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Lateral transport in boron doped SiGe quantum wells
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999 Article No. spmi.1998.0638 Available online at http://www.idealibrary.com on
Lateral transport in boron doped SiGe quantum wells M. S. K AGAN , I. V. A LTUKHOV, K. A. K OROLEV, D. V. O RLOV, V. P. S INIS Institute of Radioengineering and Electronics of RAS, 11 Mokhovaya, 103907 Moscow, Russia
S. G. T HOMAS , K. L. WANG University of California, 66-147KK Engineering IV, Los Angeles, CA 90095, U.S.A.
K. S CHMALZ ¨ Institute f¨ur Halbleiterphysik, Walter-Korsing strasse, 2, 15230 Frankfurt (Oder), Germany I. N. YASSIEVICH A.F. Ioffe Physico-Technical Institute, 26 Politechnicheskaya, 194021 St Petersburg, Russia (Received 26 October 1998) The temperature dependence of lateral conductivity and hole mobility in boron doped Si/SiGe/Si quantum well structures were studied. The conductivity at the temperatures below 20 K is shown to be due to hopping over B centers while at higher temperatures it is due to two-stage excitation consisting of thermal activation of holes from the ground to strain-split B states and the next hole tunneling into the valence band. c 1999 Academic Press
Key words: SiGe, Hall-effect, A+ states, conductivity, shallow acceptors, quantum well.
1. Introduction Selectively doped Si/SiGe/Si quantum well structures (QWS) are of great interest in the study of acceptor states which degenerate in bulk material and should be split in two-dimensional (2D) systems due to space quantization and/or strain. The energy positions of the ground and excited states of an acceptor can be controled within a wide range by alloy composition, QW width, doping level, and space position of an acceptor center.
2. Experimental results and discussion The p-type Si/SiGe/Si QWS MBE-grown pseudomorphically on the n-type Si substrate and selectively doped with boron were used for conductivity, magnetoconductivity and Hall-effect measurements at temperatures 4–100 K. The Si/SiGe/Si layer of 20 nm thickness was sandwiched between undoped Si buffer (130 nm wide) and cap (60 nm) layers. Two kinds of structures were used. In the first type of structure, the SiGe QW was uniformly doped with boron. The content of Ge, x, in the uniformly doped Si/SiGe/Si alloy was 0.1 and 0.15, respectively, and the B concentration was of 3 × 1017 cm−3 . In the second type of structure, the SiGe QW had a Ge concentration of x = 0.15 with a boron δ-doped layer in the middle of the QW at a concentration of 6 × 1011 cm−2 . Two boron δ-layers (with a B concentration of 2 × 1011 cm−2 in the first 0749–6036/99/020203 + 04
$30.00/0
c 1999 Academic Press
204
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
10–4 x = 0.15 δ-doping
10–5
Split-off state
Ground state
σ (–1)
QW
10–6 10–7 x = 0.15 10–8 x = 0.1 10–9 0
0.05
0.1 0.15 1/T (K–1)
0.2
0.25
Fig. 1. Lateral conductivity of a SiGe QW with uniform and δ-doping versus T.
σ (Ä–1)
10–5 10–7
Etr
10–9 10–11
0
0.05
0.1 0.15 1/T (K–1)
0.2
0.25
Fig. 2. Lateral conductivity of a SiGe QW in a transverse electric field versus T .
type and 4–10 × 1011 cm−2 in the second type QWS) positioned within the buffer and cap layers at a distance of 30 nm from each QW interface were used to supply holes into the QW. Figure 1 shows the dependence of conductivity, σ , along the SiGe layer on temperature, T . One can see two activation-law regions in the curves. The low-T activation energy is approximately 2 meV and practically coincides with the samples with different Ge content and doping profile. The activation energy at T ≥ 20 K was near 12 meV for x = 0.1 and 18 meV for x = 0.15; independent of the doping profile in the QW. There are two possible explanations for the σ (T ) dependence at low T . First, the origin of the 2 meV activation energy could be the thermal hole emission from A+ states (acceptors binding an additional hole [1, 2]). The calculation of the A+ binding energy [3] gives 2 meV, being weakly dependent on Ge content in the SiGe alloy. Second, it could be due to the thermally activated hopping conductivity. The hopping can be over neutral or A+ boron states and depends on the Fermi level position. The main argument against the A+ states hopping is the low conductivity observed. At the given doping level in the QW, the mean distance + between impurities (≈10 nm) is of the √ order of the effective Bohr radius of the A states, which can be estimated by the expression a B ≈ h¯ / 2mε B . Using linear interpolation of GeSi parameters between Si and Ge, we obtain a B ≈ 10 nm for A+ states [4]. Because of strong overlapping impurity states, σ cannot be less than 10−3 to 10−4 −1 (see [5] for references). This is several orders of magnitude greater than the experimental values, so, it can be only
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
205
104 µ (cm2 V–1 s–1 )
µ
mc
103 µ
H
5
10
20
30
T (K) Fig. 3. Hall mobility and ‘mobility’ found from magnetoconductivity versus T .
hopping conductivity over neutral B0 centers with a B ≈ 2.5 nm [4]. On the other hand, all boron centers should be filled (neutral) due to the δ-doping outside the QW and no hopping over B0 should appear. The only reason for B0 hopping to exist seems to be Si surface states which can accumulate almost all holes from the δ-layers so that the B0 level is partially filled. To test this hypothesis we carried out transverse field-effect measurements. The results are presented in Fig. 2. The external potential of 1.5 V applied across the QW increased the lateral conductivity by two orders of magnitude and decreased the activation energy by four times, i.e. holes are transferred by transverse electric field from the Si surface into the QW populating B levels. To clear up the origin of the low-T activation energy we have determined the hole mobility by means of magnetoconductivity and Hall-effect measurements (Fig. 3). The values of Hall and magnetoconductivity constants were taken equal to unity. The dependence of Hall mobility, µ H , on T shows that the low-T conductivity is due to hopping. Indeed, the sharp decrease of µ H at lower T indicates a change in the conductivity mechanism. The small µ H values confirm the hopping character of low-T conductivity. The coincidence of low-T activation energies for QWS with a uniform and δ-doped SiGe layer (see Fig. 1) gives additional evidence against A+ states thermally activated conductivity. In δ-doped SiGe QWS, due to inclining bands (see below), A+ states in the middle of QW should become resonant in continuum. The mobility found from magnetoconductivity, µmc , turned out to be more than µ H . It could be due to the tunneling nature of the hopping conductivity. The hopping magnetoconductivity is described by the expression [5]: σ (H )/σ = exp t (a B e2 /N c2 h¯ 2 )H 2 = exp(bH 2 ) (N is the impurity concentration, t is a numerical constant). In the low-H range we have 1σ/σ ∝ bH 2 , similar to that for classical magnetoconductivity. Thus, only the mobility found by means of the Hall-effect corresponds to the transport one at hopping. The high-T activation energies observed, 12 and 18 meV, cannot be B0 binding energy as the latter should be much larger (about 40 meV). They can be one half of B0 binding energy if the Fermi level lies between the valence band edge and the B0 ground state. In this case, the observed high-T activation energies should correspond to 24 and 36 meV B0 binding energies. These values are, however, quite surprising. Indeed, although the binding energy of shallow impurity should decrease with increasing both Ge content and strain, this is quite contrary to the experiment. The only energy which could agree with the above activation energies is the energy difference between acceptor levels split by strain. The splitting energy of the ground acceptor state found by means of linear interpolation between Si and Ge is ≈15 meV for x = 0.1 and ≈25 meV for x = 0.15. They are close to the experimental activation energies. The splitting energy can be the activation energy only if holes can pass from the split-off state into the valence band without activation, that is by tunneling. This is impossible in the scheme of flat bands. On the other hand, we have seen from the experiment that almost all
206
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
holes from the δ-layers are accumulated at the surface states, making the surface charged. So, the potential drop across the structure should appear to incline the valence bands. The scheme of potential distribution for this case is shown in the insert in Fig. 1 illustrating that the conductivity should be controled by a two-stage process. First, the thermal activation of holes from the ground to split-off state takes place and then hole tunneling into the free-hole band creates the conductivity. To estimate the possible potential drop across the structure, we can use an empirical law that for most homeopolar semiconductors the Fermi energy is fixed on the surface near 1/3 of the gap counted from the valence band edge. This is ≈0.4 eV for Si. The QW width is 10 times less than the structure width. So, the potential drop on the QW is ≈40 meV. Of course, this estimation is rather rough but it shows that the proposed model can be real. Thus, the arguments for the model are (i) the increasing activation energy of conductivity with Ge content, (ii) small additional hole concentration supplied from δ-layers into the QW, and (iii) charging the surface and giving rise to the potential drop across the QW. The experimental data presented give evidence for the hopping character of low-T conductivity of B-doped QWs rather than that due to A+ -states thermal activation. At higher temperatures, the conductivity is shown to be due to thermal activation of holes from the ground to strain-split B states following by hole tunneling into the QW valence band. Inclining the valence bands of investigated QW structures makes it possible to find the energy splitting of acceptor levels by strain from temperature dependence of conductivity. Acknowledgements—This work was supported in part by Grants 96-02-17352 and 97-02-16820 from Russian Foundation for Basic Research and 97-10-55 from Russian Ministry of Science and Technology.
References [1] [2] [3] [4] [5]
}E. M. Gershenzon, Yu. P. Ladyzhenskii, and A. P. Melnikov, JETP Lett. 14, 380 (1971). }E. E. Godik, Yu. A. Kuritsyn, and V. P. Sinis, JETP Lett. 14, 377 (1971). }I. N. Yassievich, K. Schmalz, M. A. Odnobludov, and M. S. Kagan, Solid-State Electron. 40, 97 (1996). }K. Schmalz, I. N. Yassievich, K. L. Wang, and S. G. Thomas, Phys. Rev. B57, 6579 (1998). }B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors, (Springer, Heidelberg, 1984).
Lateral transport in boron doped SiGe quantum wells M. S. K AGAN , I. V. A LTUKHOV, K. A. K OROLEV, D. V. O RLOV, V. P. S INIS Institute of Radioengineering and Electronics of RAS, 11 Mokhovaya, 103907 Moscow, Russia
S. G. T HOMAS , K. L. WANG University of California, 66-147KK Engineering IV, Los Angeles, CA 90095, U.S.A.
K. S CHMALZ ¨ Institute f¨ur Halbleiterphysik, Walter-Korsing strasse, 2, 15230 Frankfurt (Oder), Germany I. N. YASSIEVICH A.F. Ioffe Physico-Technical Institute, 26 Politechnicheskaya, 194021 St Petersburg, Russia (Received 26 October 1998) The temperature dependence of lateral conductivity and hole mobility in boron doped Si/SiGe/Si quantum well structures were studied. The conductivity at the temperatures below 20 K is shown to be due to hopping over B centers while at higher temperatures it is due to two-stage excitation consisting of thermal activation of holes from the ground to strain-split B states and the next hole tunneling into the valence band. c 1999 Academic Press
Key words: SiGe, Hall-effect, A+ states, conductivity, shallow acceptors, quantum well.
1. Introduction Selectively doped Si/SiGe/Si quantum well structures (QWS) are of great interest in the study of acceptor states which degenerate in bulk material and should be split in two-dimensional (2D) systems due to space quantization and/or strain. The energy positions of the ground and excited states of an acceptor can be controled within a wide range by alloy composition, QW width, doping level, and space position of an acceptor center.
2. Experimental results and discussion The p-type Si/SiGe/Si QWS MBE-grown pseudomorphically on the n-type Si substrate and selectively doped with boron were used for conductivity, magnetoconductivity and Hall-effect measurements at temperatures 4–100 K. The Si/SiGe/Si layer of 20 nm thickness was sandwiched between undoped Si buffer (130 nm wide) and cap (60 nm) layers. Two kinds of structures were used. In the first type of structure, the SiGe QW was uniformly doped with boron. The content of Ge, x, in the uniformly doped Si/SiGe/Si alloy was 0.1 and 0.15, respectively, and the B concentration was of 3 × 1017 cm−3 . In the second type of structure, the SiGe QW had a Ge concentration of x = 0.15 with a boron δ-doped layer in the middle of the QW at a concentration of 6 × 1011 cm−2 . Two boron δ-layers (with a B concentration of 2 × 1011 cm−2 in the first 0749–6036/99/020203 + 04
$30.00/0
c 1999 Academic Press
204
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
10–4 x = 0.15 δ-doping
10–5
Split-off state
Ground state
σ (–1)
QW
10–6 10–7 x = 0.15 10–8 x = 0.1 10–9 0
0.05
0.1 0.15 1/T (K–1)
0.2
0.25
Fig. 1. Lateral conductivity of a SiGe QW with uniform and δ-doping versus T.
σ (Ä–1)
10–5 10–7
Etr
10–9 10–11
0
0.05
0.1 0.15 1/T (K–1)
0.2
0.25
Fig. 2. Lateral conductivity of a SiGe QW in a transverse electric field versus T .
type and 4–10 × 1011 cm−2 in the second type QWS) positioned within the buffer and cap layers at a distance of 30 nm from each QW interface were used to supply holes into the QW. Figure 1 shows the dependence of conductivity, σ , along the SiGe layer on temperature, T . One can see two activation-law regions in the curves. The low-T activation energy is approximately 2 meV and practically coincides with the samples with different Ge content and doping profile. The activation energy at T ≥ 20 K was near 12 meV for x = 0.1 and 18 meV for x = 0.15; independent of the doping profile in the QW. There are two possible explanations for the σ (T ) dependence at low T . First, the origin of the 2 meV activation energy could be the thermal hole emission from A+ states (acceptors binding an additional hole [1, 2]). The calculation of the A+ binding energy [3] gives 2 meV, being weakly dependent on Ge content in the SiGe alloy. Second, it could be due to the thermally activated hopping conductivity. The hopping can be over neutral or A+ boron states and depends on the Fermi level position. The main argument against the A+ states hopping is the low conductivity observed. At the given doping level in the QW, the mean distance + between impurities (≈10 nm) is of the √ order of the effective Bohr radius of the A states, which can be estimated by the expression a B ≈ h¯ / 2mε B . Using linear interpolation of GeSi parameters between Si and Ge, we obtain a B ≈ 10 nm for A+ states [4]. Because of strong overlapping impurity states, σ cannot be less than 10−3 to 10−4 −1 (see [5] for references). This is several orders of magnitude greater than the experimental values, so, it can be only
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
205
104 µ (cm2 V–1 s–1 )
µ
mc
103 µ
H
5
10
20
30
T (K) Fig. 3. Hall mobility and ‘mobility’ found from magnetoconductivity versus T .
hopping conductivity over neutral B0 centers with a B ≈ 2.5 nm [4]. On the other hand, all boron centers should be filled (neutral) due to the δ-doping outside the QW and no hopping over B0 should appear. The only reason for B0 hopping to exist seems to be Si surface states which can accumulate almost all holes from the δ-layers so that the B0 level is partially filled. To test this hypothesis we carried out transverse field-effect measurements. The results are presented in Fig. 2. The external potential of 1.5 V applied across the QW increased the lateral conductivity by two orders of magnitude and decreased the activation energy by four times, i.e. holes are transferred by transverse electric field from the Si surface into the QW populating B levels. To clear up the origin of the low-T activation energy we have determined the hole mobility by means of magnetoconductivity and Hall-effect measurements (Fig. 3). The values of Hall and magnetoconductivity constants were taken equal to unity. The dependence of Hall mobility, µ H , on T shows that the low-T conductivity is due to hopping. Indeed, the sharp decrease of µ H at lower T indicates a change in the conductivity mechanism. The small µ H values confirm the hopping character of low-T conductivity. The coincidence of low-T activation energies for QWS with a uniform and δ-doped SiGe layer (see Fig. 1) gives additional evidence against A+ states thermally activated conductivity. In δ-doped SiGe QWS, due to inclining bands (see below), A+ states in the middle of QW should become resonant in continuum. The mobility found from magnetoconductivity, µmc , turned out to be more than µ H . It could be due to the tunneling nature of the hopping conductivity. The hopping magnetoconductivity is described by the expression [5]: σ (H )/σ = exp t (a B e2 /N c2 h¯ 2 )H 2 = exp(bH 2 ) (N is the impurity concentration, t is a numerical constant). In the low-H range we have 1σ/σ ∝ bH 2 , similar to that for classical magnetoconductivity. Thus, only the mobility found by means of the Hall-effect corresponds to the transport one at hopping. The high-T activation energies observed, 12 and 18 meV, cannot be B0 binding energy as the latter should be much larger (about 40 meV). They can be one half of B0 binding energy if the Fermi level lies between the valence band edge and the B0 ground state. In this case, the observed high-T activation energies should correspond to 24 and 36 meV B0 binding energies. These values are, however, quite surprising. Indeed, although the binding energy of shallow impurity should decrease with increasing both Ge content and strain, this is quite contrary to the experiment. The only energy which could agree with the above activation energies is the energy difference between acceptor levels split by strain. The splitting energy of the ground acceptor state found by means of linear interpolation between Si and Ge is ≈15 meV for x = 0.1 and ≈25 meV for x = 0.15. They are close to the experimental activation energies. The splitting energy can be the activation energy only if holes can pass from the split-off state into the valence band without activation, that is by tunneling. This is impossible in the scheme of flat bands. On the other hand, we have seen from the experiment that almost all
206
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
holes from the δ-layers are accumulated at the surface states, making the surface charged. So, the potential drop across the structure should appear to incline the valence bands. The scheme of potential distribution for this case is shown in the insert in Fig. 1 illustrating that the conductivity should be controled by a two-stage process. First, the thermal activation of holes from the ground to split-off state takes place and then hole tunneling into the free-hole band creates the conductivity. To estimate the possible potential drop across the structure, we can use an empirical law that for most homeopolar semiconductors the Fermi energy is fixed on the surface near 1/3 of the gap counted from the valence band edge. This is ≈0.4 eV for Si. The QW width is 10 times less than the structure width. So, the potential drop on the QW is ≈40 meV. Of course, this estimation is rather rough but it shows that the proposed model can be real. Thus, the arguments for the model are (i) the increasing activation energy of conductivity with Ge content, (ii) small additional hole concentration supplied from δ-layers into the QW, and (iii) charging the surface and giving rise to the potential drop across the QW. The experimental data presented give evidence for the hopping character of low-T conductivity of B-doped QWs rather than that due to A+ -states thermal activation. At higher temperatures, the conductivity is shown to be due to thermal activation of holes from the ground to strain-split B states following by hole tunneling into the QW valence band. Inclining the valence bands of investigated QW structures makes it possible to find the energy splitting of acceptor levels by strain from temperature dependence of conductivity. Acknowledgements—This work was supported in part by Grants 96-02-17352 and 97-02-16820 from Russian Foundation for Basic Research and 97-10-55 from Russian Ministry of Science and Technology.
References [1] [2] [3] [4] [5]
}E. M. Gershenzon, Yu. P. Ladyzhenskii, and A. P. Melnikov, JETP Lett. 14, 380 (1971). }E. E. Godik, Yu. A. Kuritsyn, and V. P. Sinis, JETP Lett. 14, 377 (1971). }I. N. Yassievich, K. Schmalz, M. A. Odnobludov, and M. S. Kagan, Solid-State Electron. 40, 97 (1996). }K. Schmalz, I. N. Yassievich, K. L. Wang, and S. G. Thomas, Phys. Rev. B57, 6579 (1998). }B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors, (Springer, Heidelberg, 1984).