the right hand side. The cross-sections at V = 0.25 and 0.40 V (arrows) are plotted in Fig. 3(b) and (c). The spectrum shape is discussed later. For 12 nm-QW, spatial variation of the STS spectra is plotted in Fig. 4(a). The number of peaks of the standingwaves along the growth direction increases by applying the higher voltage. Seven peaks can be confirmed at V = 0.45 V. The cross-sections of the LDOS spectra at V = 0.34 and 0.45 V (arrows in Fig. 4(a)) are plotted in (b) and (c). For both plots, the second peak from the right is smaller comparing with other peaks. Since the wavelength of the LDOS standingwaves along the growth direction becomes shorter with increasing the negative voltage for both QWs, we conclude the observed STS spectra represent hole subbands formed in the QW. The experimental spectrum shape is significantly asymmetric. It might be caused by the difference in the interface roughness which makes the asymmetric potential profile, because the interface of InAs grown on GaSb is relatively rougher than that of GaSb on InAs in general [10]. Subband energies were calculated using a simple quantum well potential and effective masses of 0.25m0 and 0.043m0 for heavy
7892
K. Suzuki et al. / Applied Surface Science 254 (2008) 7889–7892
and light holes, respectively, indicated as dashed lines (HH) and dotted lines (LH) on the left hand side in Figs. 3 and 4. Above calculated energies are not enough to explain the observed subband energies corresponding to the number on the right hand side. Further discussion taking into account the heavy hole–light hole mixing effect and the band nonparabolicity effect is necessary [11]. On the contrary, it might be possible to obtain the accurate valence band structure including these complicated effects experimentally. To explain the spectrum shapes roughly, we calculated observable LDOS distribution, as a sum of the squared wavefunctions for the subbands concerned with tunneling [4], plotted as dashed lines in Figs. 3(b) and (c), and 4(b) and (c). For simplicity, the fixed heavy holes effective mass is used. The observed spectrum shapes with larger peaks on both sides are reproduced well. 4. Summary We measured LDOS for GaSb/InAs QWs in the valence band by STS on the cleaved surface. Clear standingwave patterns of LDOS for confined holes were observed. We believe, using STS in the valence band, complicated valence band structures can be determined accurately.
Acknowledgements We would like to thank Lei Zhu, summer trainee from Univ. Tokyo for his experimental help. This work was partly supported by JSPS KAKENHI (16206003).
References [1] R.M. Feenstra, J.A. Strosico, J. Vac. Sci. Technol. B 5 (1987) 923. [2] K. Kanisawa, M.J. Butcher, H. Yamaguchi, Y. Hirayama, Phys. Rev. Lett. 86 (2001) 3384. [3] K. Kanisawa, M.J. Butcher, Y. Tokura, H. Yamaguchi, Y. Hirayama, Phys. Rev. Lett. 87 (2001) 196804. [4] K. Suzuki, K. Kanisawa, C. Janer, S. Perraud, K. Takashina, T. Fujisawa, Y. Hirayama, Phys. Rev. Lett. 98 (2007) 136802. [5] K. Suzuki, K. Kanisawa, S. Perraud, M. Ueki, K. Takashina, Y. Hirayama, Jpn. J. Appl. Phys. 46 (2007) 2618. [6] K. Kanisawa, S. Perraud, Y. Hirayama, in: Proceedings of the Conference on 13th International Conference on Solid Films and Surfaces (ICSFS-13) Fr-Str-16:45, San Carlos de Bariloche, Argentina, 2006. [7] M. Altarelli, Phys. Rev. B 28 (1983) 842. [8] K. Suzuki, K. Takashina, S. Miyashita, Y. Hirayama, Phys. Rev. Lett. 93 (2004) 016803. [9] G.M. Guichar, C.A. Sebenne, G.A. Garry, Phys. Rev. Lett. 37 (1976) 1158. [10] R.M. Feenstra, D.A. Collins, D.Z.-Y. Ting, M.W. Wang, T.C. McGill, Superlatt. Microstruct. 15 (1994) 215. [11] D.A. Broido, L.J. Sham, Phys. Rev. B 34 (1986) 3917.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Spatial imaging of valence band electronic structures in a GaSb/InAs quantum well K. Suzuki a,*, K. Kanisawa a, S. Perraud a,b, T. Fujisawa a a b
NTT Basic Research Laboratories, NTT Corporation, Atsugi-shi, Kanagawa 243-0198, Japan Laboratoire de Photonique et de Nanostructures, CNRS, 91460 Marcoussis, France
A R T I C L E I N F O
A B S T R A C T
Article history: Received 7 November 2007 Received in revised form 7 March 2008 Accepted 8 March 2008 Available online 16 March 2008
We measure local density of states (LDOS) for GaSb/InAs heterostructures with quantum wells in the valence band by scanning tunneling spectroscopy (STS) on the cleaved surface. Clear standingwave patterns of LDOS corresponding to the holes confined in the quantum wells are observed. ß 2008 Elsevier B.V. All rights reserved.
PACS: 73.21.Cd 68.37.Ef 81.05.Ea 81.15.Hi Keywords: Valence band Quantum well Scanning tunneling spectroscopy Local density of states Semiconductor heterostructures
1. Introduction As semiconductor devices become highly integrated with ultrafine structures, the wave properties of electrons in the devices become more and more dominant. The local analysis of the wavefunctions has been strongly desired for realizing high device performance. Scanning tunneling spectroscopy (STS) is one of the most powerful tools, which can image the spatial distribution of the electron local density of states (LDOS), corresponding to the squared wavefunction, as a function of the energy with nano-scale resolution [1–6]. Up to now, using STS, spatial distribution of LDOS showing the wave features of electrons has been observed [2–5]. However, most STS measurements have been performed focusing on electrons in the conduction band, few in the valence band [6]. Obtainable information by STS in the valence band has not been well understood. Provided LDOS imaging of holes is established, it becomes much powerful technique for investigating the complicated valence band structures, which are important feedback for
* Corresponding author. Tel.: +81 46 240 3473; fax: +81 46 240 4727. E-mail address: [email protected] (K. Suzuki). 0169-4332/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2008.03.036
device production. Furthermore, using this technique, behavior of holes and electron–hole interaction/correlation will be clarified precisely in view of nano-scale. Recently, we succeeded in observing the standingwave patterns of LDOS for the subbands formed in the quantum well (QW) in the conduction band by STS on the cleaved semiconductor heterostructure surfaces [4,5]. Here, to clarify obtainable information from the valence band by STS, we applied STS measurement to the QW in the valence band. As a result, clear standingwave patterns similar to those of the electrons confined in the QW in the conduction band were observed, showing the quantum confinement of the holes. 2. Experiments For the sample, 4 nm- and 12 nm-GaSb layers sandwiched between thick InAs layers were grown by molecular beam epitaxy on a (0 0 1) InAs substrate. In GaSb/InAs heterostructures, the conduction band bottom of InAs is lower in energy than the valence band top of GaSb, shown in Fig. 1. The band overlap of 0.15 eV is expected without consideration of the quantum confinement [7]. The GaSb layers work as a QW for holes. For
7890
K. Suzuki et al. / Applied Surface Science 254 (2008) 7889–7892
Fig. 2. Typical STM topographic image (empty state, V = +1.0 V) for the cleaved sample at 12 nm-QW.
Fig. 1. Schematic energy band profile of InAs/GaSb heterostructures.
the structure with thick layers, the Fermi level lies just below the valence band top of the GaSb [8]. For simplicity, we assume the above condition still applicable to the sample with thin layers and do not consider the effect of the band overlap in this paper.
The sample was loaded into an ultrahigh vacuum (UHV) chamber (<2 10 10 Torr) and cleaved to obtain a clean flat (1 1 0) surface. Then, the sample was transferred to the stage of the lowtemperature scanning tunneling microscope (STM) at 4.8 K cooled by liquid helium without breaking UHV. It is known that no surface Fermi level pinning states within the energy band gap are formed on the clean (1 1 0) surface of III–V compound semiconductors when cleaving is successful [9]. Scanning was performed in UHV of the order of 10 11 Torr. A bias voltage (V) was applied between the sample and the grounded tungsten STM tip, which was cleaned in situ by applying pulsed high bias voltages before measurements. A typical STM topo-
Fig. 3. (a) Spatial variation of STS spectra for 4 nm-QW; (b) and (c) cross-section at arrows in (a), V = plotted as dashed lines.
0.25 V and
0.4 V, respectively. Calculated LDOS for heavy holes are
K. Suzuki et al. / Applied Surface Science 254 (2008) 7889–7892
Fig. 4. (a) Spatial variation of STS spectra for 12 nm-QW; (b) and (c) cross-section at arrows in (a), V = plotted as dashed lines.
graphic image for the cleaved sample at 12 nm-QW is shown in Fig. 2. Clear atomic resolution was obtained. Steep interfaces can be seen. For STS measurements, differential conductance signal (dI/dV) as a function of V between the sample and the grounded tip was measured using a lock-in amplifier with a small modulation of V (5 mVpp, 700 Hz), where I is the tunneling current. Here, STS spectra represent the normalized differential conductance [(dI/ dV)/(I/V)] as a function of V(V) corresponding to the energy (eV) from the Fermi level in the sample. [(dI/dV)/(I/V)] is known to be proportional to the LDOS [1]. 3. Results and discussion Fig. 3(a–c) shows STS spectra for 4 nm-QW. The data is averaged along parallel to the layers. The gray-scale plot of LDOS [(dI/dV)/(I/V)] is shown in Fig. 3(a) as functions of the position along the growth direction and V. Contours are overlaid in an easy-to-understand manner. Bright regions correspond to high LDOS. White regions around 0 V are unavoidable divergence of LDOS due to the extremely low I for normalization. Dark regions on both sides correspond to the InAs band gap. V = 0 V is assumed to be the top of the GaSb valence band as mentioned before. LDOS are accumulated in the GaSb QW. In the lower (negative) voltage region up to 0.3 V, the LDOS curve as a
0.34 V and
7891
0.45 V, respectively. Calculated LDOS for heavy holes are
function of the position along the growth direction has a single peak at the center of the QW. In contrast, in the higher voltage region, the peak splits into two, corresponding to the shorter wavelength of the LDOS standingwaves. Observed numbers of peaks are indicated on the right hand side. The cross-sections at V = 0.25 and 0.40 V (arrows) are plotted in Fig. 3(b) and (c). The spectrum shape is discussed later. For 12 nm-QW, spatial variation of the STS spectra is plotted in Fig. 4(a). The number of peaks of the standingwaves along the growth direction increases by applying the higher voltage. Seven peaks can be confirmed at V = 0.45 V. The cross-sections of the LDOS spectra at V = 0.34 and 0.45 V (arrows in Fig. 4(a)) are plotted in (b) and (c). For both plots, the second peak from the right is smaller comparing with other peaks. Since the wavelength of the LDOS standingwaves along the growth direction becomes shorter with increasing the negative voltage for both QWs, we conclude the observed STS spectra represent hole subbands formed in the QW. The experimental spectrum shape is significantly asymmetric. It might be caused by the difference in the interface roughness which makes the asymmetric potential profile, because the interface of InAs grown on GaSb is relatively rougher than that of GaSb on InAs in general [10]. Subband energies were calculated using a simple quantum well potential and effective masses of 0.25m0 and 0.043m0 for heavy
7892
K. Suzuki et al. / Applied Surface Science 254 (2008) 7889–7892
and light holes, respectively, indicated as dashed lines (HH) and dotted lines (LH) on the left hand side in Figs. 3 and 4. Above calculated energies are not enough to explain the observed subband energies corresponding to the number on the right hand side. Further discussion taking into account the heavy hole–light hole mixing effect and the band nonparabolicity effect is necessary [11]. On the contrary, it might be possible to obtain the accurate valence band structure including these complicated effects experimentally. To explain the spectrum shapes roughly, we calculated observable LDOS distribution, as a sum of the squared wavefunctions for the subbands concerned with tunneling [4], plotted as dashed lines in Figs. 3(b) and (c), and 4(b) and (c). For simplicity, the fixed heavy holes effective mass is used. The observed spectrum shapes with larger peaks on both sides are reproduced well. 4. Summary We measured LDOS for GaSb/InAs QWs in the valence band by STS on the cleaved surface. Clear standingwave patterns of LDOS for confined holes were observed. We believe, using STS in the valence band, complicated valence band structures can be determined accurately.
Acknowledgements We would like to thank Lei Zhu, summer trainee from Univ. Tokyo for his experimental help. This work was partly supported by JSPS KAKENHI (16206003).
References [1] R.M. Feenstra, J.A. Strosico, J. Vac. Sci. Technol. B 5 (1987) 923. [2] K. Kanisawa, M.J. Butcher, H. Yamaguchi, Y. Hirayama, Phys. Rev. Lett. 86 (2001) 3384. [3] K. Kanisawa, M.J. Butcher, Y. Tokura, H. Yamaguchi, Y. Hirayama, Phys. Rev. Lett. 87 (2001) 196804. [4] K. Suzuki, K. Kanisawa, C. Janer, S. Perraud, K. Takashina, T. Fujisawa, Y. Hirayama, Phys. Rev. Lett. 98 (2007) 136802. [5] K. Suzuki, K. Kanisawa, S. Perraud, M. Ueki, K. Takashina, Y. Hirayama, Jpn. J. Appl. Phys. 46 (2007) 2618. [6] K. Kanisawa, S. Perraud, Y. Hirayama, in: Proceedings of the Conference on 13th International Conference on Solid Films and Surfaces (ICSFS-13) Fr-Str-16:45, San Carlos de Bariloche, Argentina, 2006. [7] M. Altarelli, Phys. Rev. B 28 (1983) 842. [8] K. Suzuki, K. Takashina, S. Miyashita, Y. Hirayama, Phys. Rev. Lett. 93 (2004) 016803. [9] G.M. Guichar, C.A. Sebenne, G.A. Garry, Phys. Rev. Lett. 37 (1976) 1158. [10] R.M. Feenstra, D.A. Collins, D.Z.-Y. Ting, M.W. Wang, T.C. McGill, Superlatt. Microstruct. 15 (1994) 215. [11] D.A. Broido, L.J. Sham, Phys. Rev. B 34 (1986) 3917.