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Electronic properties of single Ge/Si quantum dot grown by ion beam sputtering deposition
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Nanotechnology Nanotechnology 26 (2015) 105201 (9pp)
doi:10.1088/0957-4484/26/10/105201
Electronic properties of single Ge/Si quantum dot grown by ion beam sputtering deposition C Wang1,2, S Y Ke3, J Yang3,4, W D Hu2, F Qiu3, R F Wang3 and Y Yang1,3 1
Institute of Optoelectronic Information Materials, Yunnan University, Kunming 650091, People’s Republic of China 2 National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Science, Shanghai 200083, People’s Republic of China 3 Yunnan Key Laboratory for Micro/Nano Materials and Technology, Yunnan University, Kunming 650091, People’s Republic of China 4 State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, People’s Republic of China E-mail: [email protected] and [email protected] Received 18 November 2014, revised 21 January 2015 Accepted for publication 22 January 2015 Published 20 February 2015 Abstract
The dependence of the electronic properties of a single Ge/Si quantum dot (QD) grown by the ion-beam sputtering deposition technique on growth temperature and QD diameter is investigated by conductive atomic force microscopy (CAFM). The Si–Ge intermixing effect is demonstrated to be important for the current distribution of single QDs. The current staircase induced by the Coulomb blockade effect is observed at higher growth temperatures (>700 °C) due to the formation of an additional barrier between dislocated QDs and Si substrate for the resonant tunneling of holes. According to the proposed single-hole-tunneling model, the fact that the intermixing effect is observed to increase as the incoherent QD size decreases may explain the increase in the starting voltage of the current staircase and the decrease in the current step width. Keywords: Ge/Si single quantum dot, conductive atomic force microscopy, resonant tunneling, Coulomb blockade effect (Some figures may appear in colour only in the online journal) 1. Introduction
QDs have the natural advantage that they are able to be compatible with modern Si-based readout integrated circuits (ROICs). As a result, over the last two decades the morphology evolution and photoelectric characteristics of Ge/Si QDs have become research hotspots in the domain of condensed-matter physics and material science. The electronic properties of Ge QDs have been extensively investigated by several techniques, such as Fourier transform infrared spectroscopy, capacitance spectroscopy, deep level transient spectroscopy, and admittance spectroscopy [9–11]. However, using these traditional techniques, the electronic properties of Ge QDs are obtained by detecting several QDs in a certain area, which is a difficult way to get information about a single
Due to the confinement of carriers in three dimensions, semiconductor quantum dots (QDs) are endowed with many interesting physical properties, such as the quantum size effect, the phonon bottleneck effect, the quantum tunneling effect, the Coulomb blockade effect, and the quantum hall effect—properties that have made QDs the most promising of all candidates for developing novel electronic and optoelectronic devices [1–5]. At the same time, the carrier capture time in QDs is much shorter than that in general quantum wells and defects [6–8]. This special feature is widely applied in the field of high-speed electronic devices. Furthermore, compared with group III-V and II-VI compound QDs, Ge/Si 0957-4484/15/105201+09$33.00
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2. Experiments
quantum dot (SQD) in an array. Fortunately, atomic force microscopy (AFM) and its derived technique called conductive atomic force microscopy (CAFM) are powerful tools for studying the microstructure and located electronic characteristics of nano-materials by using their conductive tiny pinpoint and capability for high atomic resolution on the nanometer scale [12–19]. Recently a great many CAFM investigations have focused on surface characteristics and their effects on the current distribution of Ge QDs grown by molecular beam epitaxy (MBE). R Hu et al have investigated the conductive properties of Ge QDs using the CAFM technique. The results of their investigation have indicated that the electronic features of Ge QDs strongly depend on the thickness of the native Ge oxide layer [16]. S L Zhang et al have studied the topography and conductance distribution of individual Ge QDs capped by a thin Si layer. The current distributions of SQDs are observed to be extremely affected by morphology evolution during the Si capping process. This phenomenon is attributed to composition distribution and geometric factors [17]. Furthermore, F Xue et al have obtained the distribution of the lateral composition in Ge QDs by using the CAFM technique. Their results indicate that Ge QDs grown at a higher growth temperature exhibit Si–Ge intermixing behavior; this results in a significant difference in the local conductance distribution of Ge QDs grown at different temperatures [18]. However, the Si–Ge intermixing behavior and its effect on the shape evolution of two-dimensional (2D) current distribution with growth temperature are not yet identified clearly. In addition, little work has been done concerning the I-V characteristic of a single Ge QD, especially the typical current staircase in the I-V curve. At the same time, compared with MBE and chemical vapor deposition (CVD), which are both relatively mature techniques for fabricating semiconductor QDs, ion-beam sputtering deposition (IBSD) has been rarely used due to its relatively drastic growth behavior, which was once considered unsuitable for fabricating sophisticated nanostructures. Moreover, it was proposed in the previous works that the kinetic and thermodynamic behaviors involved in ion-beam QD growth are different from those in the MBE and CVD growth processes [20– 23]. So it should be of interest to study the electronic properties of Ge/Si QDs grown with the IBSD technique, what with such advantages as low cost, easy operation, and large-scale industrialization. In this article, the morphological and electronic properties of Ge/Si QDs grown at different temperatures are investigated by using the CAFM technique at room temperature. The current staircases of Ge SQDs in the samples grown at higher temperatures are observed due to the formation of an additional barrier induced by misfit dislocation. We also study the effect of base diameter and the Si–Ge intermixing effect on the I-V characteristic of Ge SQDs. A single-hole-tunneling model is proposed to interpret the different current staircases in those samples.
All samples were grown on p-Si (100) substrates with a resistivity of ∼10 Ω · cm by using the IBSD technique. Before the growth process, the substrates were chemically cleaned using modified shiraki procedures before being loaded into the vacuum chamber. The background and Ar ion bombardment pressures were set at 1 × 10−6 and 2.0 × 10−4 Torr, respectively. An ion energy of 1.0 keV and a current of 9 mA were used to sputter the target. After thermal flashing at 700 °C, a 50 nm-thick Si buffer layer and a subsequent 14.2 monolayer (ML)–Ge QD layer were grown on the Si substrates at 650, 700, and 750 °C; and the three samples were named A, B, and C, respectively. The deposition rate of the Ge layer was 6.0 ML min−1. The morphologies, current distribution images, and I-V curves of Ge QDs were detected by using a scanning probe microscope (Japan Seiko SPA-400 SPM) at atmosphere and room temperature. The ambient humidity was 40–50%. The surface morphologies of all the samples were measured by AFM in tapping mode, whereas the current distributions and I-V characteristic curves were obtained by CAFM with synchronous measurement in contact mode. The tip and reflector were coated with platinum metal, and Ag was used as the bottom electrode. Raman scattering spectra were obtained by employing a Renishaw inVia Raman microscope equipped with an excitation laser operating at 514.5 nm in back-scattering geometry at room temperature.
3. Results and discussion The surface morphologies and current distributions of the three QD samples grown at different temperatures are shown in figures 1(a)–(f), respectively. It can be observed that almost all of the Ge QDs in the three samples exhibit a dome shape, and only a small part of the QDs in sample C show a pyramid shape. When the growth temperature is increased from 650 to 750 °C, the QD density increases from 3.8 × 109 to 7.1 × 109 cm−2, and the QD distribution on a (100) surface and QD size uniformity are also improved. Moreover, the QD diameter (D) and height (H) show a downward trend. This is a special feature that occurs during the process of ion-beam growth of the Ge QDs. To further illuminate the evolution details of the Ge QDs relative to growth temperature, the parameters of the deposited Ge QDs are obtained by means of a line-scan profile and a statistical histogram, as listed in table 1. The peak values of normal distributions of the QD diameters are 70, 55, and 45 nm; and those of the heights are 12, 9, and 7 nm, respectively, for the three samples. We believe that this kind of QD evolution according to growth temperature can be attributed to some natural characteristics of the IBSD technique. During the sputtering process, the ion-beam energy and the Ar plasma density are relatively high. This generally leads to high kinetic energy of sputtering atoms on the substrate surface. Therefore, the diffusion of Ge atoms and the nucleation of Ge QDs are 2
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Figure 1. (a)–(c) Morphology images and (d)–(f) current distributions of samples A, B, and C measured by the tapping and contact modes of AFM, respectively. The red circles show the detected SQD in each sample. Table 1. Statistical Ge QD parameters in samples A, B, and C.
Sample
Density (cm−2)
Distribution range of D (nm)
Peak value of the D normal distribution (nm)
Distribution range of H (nm)
Peak value of the H normal distribution (nm)
A B C
3.8 × 109 5.4 × 109 7.1 × 109
45–90 40–70 25–65
∼70 ∼55 ∼45
8–15 6–11 4–9
∼12 ∼9 ∼7
modulated not only by the thermodynamic but also by the surface kinetic mechanism. It was demonstrated recently that ion-beam energy plays an important role in QD evolution [23]. When the Ar ion energy is lower than 0.6 keV, the QD size increases and the QD density decreases with the increase in the growth temperature. However, the opposite trends occur when the Ar ion energy is larger than ∼1.0 keV, and similar behavior seems to be repeated in this work. It was suggested that the higher Ar ion energy induces a mechanism of supersaturation-driven nucleation. The decomposition of a super-strained wetting layer was demonstrated to enhance the QD nucleation rate effectively at high growth temperatures. On the other hand, according to the thermodynamic theories [24], if the surface energy decreases during QD formation, the energy per atom is of a minimum value versus size, and the lowest energy state for a QD array may be a uniform ensemble at this size. Thus, rising growth temperatures generally drive QD distributions toward smaller sizes, with an increase in entropy S. This can be attributed to the fact that there are more possible arrangements of atoms into smaller QDs than into larger ones. Figure 2 shows the Raman spectra of the three samples. A broadening wave packet with its center at ∼480 cm−1 is
Figure 2. Raman spectra of samples A, B, and C at room
temperature.
observed in sample A. This is attributed to the amorphous Si– Si (a-Si–Si) vibration mode of the Si buffer layer [21, 25]. It was concluded in our previous work [20, 21] that a Si buffer layer grown at a low temperature exhibits a mixed-phase 3
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structure (so-called microcrystalline Si), which includes a-Si and crystalline Si (c-Si); Ge QDs can be formed on the c-Si due to relaxation of the strain of lattice mismatch. Furthermore, the Ge–Ge vibration mode of the QDs in sample A is located at ∼295 cm−1, and the standard amorphous Ge–Ge wave packet (∼270 cm−1 [20, 25]) seems not to be observed in figure 2. This indicates that Ge QDs already crystallize at 650 °C. With the increase in growth temperature, the a-Si–Si peak disappears and the full width at half maximum (FWHM) of the Ge–Ge peak decreases, accompanied by a blueshift from 295 to 299 cm−1. These suggest that the crystal quality of the Si buffer layer and Ge QDs is improved. It is worth noting that an obvious vibration mode located at ∼386 cm−1 is observed in both samples B and C. As reported elsewhere [22, 26, 27], the peak located at ∼390 cm−1 was identified to be the Si–Ge vibration mode of SiGe-alloy QDs, and its peak position may be slightly modulated by residual strain and the Ge content in the QDs [28, 29]. Thus, this obvious peak with its center at 386 cm−1 can be attributed to the Si–Ge vibration mode of SiGe-alloy QDs. This observation of a Si–Ge peak results from the Si–Ge intermixing induced by the uphill diffusion of Si atoms into Ge QDs at higher growth temperatures. Based on the foregoing analysis, it is suggested that the interdiffusion between the Ge and Si atoms occurring at the interface of the two textures becomes significant after the growth temperature is increased. Unexpectedly, this intermixing behavior can also be demonstrated by the current distribution, as shown in figures 1(d)–(f). Overall, the current distribution of the Ge QDs in the 650 °C-grown sample (sample A) is homogeneous. The measured results indicate that the maximum current value is −114 nA, which is obtained in the region of the QDs. However, the current distributions of almost all the Ge QDs in sample B exhibit an annular shape, and that of some QDs with smaller sizes in sample C show a disklike shape; this is an interesting phenomenon. As is known, the conductivity of a Si atom is smaller than that of a Ge atom. Therefore, the current values at the region where the Si atoms aggregate are lower and the color is brighter, whereas the opposite behaviors occur in the region where the Ge atoms aggregate. This implies that the Si–Ge intermixing effect at higher growth temperatures may be responsible for these annular and disklike current distributions. Since the diffusion behavior of Ge atoms can be activated even at lower growth temperatures, it is important for Si atoms that the diffusion lengths increase as the growth temperature increases [30]. In those samples grown at lower temperatures (i.e., sample A), the Si–Ge interdiffusion behavior reflected in the current distribution image is not obvious, which is in good agreement with the Raman spectra. In sample B, the bright region in the current distribution image tends to be located in the middle of the Ge QDs. This indicates that the Si atoms are inclined to accumulate at the center of the QDs. However, in sample C, the lower current region is not only at the center but extends to almost all the QDs, which present a disklike current distribution. This implies that Si–Ge intermixing becomes stronger in QDs grown at 750 °C.
Figure 3. I-V curves of the Ge SQDs ∼60 nm in diameter and ∼6 nm
in height in the three samples detected at room temperature.
A reasonable explanation for the different shapes of current distributions is as follows. The interface of the Ge QDs and the Si buffer layer undergoes the maximum stress amplitudes. Thus, the Si–Ge alloying occurs in the QD region as a result of the largest amount stress relaxation. Since Ge atoms are continually deposited during the QD growth process, the intermixing region near the edge of the QDs is continually buried by newly arriving Ge atoms as the QD diameter increases [31]. Thus, the Si atoms aggregate at the center region at 700 °C, leading to the appearance of annular current distributions of QDs. With the increase in the growth temperature, the Si atoms become more active, which may trigger more intensive uphill diffusion. The buried rate of Si atoms is slower than the Si–Ge alloying rate at 750 °C. Hence, disklike current distributions form in the QD region of sample C. Figure 3 shows the detected I-V curves of the SQDs selected from the three samples and marked by the red circles in the current distribution images of figure 1. The three selected SQDs share similar diameters of ∼60 nm and heights of ∼6 nm. In contrast with samples B and C, the current staircase, which is one of the typical properties of semiconductor QDs induced by the Coulomb blockade effect, is not observed in sample A. The current increases monotonously as the bias voltage increases until the saturation value (100 nA) of the measurement system is achieved. It is well known that the current staircase can be attributed to the resonant tunneling of carriers. The step number is generally related to the number of the confined energy level for resonant tunneling. For better understanding of the origin of the tunneling behavior, the diagrams of the CAFM test system and the equivalent circuit are mapped in figures 4(a) and (b), respectively. R1 and C1 are the resistance and capacitance, respectively, of the tip/QD interface, and R2 and C2 are those of the QD/Si interface. The gray circle in figure 4(b) represents the contact point of the tip and the SQD. Before ex situ examination, a thin native GeO2 layer (barrier) has already existed on the surface of the Ge QDs. In addition, H C Chung et al showed that the misfit dislocation generally produces a 4
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Figure 4. Schematic diagrams of (a) the CAFM test system, (b) the equivalent circuit, and the single-hole-tunneling model (c) in the thermal equilibrium state and (d) with reverse bias.
interface. Compared with that at low-temperature growth, a high growth temperature induces a significantly high nucleation rate for these loops. Thus, at higher growth temperatures, under the lattice strain between Ge and Si, the formation of misfit dislocations under Ge QDs becomes easier [33]. This mechanism for misfit dislocation growth may explain our results. The Ge QDs in sample A are dislocationfree due to the lower temperature growth; they are also named coherent QDs generally. Hence, the disorder layer is absent between the coherent Ge QDs and the Si buffer layer. The holes can first be captured by the Ge well, and then they tunnel through the GeO2 barrier under forward bias voltage. Consequently, the current staircase cannot be observed in sample A. When the growth temperature increases to 700 or even 750 °C, misfit dislocations form at the interface of the QDs and the Si layer, at which point the QDs in samples B and C become incoherent ones. The disorder layer formed at the interface leads to the formation of another additional barrier for the holes. Thus, the holes can achieve a resonant tunneling through the double valence-band barriers under forward bias voltage. This results in the appearance of the current staircase in samples B and C. However, under reverse bias voltage, as shown in figure 4(d), the EF of the Pt metal deviates from the conduction band. The holes cannot be transported on the
disorder layer between the Ge QDs and the Si buffer layer, which acts as a tunneling barrier [4]. Therefore, a doublebarrier tunneling system can be formed during the electronic measurement of the dislocated QDs. Under reverse bias voltage, the electrons in the Si buffer layer can easily achieve resonant tunneling and be captured by the Pt electrode, which induces the appearance of the current staircase in the I-V curve [4]. However, current staircases under reverse bias voltage in this work are not observed in all of our three samples. It suggests that the model of electron resonant tunneling through the double conductionband barriers is unsuitable for clarifying these staircase behaviors. Based on the special feature of the I-V curve and the foregoing analysis, a single-hole-tunneling model is proposed to interpret the current staircase. The energy band diagram of this model is mapped in figure 4(c). During the QD growth process, the energy provided by the heater system is enough generally to nucleate partial half dislocation loops [32]. The further growth of most loops is restrained by the dislocation line tension, whereas a small part of the loops can overcome the energy barrier either by being pinned or by fluctuations in local stresses, and then they undergo a spontaneous growth process. When the size of the loop reaches a critical value, the loop front extends to the island/buffer–layer interface and then forms a misfit dislocation along the 5
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Figure 5. (a)–(d) Morphology images, (e)–(g) current distributions, and (i)–(l) I-V curves of the SQDs selected from sample C with heights of ∼6 nm and diameters of ∼60 (first line), ∼50 (second line), ∼40 (third line), and ∼30 nm (fourth line), respectively.
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the starting voltage V0 for the first current step increases, whereas the ΔV value decreases with the decrease in the QD diameter.
Table 2. Electronic parameters of QDs of different diameters selected
from sample C. D/nm
V0/V
ΔV/V
∼60 ∼50 ∼40 ∼30
∼3.5 ∼5.2 ∼7.6 ∼8.7
∼3.4 ∼2.0 ∼1.5 ∼0.9
RT/kΩ
Caq/F 3
3.4 × 10 2.0 × 103 1.5 × 103 9.0 × 102
EC/J −19
9.4 × 10 1.6 × 10−18 2.1 × 10−18 3.6 × 10−18
1.4 × 10−20 8.0 × 10−21 6.0 × 10−21 3.6 × 10−21
E lkn =
π 2ℏ2 ⎛⎜ l 2 k2 n2 ⎞⎟ π 2ℏ2 ⎛⎜ 2l 2 n2 ⎞⎟ + + = + ⎟ (1) ⎟ 2 2m* ⎜⎝ d x2 2m* ⎜⎝ d xy d y2 d z2 ⎠ d z2 ⎠
According to the single-hole-tunneling model proposed in figure 4, the confined state energies in the QD potential well can be obtained by solving equation (1). As previously mentioned, Si–Ge intermixing increases as the QD diameter decreases; that is, the intermixing in a QD 60 nm in diameter is not so obvious compared with that in a QD of smaller diameter, so the Si–Ge intermixing effect is ignored tentatively in the calculation of confined energy levels in a domeshaped QD 6 nm in height and 60 nm in diameter to interpret the current-jump phenomenon in I-V curves under forward bias voltage. The effective mass of light and heavy holes (mhh* and mlh*) is taken as 0.044 and 0.28m0 [37], respectively. The valence band diagram of the double-barrier system without bias voltage is shown in figure 6(a). The EF of all the layers is equal at thermal equilibrium state. According to the calculation based on equation (1), two quantum states confined in the SQD potential well, the fourth heavy-hole energy level and the second light-hole one with energies of 583 and 928 meV, located between the valence bands of the Si and the disorder layer, are labeled Ehh4 and Elh2, respectively, in this diagram. Under forward bias voltage, as shown in figure 6(b), the energy band of the total system is tilted. Relative to the valence band of Ge QDs, the Si valence band undergoes a downward shift with the increase in bias voltage due to the increasing energy difference (ΔE) in the two edges of the barrier of the disorder layer after the tilt of the energy band. When the forward bias voltage is increased to V0, the Si valence band descends to the level of the Ehh4 state, and the first resonant tunneling of holes occurs. Due to the Coulomb blockage effect, holes can tunnel through the SQD one by one only. Thus, the hole current is changeless until the bias voltage is increased to V1 to further push the Si valence band to be in parallel with the Elh2 level to open the second tunneling pathway for holes. As mentioned, the V0 value increases whereas the ΔV value decreases with the decrease in QD diameter. This interesting behavior can probably be understood in terms of the Si–Ge intermixing occurring in the QDs. With the Si–Ge intermixing, the Ge QDs evolve into Si1−xGex-alloy QDs gradually. The band gap of the Si1−xGex QDs increases with the increase in Si content. Due to the small conduction-band offset at the Ge/Si interface, the valence band of the QDs undertakes most of the band-gap increment. As a result, the valence-band offset at the Ge/Si interface decreases with the decrease in QD size. This leads to an increase in the V0 value. At the same time, the effective mass can be obtained by the method of linear interpolation as expressed in the following. (The stress is not taken into account because the residual stress accumulated in the dislocated QDs can be neglected
valence band to form the hole current due to the fact that the Pt metal cannot emit holes, and the holes in the Si layer move toward the Ag/Si electrode. As a result, the current characteristic under reverse bias voltage can be explained only by the single-barrier electron-tunneling model. As observed in figure 4(d), due to the lower conduction-band offset between the Si and the disorder layer, the electrons in the conduction band of Si can overcome the barrier of the disorder layer and then tunnel through the GeO2 single barrier easily; the resonant tunneling behavior of the electrons cannot be triggered. Thus, the staircase phenomenon does not appear under reverse bias. As we all know, QD size is one of the major factors that affect the properties of photoelectric devices. To clarify the diameter dependence of the electronic characteristics, four SQDs with heights of ∼6 nm and diameters of ∼60, ∼50, ∼40, and ∼30 nm were selected from sample C for the electronic measurement. The morphologies, current distributions, and I-V curves of these four SQDs are shown in figure 5. The bright area in the current distribution image of the QD region increases as the QD diameter decreases, indicating that the Si–Ge interdiffusion becomes stronger as the QD diameter decreases. A similar phenomenon can be observed in reference [34], in which the Ge content in QDs of larger sizes is larger than that in QDs of small sizes. Results of the investigation of tree-ring structures below dislocated SiGe QDs performed by T Merdzhanova et al may explain this phenomenon [35]. When the QD growth temperature is higher than 740 °C, the Ge content in those incoherent (dislocated) SiGe QDs increases with the increase in the QD base area due to the introduction of misfit dislocations rather than serious Si–Ge intermixing. Therefore, as to our results, the formation of dislocated SiGe QDs at 750 °C may be responsible for the intermixing evolution commensurate with the QD diameter. In a double-tunnel structure [36], the Coulomb capacity Caq and the tunneling junction resistance RT of a QD can be expressed as Caq = C1 + C2 = 2e(ΔV)−1 and RT = e · (ΔI · Caq)−1, respectively, where ΔV is the difference between the two adjacent starting voltages for the current jump and ΔI is the current difference between two adjacent current steps. Based on the two equations, some electronic parameters of these SQDs are calculated and listed in table 2. The resistance RT of all four SQDs is larger than the quantum resistance RQ of 25.8 kΩ, and the charging energies EC are higher than the thermal energy at room temperature (∼26 meV). These are the two basic conditions for producing the Coulomb blockade effect in QDs. Thus, the current staircase can be observed in the I-V curves of all four SQDs. It is interesting to note that 7
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Figure 6. Energy band diagrams of SiGe alloy QDs (a) in the thermal equilibrium state and (b) with forward bias voltage.
Acknowledgments
after relaxation.) ⁎ m hh = 0.53−0.25x
(2)
m lh⁎ = 0.16−0.116x
(3)
This work was financially supported by the National Science Foundation of China (No. 11274266), the Open Project launched by the National Laboratory for Infrared Physics (No. M201405), the Key Project of the Applied Basic Research Project of Yunnan Province of China (No. 2013FA029), and the Introducing Talent Project launched by the government of Yunnan Province.
According to equations (2) and (3), mhh* and mlh* increase with the decrease in the Ge content in Si1−xGex-alloy QDs. Consequently, using relation (1), it can be concluded that both Ehh4 and Elh2 increase with the decrease in Ge content in SiGe QDs, whereas the rate of increase of Ehh4 is larger than that of Elh2; in other words, the energy level difference (ΔEL) between Ehh4 and Elh2 decreases gradually. This is probably what is responsible for the decrease in the current step width ΔV observed in figure 5.
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4. Conclusions Three Ge/Si quantum dot samples as well as their own Si buffer layer were grown at different temperatures by using the ion-beam sputtering technique. The surface morphologies and the electronic properties were studied by the tapping and contact models of AFM, respectively. The current distribution with different shapes was demonstrated to be dominated by Si–Ge intermixing in QDs—actually, in accordance with the growth temperature. Current staircases were observed in those incoherent QDs instead of in the coherent QDs. The disorder layer induced by the dislocation acts as a thin and high potential barrier which results in the resonant tunneling of holes and the appearance of the Coulomb staircase. The enhancement of intermixing with the decrease in QD sizes was demonstrated to be responsible for the increase in starting voltage of the staircase and the decrease in the current step width. We believe that our results are helpful for fabricating sophisticated electronic and optoelectronic devices based on group IV semiconductor quantum dots. 8
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[18] Xue F, Qin J, Cui J, Fan Y L, Jiang Z M and Yang X J 2005 Surf. Sci. 592 65 [19] Vicaro K O, Cotta M A, Gutierrez H R and Bortoleto J R R 2003 Nanotechnology 14 509 [20] Ke S Y, Ye S, Yang J, Wang Z Q, Wang C and Yang Y 2014 Appl. Surf. Sci. 328 387 [21] Yang J, Wang C, Tao D P and Yang Y 2012 Mater. Tech. 27 133 [22] Yang J, Jin Y X, Wang C, Li L, Tao D P and Yang Y 2012 Appl. Surf. Sci. 258 3637 [23] Chung H C, Liu C P and Lai Y L 2008 Appl. Phys A 91 267 [24] Wagner R J and Gulari E 2005 Surf. Sci. 590 8 [25] Olivares J, Martın P, Rodrıguez A, Sangrador J, Jimenez J and Rodrıguez T 2000 Thin Solid Films 358 56 [26] Valakh M Y, Lytvyn P M, Nikolenko A S, Strelchuk V V, Krasilnik Z F, Lobanov D N and Novikov A V 2010 Appl. Phys. Lett. 96 141909 [27] Singha R K, Das S, Majumdar S, Das K, Dhar A and Ray S K 2008 J. Appl. Phys. 103 114301 [28] Valakh M Y, Lytvyn P M, Nikolenko A S, Strelchuk V V, Krasilnik Z F, Lobanov D N and Novikov A V 2010 Appl. Phys. Lett. 96 141909
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Electronic properties of single Ge/Si quantum dot grown by ion beam sputtering deposition
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Nanotechnology Nanotechnology 26 (2015) 105201 (9pp)
doi:10.1088/0957-4484/26/10/105201
Electronic properties of single Ge/Si quantum dot grown by ion beam sputtering deposition C Wang1,2, S Y Ke3, J Yang3,4, W D Hu2, F Qiu3, R F Wang3 and Y Yang1,3 1
Institute of Optoelectronic Information Materials, Yunnan University, Kunming 650091, People’s Republic of China 2 National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Science, Shanghai 200083, People’s Republic of China 3 Yunnan Key Laboratory for Micro/Nano Materials and Technology, Yunnan University, Kunming 650091, People’s Republic of China 4 State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, People’s Republic of China E-mail: [email protected] and [email protected] Received 18 November 2014, revised 21 January 2015 Accepted for publication 22 January 2015 Published 20 February 2015 Abstract
The dependence of the electronic properties of a single Ge/Si quantum dot (QD) grown by the ion-beam sputtering deposition technique on growth temperature and QD diameter is investigated by conductive atomic force microscopy (CAFM). The Si–Ge intermixing effect is demonstrated to be important for the current distribution of single QDs. The current staircase induced by the Coulomb blockade effect is observed at higher growth temperatures (>700 °C) due to the formation of an additional barrier between dislocated QDs and Si substrate for the resonant tunneling of holes. According to the proposed single-hole-tunneling model, the fact that the intermixing effect is observed to increase as the incoherent QD size decreases may explain the increase in the starting voltage of the current staircase and the decrease in the current step width. Keywords: Ge/Si single quantum dot, conductive atomic force microscopy, resonant tunneling, Coulomb blockade effect (Some figures may appear in colour only in the online journal) 1. Introduction
QDs have the natural advantage that they are able to be compatible with modern Si-based readout integrated circuits (ROICs). As a result, over the last two decades the morphology evolution and photoelectric characteristics of Ge/Si QDs have become research hotspots in the domain of condensed-matter physics and material science. The electronic properties of Ge QDs have been extensively investigated by several techniques, such as Fourier transform infrared spectroscopy, capacitance spectroscopy, deep level transient spectroscopy, and admittance spectroscopy [9–11]. However, using these traditional techniques, the electronic properties of Ge QDs are obtained by detecting several QDs in a certain area, which is a difficult way to get information about a single
Due to the confinement of carriers in three dimensions, semiconductor quantum dots (QDs) are endowed with many interesting physical properties, such as the quantum size effect, the phonon bottleneck effect, the quantum tunneling effect, the Coulomb blockade effect, and the quantum hall effect—properties that have made QDs the most promising of all candidates for developing novel electronic and optoelectronic devices [1–5]. At the same time, the carrier capture time in QDs is much shorter than that in general quantum wells and defects [6–8]. This special feature is widely applied in the field of high-speed electronic devices. Furthermore, compared with group III-V and II-VI compound QDs, Ge/Si 0957-4484/15/105201+09$33.00
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2. Experiments
quantum dot (SQD) in an array. Fortunately, atomic force microscopy (AFM) and its derived technique called conductive atomic force microscopy (CAFM) are powerful tools for studying the microstructure and located electronic characteristics of nano-materials by using their conductive tiny pinpoint and capability for high atomic resolution on the nanometer scale [12–19]. Recently a great many CAFM investigations have focused on surface characteristics and their effects on the current distribution of Ge QDs grown by molecular beam epitaxy (MBE). R Hu et al have investigated the conductive properties of Ge QDs using the CAFM technique. The results of their investigation have indicated that the electronic features of Ge QDs strongly depend on the thickness of the native Ge oxide layer [16]. S L Zhang et al have studied the topography and conductance distribution of individual Ge QDs capped by a thin Si layer. The current distributions of SQDs are observed to be extremely affected by morphology evolution during the Si capping process. This phenomenon is attributed to composition distribution and geometric factors [17]. Furthermore, F Xue et al have obtained the distribution of the lateral composition in Ge QDs by using the CAFM technique. Their results indicate that Ge QDs grown at a higher growth temperature exhibit Si–Ge intermixing behavior; this results in a significant difference in the local conductance distribution of Ge QDs grown at different temperatures [18]. However, the Si–Ge intermixing behavior and its effect on the shape evolution of two-dimensional (2D) current distribution with growth temperature are not yet identified clearly. In addition, little work has been done concerning the I-V characteristic of a single Ge QD, especially the typical current staircase in the I-V curve. At the same time, compared with MBE and chemical vapor deposition (CVD), which are both relatively mature techniques for fabricating semiconductor QDs, ion-beam sputtering deposition (IBSD) has been rarely used due to its relatively drastic growth behavior, which was once considered unsuitable for fabricating sophisticated nanostructures. Moreover, it was proposed in the previous works that the kinetic and thermodynamic behaviors involved in ion-beam QD growth are different from those in the MBE and CVD growth processes [20– 23]. So it should be of interest to study the electronic properties of Ge/Si QDs grown with the IBSD technique, what with such advantages as low cost, easy operation, and large-scale industrialization. In this article, the morphological and electronic properties of Ge/Si QDs grown at different temperatures are investigated by using the CAFM technique at room temperature. The current staircases of Ge SQDs in the samples grown at higher temperatures are observed due to the formation of an additional barrier induced by misfit dislocation. We also study the effect of base diameter and the Si–Ge intermixing effect on the I-V characteristic of Ge SQDs. A single-hole-tunneling model is proposed to interpret the different current staircases in those samples.
All samples were grown on p-Si (100) substrates with a resistivity of ∼10 Ω · cm by using the IBSD technique. Before the growth process, the substrates were chemically cleaned using modified shiraki procedures before being loaded into the vacuum chamber. The background and Ar ion bombardment pressures were set at 1 × 10−6 and 2.0 × 10−4 Torr, respectively. An ion energy of 1.0 keV and a current of 9 mA were used to sputter the target. After thermal flashing at 700 °C, a 50 nm-thick Si buffer layer and a subsequent 14.2 monolayer (ML)–Ge QD layer were grown on the Si substrates at 650, 700, and 750 °C; and the three samples were named A, B, and C, respectively. The deposition rate of the Ge layer was 6.0 ML min−1. The morphologies, current distribution images, and I-V curves of Ge QDs were detected by using a scanning probe microscope (Japan Seiko SPA-400 SPM) at atmosphere and room temperature. The ambient humidity was 40–50%. The surface morphologies of all the samples were measured by AFM in tapping mode, whereas the current distributions and I-V characteristic curves were obtained by CAFM with synchronous measurement in contact mode. The tip and reflector were coated with platinum metal, and Ag was used as the bottom electrode. Raman scattering spectra were obtained by employing a Renishaw inVia Raman microscope equipped with an excitation laser operating at 514.5 nm in back-scattering geometry at room temperature.
3. Results and discussion The surface morphologies and current distributions of the three QD samples grown at different temperatures are shown in figures 1(a)–(f), respectively. It can be observed that almost all of the Ge QDs in the three samples exhibit a dome shape, and only a small part of the QDs in sample C show a pyramid shape. When the growth temperature is increased from 650 to 750 °C, the QD density increases from 3.8 × 109 to 7.1 × 109 cm−2, and the QD distribution on a (100) surface and QD size uniformity are also improved. Moreover, the QD diameter (D) and height (H) show a downward trend. This is a special feature that occurs during the process of ion-beam growth of the Ge QDs. To further illuminate the evolution details of the Ge QDs relative to growth temperature, the parameters of the deposited Ge QDs are obtained by means of a line-scan profile and a statistical histogram, as listed in table 1. The peak values of normal distributions of the QD diameters are 70, 55, and 45 nm; and those of the heights are 12, 9, and 7 nm, respectively, for the three samples. We believe that this kind of QD evolution according to growth temperature can be attributed to some natural characteristics of the IBSD technique. During the sputtering process, the ion-beam energy and the Ar plasma density are relatively high. This generally leads to high kinetic energy of sputtering atoms on the substrate surface. Therefore, the diffusion of Ge atoms and the nucleation of Ge QDs are 2
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Figure 1. (a)–(c) Morphology images and (d)–(f) current distributions of samples A, B, and C measured by the tapping and contact modes of AFM, respectively. The red circles show the detected SQD in each sample. Table 1. Statistical Ge QD parameters in samples A, B, and C.
Sample
Density (cm−2)
Distribution range of D (nm)
Peak value of the D normal distribution (nm)
Distribution range of H (nm)
Peak value of the H normal distribution (nm)
A B C
3.8 × 109 5.4 × 109 7.1 × 109
45–90 40–70 25–65
∼70 ∼55 ∼45
8–15 6–11 4–9
∼12 ∼9 ∼7
modulated not only by the thermodynamic but also by the surface kinetic mechanism. It was demonstrated recently that ion-beam energy plays an important role in QD evolution [23]. When the Ar ion energy is lower than 0.6 keV, the QD size increases and the QD density decreases with the increase in the growth temperature. However, the opposite trends occur when the Ar ion energy is larger than ∼1.0 keV, and similar behavior seems to be repeated in this work. It was suggested that the higher Ar ion energy induces a mechanism of supersaturation-driven nucleation. The decomposition of a super-strained wetting layer was demonstrated to enhance the QD nucleation rate effectively at high growth temperatures. On the other hand, according to the thermodynamic theories [24], if the surface energy decreases during QD formation, the energy per atom is of a minimum value versus size, and the lowest energy state for a QD array may be a uniform ensemble at this size. Thus, rising growth temperatures generally drive QD distributions toward smaller sizes, with an increase in entropy S. This can be attributed to the fact that there are more possible arrangements of atoms into smaller QDs than into larger ones. Figure 2 shows the Raman spectra of the three samples. A broadening wave packet with its center at ∼480 cm−1 is
Figure 2. Raman spectra of samples A, B, and C at room
temperature.
observed in sample A. This is attributed to the amorphous Si– Si (a-Si–Si) vibration mode of the Si buffer layer [21, 25]. It was concluded in our previous work [20, 21] that a Si buffer layer grown at a low temperature exhibits a mixed-phase 3
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structure (so-called microcrystalline Si), which includes a-Si and crystalline Si (c-Si); Ge QDs can be formed on the c-Si due to relaxation of the strain of lattice mismatch. Furthermore, the Ge–Ge vibration mode of the QDs in sample A is located at ∼295 cm−1, and the standard amorphous Ge–Ge wave packet (∼270 cm−1 [20, 25]) seems not to be observed in figure 2. This indicates that Ge QDs already crystallize at 650 °C. With the increase in growth temperature, the a-Si–Si peak disappears and the full width at half maximum (FWHM) of the Ge–Ge peak decreases, accompanied by a blueshift from 295 to 299 cm−1. These suggest that the crystal quality of the Si buffer layer and Ge QDs is improved. It is worth noting that an obvious vibration mode located at ∼386 cm−1 is observed in both samples B and C. As reported elsewhere [22, 26, 27], the peak located at ∼390 cm−1 was identified to be the Si–Ge vibration mode of SiGe-alloy QDs, and its peak position may be slightly modulated by residual strain and the Ge content in the QDs [28, 29]. Thus, this obvious peak with its center at 386 cm−1 can be attributed to the Si–Ge vibration mode of SiGe-alloy QDs. This observation of a Si–Ge peak results from the Si–Ge intermixing induced by the uphill diffusion of Si atoms into Ge QDs at higher growth temperatures. Based on the foregoing analysis, it is suggested that the interdiffusion between the Ge and Si atoms occurring at the interface of the two textures becomes significant after the growth temperature is increased. Unexpectedly, this intermixing behavior can also be demonstrated by the current distribution, as shown in figures 1(d)–(f). Overall, the current distribution of the Ge QDs in the 650 °C-grown sample (sample A) is homogeneous. The measured results indicate that the maximum current value is −114 nA, which is obtained in the region of the QDs. However, the current distributions of almost all the Ge QDs in sample B exhibit an annular shape, and that of some QDs with smaller sizes in sample C show a disklike shape; this is an interesting phenomenon. As is known, the conductivity of a Si atom is smaller than that of a Ge atom. Therefore, the current values at the region where the Si atoms aggregate are lower and the color is brighter, whereas the opposite behaviors occur in the region where the Ge atoms aggregate. This implies that the Si–Ge intermixing effect at higher growth temperatures may be responsible for these annular and disklike current distributions. Since the diffusion behavior of Ge atoms can be activated even at lower growth temperatures, it is important for Si atoms that the diffusion lengths increase as the growth temperature increases [30]. In those samples grown at lower temperatures (i.e., sample A), the Si–Ge interdiffusion behavior reflected in the current distribution image is not obvious, which is in good agreement with the Raman spectra. In sample B, the bright region in the current distribution image tends to be located in the middle of the Ge QDs. This indicates that the Si atoms are inclined to accumulate at the center of the QDs. However, in sample C, the lower current region is not only at the center but extends to almost all the QDs, which present a disklike current distribution. This implies that Si–Ge intermixing becomes stronger in QDs grown at 750 °C.
Figure 3. I-V curves of the Ge SQDs ∼60 nm in diameter and ∼6 nm
in height in the three samples detected at room temperature.
A reasonable explanation for the different shapes of current distributions is as follows. The interface of the Ge QDs and the Si buffer layer undergoes the maximum stress amplitudes. Thus, the Si–Ge alloying occurs in the QD region as a result of the largest amount stress relaxation. Since Ge atoms are continually deposited during the QD growth process, the intermixing region near the edge of the QDs is continually buried by newly arriving Ge atoms as the QD diameter increases [31]. Thus, the Si atoms aggregate at the center region at 700 °C, leading to the appearance of annular current distributions of QDs. With the increase in the growth temperature, the Si atoms become more active, which may trigger more intensive uphill diffusion. The buried rate of Si atoms is slower than the Si–Ge alloying rate at 750 °C. Hence, disklike current distributions form in the QD region of sample C. Figure 3 shows the detected I-V curves of the SQDs selected from the three samples and marked by the red circles in the current distribution images of figure 1. The three selected SQDs share similar diameters of ∼60 nm and heights of ∼6 nm. In contrast with samples B and C, the current staircase, which is one of the typical properties of semiconductor QDs induced by the Coulomb blockade effect, is not observed in sample A. The current increases monotonously as the bias voltage increases until the saturation value (100 nA) of the measurement system is achieved. It is well known that the current staircase can be attributed to the resonant tunneling of carriers. The step number is generally related to the number of the confined energy level for resonant tunneling. For better understanding of the origin of the tunneling behavior, the diagrams of the CAFM test system and the equivalent circuit are mapped in figures 4(a) and (b), respectively. R1 and C1 are the resistance and capacitance, respectively, of the tip/QD interface, and R2 and C2 are those of the QD/Si interface. The gray circle in figure 4(b) represents the contact point of the tip and the SQD. Before ex situ examination, a thin native GeO2 layer (barrier) has already existed on the surface of the Ge QDs. In addition, H C Chung et al showed that the misfit dislocation generally produces a 4
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Figure 4. Schematic diagrams of (a) the CAFM test system, (b) the equivalent circuit, and the single-hole-tunneling model (c) in the thermal equilibrium state and (d) with reverse bias.
interface. Compared with that at low-temperature growth, a high growth temperature induces a significantly high nucleation rate for these loops. Thus, at higher growth temperatures, under the lattice strain between Ge and Si, the formation of misfit dislocations under Ge QDs becomes easier [33]. This mechanism for misfit dislocation growth may explain our results. The Ge QDs in sample A are dislocationfree due to the lower temperature growth; they are also named coherent QDs generally. Hence, the disorder layer is absent between the coherent Ge QDs and the Si buffer layer. The holes can first be captured by the Ge well, and then they tunnel through the GeO2 barrier under forward bias voltage. Consequently, the current staircase cannot be observed in sample A. When the growth temperature increases to 700 or even 750 °C, misfit dislocations form at the interface of the QDs and the Si layer, at which point the QDs in samples B and C become incoherent ones. The disorder layer formed at the interface leads to the formation of another additional barrier for the holes. Thus, the holes can achieve a resonant tunneling through the double valence-band barriers under forward bias voltage. This results in the appearance of the current staircase in samples B and C. However, under reverse bias voltage, as shown in figure 4(d), the EF of the Pt metal deviates from the conduction band. The holes cannot be transported on the
disorder layer between the Ge QDs and the Si buffer layer, which acts as a tunneling barrier [4]. Therefore, a doublebarrier tunneling system can be formed during the electronic measurement of the dislocated QDs. Under reverse bias voltage, the electrons in the Si buffer layer can easily achieve resonant tunneling and be captured by the Pt electrode, which induces the appearance of the current staircase in the I-V curve [4]. However, current staircases under reverse bias voltage in this work are not observed in all of our three samples. It suggests that the model of electron resonant tunneling through the double conductionband barriers is unsuitable for clarifying these staircase behaviors. Based on the special feature of the I-V curve and the foregoing analysis, a single-hole-tunneling model is proposed to interpret the current staircase. The energy band diagram of this model is mapped in figure 4(c). During the QD growth process, the energy provided by the heater system is enough generally to nucleate partial half dislocation loops [32]. The further growth of most loops is restrained by the dislocation line tension, whereas a small part of the loops can overcome the energy barrier either by being pinned or by fluctuations in local stresses, and then they undergo a spontaneous growth process. When the size of the loop reaches a critical value, the loop front extends to the island/buffer–layer interface and then forms a misfit dislocation along the 5
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Figure 5. (a)–(d) Morphology images, (e)–(g) current distributions, and (i)–(l) I-V curves of the SQDs selected from sample C with heights of ∼6 nm and diameters of ∼60 (first line), ∼50 (second line), ∼40 (third line), and ∼30 nm (fourth line), respectively.
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the starting voltage V0 for the first current step increases, whereas the ΔV value decreases with the decrease in the QD diameter.
Table 2. Electronic parameters of QDs of different diameters selected
from sample C. D/nm
V0/V
ΔV/V
∼60 ∼50 ∼40 ∼30
∼3.5 ∼5.2 ∼7.6 ∼8.7
∼3.4 ∼2.0 ∼1.5 ∼0.9
RT/kΩ
Caq/F 3
3.4 × 10 2.0 × 103 1.5 × 103 9.0 × 102
EC/J −19
9.4 × 10 1.6 × 10−18 2.1 × 10−18 3.6 × 10−18
1.4 × 10−20 8.0 × 10−21 6.0 × 10−21 3.6 × 10−21
E lkn =
π 2ℏ2 ⎛⎜ l 2 k2 n2 ⎞⎟ π 2ℏ2 ⎛⎜ 2l 2 n2 ⎞⎟ + + = + ⎟ (1) ⎟ 2 2m* ⎜⎝ d x2 2m* ⎜⎝ d xy d y2 d z2 ⎠ d z2 ⎠
According to the single-hole-tunneling model proposed in figure 4, the confined state energies in the QD potential well can be obtained by solving equation (1). As previously mentioned, Si–Ge intermixing increases as the QD diameter decreases; that is, the intermixing in a QD 60 nm in diameter is not so obvious compared with that in a QD of smaller diameter, so the Si–Ge intermixing effect is ignored tentatively in the calculation of confined energy levels in a domeshaped QD 6 nm in height and 60 nm in diameter to interpret the current-jump phenomenon in I-V curves under forward bias voltage. The effective mass of light and heavy holes (mhh* and mlh*) is taken as 0.044 and 0.28m0 [37], respectively. The valence band diagram of the double-barrier system without bias voltage is shown in figure 6(a). The EF of all the layers is equal at thermal equilibrium state. According to the calculation based on equation (1), two quantum states confined in the SQD potential well, the fourth heavy-hole energy level and the second light-hole one with energies of 583 and 928 meV, located between the valence bands of the Si and the disorder layer, are labeled Ehh4 and Elh2, respectively, in this diagram. Under forward bias voltage, as shown in figure 6(b), the energy band of the total system is tilted. Relative to the valence band of Ge QDs, the Si valence band undergoes a downward shift with the increase in bias voltage due to the increasing energy difference (ΔE) in the two edges of the barrier of the disorder layer after the tilt of the energy band. When the forward bias voltage is increased to V0, the Si valence band descends to the level of the Ehh4 state, and the first resonant tunneling of holes occurs. Due to the Coulomb blockage effect, holes can tunnel through the SQD one by one only. Thus, the hole current is changeless until the bias voltage is increased to V1 to further push the Si valence band to be in parallel with the Elh2 level to open the second tunneling pathway for holes. As mentioned, the V0 value increases whereas the ΔV value decreases with the decrease in QD diameter. This interesting behavior can probably be understood in terms of the Si–Ge intermixing occurring in the QDs. With the Si–Ge intermixing, the Ge QDs evolve into Si1−xGex-alloy QDs gradually. The band gap of the Si1−xGex QDs increases with the increase in Si content. Due to the small conduction-band offset at the Ge/Si interface, the valence band of the QDs undertakes most of the band-gap increment. As a result, the valence-band offset at the Ge/Si interface decreases with the decrease in QD size. This leads to an increase in the V0 value. At the same time, the effective mass can be obtained by the method of linear interpolation as expressed in the following. (The stress is not taken into account because the residual stress accumulated in the dislocated QDs can be neglected
valence band to form the hole current due to the fact that the Pt metal cannot emit holes, and the holes in the Si layer move toward the Ag/Si electrode. As a result, the current characteristic under reverse bias voltage can be explained only by the single-barrier electron-tunneling model. As observed in figure 4(d), due to the lower conduction-band offset between the Si and the disorder layer, the electrons in the conduction band of Si can overcome the barrier of the disorder layer and then tunnel through the GeO2 single barrier easily; the resonant tunneling behavior of the electrons cannot be triggered. Thus, the staircase phenomenon does not appear under reverse bias. As we all know, QD size is one of the major factors that affect the properties of photoelectric devices. To clarify the diameter dependence of the electronic characteristics, four SQDs with heights of ∼6 nm and diameters of ∼60, ∼50, ∼40, and ∼30 nm were selected from sample C for the electronic measurement. The morphologies, current distributions, and I-V curves of these four SQDs are shown in figure 5. The bright area in the current distribution image of the QD region increases as the QD diameter decreases, indicating that the Si–Ge interdiffusion becomes stronger as the QD diameter decreases. A similar phenomenon can be observed in reference [34], in which the Ge content in QDs of larger sizes is larger than that in QDs of small sizes. Results of the investigation of tree-ring structures below dislocated SiGe QDs performed by T Merdzhanova et al may explain this phenomenon [35]. When the QD growth temperature is higher than 740 °C, the Ge content in those incoherent (dislocated) SiGe QDs increases with the increase in the QD base area due to the introduction of misfit dislocations rather than serious Si–Ge intermixing. Therefore, as to our results, the formation of dislocated SiGe QDs at 750 °C may be responsible for the intermixing evolution commensurate with the QD diameter. In a double-tunnel structure [36], the Coulomb capacity Caq and the tunneling junction resistance RT of a QD can be expressed as Caq = C1 + C2 = 2e(ΔV)−1 and RT = e · (ΔI · Caq)−1, respectively, where ΔV is the difference between the two adjacent starting voltages for the current jump and ΔI is the current difference between two adjacent current steps. Based on the two equations, some electronic parameters of these SQDs are calculated and listed in table 2. The resistance RT of all four SQDs is larger than the quantum resistance RQ of 25.8 kΩ, and the charging energies EC are higher than the thermal energy at room temperature (∼26 meV). These are the two basic conditions for producing the Coulomb blockade effect in QDs. Thus, the current staircase can be observed in the I-V curves of all four SQDs. It is interesting to note that 7
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Figure 6. Energy band diagrams of SiGe alloy QDs (a) in the thermal equilibrium state and (b) with forward bias voltage.
Acknowledgments
after relaxation.) ⁎ m hh = 0.53−0.25x
(2)
m lh⁎ = 0.16−0.116x
(3)
This work was financially supported by the National Science Foundation of China (No. 11274266), the Open Project launched by the National Laboratory for Infrared Physics (No. M201405), the Key Project of the Applied Basic Research Project of Yunnan Province of China (No. 2013FA029), and the Introducing Talent Project launched by the government of Yunnan Province.
According to equations (2) and (3), mhh* and mlh* increase with the decrease in the Ge content in Si1−xGex-alloy QDs. Consequently, using relation (1), it can be concluded that both Ehh4 and Elh2 increase with the decrease in Ge content in SiGe QDs, whereas the rate of increase of Ehh4 is larger than that of Elh2; in other words, the energy level difference (ΔEL) between Ehh4 and Elh2 decreases gradually. This is probably what is responsible for the decrease in the current step width ΔV observed in figure 5.
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4. Conclusions Three Ge/Si quantum dot samples as well as their own Si buffer layer were grown at different temperatures by using the ion-beam sputtering technique. The surface morphologies and the electronic properties were studied by the tapping and contact models of AFM, respectively. The current distribution with different shapes was demonstrated to be dominated by Si–Ge intermixing in QDs—actually, in accordance with the growth temperature. Current staircases were observed in those incoherent QDs instead of in the coherent QDs. The disorder layer induced by the dislocation acts as a thin and high potential barrier which results in the resonant tunneling of holes and the appearance of the Coulomb staircase. The enhancement of intermixing with the decrease in QD sizes was demonstrated to be responsible for the increase in starting voltage of the staircase and the decrease in the current step width. We believe that our results are helpful for fabricating sophisticated electronic and optoelectronic devices based on group IV semiconductor quantum dots. 8
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Nanotechnology 26 (2015) 105201
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