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Polarization dependence of intersubband absorption and photoconductivity in p-type SiGe quantum wells
SM ARTICLE 745 Revise 1st proof 22.7.96
Superlattices and Microstructures, Vol. 20, No. 2, 1996
Polarization dependence of intersubband absorption and photoconductivity in p-type SiGe quantum wells T. F, P. K, M. H, G. B Institut fu¨r Halbleiterphysik, Universita¨t Linz, A-4040 Linz, Austria
J. F. N¨ , G. A Walter Schottky Institut, TU Mu¨nchen, D-85784 Garching, Germany (Received 25 November 1995) We present a detailed study of the polarization dependence of subband absorption and photoconductivity in Si/SiGe quantum wells. For samples with a hole concentration of p \2.8]1012 cm~2, both p- and s-polarized absorptions have been observed and transitions to4 several excited states are clearly identified by comparison with self-consistent Luttinger– Kohn type calculations. The photoconductivity is surprisingly insensitive to the polarization, which indicates the importance of the subsequent transport process on the photocurrent responsitivity. ( 1996 Academic Press Limited
1. Introduction The absorption of infrared radiation through intersubband transitions in quantum wells has been studied extensively in the past few years, because of its possible application in infrared detectors [1]. Besides the GaAs/AlGaAs system, the Si/SiGe system has attracted much attention recently because it offers the possibility of a direct integration of SiGe quantum wells with Si devices. For the realization of quantum well infrared photodetectors (QWIPs), valence band quantum wells are especially attractive, since due to the coupling of the heavy hole (HH), light hole (LH) and spin split-off (SO) valence bands, intersubband absorption is allowed for light polarized both parallel and perpendicular to the growth direction [1–11]. Therefore, normal-incidence QWIPs can be realized without the need of a grating coupler, as has been demonstrated both for III-V and Si/SiGe quantum wells [1,3,4]. Interestingly, the reported normal-incidence (or s-polarized) photoconductivity is actually much larger than predicted theoretically [1,3,4,11]. From transmission experiments, the evidence for s-polarized absorption is much scarcer however [3,4,6,9], and in our opinion a detailed understanding of these observations, including a correlation with theoretical calculations, is lacking so far. In this work we present transmission data which clearly show both p- and s-polarized absorption, whose origin and spectral positions can be quantitatively understood on the basis of a self-consistent 6-band Luttinger–Kohn calculation [10]. As in previous work, we observe a striking difference between transmission and photoconductivity results. 0749–6036/96/060237]07 $18.00/0
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2. Basic properties of Si/SiGe quantum wells Before we discuss the experimental results, a short summary of the basic properties of p-type Si/SiGe quantum wells (QWs) is given in the following. In addition, the selection rules governing the optical transitions in p-type QWs are discussed. A detailed description of our calculations has been published elsewhere [10]. In Si and Ge the three top-most valence bands (heavy-hole band (HH), light-hole band (LH) and spin split-off band (SO)) are degenerate (HH, LH) or nearly degenerate (HH, SO) at the C-point. Therefore, these three bands have to be considered in calculating valence band QW states and a simple single-band calculation, as in the case of conduction band QWs, is no longer applicable. A suitable description of the QW valence band structure near the C-point is provided by the Luttinger– Kohn Hamiltonian, as has been shown in Refs [2,6,8,10]. In the multi-quantum wells investigated in this work the SiGe layers forming the wells are grown pseudomorphically on the Si barriers, resulting in highly biaxial compressively strained SiGe layers. It is well known that this strain lifts the degeneracy of the HH and LH bands, leaving the HH band top-most. It also leads to a mixing of the LH and the SO band at the C-point which has, therefore, to be included in the calculation [12,13]. In addition, many-body interactions (Coulomb interaction and exchange-correlation interaction) have been taken into account self-consistently within the local density approximation. As a result of our calculations we obtain the energies of the various subbands, their dispersions parallel and perpendicular to the growth (z) direction and the corresponding envelope functions. Due to the non-diagonal elements in the Luttinger–Kohn Hamiltonian, these envelope functions are generally built up from all three valence bands. Therefore, a classification by HH, LH or SO no longer appears sensible. However, in the following we will label the eigenstates corresponding to the valence band which predominately builds up the eigenstate, remembering that this is only a coarse classification. For all QWs investigated in this work the ground state is built up mainly from HH contribu˚ ~1). This is a tions even for in-plane wavevectors as large as the Fermi wavevector (k ¹0.043 A f consequence of the large strain-induced splitting of the HH and LH bands which suppresses the mixing of these bands. In the following, the selection rules for optical transitions from the HH ground state to excited states are discussed: for vanishing in-plane wavevector, only transitions between states with opposite parity are allowed (dipole transitions) whereas for finite in-plane wavevectors transitions between states with the same parity also become allowed (overlap transitions). Transitions within the HH band (e.g. HH1]HH2) are allowed for light polarized parallel to the growth direction (z-polarization) and are forbidden for light polarized perpendicular to it (xypolarization). Within the HH band, only dipole transitions are allowed. Since these selection rules determine the transitions within one band (HH), they are identical to the selection rules known from a one-band model. Optical transitions from the HH ground state to states built up from the LH and SO valence bands are allowed for light polarized both in z and xy direction. For the former polarization, the initial state (HH) and the final state (LH, SO) must have the same parity (overlap transitions), whereas for the latter polarization both dipole and overlap transitions are allowed.
3. Experimental results and discussion Infrared transmission experiments were performed in multipass waveguide geometry [10]. The radiation is coupled into the sample at one facet which is wedged at an angle of 38° and then undergoes approximately 7 (depending on the ratio of the thickness to the length of the sample) total internal reflections at a reflection angle of 52°. This geometry in principle allows one to couple both
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0.4 0.2 0 0.8 0.6
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0.4 0.2
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500
1000
1500
2000
2500
3000
–1
Wave number (cm )
Fig. 1. Low temperature (T\10 K) measurement (lines without symbols) and calculation (lines with symbols) of the waveguide transmission spectra for a Si/SiGe multi-quantum-well sample with structural parameters indicated in the plot.
directions of polarization to the QW excitations (s-polarization, where the electric field vector is perpendicular to the z-direction, and p-polarization, where it is tilted by 38° from the z-direction). However, if the QW layers are close to the sample surface (compared to the wavelength of the radiation in the medium), the coupling of the radiation to the intersubband excitations is dominated by the boundary conditions for total internal reflection of the electromagnetic field. In this case the transitions allowed for z-polarized light are only observable if the sample surface is covered with a metal layer [10]. However, the metal layer shorts out any component of the electromagnetic field parallel to the surface (i.e. xy component), thereby inhibiting the absorption of xy-polarized radiation [10]. A large number of QW structures with widely varying parameters has been investigated previously by us and their absorption spectra could be well explained in the framework of the above mentioned calculation [10,14]. In the present study, which is aimed at the investigation of the xypolarized absorption, the active QW layers are set back from the surface by growing a 1.25 lm thick Si cap layer, which relaxes the above mentioned restriction. This sample was pseudomorphically ˚ Si grown on a (001) semi-insulating Si substrate by MBE. It consists of 30 periods of 30 A Ge 0.29 ˚ Si barriers. Due to the lattice mismatch, the strain in0.71 quantum wells separated by 150 A the SiGe ˚ of the barrier giving layers is e \e B[1.2%. The QWs were modulation doped in the center 60 A 99 :: a sheet concentration of p \2.8]1012 cm~2. Transmission measurements were performed in a s Fourier-transform infrared (FTIR) spectrometer at a temperature of T\10 K. In Fig. 1 the infrared transmission spectra of the sample described above are shown for both polarization directions. The sample spectra (thick lines without symbols) were normalized to the spectra measured for an undoped Si waveguide. For the data below 500 cm~1, the far infrared (FIR) setup of the FTIR (Hg lamp, Mylar beamsplitter, Si bolometer) was used, whereas the data above
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Fig. 2. Contour plot of the oscillator strength for transitions from the HH ground state at kz=0 as a function of the final state’s band number and the in-plane wavevector along the [110] direction. The left (right) part shows the oscillator strength for z (xy)-polarization calculated for the QW shown in Fig. 1, where each contour corresponds to an increase of the oscillator strength of 0.33 (0.16), the maximum oscillator strength being 6 (1.6). The triplet of numbers (normalized to unity) next to the regions of significant oscillator strength indicates the composition of the final state, where the upper, middle and lower number denotes the relative contributions of the HH, LH, and SO band to the final state, respectively.
650 cm"1 were measured in the mid-infrared (MIR) configuration (glow-bar, KBr beamsplitter, HgCdTe detector). Between these two ranges the data are very noisy and therefore not shown. Both the p- and s-polarized spectra shown in Fig. 1 appear to contain a wavenumber-dependent background that decreases steeply below 300 cm"1 and has a slowly varying tail for wavenumbers up to 3000 cm"1. Simulations of the waveguide transmission including the free carrier absorption (similar to Ref. [9]) have shown that the spectral shape of the background cannot be explained by this effect but might rather be due to a difference in the preparation of the sample and reference waveguides (i.e. thickness, facet wedging, etc.). However, in order not to introduce any ambiguity in the measured spectra, no attempt was made to correct this background. In the lower part of Fig. 1, the transmission spectrum measured in s-polarization is shown. As discussed above, in this polarization only transitions to LH and SO final states are allowed. The spectrum shows a narrow absorption line around 400 cm"1 and a broad absorption band between 1200 cm"1 and 2500 cm"1. Also shown in Fig. 1 are the theoretical results (thin lines with symbols). These results are obtained by a calculation of the absorption spectrum and a subsequent simulation of the waveguide transmission [10]. The agreement between theory and experiment is quite remarkable, especially if the large background at low wavenumbers is considered. (Note, that in the experimental spectrum the strength of the absorption at 2400 cm"1 is approximately 40% relative to the obvious baseline.) The upper part of Fig. 1 shows both the experimental and the theoretical results for p-polarized radiation. Again the agreement between experimental and calculated transmission spectra is excellent. The dominant peak for this polarization is centered around 21000 cm"1. At this energy, no peak is observed in the spectrum for the s-polarized light. Since the electric field vector for p-polarized radiation contains also a component in the xy direction, similar structures as for spolarization are observed in addition (at 400 cm"1 and at 1200–2500 cm"1). The transitions that correspond to the absorption lines shown in Fig. 1 can be identified by plotting the oscillator strengths from the HH ground state to the various excited states as a function
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–150
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SO2
–200 ° 29% Ge 30 A, –250 0.00
0.01
xy-pol. 0.02 k[110] (A–1)
z-pol. 0.03
0.04
Fig. 3. In-plane dispersion along [110] direction at k \0 for the first 20 eigenstates of the QW shown in Fig. z 1. According to Fig. 2, the solid (dashed) arrows indicate the z- (xy-) polarized transitions with the highest oscillator strengths. If sensible, the final states of the transitions are labeled according to the valence band that predominantly builds up this state.
of the in-plane wave vector. Figure 2 shows a contour plot of these oscillator strengths for vanishing wavevector along growth direction, k \0, as a function of the number of the subband of the final z state (abscissa axis) and the in-plane wave vector along the [110] direction (ordinate axis). The ˚ ~1). The left (right) panel of Fig. 2 shows wavevector axis ends at the Fermi wavevector (k \0.043 A f the oscillator strength for light polarized parallel to the z (xy) direction. In these plots each contour line corresponds to an increase of the oscillator strength by 0.33 (0.16), the maximum oscillator strength is 6 (1.6). In Fig. 2, the transitions with significant oscillator strengths are labeled with a triplet of numbers (p , p , p ). These numbers are normalized to unity and indicate the relative HH LH SO contribution of the HH, LH and SO band to the final state, respectively. According to Fig. 2 the strongest transition is allowed for light polarized parallel to the z direction and occurs at vanishing in-plane wavevector with a HH-like final state in the 9th band (HH1-HH2 transition). From Fig. 3, which shows the in-plane dispersion of the various energy bands for wavevectors parallel to the [110] direction, a transition energy of 135 meV (1080 cm~1) is obtained. As discussed in Ref. [10], for the dimensions of the quantum well investigated in this work, the energy level of the HH2-like final state is close to the top of the barrier and, therefore, is broadened due to miniband formation (k -dispersion). Consequently, the corresponding absorption z line in Fig. 1 is rather broad and asymmetric. In xy-polarization (Fig. 2, right panel), the strongest transition has a LH-like final state in the
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˚ ~1, the transition energy is third band and occurs for an in-plane wavevector k \0.035 A *110+ B400 cm~1 (or 50 meV, see Fig. 3). This transition is forbidden at k \0 and, therefore, is an *110+ ˚ ~1, the oscillator strength overlap transition (HH1]LH1). At k B0.02 A for this transition is *110+ concentrated still in the second band and it eventually jumps to the third band for increasing k . *110+ This behavior is due to the anti-crossing of the second and the third band also shown in Fig. 3. For xy-polarization, some transitions are also allowed at the C-point (dipole transitions): In the present sample, the final state of such transitions is in the 17th band and is SO-like (HH1]SO2). Again due to anti-crossing, the oscillator strength of these transitions jumps to higher energy bands for increasing in-plane wavevector, preserving the SO character of the final state up to the Fermi wavevector. According to Fig. 3, the energy of these transitions varies from 1800 cm~1 to 2400 cm~1 (225– 300 meV) for increasing in-plane wavevector. The absorption between 1200 cm~1 and 1800 cm~1 (150–225 meV, see Fig. 1) is due to transitions to the 14th and 15th band at in-plane wavevectors ˚ ~1. Due to the strong mixing of the HH, LH, and SO bands, for these transitions a around 0.035 A classification according to their final state does not appear sensible. All these transitions are observed in the present experiment (compare Fig. 1 and Fig. 3). The absorption band between 1200 cm~1 and 2400 cm~1 shown in Fig. 1 is due to transitions with the final state above the barrier of the quantum well. It is well known that for such bound-tocontinuum transitions maximum QWIP detectivity is achieved [1]. In addition, these transitions are allowed in xy-polarization and, therefore, they are ideally suited for the design of normal incidence Si/SiGe QWIPs. In the following, results of photoconductivity measurements for SiGe quantum wells with structural parameters similar to the quantum wells described above are reported. The sample for the photoconductivity measurements consists of 10 periods of Si Ge 0.36 ˚ thickness separated by 320 A ˚ Si barriers. They are doped in the0.64 quantum wells with 25 A well with a sheet carrier concentration of p \1.2]1012 cm~2. The multi-quantum well sequence is grown on s a 300 nm Si bottom contact layer and is terminated by a 100 nm Si top contact layer, both doped to p\4]1018 cm~3. The samples were processed into 200 lm]200 lm square mesas by reactive ion etching. In order to be able to investigate the dependence of the photocurrent on the polarization, the radiation was coupled into the detector via a wedged (38°) sample facet. For this sample, the transmission experiments are not as conclusive as for the sample described above, since it contains no thick undoped cap layer, but heavily doped contacts instead. Furthermore, it is doped in the wells, which leads to excessive line broadening. The results of the photoconductivity measurements are shown in Fig. 4A. For both directions of polarization a photoresponse of quite similar spectral shape is observed, with a higher signal in s-polarization than in p-polarization. This result is rather surprising, since in the transmission spectra presented above a strong polarization dependence with higher absorption in p-polarization was observed. Also from our calculations we expect a peak absorption that is much larger for z-polarized radiation than for xy-polarization: in Fig. 4B, the calculated absorption coefficients for this sample are shown for z- (solid line) and xy- (broken line) polarization. (The increase of the calculated absorption coefficient for xy-polarization below 800 cm~1 is due the HH1-LH1 transition at D450 cm~1.) Although the calculations reproduce some aspects of the measured photoresponse (for example the different onsets for p- and s-polarization) they fail to explain the relative strengths for the two polarizations. (Note that in Fig. 4B the absorption spectrum for z-polarized radiation has been divided by 10.) Since our calculations have proven to give accurate results for the absorption spectra of SiGe quantum wells over a wide range of structural parameters [10,14], we conclude that the shape of the photoresponse spectrum is dominated not only by the absorption coefficient, but rather by the vertical transport properties of the photo-excited carriers [11,15]. One possible mechanism to explain our photocurrent data is an energy-dependent photoconductive gain: for QWIPs, the photoconductive gain decreases with increasing time that a photo-excited carrier needs to escape
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Photoresponse (a.u.)
s-pol. p-pol.
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° 36% Ge w: 25 A, ° b: 320 A 10 periods well-doped 12 –2 ps = 1.2 × 10 cm
100 Absorption coeff. (cm–1)
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80 60 40
× 0.1
20
1000 1500 2000 2500 3000 3500 4000 Wave number (cm–1)
0 500
1000 1500 2000 2500 3000 3500 4000 Wave number (cm–1)
Fig. 4. A, Photoresponse of well doped Si/SiGe QWs with dimensions indicated in the plot. The radiation is coupled into the detector via a 38° wedged facet. The solid (broken) line shows the result measured in p(s)-polarization. B, Calculated absorption spectra of this sample (solid line: z-polarization, broken line: xypolarization).
from the quantum well [15]. Therefore, the gain vanishes for transitions with a strongly bound final state (infinite escape time) and becomes finite for transitions to a delocalized final state close to the top of the barrier. Since in our samples, the final states of the transitions allowed in xy-polarization (LH, SO states) are less localized than the final state of the z-polarized transition (HH2), a higher photoconductive gain is expected for the former. However, these considerations are only speculative and clearly more work has to be done for a better understanding of the dependence of the photocurrent on the polarization. Acknowledgements—This work was supported in part by the FWF (Austria) under Project No. 9119, by GhE and BMfWFK
References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
B. F. Levine, J. Appl. Phys. 74, R1 (1993). J. C. Chang and R. B. James, Phys. Rev. B 39, 12 672 (1989). P. People, J. C. Bean, C. G. Bethea, S. K. Sputz and L. J. Peticolas, Appl. Phys. Lett. 61, 1122 (1992). J. S. Park, R. P. G. Karunasiri and K. L. Wang, Appl. Phys. Lett. 61, 681 (1992); R. P. G. Karunasiri, J. S. Park and K. L. Wang, ibid. 61, 2434 (1992). K. L. Wang and R. P. G. Karunasiri, in: Semiconductor Quantum Wells and Superlattices for Long-Wavelength Infrared Detectors, Edited by M. O. Manasreh, Artech House, Boston (1993). P. Man and D. S. Pan, Appl. Phys. Lett. 61, 2799 (1992). S. K. Chun, D. S. Pan and K. L. Wang, Phys. Rev. B 47, 15 638 (1993). E. Corbin, K. B. Wong and M. Jaros, Phys. Rev. B 50, 2339 (1994). F. Szmulowicz and G. J. Brown, Phys. Rev. B 51, 13 203 (1995). S. Zanier, J. M. Berroir, Y. Guldner, J. P. Vieren, I. Sagnes, F. Glowacki, Y. Campidelli and P. A. Badoz, Phys. Rev. B 51, 14 311 (1995). T. Fromherz, E. Koppensteiner, M. Helm, G. Bauer, J. F. Nu¨tzel and G. Abstreiter, Phys. Rev. B 50, 15 073 (1994). A. Fenigstein, E. Finkman, G. Bahir and S. E. Schacham, J. Appl. Phys. 76, 1998 (1994). R. People and S. K. Sputz, Phys. Rev. B 41, 8431 (1990). F. H. Pollak and M. Cardona, Phys. Rev. 172, 816 (1968). T. Fromherz, E. Koppensteiner, M. Helm, G. Bauer, J. F. Nu¨tzel and G. Abstreiter, Superlatt. Microstruct. 15, 229 (1994). H. C. Liu, Appl. Phys. Lett. 60, 1507 (1992).
Superlattices and Microstructures, Vol. 20, No. 2, 1996
Polarization dependence of intersubband absorption and photoconductivity in p-type SiGe quantum wells T. F, P. K, M. H, G. B Institut fu¨r Halbleiterphysik, Universita¨t Linz, A-4040 Linz, Austria
J. F. N¨ , G. A Walter Schottky Institut, TU Mu¨nchen, D-85784 Garching, Germany (Received 25 November 1995) We present a detailed study of the polarization dependence of subband absorption and photoconductivity in Si/SiGe quantum wells. For samples with a hole concentration of p \2.8]1012 cm~2, both p- and s-polarized absorptions have been observed and transitions to4 several excited states are clearly identified by comparison with self-consistent Luttinger– Kohn type calculations. The photoconductivity is surprisingly insensitive to the polarization, which indicates the importance of the subsequent transport process on the photocurrent responsitivity. ( 1996 Academic Press Limited
1. Introduction The absorption of infrared radiation through intersubband transitions in quantum wells has been studied extensively in the past few years, because of its possible application in infrared detectors [1]. Besides the GaAs/AlGaAs system, the Si/SiGe system has attracted much attention recently because it offers the possibility of a direct integration of SiGe quantum wells with Si devices. For the realization of quantum well infrared photodetectors (QWIPs), valence band quantum wells are especially attractive, since due to the coupling of the heavy hole (HH), light hole (LH) and spin split-off (SO) valence bands, intersubband absorption is allowed for light polarized both parallel and perpendicular to the growth direction [1–11]. Therefore, normal-incidence QWIPs can be realized without the need of a grating coupler, as has been demonstrated both for III-V and Si/SiGe quantum wells [1,3,4]. Interestingly, the reported normal-incidence (or s-polarized) photoconductivity is actually much larger than predicted theoretically [1,3,4,11]. From transmission experiments, the evidence for s-polarized absorption is much scarcer however [3,4,6,9], and in our opinion a detailed understanding of these observations, including a correlation with theoretical calculations, is lacking so far. In this work we present transmission data which clearly show both p- and s-polarized absorption, whose origin and spectral positions can be quantitatively understood on the basis of a self-consistent 6-band Luttinger–Kohn calculation [10]. As in previous work, we observe a striking difference between transmission and photoconductivity results. 0749–6036/96/060237]07 $18.00/0
( 1996 Academic Press Limited
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2. Basic properties of Si/SiGe quantum wells Before we discuss the experimental results, a short summary of the basic properties of p-type Si/SiGe quantum wells (QWs) is given in the following. In addition, the selection rules governing the optical transitions in p-type QWs are discussed. A detailed description of our calculations has been published elsewhere [10]. In Si and Ge the three top-most valence bands (heavy-hole band (HH), light-hole band (LH) and spin split-off band (SO)) are degenerate (HH, LH) or nearly degenerate (HH, SO) at the C-point. Therefore, these three bands have to be considered in calculating valence band QW states and a simple single-band calculation, as in the case of conduction band QWs, is no longer applicable. A suitable description of the QW valence band structure near the C-point is provided by the Luttinger– Kohn Hamiltonian, as has been shown in Refs [2,6,8,10]. In the multi-quantum wells investigated in this work the SiGe layers forming the wells are grown pseudomorphically on the Si barriers, resulting in highly biaxial compressively strained SiGe layers. It is well known that this strain lifts the degeneracy of the HH and LH bands, leaving the HH band top-most. It also leads to a mixing of the LH and the SO band at the C-point which has, therefore, to be included in the calculation [12,13]. In addition, many-body interactions (Coulomb interaction and exchange-correlation interaction) have been taken into account self-consistently within the local density approximation. As a result of our calculations we obtain the energies of the various subbands, their dispersions parallel and perpendicular to the growth (z) direction and the corresponding envelope functions. Due to the non-diagonal elements in the Luttinger–Kohn Hamiltonian, these envelope functions are generally built up from all three valence bands. Therefore, a classification by HH, LH or SO no longer appears sensible. However, in the following we will label the eigenstates corresponding to the valence band which predominately builds up the eigenstate, remembering that this is only a coarse classification. For all QWs investigated in this work the ground state is built up mainly from HH contribu˚ ~1). This is a tions even for in-plane wavevectors as large as the Fermi wavevector (k ¹0.043 A f consequence of the large strain-induced splitting of the HH and LH bands which suppresses the mixing of these bands. In the following, the selection rules for optical transitions from the HH ground state to excited states are discussed: for vanishing in-plane wavevector, only transitions between states with opposite parity are allowed (dipole transitions) whereas for finite in-plane wavevectors transitions between states with the same parity also become allowed (overlap transitions). Transitions within the HH band (e.g. HH1]HH2) are allowed for light polarized parallel to the growth direction (z-polarization) and are forbidden for light polarized perpendicular to it (xypolarization). Within the HH band, only dipole transitions are allowed. Since these selection rules determine the transitions within one band (HH), they are identical to the selection rules known from a one-band model. Optical transitions from the HH ground state to states built up from the LH and SO valence bands are allowed for light polarized both in z and xy direction. For the former polarization, the initial state (HH) and the final state (LH, SO) must have the same parity (overlap transitions), whereas for the latter polarization both dipole and overlap transitions are allowed.
3. Experimental results and discussion Infrared transmission experiments were performed in multipass waveguide geometry [10]. The radiation is coupled into the sample at one facet which is wedged at an angle of 38° and then undergoes approximately 7 (depending on the ratio of the thickness to the length of the sample) total internal reflections at a reflection angle of 52°. This geometry in principle allows one to couple both
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1.0 0.8
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0.6 ° 29% Ge well: 30 A, ° barrier: 150 A 30 periods 1.25 µ m Si cap 12 –2 ps = 2.8 × 10 cm
Transmission
0.4 0.2 0 0.8 0.6
s-pol.
0.4 0.2
0
500
1000
1500
2000
2500
3000
–1
Wave number (cm )
Fig. 1. Low temperature (T\10 K) measurement (lines without symbols) and calculation (lines with symbols) of the waveguide transmission spectra for a Si/SiGe multi-quantum-well sample with structural parameters indicated in the plot.
directions of polarization to the QW excitations (s-polarization, where the electric field vector is perpendicular to the z-direction, and p-polarization, where it is tilted by 38° from the z-direction). However, if the QW layers are close to the sample surface (compared to the wavelength of the radiation in the medium), the coupling of the radiation to the intersubband excitations is dominated by the boundary conditions for total internal reflection of the electromagnetic field. In this case the transitions allowed for z-polarized light are only observable if the sample surface is covered with a metal layer [10]. However, the metal layer shorts out any component of the electromagnetic field parallel to the surface (i.e. xy component), thereby inhibiting the absorption of xy-polarized radiation [10]. A large number of QW structures with widely varying parameters has been investigated previously by us and their absorption spectra could be well explained in the framework of the above mentioned calculation [10,14]. In the present study, which is aimed at the investigation of the xypolarized absorption, the active QW layers are set back from the surface by growing a 1.25 lm thick Si cap layer, which relaxes the above mentioned restriction. This sample was pseudomorphically ˚ Si grown on a (001) semi-insulating Si substrate by MBE. It consists of 30 periods of 30 A Ge 0.29 ˚ Si barriers. Due to the lattice mismatch, the strain in0.71 quantum wells separated by 150 A the SiGe ˚ of the barrier giving layers is e \e B[1.2%. The QWs were modulation doped in the center 60 A 99 :: a sheet concentration of p \2.8]1012 cm~2. Transmission measurements were performed in a s Fourier-transform infrared (FTIR) spectrometer at a temperature of T\10 K. In Fig. 1 the infrared transmission spectra of the sample described above are shown for both polarization directions. The sample spectra (thick lines without symbols) were normalized to the spectra measured for an undoped Si waveguide. For the data below 500 cm~1, the far infrared (FIR) setup of the FTIR (Hg lamp, Mylar beamsplitter, Si bolometer) was used, whereas the data above
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Fig. 2. Contour plot of the oscillator strength for transitions from the HH ground state at kz=0 as a function of the final state’s band number and the in-plane wavevector along the [110] direction. The left (right) part shows the oscillator strength for z (xy)-polarization calculated for the QW shown in Fig. 1, where each contour corresponds to an increase of the oscillator strength of 0.33 (0.16), the maximum oscillator strength being 6 (1.6). The triplet of numbers (normalized to unity) next to the regions of significant oscillator strength indicates the composition of the final state, where the upper, middle and lower number denotes the relative contributions of the HH, LH, and SO band to the final state, respectively.
650 cm"1 were measured in the mid-infrared (MIR) configuration (glow-bar, KBr beamsplitter, HgCdTe detector). Between these two ranges the data are very noisy and therefore not shown. Both the p- and s-polarized spectra shown in Fig. 1 appear to contain a wavenumber-dependent background that decreases steeply below 300 cm"1 and has a slowly varying tail for wavenumbers up to 3000 cm"1. Simulations of the waveguide transmission including the free carrier absorption (similar to Ref. [9]) have shown that the spectral shape of the background cannot be explained by this effect but might rather be due to a difference in the preparation of the sample and reference waveguides (i.e. thickness, facet wedging, etc.). However, in order not to introduce any ambiguity in the measured spectra, no attempt was made to correct this background. In the lower part of Fig. 1, the transmission spectrum measured in s-polarization is shown. As discussed above, in this polarization only transitions to LH and SO final states are allowed. The spectrum shows a narrow absorption line around 400 cm"1 and a broad absorption band between 1200 cm"1 and 2500 cm"1. Also shown in Fig. 1 are the theoretical results (thin lines with symbols). These results are obtained by a calculation of the absorption spectrum and a subsequent simulation of the waveguide transmission [10]. The agreement between theory and experiment is quite remarkable, especially if the large background at low wavenumbers is considered. (Note, that in the experimental spectrum the strength of the absorption at 2400 cm"1 is approximately 40% relative to the obvious baseline.) The upper part of Fig. 1 shows both the experimental and the theoretical results for p-polarized radiation. Again the agreement between experimental and calculated transmission spectra is excellent. The dominant peak for this polarization is centered around 21000 cm"1. At this energy, no peak is observed in the spectrum for the s-polarized light. Since the electric field vector for p-polarized radiation contains also a component in the xy direction, similar structures as for spolarization are observed in addition (at 400 cm"1 and at 1200–2500 cm"1). The transitions that correspond to the absorption lines shown in Fig. 1 can be identified by plotting the oscillator strengths from the HH ground state to the various excited states as a function
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241
100 LH1 50
0 Energy (meV)
HH2 –50 SO2 –100
–150
SO2
SO2
–200 ° 29% Ge 30 A, –250 0.00
0.01
xy-pol. 0.02 k[110] (A–1)
z-pol. 0.03
0.04
Fig. 3. In-plane dispersion along [110] direction at k \0 for the first 20 eigenstates of the QW shown in Fig. z 1. According to Fig. 2, the solid (dashed) arrows indicate the z- (xy-) polarized transitions with the highest oscillator strengths. If sensible, the final states of the transitions are labeled according to the valence band that predominantly builds up this state.
of the in-plane wave vector. Figure 2 shows a contour plot of these oscillator strengths for vanishing wavevector along growth direction, k \0, as a function of the number of the subband of the final z state (abscissa axis) and the in-plane wave vector along the [110] direction (ordinate axis). The ˚ ~1). The left (right) panel of Fig. 2 shows wavevector axis ends at the Fermi wavevector (k \0.043 A f the oscillator strength for light polarized parallel to the z (xy) direction. In these plots each contour line corresponds to an increase of the oscillator strength by 0.33 (0.16), the maximum oscillator strength is 6 (1.6). In Fig. 2, the transitions with significant oscillator strengths are labeled with a triplet of numbers (p , p , p ). These numbers are normalized to unity and indicate the relative HH LH SO contribution of the HH, LH and SO band to the final state, respectively. According to Fig. 2 the strongest transition is allowed for light polarized parallel to the z direction and occurs at vanishing in-plane wavevector with a HH-like final state in the 9th band (HH1-HH2 transition). From Fig. 3, which shows the in-plane dispersion of the various energy bands for wavevectors parallel to the [110] direction, a transition energy of 135 meV (1080 cm~1) is obtained. As discussed in Ref. [10], for the dimensions of the quantum well investigated in this work, the energy level of the HH2-like final state is close to the top of the barrier and, therefore, is broadened due to miniband formation (k -dispersion). Consequently, the corresponding absorption z line in Fig. 1 is rather broad and asymmetric. In xy-polarization (Fig. 2, right panel), the strongest transition has a LH-like final state in the
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˚ ~1, the transition energy is third band and occurs for an in-plane wavevector k \0.035 A *110+ B400 cm~1 (or 50 meV, see Fig. 3). This transition is forbidden at k \0 and, therefore, is an *110+ ˚ ~1, the oscillator strength overlap transition (HH1]LH1). At k B0.02 A for this transition is *110+ concentrated still in the second band and it eventually jumps to the third band for increasing k . *110+ This behavior is due to the anti-crossing of the second and the third band also shown in Fig. 3. For xy-polarization, some transitions are also allowed at the C-point (dipole transitions): In the present sample, the final state of such transitions is in the 17th band and is SO-like (HH1]SO2). Again due to anti-crossing, the oscillator strength of these transitions jumps to higher energy bands for increasing in-plane wavevector, preserving the SO character of the final state up to the Fermi wavevector. According to Fig. 3, the energy of these transitions varies from 1800 cm~1 to 2400 cm~1 (225– 300 meV) for increasing in-plane wavevector. The absorption between 1200 cm~1 and 1800 cm~1 (150–225 meV, see Fig. 1) is due to transitions to the 14th and 15th band at in-plane wavevectors ˚ ~1. Due to the strong mixing of the HH, LH, and SO bands, for these transitions a around 0.035 A classification according to their final state does not appear sensible. All these transitions are observed in the present experiment (compare Fig. 1 and Fig. 3). The absorption band between 1200 cm~1 and 2400 cm~1 shown in Fig. 1 is due to transitions with the final state above the barrier of the quantum well. It is well known that for such bound-tocontinuum transitions maximum QWIP detectivity is achieved [1]. In addition, these transitions are allowed in xy-polarization and, therefore, they are ideally suited for the design of normal incidence Si/SiGe QWIPs. In the following, results of photoconductivity measurements for SiGe quantum wells with structural parameters similar to the quantum wells described above are reported. The sample for the photoconductivity measurements consists of 10 periods of Si Ge 0.36 ˚ thickness separated by 320 A ˚ Si barriers. They are doped in the0.64 quantum wells with 25 A well with a sheet carrier concentration of p \1.2]1012 cm~2. The multi-quantum well sequence is grown on s a 300 nm Si bottom contact layer and is terminated by a 100 nm Si top contact layer, both doped to p\4]1018 cm~3. The samples were processed into 200 lm]200 lm square mesas by reactive ion etching. In order to be able to investigate the dependence of the photocurrent on the polarization, the radiation was coupled into the detector via a wedged (38°) sample facet. For this sample, the transmission experiments are not as conclusive as for the sample described above, since it contains no thick undoped cap layer, but heavily doped contacts instead. Furthermore, it is doped in the wells, which leads to excessive line broadening. The results of the photoconductivity measurements are shown in Fig. 4A. For both directions of polarization a photoresponse of quite similar spectral shape is observed, with a higher signal in s-polarization than in p-polarization. This result is rather surprising, since in the transmission spectra presented above a strong polarization dependence with higher absorption in p-polarization was observed. Also from our calculations we expect a peak absorption that is much larger for z-polarized radiation than for xy-polarization: in Fig. 4B, the calculated absorption coefficients for this sample are shown for z- (solid line) and xy- (broken line) polarization. (The increase of the calculated absorption coefficient for xy-polarization below 800 cm~1 is due the HH1-LH1 transition at D450 cm~1.) Although the calculations reproduce some aspects of the measured photoresponse (for example the different onsets for p- and s-polarization) they fail to explain the relative strengths for the two polarizations. (Note that in Fig. 4B the absorption spectrum for z-polarized radiation has been divided by 10.) Since our calculations have proven to give accurate results for the absorption spectra of SiGe quantum wells over a wide range of structural parameters [10,14], we conclude that the shape of the photoresponse spectrum is dominated not only by the absorption coefficient, but rather by the vertical transport properties of the photo-excited carriers [11,15]. One possible mechanism to explain our photocurrent data is an energy-dependent photoconductive gain: for QWIPs, the photoconductive gain decreases with increasing time that a photo-excited carrier needs to escape
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Photoresponse (a.u.)
s-pol. p-pol.
500
° 36% Ge w: 25 A, ° b: 320 A 10 periods well-doped 12 –2 ps = 1.2 × 10 cm
100 Absorption coeff. (cm–1)
A
243 B xy-pol. z-pol.
80 60 40
× 0.1
20
1000 1500 2000 2500 3000 3500 4000 Wave number (cm–1)
0 500
1000 1500 2000 2500 3000 3500 4000 Wave number (cm–1)
Fig. 4. A, Photoresponse of well doped Si/SiGe QWs with dimensions indicated in the plot. The radiation is coupled into the detector via a 38° wedged facet. The solid (broken) line shows the result measured in p(s)-polarization. B, Calculated absorption spectra of this sample (solid line: z-polarization, broken line: xypolarization).
from the quantum well [15]. Therefore, the gain vanishes for transitions with a strongly bound final state (infinite escape time) and becomes finite for transitions to a delocalized final state close to the top of the barrier. Since in our samples, the final states of the transitions allowed in xy-polarization (LH, SO states) are less localized than the final state of the z-polarized transition (HH2), a higher photoconductive gain is expected for the former. However, these considerations are only speculative and clearly more work has to be done for a better understanding of the dependence of the photocurrent on the polarization. Acknowledgements—This work was supported in part by the FWF (Austria) under Project No. 9119, by GhE and BMfWFK
References [1] [2] [3] [4]
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