- Email: [email protected]
Incorporation of dopant atoms and defects in semiconductors: a microscopic view
ARTICLE IN PRESS
Physica B 340–342 (2003) 1159–1165
Incorporation of dopant atoms and defects in semiconductors: a microscopic view Ph. Ebert* Institut fur Forschungszentrum Julich GmbH, 52425 Julich, Germany . Festkorperforschung, . . .
Abstract We demonstrate that scanning tunneling microscopy is an ideal tool for the investigation of individual bulk defects and dopant atoms in semiconductors. This technique allows not only an atomically resolved imaging of individual defects and dopant atoms, but rather a detailed determination of their nanoscale electronic as well as structural properties and their concentrations. The capacities of scanning tunneling microscopy for defect investigations will be presented with help of selected examples. r 2003 Elsevier B.V. All rights reserved. Keywords: Dopant atoms; Point defects; Compensation; Scanning tunneling microscopy; InP; GaAs
1. Introduction Since the early stages of semiconductor technology, the importance of defects and dopant atoms became obvious. Therefore, considerable research efforts focused on the determination of the nanoscale physics governing the formation of point defects, the incorporation behavior of impurities, and their respective electronic properties. However, a direct access to point defects in semiconductors is a difficult task. Most conventional experimental techniques relied on the interpretation of macroscopic data of differently processed crystals or on signals integrating over a large set of usually unknown defects. Thus conclusions about individual defects on the atomic level were limited. In view of this situation the possibility to directly image with atomic resolution *Tel.: +49-2461-61-5023; fax: +49-2461-61-6444. E-mail address: [email protected] (P. Ebert).
individual bulk point defects and dopant atoms by cross-sectional scanning tunneling microscopy (STM) [1–4] is particularly intriguing. The aim of this paper is to illustrate the methodology by presenting the recent progress gained in the extraction of the physical mechanisms governing the incorporation behavior of defects and dopants.
2. Experimental approach Cross-sectional scanning tunneling microscopy is based on a rather simple concept. In order to take advantage of its atomic resolution, the bulk defects and dopant atoms as well as other structures of interest, e.g., interfaces, are exposed by cleavage on a cross-sectional surface (Fig. 1). On the cleavage surface the STM is then not only capable of directly imaging of the individual bulk point defects and dopant atoms with atomic resolution, but also able to identify them and
0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.10.005
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1160
tip of STM
VP-ZnIn
cleaved off
VP
defects and dopant atoms
ZnIn (110)
[001] (001)
substrate
(a)
5 nm
[110]
epitaxial layer
Fig. 1. Principle of cross-sectional scanning tunneling microscopy.
(b)
characterize their nanoscale electronic properties [5]. This technique works astonishigly well for almost all III–V and II–VI compound semiconductors, since most of them exhibit (i) a very good cleavage behavior, (ii) a 1 1 surface relaxation, and (iii) essentially no surface states in the band gap [5]. In the following we show selected examples of cross-sectional STM of defects and dopants in semiconductor substrates and spatially confined structures.
3. Imaging dopant atoms in semiconductors Fig. 2 shows a typical InP(1 1 0) cleavage surface as imaged by STM at negative voltages applied to the sample. First, one can observe the atomic rows along the ½1 1% 0 direction consisting of occupied dangling bonds localized above each anion. Thus the image essentially shows the phosphorus (P) sublattice. In contrast, at positive voltages the cation sublattice is visible [6,7]. Second, one can distinguish three types of defects/dopants by their contrast: (i) White elevations, which arise from the screened Coulomb potential around negatively charged ZnIn dopant atoms on In lattice sites [2–5,8,9]. (ii) Missing ‘atoms’ surrounded by dark
(c)
2nd layer Zn
_
[110]
(d)
surface cation surface anion surface Zn dopant atom
(e) Fig. 2. (a) STM image of a p-doped InP(1 1 0) surface. Six ZnIn dopant atoms in different subsurface layers, one P vacancy (VP), and one vacancy-dopant complex (VP–ZnIn) are visible. (b) to (d) Zn-dopant atoms (b) in the first, (c) second, and (d) third subsurface layer. The crosses in (b) to (d) mark the projected positions of the dopants, identifies using the altenating mirror plane of the dopant atom-induced contrast arising from the screened Coulomb potential around the ionized dopants. (e) Schematic drawing of the positions of the dopants atoms in the lattice. All images shows the occupied states. Adapted with permission from Ebert et al. [8]. r 1996 American Physical Society.
contrasts, arising from positively charged surface P monovacancies (VP) [5,10–14], formed after cleavage by Langmiur evaporation of anions [15]. They are thus not bulk defects. (iii) The vacancy
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1161
sublattice, on which the Zn dopant atoms reside, with respect to the surface P sublattice as illustrated in Fig. 2e. Thus Fig. 2b–d show dopant atoms in the surface first, second, and third subsurface layers. This allows a three-dimensional mapping of dopant atoms in semiconductors and on basis of observing directly individual dopant atoms.
formation leads to the third type of defect, an electrically compensated complex consisting of a surface vacancy and an adjacent Zn dopant atom [8,13]. Here we concentrate only on bulk defects and dopants, although a large number of investigations addressed surface defects [5]. The images of the dopant atoms differ at closer look in intensity and symmetry. High resolution STM images of the three most intensive dopant atom features (Fig. 2b–d) show distinct changes in symmetry characterized by a (½1 1% 0) mirror plane between and on top the atomic rows along the [0 0 1] direction. In order to understand this effect, one has to recall that in addition to the filled dangling bond states above the P atoms, the contrast of a dopant consists of a long range elevation arising from the imaging of the screened Coulomb potential [16], which is centered at the ionized dopant. Therefore, its center tells us where the Zn dopant atom is incorporated relative to the imaged P sublattice, while the intensity of the contrast decreases with increasing depth of the dopant atom. With decreasing intensity of the white contrast (i.e., increasing depth of the dopant), the (½1 1% 0) mirror plane and thus the dopant itself alternately is located between the atomic rows along the [0 0 1] direction (Fig. 2b and d) or on top of the atomic rows (Fig. 2c) (see crosses). This alternating geometry reflects with increasing subsurface depth the position of the In
4. Clustering of charged dopant atoms The atomically resolved mapping ability allows one to address dopant incorporation in nanometer-scale systems. The generally accepted view is that at such dimensions the repulsive screened Coulomb interaction between the charged dopants governs their incorporation. Such a repulsion in turn should lead to a rather homogeneous distribution of the dopant atoms in the semiconductor. This is, however, not the case: Fig. 3a shows a STM image of a cleaved 2.5 1020 cm3 Zn-doped GaAs crystal, where each individual Zn dopant atom appears as a bright contrast. From the dopant positions we calculated the local dopant concentration (Fig. 3b), which shows that the distribution of the dopants exhibits strong fluctuations leading to clusters of electrically active dopants with dimensions of about 10 nm [17].
10 nm (a)
(b)
Fig. 3. (a) STM image of a (1 1 0) cleavage surface of 2.5 10 cm3 Zn-doped GaAs acquired at 2:4 V. The white hillocks superposed onto the atomic-scale corrugation of the atomic rows along the ½1 1% 0 direction are Zn dopant atoms. (b) Local concentration of the dopants calculated from the measured position in (a). A high concentration is shown as white contrast. The images show a clustering of the dopant atoms. Adapted with permission from Ebert et al. [17]. r 1999 American Physical Society. 20
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1162
6 2.5·1018 cm-3 1.1·1019 cm-3
5
2.5·1020 cm-3
-ln [c(r)]
4 3
Screening length R S (nm)
At first sight, the clustering behavior seems to suggest the existence of a possible attractive interaction in addition to the screened Coulomb repulsion. However, a quantitative analysis of the dopant distributions proved different: The negative logarithm of the pair correlation function of the dopants (Fig. 4) is proportional to the so called mean force potential [18]. In case of low dopant concentration (i.e., the average distance between dopants is larger than the extend of the interaction potential), the mean force potential equals the repulsive screened Coulomb interaction between two charged dopants given by V ðrÞ ¼ e=ð4pe0 er Þ 1=r expðr=RS Þ [19]. On this basis we extracted from the data in Fig. 4 the screening length RS (open squares in inset of Fig. 4). As expected, the screening length increases with decreasing carrier concentration. However, the data does not agree quantitatively with the theoretical values (solid line) determined for a freeze-in temperature of 900 K [19]. However, when taking many-body effects in the otherwise repulsive interaction
5 4 3 2 1 18
19
20
10 10 10 Carrier concentration (cm-3)
2 1 0 -1
0
2
4
6
8
10
Distance r (nm) Fig. 4. Measured negative logarithm of the pair correlation function for three carrier concentrations. The arrows indicate attractive minima increasing in distance with decreasing carrier concentration. Inset: Values for screening lengths RS as a function of the carrier concentration (empty squares). The solid line represents the theoretical screening length calculated according to Ref. [19] for 900 K. The filled squares show the screening length corrected for many-body interactions. Adapted with permission from Ebert et al. [17]. r 1999 American Physical Society.
between the dopants into account, we obtained the screening length around an isolated dopant (filled squares) [17], which agrees well with the theoretical expectation. This shows that the present system can be well described by classical screening. The importance of many-body effects is found in a weak attractive part beyond a shortrange repulsive core (see arrows in Fig. 4 marking minima in ln[c(r)]), leading to the clustering of dopant atoms observed.
5. Dopant-induced dots and potential fluctuations The above results show that at the dimensions of 20–30 nm aimed for future transistors, the electrical potential distribution within the devices cannot be treated as continuous anymore. The potential is rather governed by individual, discrete ionized dopant atoms and by fluctuations in the dopant distribution. Fig. 5a demonstrates that a clustering of dopant atoms occurs also in nanostructures [20]. In this example, a GaAs p–n multilayer structure, one can see several p- and ndoped layers separated by a depletion zone giving rise to a dark line at the interface in the STM images [21]. This dark line is the electronic interface, which is very rough due to a clustering of dopant atoms [22]. This roughness creates in a nominally p-doped layer, sandwiched between two n-doped layers, several electronically decoupled clusters of dopant atoms labeled d2, d4, and d14 according to the number of dopant atoms within the cluster. These clusters are surrounded by confining potentials for free holes in the order of a few tenths of eV (border toward depleted zones with no dopants d0 ) to 1.4 eV (toward n-doped layer). Fig. 5b shows that each of these clusters of dopant atoms has drastically different current– voltage characteristics. This is due to the spatial confinement of the free charge carriers within the cluster, which reduces the ability to screen the electric field of the tip, because the charge carriers cannot be moved out of the cluster. Thus the band bending is larger compared to spatially nonconfined material and as consequence the current is lower [17]. The similarity of the tip-dot configuration with n–p–n transistors suggests that the
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1163
6. Dopant compensation by defects
p
d4 d0
d2
d0 d14
(a)
_ [110]
d0
[001]
10 nm
p
n
p
d0 d2 d4 d 14 p -layer
current (nA)
0.1
0.01
-3 (b)
n
-2
-1
1
2
3
sample voltage (V)
Fig. 5. (a) Atomically resolved scanning tunneling microscope images of a GaAs p–n structure. The bright hillocks in the pand n-doped layers are signatures of C and Si dopant atoms, respectively. The encircled areas d2 ; d4 ; and d14 are dopantinduced dots confined by potential barriers due to the doping of the surrounding areas (n-type and lack of dopants). The growth direction is [0 0 1]. (b) Current–voltage curves for the dopantinduced dots marked in (a). Adapted with permission from J.ager et al. [20]. r 2003 American Institute of Physics.
effects found here will also affect future miniaturized semiconductor devices, once they reach dimensions as small as the fluctuations of the dopant concentration [20].
The STM can also image a variety of bulk defects exposed by cleavage on the surface. This opens the way to address the compensation of dopants by defects as shown especially for Sidoped GaAs [23,24]. Si-doped GaAs exhibits a strong compensation, which has been attributed [25–33] to many different compensation mechanisms based of a zoo of defects. The STM investigations [23] performed on as-grown GaAs with Si concentrations ranging from 2.7 1018 (55% electr. inactive Si) to (2.56) 1019 cm3 (95% compensated Si), were able to clarify the compensation. With increasing Si concentration, the STM images revealed a strong increase of the concentration of various defects, showing that defects play a crucial role in the compensation. Fig. 6 shows the occupied states (arsenic sublattice, upper row) and empty states (Ga sublattice) of all bulk defects and dopant atoms observed by STM [23]. These are SiGa donors (frames (a1) and (a2)), SiAs acceptors (b1, b2), Si donor-Ga vacancy complexes (SiGa–VGa) (c1, c2), and planar Si clusters on (1 1 1) planes (d) [23]. Once these defects are identified, it is possible to directly extract the bulk concentrations of every type of defect separately, by counting of the individual dopant atoms and point defects located in a particular surface and/or subsurface layer (depth resolution see Fig. 2). Fig. 7 shows the obtained result: SiGa donors are consecutively compensated by SiAs acceptors, Si clusters, and SiGa–Ga-vacancy complexes at critical Si concentrations, something explaining the prior contradicting literature. Many of the proposed mechanisms contribute indeed, but dominate only in certain ranges of Si concentrations. The order of occurrence of the different compensating defects arises from the amphotericity, followed by enhanced screened Coulomb interactions, due to a reduced screening, driving the Si pair formation and thus governing the solubility limit of Si in GaAs [23]. Finally, only at very high dopant concentration Ga vacancies form due to the Fermi level effect, something occurring also in GaAs doped with non-amphoteric Te dopants [34].
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1164
(a1)
(b1)
(c1)
(d1)
(a2)
(b2)
(c2)
(d2)
Fig. 6. STM images of occupied (upper frames, measured at 2.0 to 2.2 V) and empty (lower frames, +1.4 to +1.5 V) density of states of the major bulk defects in cleavage surfaces of Si-doped as-grown GaAs. (a1) and (a2) show a SiGa donor, (b1) and (b2) a SiAs acceptor, (c1) and (c2) a SiGa–Ga-vacancy complex, and (d1) and (d2) the intersection line of a planar Si cluster. Adapted with permission from Domke et al. [23]. r 1996 American Physical Society.
Concentration (cm-3)
1020
7. Conclusions SiGa donor SiAs acceptor VGa-SiGa complex Si cluster total Si conc.
The selected examples illustrate that crosssectional scanning tunneling microscopy is a very successful tool for identifying the bulk point defects as well as dopant atoms and their concentration present in semiconductors. It even provides a three-dimensional mapping of dopants with atomic precision. This unique access to detailed microscopic data allows a direct derivation of the physics governing the incorporation of defects and dopant atoms, leading to an atomic level understanding of materials’ properties.
1019
1018
Acknowledgements 1018
1019
1020
Incorporated Si concentration (cm-3) Fig. 7. Si concentration present in SiGa donors, SiAs acceptors, Si clusters, and VGa–SiGa complexes as a function of the Si doping concentration incorporated into the crystals during growth (measured by SIMS). The sum of the Si concentrations of the different defects measured in the STM images ( ) agrees well with that measured by SIMS (solid line). The horizontal error bars originate from the SIMS measurements. They should be applied to all the respective data points. All vertical error bars show the reproducibility of the STM measurements. Adapted with permission from Domke et al. [23]. r 1996 American Physical Society.
The author thanks C. Domke, N. J.ager, F. Kluge, K. Urban, E.R. Weber, and Zhenyu Zhang, for fruitful cooperations and the Deutsche Forschungsgemeinschaft for financial support under Grant Eb 197/2-1.
References [1] R.M. Feenstra, et al., Phys. Rev. Lett. 71 (1993) 1176. [2] Ph. Ebert, K. Urban, Ultramicroscopy 49 (1993) 344. [3] M.B. Johnson, et al., Appl. Phys. Lett. 63 (1993) 2923.
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165 [4] J.F. Zheng, et al., Phys. Rev. Lett. 72 (1994) 1490. [5] Ph. Ebert, Surf. Sci. Rep. 33 (1999) 121; Ph. Ebert, Current Opinion in Sol. St. Mat. Sci. 5 (2001) 211. [6] R.M. Feenstra, et al., Phys. Rev. Lett. 58 (1987) 1192. [7] Ph. Ebert, et al., Phys. Rev. Lett. 77 (1996) 2997. [8] Ph. Ebert, et al., Phys. Rev. B 53 (1996) 4580. [9] M.B. Johnson, et al., Appl. Phys. Lett. 63 (1993) 3636. [10] G. Lengel, et al., Phys. Rev. Lett. 72 (1994) 836. [11] Ph. Ebert, et al., Phys. Rev. Lett. 72 (1994) 840. [12] Ph. Ebert, et al., Phys. Rev. Lett. 76 (1996) 2089. [13] K.J. Chao, et al., Phys. Rev. B 53 (1996) 6935. [14] Ph. Ebert, et al., Phys. Rev. Lett. 84 (2000) 5816. [15] Ph. Ebert, et al., Phys. Rev. B 51 (1995) 9696. [16] C. Domke, et al., J. Vac. Sci. Technol. B 16 (1998) 2825. [17] Ph. Ebert, et al., Phys. Rev. Lett. 83 (1999) 757. [18] T.L. Hill, Statistical Mechanics, McGraw-Hill, New York, 1956, p. 432. [19] R.B. Dingle, Phil. Mag. 46 (1955) 831. [20] N.D. J.ager, et al., Appl. Phys. Lett. 82 (2003) 2700.
[21] [22] [23] [24] [25]
[26] [27] [28]
[29] [30] [31] [32] [33] [34]
1165
N.D. J.ager, et al., Phys. Rev. B 67 (2003) 165307. N.D. J.ager, et al., Phys. Rev. B 65 (2002) 235302. C. Domke, et al., Phys. Rev. B 54 (1996) 10288. C. Domke, et al., Phys. Rev. B 57 (1998) 4482. J.M. Whelan, et al., in: Proceedings of the International Conference on Semiconductor Physics, Publishig House Czechoslovac Academy of Science, Prague, 1961, p. 943. C. Kolm, et al., Phys. Rev. 108 (1957) 965. S. Muto, et al., Phil. Mag. A 66 (1992) 257. J. Maguire, et al., Appl. Phys. Lett. 50 (1987) 516; J. Wagner, et al., Mat. Sci. Forum 38–41 (1989) 815; W.M. Theis, W.G. Spitzer, J. Appl. Phys. 56 (1984) 890. T.N. Theis, et al., Phys. Rev. Lett. 60 (1988) 361. C.K. The, et al., Can. J. Phys. 67 (1989) 375. J. Maguire, et al., J. Phys. C: Solid State Phys. 19 (1986) 1897. A.N. Morozov, V.T. Bublik, J. Crystal Growth 97 (1989) 475. S. Schuppler, et al., Appl. Phys. Lett. 63 (1993) 2357. J. Gebauer, et al., Appl. Phys. Lett. 82 (2003) 2059.
Physica B 340–342 (2003) 1159–1165
Incorporation of dopant atoms and defects in semiconductors: a microscopic view Ph. Ebert* Institut fur Forschungszentrum Julich GmbH, 52425 Julich, Germany . Festkorperforschung, . . .
Abstract We demonstrate that scanning tunneling microscopy is an ideal tool for the investigation of individual bulk defects and dopant atoms in semiconductors. This technique allows not only an atomically resolved imaging of individual defects and dopant atoms, but rather a detailed determination of their nanoscale electronic as well as structural properties and their concentrations. The capacities of scanning tunneling microscopy for defect investigations will be presented with help of selected examples. r 2003 Elsevier B.V. All rights reserved. Keywords: Dopant atoms; Point defects; Compensation; Scanning tunneling microscopy; InP; GaAs
1. Introduction Since the early stages of semiconductor technology, the importance of defects and dopant atoms became obvious. Therefore, considerable research efforts focused on the determination of the nanoscale physics governing the formation of point defects, the incorporation behavior of impurities, and their respective electronic properties. However, a direct access to point defects in semiconductors is a difficult task. Most conventional experimental techniques relied on the interpretation of macroscopic data of differently processed crystals or on signals integrating over a large set of usually unknown defects. Thus conclusions about individual defects on the atomic level were limited. In view of this situation the possibility to directly image with atomic resolution *Tel.: +49-2461-61-5023; fax: +49-2461-61-6444. E-mail address: [email protected] (P. Ebert).
individual bulk point defects and dopant atoms by cross-sectional scanning tunneling microscopy (STM) [1–4] is particularly intriguing. The aim of this paper is to illustrate the methodology by presenting the recent progress gained in the extraction of the physical mechanisms governing the incorporation behavior of defects and dopants.
2. Experimental approach Cross-sectional scanning tunneling microscopy is based on a rather simple concept. In order to take advantage of its atomic resolution, the bulk defects and dopant atoms as well as other structures of interest, e.g., interfaces, are exposed by cleavage on a cross-sectional surface (Fig. 1). On the cleavage surface the STM is then not only capable of directly imaging of the individual bulk point defects and dopant atoms with atomic resolution, but also able to identify them and
0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.10.005
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1160
tip of STM
VP-ZnIn
cleaved off
VP
defects and dopant atoms
ZnIn (110)
[001] (001)
substrate
(a)
5 nm
[110]
epitaxial layer
Fig. 1. Principle of cross-sectional scanning tunneling microscopy.
(b)
characterize their nanoscale electronic properties [5]. This technique works astonishigly well for almost all III–V and II–VI compound semiconductors, since most of them exhibit (i) a very good cleavage behavior, (ii) a 1 1 surface relaxation, and (iii) essentially no surface states in the band gap [5]. In the following we show selected examples of cross-sectional STM of defects and dopants in semiconductor substrates and spatially confined structures.
3. Imaging dopant atoms in semiconductors Fig. 2 shows a typical InP(1 1 0) cleavage surface as imaged by STM at negative voltages applied to the sample. First, one can observe the atomic rows along the ½1 1% 0 direction consisting of occupied dangling bonds localized above each anion. Thus the image essentially shows the phosphorus (P) sublattice. In contrast, at positive voltages the cation sublattice is visible [6,7]. Second, one can distinguish three types of defects/dopants by their contrast: (i) White elevations, which arise from the screened Coulomb potential around negatively charged ZnIn dopant atoms on In lattice sites [2–5,8,9]. (ii) Missing ‘atoms’ surrounded by dark
(c)
2nd layer Zn
_
[110]
(d)
surface cation surface anion surface Zn dopant atom
(e) Fig. 2. (a) STM image of a p-doped InP(1 1 0) surface. Six ZnIn dopant atoms in different subsurface layers, one P vacancy (VP), and one vacancy-dopant complex (VP–ZnIn) are visible. (b) to (d) Zn-dopant atoms (b) in the first, (c) second, and (d) third subsurface layer. The crosses in (b) to (d) mark the projected positions of the dopants, identifies using the altenating mirror plane of the dopant atom-induced contrast arising from the screened Coulomb potential around the ionized dopants. (e) Schematic drawing of the positions of the dopants atoms in the lattice. All images shows the occupied states. Adapted with permission from Ebert et al. [8]. r 1996 American Physical Society.
contrasts, arising from positively charged surface P monovacancies (VP) [5,10–14], formed after cleavage by Langmiur evaporation of anions [15]. They are thus not bulk defects. (iii) The vacancy
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1161
sublattice, on which the Zn dopant atoms reside, with respect to the surface P sublattice as illustrated in Fig. 2e. Thus Fig. 2b–d show dopant atoms in the surface first, second, and third subsurface layers. This allows a three-dimensional mapping of dopant atoms in semiconductors and on basis of observing directly individual dopant atoms.
formation leads to the third type of defect, an electrically compensated complex consisting of a surface vacancy and an adjacent Zn dopant atom [8,13]. Here we concentrate only on bulk defects and dopants, although a large number of investigations addressed surface defects [5]. The images of the dopant atoms differ at closer look in intensity and symmetry. High resolution STM images of the three most intensive dopant atom features (Fig. 2b–d) show distinct changes in symmetry characterized by a (½1 1% 0) mirror plane between and on top the atomic rows along the [0 0 1] direction. In order to understand this effect, one has to recall that in addition to the filled dangling bond states above the P atoms, the contrast of a dopant consists of a long range elevation arising from the imaging of the screened Coulomb potential [16], which is centered at the ionized dopant. Therefore, its center tells us where the Zn dopant atom is incorporated relative to the imaged P sublattice, while the intensity of the contrast decreases with increasing depth of the dopant atom. With decreasing intensity of the white contrast (i.e., increasing depth of the dopant), the (½1 1% 0) mirror plane and thus the dopant itself alternately is located between the atomic rows along the [0 0 1] direction (Fig. 2b and d) or on top of the atomic rows (Fig. 2c) (see crosses). This alternating geometry reflects with increasing subsurface depth the position of the In
4. Clustering of charged dopant atoms The atomically resolved mapping ability allows one to address dopant incorporation in nanometer-scale systems. The generally accepted view is that at such dimensions the repulsive screened Coulomb interaction between the charged dopants governs their incorporation. Such a repulsion in turn should lead to a rather homogeneous distribution of the dopant atoms in the semiconductor. This is, however, not the case: Fig. 3a shows a STM image of a cleaved 2.5 1020 cm3 Zn-doped GaAs crystal, where each individual Zn dopant atom appears as a bright contrast. From the dopant positions we calculated the local dopant concentration (Fig. 3b), which shows that the distribution of the dopants exhibits strong fluctuations leading to clusters of electrically active dopants with dimensions of about 10 nm [17].
10 nm (a)
(b)
Fig. 3. (a) STM image of a (1 1 0) cleavage surface of 2.5 10 cm3 Zn-doped GaAs acquired at 2:4 V. The white hillocks superposed onto the atomic-scale corrugation of the atomic rows along the ½1 1% 0 direction are Zn dopant atoms. (b) Local concentration of the dopants calculated from the measured position in (a). A high concentration is shown as white contrast. The images show a clustering of the dopant atoms. Adapted with permission from Ebert et al. [17]. r 1999 American Physical Society. 20
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1162
6 2.5·1018 cm-3 1.1·1019 cm-3
5
2.5·1020 cm-3
-ln [c(r)]
4 3
Screening length R S (nm)
At first sight, the clustering behavior seems to suggest the existence of a possible attractive interaction in addition to the screened Coulomb repulsion. However, a quantitative analysis of the dopant distributions proved different: The negative logarithm of the pair correlation function of the dopants (Fig. 4) is proportional to the so called mean force potential [18]. In case of low dopant concentration (i.e., the average distance between dopants is larger than the extend of the interaction potential), the mean force potential equals the repulsive screened Coulomb interaction between two charged dopants given by V ðrÞ ¼ e=ð4pe0 er Þ 1=r expðr=RS Þ [19]. On this basis we extracted from the data in Fig. 4 the screening length RS (open squares in inset of Fig. 4). As expected, the screening length increases with decreasing carrier concentration. However, the data does not agree quantitatively with the theoretical values (solid line) determined for a freeze-in temperature of 900 K [19]. However, when taking many-body effects in the otherwise repulsive interaction
5 4 3 2 1 18
19
20
10 10 10 Carrier concentration (cm-3)
2 1 0 -1
0
2
4
6
8
10
Distance r (nm) Fig. 4. Measured negative logarithm of the pair correlation function for three carrier concentrations. The arrows indicate attractive minima increasing in distance with decreasing carrier concentration. Inset: Values for screening lengths RS as a function of the carrier concentration (empty squares). The solid line represents the theoretical screening length calculated according to Ref. [19] for 900 K. The filled squares show the screening length corrected for many-body interactions. Adapted with permission from Ebert et al. [17]. r 1999 American Physical Society.
between the dopants into account, we obtained the screening length around an isolated dopant (filled squares) [17], which agrees well with the theoretical expectation. This shows that the present system can be well described by classical screening. The importance of many-body effects is found in a weak attractive part beyond a shortrange repulsive core (see arrows in Fig. 4 marking minima in ln[c(r)]), leading to the clustering of dopant atoms observed.
5. Dopant-induced dots and potential fluctuations The above results show that at the dimensions of 20–30 nm aimed for future transistors, the electrical potential distribution within the devices cannot be treated as continuous anymore. The potential is rather governed by individual, discrete ionized dopant atoms and by fluctuations in the dopant distribution. Fig. 5a demonstrates that a clustering of dopant atoms occurs also in nanostructures [20]. In this example, a GaAs p–n multilayer structure, one can see several p- and ndoped layers separated by a depletion zone giving rise to a dark line at the interface in the STM images [21]. This dark line is the electronic interface, which is very rough due to a clustering of dopant atoms [22]. This roughness creates in a nominally p-doped layer, sandwiched between two n-doped layers, several electronically decoupled clusters of dopant atoms labeled d2, d4, and d14 according to the number of dopant atoms within the cluster. These clusters are surrounded by confining potentials for free holes in the order of a few tenths of eV (border toward depleted zones with no dopants d0 ) to 1.4 eV (toward n-doped layer). Fig. 5b shows that each of these clusters of dopant atoms has drastically different current– voltage characteristics. This is due to the spatial confinement of the free charge carriers within the cluster, which reduces the ability to screen the electric field of the tip, because the charge carriers cannot be moved out of the cluster. Thus the band bending is larger compared to spatially nonconfined material and as consequence the current is lower [17]. The similarity of the tip-dot configuration with n–p–n transistors suggests that the
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1163
6. Dopant compensation by defects
p
d4 d0
d2
d0 d14
(a)
_ [110]
d0
[001]
10 nm
p
n
p
d0 d2 d4 d 14 p -layer
current (nA)
0.1
0.01
-3 (b)
n
-2
-1
1
2
3
sample voltage (V)
Fig. 5. (a) Atomically resolved scanning tunneling microscope images of a GaAs p–n structure. The bright hillocks in the pand n-doped layers are signatures of C and Si dopant atoms, respectively. The encircled areas d2 ; d4 ; and d14 are dopantinduced dots confined by potential barriers due to the doping of the surrounding areas (n-type and lack of dopants). The growth direction is [0 0 1]. (b) Current–voltage curves for the dopantinduced dots marked in (a). Adapted with permission from J.ager et al. [20]. r 2003 American Institute of Physics.
effects found here will also affect future miniaturized semiconductor devices, once they reach dimensions as small as the fluctuations of the dopant concentration [20].
The STM can also image a variety of bulk defects exposed by cleavage on the surface. This opens the way to address the compensation of dopants by defects as shown especially for Sidoped GaAs [23,24]. Si-doped GaAs exhibits a strong compensation, which has been attributed [25–33] to many different compensation mechanisms based of a zoo of defects. The STM investigations [23] performed on as-grown GaAs with Si concentrations ranging from 2.7 1018 (55% electr. inactive Si) to (2.56) 1019 cm3 (95% compensated Si), were able to clarify the compensation. With increasing Si concentration, the STM images revealed a strong increase of the concentration of various defects, showing that defects play a crucial role in the compensation. Fig. 6 shows the occupied states (arsenic sublattice, upper row) and empty states (Ga sublattice) of all bulk defects and dopant atoms observed by STM [23]. These are SiGa donors (frames (a1) and (a2)), SiAs acceptors (b1, b2), Si donor-Ga vacancy complexes (SiGa–VGa) (c1, c2), and planar Si clusters on (1 1 1) planes (d) [23]. Once these defects are identified, it is possible to directly extract the bulk concentrations of every type of defect separately, by counting of the individual dopant atoms and point defects located in a particular surface and/or subsurface layer (depth resolution see Fig. 2). Fig. 7 shows the obtained result: SiGa donors are consecutively compensated by SiAs acceptors, Si clusters, and SiGa–Ga-vacancy complexes at critical Si concentrations, something explaining the prior contradicting literature. Many of the proposed mechanisms contribute indeed, but dominate only in certain ranges of Si concentrations. The order of occurrence of the different compensating defects arises from the amphotericity, followed by enhanced screened Coulomb interactions, due to a reduced screening, driving the Si pair formation and thus governing the solubility limit of Si in GaAs [23]. Finally, only at very high dopant concentration Ga vacancies form due to the Fermi level effect, something occurring also in GaAs doped with non-amphoteric Te dopants [34].
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165
1164
(a1)
(b1)
(c1)
(d1)
(a2)
(b2)
(c2)
(d2)
Fig. 6. STM images of occupied (upper frames, measured at 2.0 to 2.2 V) and empty (lower frames, +1.4 to +1.5 V) density of states of the major bulk defects in cleavage surfaces of Si-doped as-grown GaAs. (a1) and (a2) show a SiGa donor, (b1) and (b2) a SiAs acceptor, (c1) and (c2) a SiGa–Ga-vacancy complex, and (d1) and (d2) the intersection line of a planar Si cluster. Adapted with permission from Domke et al. [23]. r 1996 American Physical Society.
Concentration (cm-3)
1020
7. Conclusions SiGa donor SiAs acceptor VGa-SiGa complex Si cluster total Si conc.
The selected examples illustrate that crosssectional scanning tunneling microscopy is a very successful tool for identifying the bulk point defects as well as dopant atoms and their concentration present in semiconductors. It even provides a three-dimensional mapping of dopants with atomic precision. This unique access to detailed microscopic data allows a direct derivation of the physics governing the incorporation of defects and dopant atoms, leading to an atomic level understanding of materials’ properties.
1019
1018
Acknowledgements 1018
1019
1020
Incorporated Si concentration (cm-3) Fig. 7. Si concentration present in SiGa donors, SiAs acceptors, Si clusters, and VGa–SiGa complexes as a function of the Si doping concentration incorporated into the crystals during growth (measured by SIMS). The sum of the Si concentrations of the different defects measured in the STM images ( ) agrees well with that measured by SIMS (solid line). The horizontal error bars originate from the SIMS measurements. They should be applied to all the respective data points. All vertical error bars show the reproducibility of the STM measurements. Adapted with permission from Domke et al. [23]. r 1996 American Physical Society.
The author thanks C. Domke, N. J.ager, F. Kluge, K. Urban, E.R. Weber, and Zhenyu Zhang, for fruitful cooperations and the Deutsche Forschungsgemeinschaft for financial support under Grant Eb 197/2-1.
References [1] R.M. Feenstra, et al., Phys. Rev. Lett. 71 (1993) 1176. [2] Ph. Ebert, K. Urban, Ultramicroscopy 49 (1993) 344. [3] M.B. Johnson, et al., Appl. Phys. Lett. 63 (1993) 2923.
ARTICLE IN PRESS P. Ebert / Physica B 340–342 (2003) 1159–1165 [4] J.F. Zheng, et al., Phys. Rev. Lett. 72 (1994) 1490. [5] Ph. Ebert, Surf. Sci. Rep. 33 (1999) 121; Ph. Ebert, Current Opinion in Sol. St. Mat. Sci. 5 (2001) 211. [6] R.M. Feenstra, et al., Phys. Rev. Lett. 58 (1987) 1192. [7] Ph. Ebert, et al., Phys. Rev. Lett. 77 (1996) 2997. [8] Ph. Ebert, et al., Phys. Rev. B 53 (1996) 4580. [9] M.B. Johnson, et al., Appl. Phys. Lett. 63 (1993) 3636. [10] G. Lengel, et al., Phys. Rev. Lett. 72 (1994) 836. [11] Ph. Ebert, et al., Phys. Rev. Lett. 72 (1994) 840. [12] Ph. Ebert, et al., Phys. Rev. Lett. 76 (1996) 2089. [13] K.J. Chao, et al., Phys. Rev. B 53 (1996) 6935. [14] Ph. Ebert, et al., Phys. Rev. Lett. 84 (2000) 5816. [15] Ph. Ebert, et al., Phys. Rev. B 51 (1995) 9696. [16] C. Domke, et al., J. Vac. Sci. Technol. B 16 (1998) 2825. [17] Ph. Ebert, et al., Phys. Rev. Lett. 83 (1999) 757. [18] T.L. Hill, Statistical Mechanics, McGraw-Hill, New York, 1956, p. 432. [19] R.B. Dingle, Phil. Mag. 46 (1955) 831. [20] N.D. J.ager, et al., Appl. Phys. Lett. 82 (2003) 2700.
[21] [22] [23] [24] [25]
[26] [27] [28]
[29] [30] [31] [32] [33] [34]
1165
N.D. J.ager, et al., Phys. Rev. B 67 (2003) 165307. N.D. J.ager, et al., Phys. Rev. B 65 (2002) 235302. C. Domke, et al., Phys. Rev. B 54 (1996) 10288. C. Domke, et al., Phys. Rev. B 57 (1998) 4482. J.M. Whelan, et al., in: Proceedings of the International Conference on Semiconductor Physics, Publishig House Czechoslovac Academy of Science, Prague, 1961, p. 943. C. Kolm, et al., Phys. Rev. 108 (1957) 965. S. Muto, et al., Phil. Mag. A 66 (1992) 257. J. Maguire, et al., Appl. Phys. Lett. 50 (1987) 516; J. Wagner, et al., Mat. Sci. Forum 38–41 (1989) 815; W.M. Theis, W.G. Spitzer, J. Appl. Phys. 56 (1984) 890. T.N. Theis, et al., Phys. Rev. Lett. 60 (1988) 361. C.K. The, et al., Can. J. Phys. 67 (1989) 375. J. Maguire, et al., J. Phys. C: Solid State Phys. 19 (1986) 1897. A.N. Morozov, V.T. Bublik, J. Crystal Growth 97 (1989) 475. S. Schuppler, et al., Appl. Phys. Lett. 63 (1993) 2357. J. Gebauer, et al., Appl. Phys. Lett. 82 (2003) 2059.