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Morphology control and growth dynamics of in-plane solid–liquid–solid silicon nanowires
Physica E 44 (2012) 1045–1049
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Morphology control and growth dynamics of in-plane solid–liquid–solid silicon nanowires Linwei Yu n, Pere Roca i Cabarrocas Laboratoire de Physique des Interfaces et des Couches Minces (LPICM), Ecole Polytechnique/CNRS, 91128 Palaiseau, France
a r t i c l e i n f o
abstract
Article history: Received 7 June 2010 Received in revised form 30 May 2011 Accepted 2 June 2011 Available online 17 June 2011
In-plane silicon nanowires (SiNWs) growth, via a newly proposed in-plane solid–liquid–solid (IPSLS) mode, is mediated by nanoscale indium drops that transform amorphous silicon precursors to well-defined SiNWs during a reactive-gas-free annealing process. Compared to the well-known vapor–liquid–solid process, the movement of the front and rear interfaces are coupled to each other via the liquid catalyst drop, which causes the deformation of the liquid catalyst drop (either squeezed or stretched). We show that this growth dynamics indicates an effective way to control and design the morphology of the in-plane SiNWs. We also develop an in-depth insight of this morphology control mechanism via the IPSLS mode, and further address their direct influence on the strain built up in the crystalline SiNWs during their in-situ growth. & 2011 Elsevier B.V. All rights reserved.
1. Introduction Silicon nanowires (SiNWs) are promising building elements for future nano electronics [1–3] and optoelectronic [4,5] devices. Morphological control of the quasi one-dimensional (1D) channel is an important aspect for the design and realization of different functionalities based on SiNWs structure. We recently proposed an in-plane solid–liquid–solid (IPSLS) growth mode of SiNWs, which opens up new possibilities to impose effective growth control and tailor the morphology of the in-plane SiNWs network [6–9]. The IPSLS growth mode also enables precise position control of the inplane SiNWs during in-situ growth, which opens new perspectives for large-scale implementation of the SiNWs-based functionalities. In general, the IPSLS mode shares many similarities with the wellknown vapor–liquid–solid (VLS) mode, for example, both of them are mediated by nano-scaled catalyst drops with the diameter of the SiNWs being determined by the size of catalyst drops. Meanwhile, they differ strikingly in the growth balance conditions and the principles in morphology control. All these differences arise from the solid state precursor in an IPSLS process, which is usually provided by a thin layer of hydrogenated amorphous Si (a-Si:H) with a higher Gibbs energy of Si atoms than that in crystalline Si phase. In this study, we use indium (In) drops as catalysts to absorb and transform the a-Si:H matrix to crystalline SiNWs. It is also worthy to note, during our experiences in trying different material systems, In stands out as
n
Corresponding author. Tel.: þ33 1 69 33 43 53. E-mail address: [email protected] (L. Yu).
1386-9477/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2011.06.005
an ideal choice largely because of its slow diffusion process among the a-Si:H matrix, which is an important criteria to produce well-defined nanowire structures. Looking at detailed growth balance condition of the catalyst drop in a IPSLS process, we found that both the front a-Si/catalyst interface and the rear catalyst/SiNW interfaces are a hard solid/liquid interface, in contrast to the soft gas/liquid interface in the VLS process [10,11]. As a consequence, the movement of the front (absorption) and the rear (deposition) interfaces are coupled via the liquid catalyst drop in between. Any speed difference between the two interfaces will lead to a deformation (squeezing or stretching) of the liquid catalyst drop and in return modify the size and morphology of the produced SiNWs. This scenario is unique to the IPSLS process and can be exploited to tailor the morphology, size and position of the in-plane SiNW network for specific applications. For this purpose, we need to gain further insight of this interface–interplay mechanism and their impact on the in-plane SiNWs. Here, we will focus on understanding this interface– interplay dynamics and their influences on the development and morphological and structural properties of the in-plane SiNWs.
2. Experiment The growth of the in-plane SiNWs, performed in a plasma enhanced chemical vapor deposition (PECVD) system, involves the following steps: first, nano-scale indium (In) catalyst drops are produced during a H2 plasma treatment of a thin sacrificial ITO layer at around 250–350 1C; then, a thin a-Si:H layer is deposited at low temperature (typically at 100 1C) in order to
1046
L. Yu, P. Roca i Cabarrocas / Physica E 44 (2012) 1045–1049
keep the indium (In) drops in solid state; finally, the substrate is heated up to 300–500 1C. The melted In catalyst drops were activated to absorb the covering a-Si:H layer and produce crystalline SiNWs during its in-plane movement on the sample surface. The structural properties and crystallinity were also characterized by high resolution using transmission electron microscopy (HR-TEM). Further details on the experimental conditions are available in our earlier reports [6–9,12,13].
3. Results and discussion To give a first impression of the rich morphologies of the IPSLS-SiNWs, we show in Fig. 1 the scanning electron microscopy (SEM) images of the SiNWs grown under different growth conditions (as will be explained later). As we can see, though the SiNWs are crystalline (as confirmed by HR-TEM characterizations shown in Fig. 2 and also by the local Raman spectrum mapping in Ref. [9]) and rigid by themselves, their morphologies/line-shape can still be readily controlled to grow as a straight-line or a bending wire. This ability, without the aid of any patterns or templates, is actually enabled by the unique interface interplay in the IPSLS process. Compared to the well-known VLS mode, where the top vapor–liquid (V–L) interface on the top of the liquid catalyst drop is soft, both the front absorption and the rear deposition interfaces are hard liquid–solid (L–S) interfaces, as illustrated in Fig. 3(a) and
(b). As a consequence, the liquid catalyst in IPSLS mode is subjected to a stringent constraint imposed by the front and rear hard L–S interfaces. If the absorption interface (va) and the deposition interface (vd) are moving at different rates, the liquid catalyst drop has to be deformed (either stretched or squeezed) to reach a new growth balance condition, and in return modifies the morphology of the produced SiNWs. This is a unique aspect of the IPSLS growth mode, which indicates an unprecedented opportunity to control and tailor the nanowires structures. Before detailed discussion of the interface interplay, we first examine the driving force and the mass transport process of an IPSLS process. As illustrated in Fig. 3(b), during the IPSLS process, a liquid catalyst drop is in contact with the front a-Si:H matrix and the rear c-SiNW, which have different Gibbs energies (for Si atoms), DEac Ea Ec E0.12 eV [14,15]. The absorption and transformation of the a-Si:H matrix to SiNWs is energetically favorable, and drives the in-plane movement of the catalyst drops. In more details, since the higher Gibbs energy of Si in a-Si:H matrix establishes a higher local equilibrium Si concentration (in catalyst a c DEac =kT liquid) at the front catalyst/a-Si:H interface, with Ceq ¼ Ceq e , c than that at the catalyst/c-Si interface Ceq , the absorbed Si atoms at the front interface will diffuse across the catalyst drop towards the deposition interface and build up a Si supersaturation c a c S ¼ CSi =Ceq rCeq =Ceq ¼ eDEac =kT :
ð1Þ
Fig. 1. SEM images of (a) a thick SiNW ( 300 nm) grown under growth condition Z o 1 and of a thin SiNWs ( 150 nm) grown under Z 41, with the enlarged view of the straight SiNW presented in the inset, (b) a zigzag SiNW with regular growth orientations switching obtained under a condition of Z 41 and (c) in-situ real-time SEM images captured during in-plane growth of such a zigzag bending SiNW.
Fig. 2. (a)–(c) HR-TEM characterizations of an in-plane SiNWs, with enlarged views of the Si lattice indicating the crystallinity of the SiNWs grown in IPSLS mode.
L. Yu, P. Roca i Cabarrocas / Physica E 44 (2012) 1045–1049
1047
SiHx (gas) G-L (soft) Catalyst
Catalyst
SiNW in LPSLS
Ea
CSi
Ec (=0 as ground state)
liquid
a-Si:H
Absorption
ion Diffus J ( Si)
Nucleation & Deposition
S-L (hard)
c-SiNWs
S-L (hard)
Catalyst liquid
c-SiNWs
dc
vd
va
a-Si:H (solid)
lc
Fig. 3. Illustration of the different absorption and deposition interfaces involved in (a) the VLS mode and (b) the In-plane (IPSLS) mode. The top-right inset depicts the relative Gibbs energy state of Si atoms in a-Si:H matrix, catalyst drop and SiNWs, respectively.
Thus, the mass transport flux, in a diffusion process, through the catalyst drop can be described as
with lc and Ds being the length of catalyst drop and the diffusion coefficient of dissolved Si atoms in the catalyst drop, respectively. At the front catalyst/a-Si:H absorption interface, the advancing rate depends on the incorporation rate of Si atoms from the a-Si:H matrix into the catalyst drop. This process breaks further into two sub-steps: (1) the breaking of Si–Si atoms at the catalyst/a-Si:H interface and (2) the transport of Si atoms across the catalyst drop in a diffusion process, as depicted in Fig. 3(b). As discussed in our previous works, the first step is usually a fast process and thus not a rate-limiting factor [6]. The mass transport of dissolved Si atoms is limited by the Si concentration gradient DCSi/lc, which is in turn fundamentally limited by the nucleation/deposition rate at the SiNW/In interface, at least under the current experimental conditions [6]. The absorption (or diffusion transport) flux, related to the velocity by JSi ¼ vSi/OSi, can be depicted in Fig. 3 as a linear line a intersecting the Si concentration x-axis at CSi , with a slope inversely proportional to the length of catalyst drop. Note that c the maximum (or the minimum) flux is reached when CSi ¼ CSi a with S ¼Smin (or CSi ¼ CSi with S¼ Smax). At the rear SiNW/catalyst deposition interface, the growth environment seen by the SiNW is essentially identical to that of a typical VLS process. According to the established understanding achieved in the VLS mode, [1,10,16,17] the nucleation and deposition process is driven by the local supersaturation built up at the SiNW/catalyst interface, as indicated in Figs. 3(b) and 4. Putting aside the detailed non-linear relation between the deposition rate and supersaturation, it is reasonable to assume, without loosing generality, that the deposition rate increases monotonically with the Si concentration, with a trend approximated by the red curve in Fig. 4. Now, considering an initial situation where a spherical catalyst drop is placed in contact with an a-Si:H layer of thickness of ha, a stable and balanced movement of the catalyst drop requires that vd ¼ va ,
Strain-free
Squeezed
ð2Þ
ð3Þ
which, as indicated by the intersect point between the deposition and absorption curves in Fig. 4, determines also a corresponding Si concentration CSi. However, this strain-free spherical shape
<1 Interface speed
a JSi ¼ Ds ðCeq CSi Þ=lc ,
Deformations & balance conditions Stretched
∼1
>1 vd
va = ΔCSi
dc ~ dcr (dc ~ lc)
Ds lc
dc < dcr lc decreases
dc > dcr lc increases 0 a
c
CSi (Smin)
CSi
CSi (Smax)
Fig. 4. Speeds of the front absorption (va) and the rear deposition (vd) interfaces, as a function of the dissolved Si concentration at the SiNW/catalyst interface. The top insets indicate the three possible strain states and corresponding deformations of the catalysts, as well as the typical SiNWs produced under the different growth balance conditions. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
with dc lc cannot be achieved for all the catalysts of different sizes, since the mass conservation condition imposes that va ha dc a ¼ vd d2w ) Z va =vd ¼ fdc =ðha aÞ, 2
ð4Þ
where the ratios of f (dw/dc) and a ra Si/rc Si can be considered as constants. So, by combining Eqs. (3) and (4), we can obtain, for a specific a-Si:H thickness ha, a critical catalyst size of dcr ha a/f. It is important to note that, it is the ratio of the size of catalyst drop over the a-Si:H layer as seen in Eq. (4), Z dc/ha, instead of their absolute values, that determines the balance condition. Since ha can be precisely controlled during a plasma deposition process, this feature enables actually a broad range of tunability of the morphology of the in-plane SiNWs. Given an a-Si:H thickness of ha, for a catalyst drop with an initial size of dc 4 dcr (or dc odcr), as shown in Fig. 4, the rear deposition interface will move slower (or faster) than the front absorption interface. This situation will force the catalyst drop to deform into
L. Yu, P. Roca i Cabarrocas / Physica E 44 (2012) 1045–1049
a elongated (squashed) shape, and a new balanced intersect-point can be sought by changing the slope of the absorption line according to 1/lc. According to the different balance positions for the small and large catalyst drops, a small catalyst drop will develop in general faster than a large one, since the corresponding CSi at the SiNW/catalyst interface, as determined by the intersected position, is higher in the small catalyst drops. The deformation of the catalyst drop has a direct impact on the morphology of the produced SiNWs. As shown in Fig. 4, given a thickness of the a-Si:H covering layer, a larger catalyst drop will tend to grow under a condition of being stretched (with dc olc) and exert a tensile stress on the SiNW during growth. The SiNWs grown under this condition are usually straight and long, in analogy to a tensilestrained string. This can be seen for example in Fig. 1(a), where a thicker SiNW (of 300 nm in diameter), featuring a long and straight morphology with a rather uniform size and smooth surface, was catalyzed by a large In catalyst under a stretching condition (Z o1). An enlarged view of the SiNW segment is presented in the inset of Fig. 1(a). On the contrary, a smaller catalyst drop will experience, on average, a state of being squeezed (with dc 4lc) and thus exert a compressive stress on the produced SiNWs. In this case (Z 41), the catalyst drop tends to change its growth direction frequently to release the compressive stress. This situation produces bending SiNWs, as seen in Fig. 1(a) for a thin SiNW (of 150 nm). Interestingly, under this condition, the interface interplay could also couple or trigger the switching of the preferential growth directions of the SiNWs (between different crystallographic orientations), and produce zigzag SiNWs with regular turnings, as shown in Fig. 1(b). Since the growth of the in-plane SiNWs can be activated during a reacting-gas-free annealing environment, we are able to observe the growth of SiNWs in real-time in a SEM system equipped with an insitu heating stage. The SEM image of such a zigzag bending SiNW, guided by a running indium catalyst drop ahead, is shown in Fig. 1(c), where we can see the liquid catalyst drop is squeezed (at this specific moment) by the rear SiNW/catalyst interface into an elliptic shape. Details of the in-situ real-time observation are available in Ref. [9]. It is also interesting to estimate the stretching or squeezing force experienced by the in-plane SiNWs during growth, when they develop under condition deviating from the balance condition of Z ¼1. Since the liquid catalyst drop favors always a spherical shape with lc ¼dc to minimize the exposed surface energy, we assume in a simplified situation that the strain energy of the liquid catalyst drop manifests itself mainly in terms of the change of the total exposed surface energy of the liquid catalyst drop, that is Estr ¼ sIn ð2d2c þ 4dc lc Þ,
ð5Þ
with sIn being the average surface and interface energy of the liquid In catalyst drop. Then, the pressure exerted on the SiNW/catalyst interface, due to the deformation of catalyst drop, can be written as 1 dEstr 4sIn ddc ddc lc p¼ 2 ¼ þ þ1 : ð6Þ fdc dlc dlc dc fdc dlc Since the volume of the catalyst drop can be considered as a constant V ¼ d2c lc , the deviations in the width and the length of the liquid catalyst drop are correlated as ddc dc ¼ : dlc 2lc Combining Eqs. (6) and (7), we obtain 2sIn dc 2sIn 1 ¼ 1=3 ðr 2=3 r 1=3 Þ: p¼ fdc lc fV
ð7Þ
ð8Þ
So, the pressure or stress exerted at the SiNW end (the SiNW/ catalyst interface), being positive for compressive and negative for tensile, is related to the deformation ratio defined as rdc/lc, and
75 Diameter of the In catalyst drop 50
100 nm p ~ (r 2/3 − r −1/3)
250 nm Pressure on SiNW (MPa)
1048
25
500 nm
0
-25
-50
Tension strain (η<1)
Compression strain (>1)
-75 0.8
1.0 Deformation ratio r = dc/lc
1.2
Fig. 5. Stress or pressure on the SiNWs/catalyst interface, as a function of the deformation ratio r dc/lc, guided by catalyst drops of different diameters.
scales up in general inversely with the mean size of catalyst drop V 1/3. In Fig. 5, we plot this pressure as a function of r, which according to our in-situ SEM observation could assume usually a range of at least 0.7–1.3 under different balance conditions. For a catalyst drop of around several hundreds nanometers, this pressure increases monotonically with Z and can easily reach a few tens of MPa. It is worthy to note that, when the compressive stress will be usually released by frequent direction-changing of the catalyst drop and lead to bending SiNWs as discussed before, the tensile strain introduced in the SiNWs during growth can be kept in the nanowires by their contact to the solid substrate. The conductivity, carrier mobility or structural properties of the SiNWs channels can be affected and modulated by this non-trivial strain of the SiNW (which scales up inversely to the size of catalyst). Further investigations of these aspects are still needed.
4. Summary In this paper, we have investigated the unique interfaces coupling behaviors in the IPSLS process and highlighted their impacts on the morphological and structural properties of the in-plane SiNWs. We have studied in detail the balance condition between the front absorption and rear deposition interfaces, and the deformation of the liquid catalyst drop in response to the interface interplay. We also establish a model to estimate the stress or strain that could be introduced in the SiNWs when guided by a deformed catalyst drop. These results help to establish a comprehensive understanding of this new IPSLS process and lay a basis for their various SiNWs-based device applications. References [1] S. Volker, V.W. Joerg, S. Stephan, G. Ulrich, Adv. Mater. 21 (25–26) (2009) 2681. [2] Y. Cui, Z. Zhong, D. Wang, W.U. Wang, C.M. Lieber, Nano Lett. 3 (2003) 149. [3] Y. Huang, X. Duan, Q. Wei, C.M. Lieber, Science 291 (5504) (2001) 630. [4] M. Dovrat, N. Arad, X.H. Zhang, S.T. Lee, A. Sa’ar, Phys. Rev. B 75 (20) (2007). [5] J.F. Qi, A.M. Belcher, J.M. White, Appl. Phys. Lett. 82 (16) (2003) 2616. [6] L. Yu, P. Roca i Cabarrocas, Phys. Rev. B 81 (2010) 085323. [7] L. Yu, P. Roca i Cabarrocas, Phys. Rev. B: Condens. Matter Mater. Phys. 80 (8) (2009) 085313. [8] L. Yu, M. Oudwan, O. Moustapha, F. Franck, P. Roca i Cabarrocas, Appl. Phys. Lett. 95 (11) (2009) 113106.
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[9] L. Yu, P.-J. Alet, G. Picardi, P. Roca i Cabarrocas, Phys. Rev. Lett. 102 (12) (2009) 125501. ¨ [10] Brent A. Wacaser, Kimberly A. Dick, Jonas Johansson, Magnus T. Borgstrom, Knut Deppert, L. Samuelson, Adv. Mater. 21 (2) (2009) 153. [11] R.S. Wagner, W.C. Ellis, Appl. Phys. Lett. 4 (5) (1964) 89. [12] L. Yu, B. O’Donnell, P.-J. Alet, S. Conesa-Boj, F. Peiro, J. Arbiol, P.R. i. Cabarrocas, Nanotechnology 20 (22) (2009) 225604.
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[13] L. Yu, O. Moustapha, M. Oudwan, P. Roca i Cabarrocas, Mater. Res. Soc. Symp. Proc. 1178E (2009) AA07-07. [14] I. Stich, R. Car, M. Parrinello, Phys. Rev. B 44 (20) (1991) 11092. [15] S. Roorda, S. Doorn, W.C. Sinke, P.M.L.O. Scholte, E. van Loenen, Phys. Rev. Lett. 62 (16) (1989) 1880. [16] E.I. Givargizov, J. Cryst. Growth 31 (1975) 20. [17] C.Y. Wen, M.C. Reuter, J. Tersoff, E.A. Stach, F.M. Ross, Nano Lett. (2009).
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Morphology control and growth dynamics of in-plane solid–liquid–solid silicon nanowires Linwei Yu n, Pere Roca i Cabarrocas Laboratoire de Physique des Interfaces et des Couches Minces (LPICM), Ecole Polytechnique/CNRS, 91128 Palaiseau, France
a r t i c l e i n f o
abstract
Article history: Received 7 June 2010 Received in revised form 30 May 2011 Accepted 2 June 2011 Available online 17 June 2011
In-plane silicon nanowires (SiNWs) growth, via a newly proposed in-plane solid–liquid–solid (IPSLS) mode, is mediated by nanoscale indium drops that transform amorphous silicon precursors to well-defined SiNWs during a reactive-gas-free annealing process. Compared to the well-known vapor–liquid–solid process, the movement of the front and rear interfaces are coupled to each other via the liquid catalyst drop, which causes the deformation of the liquid catalyst drop (either squeezed or stretched). We show that this growth dynamics indicates an effective way to control and design the morphology of the in-plane SiNWs. We also develop an in-depth insight of this morphology control mechanism via the IPSLS mode, and further address their direct influence on the strain built up in the crystalline SiNWs during their in-situ growth. & 2011 Elsevier B.V. All rights reserved.
1. Introduction Silicon nanowires (SiNWs) are promising building elements for future nano electronics [1–3] and optoelectronic [4,5] devices. Morphological control of the quasi one-dimensional (1D) channel is an important aspect for the design and realization of different functionalities based on SiNWs structure. We recently proposed an in-plane solid–liquid–solid (IPSLS) growth mode of SiNWs, which opens up new possibilities to impose effective growth control and tailor the morphology of the in-plane SiNWs network [6–9]. The IPSLS growth mode also enables precise position control of the inplane SiNWs during in-situ growth, which opens new perspectives for large-scale implementation of the SiNWs-based functionalities. In general, the IPSLS mode shares many similarities with the wellknown vapor–liquid–solid (VLS) mode, for example, both of them are mediated by nano-scaled catalyst drops with the diameter of the SiNWs being determined by the size of catalyst drops. Meanwhile, they differ strikingly in the growth balance conditions and the principles in morphology control. All these differences arise from the solid state precursor in an IPSLS process, which is usually provided by a thin layer of hydrogenated amorphous Si (a-Si:H) with a higher Gibbs energy of Si atoms than that in crystalline Si phase. In this study, we use indium (In) drops as catalysts to absorb and transform the a-Si:H matrix to crystalline SiNWs. It is also worthy to note, during our experiences in trying different material systems, In stands out as
n
Corresponding author. Tel.: þ33 1 69 33 43 53. E-mail address: [email protected] (L. Yu).
1386-9477/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2011.06.005
an ideal choice largely because of its slow diffusion process among the a-Si:H matrix, which is an important criteria to produce well-defined nanowire structures. Looking at detailed growth balance condition of the catalyst drop in a IPSLS process, we found that both the front a-Si/catalyst interface and the rear catalyst/SiNW interfaces are a hard solid/liquid interface, in contrast to the soft gas/liquid interface in the VLS process [10,11]. As a consequence, the movement of the front (absorption) and the rear (deposition) interfaces are coupled via the liquid catalyst drop in between. Any speed difference between the two interfaces will lead to a deformation (squeezing or stretching) of the liquid catalyst drop and in return modify the size and morphology of the produced SiNWs. This scenario is unique to the IPSLS process and can be exploited to tailor the morphology, size and position of the in-plane SiNW network for specific applications. For this purpose, we need to gain further insight of this interface–interplay mechanism and their impact on the in-plane SiNWs. Here, we will focus on understanding this interface– interplay dynamics and their influences on the development and morphological and structural properties of the in-plane SiNWs.
2. Experiment The growth of the in-plane SiNWs, performed in a plasma enhanced chemical vapor deposition (PECVD) system, involves the following steps: first, nano-scale indium (In) catalyst drops are produced during a H2 plasma treatment of a thin sacrificial ITO layer at around 250–350 1C; then, a thin a-Si:H layer is deposited at low temperature (typically at 100 1C) in order to
1046
L. Yu, P. Roca i Cabarrocas / Physica E 44 (2012) 1045–1049
keep the indium (In) drops in solid state; finally, the substrate is heated up to 300–500 1C. The melted In catalyst drops were activated to absorb the covering a-Si:H layer and produce crystalline SiNWs during its in-plane movement on the sample surface. The structural properties and crystallinity were also characterized by high resolution using transmission electron microscopy (HR-TEM). Further details on the experimental conditions are available in our earlier reports [6–9,12,13].
3. Results and discussion To give a first impression of the rich morphologies of the IPSLS-SiNWs, we show in Fig. 1 the scanning electron microscopy (SEM) images of the SiNWs grown under different growth conditions (as will be explained later). As we can see, though the SiNWs are crystalline (as confirmed by HR-TEM characterizations shown in Fig. 2 and also by the local Raman spectrum mapping in Ref. [9]) and rigid by themselves, their morphologies/line-shape can still be readily controlled to grow as a straight-line or a bending wire. This ability, without the aid of any patterns or templates, is actually enabled by the unique interface interplay in the IPSLS process. Compared to the well-known VLS mode, where the top vapor–liquid (V–L) interface on the top of the liquid catalyst drop is soft, both the front absorption and the rear deposition interfaces are hard liquid–solid (L–S) interfaces, as illustrated in Fig. 3(a) and
(b). As a consequence, the liquid catalyst in IPSLS mode is subjected to a stringent constraint imposed by the front and rear hard L–S interfaces. If the absorption interface (va) and the deposition interface (vd) are moving at different rates, the liquid catalyst drop has to be deformed (either stretched or squeezed) to reach a new growth balance condition, and in return modifies the morphology of the produced SiNWs. This is a unique aspect of the IPSLS growth mode, which indicates an unprecedented opportunity to control and tailor the nanowires structures. Before detailed discussion of the interface interplay, we first examine the driving force and the mass transport process of an IPSLS process. As illustrated in Fig. 3(b), during the IPSLS process, a liquid catalyst drop is in contact with the front a-Si:H matrix and the rear c-SiNW, which have different Gibbs energies (for Si atoms), DEac Ea Ec E0.12 eV [14,15]. The absorption and transformation of the a-Si:H matrix to SiNWs is energetically favorable, and drives the in-plane movement of the catalyst drops. In more details, since the higher Gibbs energy of Si in a-Si:H matrix establishes a higher local equilibrium Si concentration (in catalyst a c DEac =kT liquid) at the front catalyst/a-Si:H interface, with Ceq ¼ Ceq e , c than that at the catalyst/c-Si interface Ceq , the absorbed Si atoms at the front interface will diffuse across the catalyst drop towards the deposition interface and build up a Si supersaturation c a c S ¼ CSi =Ceq rCeq =Ceq ¼ eDEac =kT :
ð1Þ
Fig. 1. SEM images of (a) a thick SiNW ( 300 nm) grown under growth condition Z o 1 and of a thin SiNWs ( 150 nm) grown under Z 41, with the enlarged view of the straight SiNW presented in the inset, (b) a zigzag SiNW with regular growth orientations switching obtained under a condition of Z 41 and (c) in-situ real-time SEM images captured during in-plane growth of such a zigzag bending SiNW.
Fig. 2. (a)–(c) HR-TEM characterizations of an in-plane SiNWs, with enlarged views of the Si lattice indicating the crystallinity of the SiNWs grown in IPSLS mode.
L. Yu, P. Roca i Cabarrocas / Physica E 44 (2012) 1045–1049
1047
SiHx (gas) G-L (soft) Catalyst
Catalyst
SiNW in LPSLS
Ea
CSi
Ec (=0 as ground state)
liquid
a-Si:H
Absorption
ion Diffus J ( Si)
Nucleation & Deposition
S-L (hard)
c-SiNWs
S-L (hard)
Catalyst liquid
c-SiNWs
dc
vd
va
a-Si:H (solid)
lc
Fig. 3. Illustration of the different absorption and deposition interfaces involved in (a) the VLS mode and (b) the In-plane (IPSLS) mode. The top-right inset depicts the relative Gibbs energy state of Si atoms in a-Si:H matrix, catalyst drop and SiNWs, respectively.
Thus, the mass transport flux, in a diffusion process, through the catalyst drop can be described as
with lc and Ds being the length of catalyst drop and the diffusion coefficient of dissolved Si atoms in the catalyst drop, respectively. At the front catalyst/a-Si:H absorption interface, the advancing rate depends on the incorporation rate of Si atoms from the a-Si:H matrix into the catalyst drop. This process breaks further into two sub-steps: (1) the breaking of Si–Si atoms at the catalyst/a-Si:H interface and (2) the transport of Si atoms across the catalyst drop in a diffusion process, as depicted in Fig. 3(b). As discussed in our previous works, the first step is usually a fast process and thus not a rate-limiting factor [6]. The mass transport of dissolved Si atoms is limited by the Si concentration gradient DCSi/lc, which is in turn fundamentally limited by the nucleation/deposition rate at the SiNW/In interface, at least under the current experimental conditions [6]. The absorption (or diffusion transport) flux, related to the velocity by JSi ¼ vSi/OSi, can be depicted in Fig. 3 as a linear line a intersecting the Si concentration x-axis at CSi , with a slope inversely proportional to the length of catalyst drop. Note that c the maximum (or the minimum) flux is reached when CSi ¼ CSi a with S ¼Smin (or CSi ¼ CSi with S¼ Smax). At the rear SiNW/catalyst deposition interface, the growth environment seen by the SiNW is essentially identical to that of a typical VLS process. According to the established understanding achieved in the VLS mode, [1,10,16,17] the nucleation and deposition process is driven by the local supersaturation built up at the SiNW/catalyst interface, as indicated in Figs. 3(b) and 4. Putting aside the detailed non-linear relation between the deposition rate and supersaturation, it is reasonable to assume, without loosing generality, that the deposition rate increases monotonically with the Si concentration, with a trend approximated by the red curve in Fig. 4. Now, considering an initial situation where a spherical catalyst drop is placed in contact with an a-Si:H layer of thickness of ha, a stable and balanced movement of the catalyst drop requires that vd ¼ va ,
Strain-free
Squeezed
ð2Þ
ð3Þ
which, as indicated by the intersect point between the deposition and absorption curves in Fig. 4, determines also a corresponding Si concentration CSi. However, this strain-free spherical shape
<1 Interface speed
a JSi ¼ Ds ðCeq CSi Þ=lc ,
Deformations & balance conditions Stretched
∼1
>1 vd
va = ΔCSi
dc ~ dcr (dc ~ lc)
Ds lc
dc < dcr lc decreases
dc > dcr lc increases 0 a
c
CSi (Smin)
CSi
CSi (Smax)
Fig. 4. Speeds of the front absorption (va) and the rear deposition (vd) interfaces, as a function of the dissolved Si concentration at the SiNW/catalyst interface. The top insets indicate the three possible strain states and corresponding deformations of the catalysts, as well as the typical SiNWs produced under the different growth balance conditions. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
with dc lc cannot be achieved for all the catalysts of different sizes, since the mass conservation condition imposes that va ha dc a ¼ vd d2w ) Z va =vd ¼ fdc =ðha aÞ, 2
ð4Þ
where the ratios of f (dw/dc) and a ra Si/rc Si can be considered as constants. So, by combining Eqs. (3) and (4), we can obtain, for a specific a-Si:H thickness ha, a critical catalyst size of dcr ha a/f. It is important to note that, it is the ratio of the size of catalyst drop over the a-Si:H layer as seen in Eq. (4), Z dc/ha, instead of their absolute values, that determines the balance condition. Since ha can be precisely controlled during a plasma deposition process, this feature enables actually a broad range of tunability of the morphology of the in-plane SiNWs. Given an a-Si:H thickness of ha, for a catalyst drop with an initial size of dc 4 dcr (or dc odcr), as shown in Fig. 4, the rear deposition interface will move slower (or faster) than the front absorption interface. This situation will force the catalyst drop to deform into
L. Yu, P. Roca i Cabarrocas / Physica E 44 (2012) 1045–1049
a elongated (squashed) shape, and a new balanced intersect-point can be sought by changing the slope of the absorption line according to 1/lc. According to the different balance positions for the small and large catalyst drops, a small catalyst drop will develop in general faster than a large one, since the corresponding CSi at the SiNW/catalyst interface, as determined by the intersected position, is higher in the small catalyst drops. The deformation of the catalyst drop has a direct impact on the morphology of the produced SiNWs. As shown in Fig. 4, given a thickness of the a-Si:H covering layer, a larger catalyst drop will tend to grow under a condition of being stretched (with dc olc) and exert a tensile stress on the SiNW during growth. The SiNWs grown under this condition are usually straight and long, in analogy to a tensilestrained string. This can be seen for example in Fig. 1(a), where a thicker SiNW (of 300 nm in diameter), featuring a long and straight morphology with a rather uniform size and smooth surface, was catalyzed by a large In catalyst under a stretching condition (Z o1). An enlarged view of the SiNW segment is presented in the inset of Fig. 1(a). On the contrary, a smaller catalyst drop will experience, on average, a state of being squeezed (with dc 4lc) and thus exert a compressive stress on the produced SiNWs. In this case (Z 41), the catalyst drop tends to change its growth direction frequently to release the compressive stress. This situation produces bending SiNWs, as seen in Fig. 1(a) for a thin SiNW (of 150 nm). Interestingly, under this condition, the interface interplay could also couple or trigger the switching of the preferential growth directions of the SiNWs (between different crystallographic orientations), and produce zigzag SiNWs with regular turnings, as shown in Fig. 1(b). Since the growth of the in-plane SiNWs can be activated during a reacting-gas-free annealing environment, we are able to observe the growth of SiNWs in real-time in a SEM system equipped with an insitu heating stage. The SEM image of such a zigzag bending SiNW, guided by a running indium catalyst drop ahead, is shown in Fig. 1(c), where we can see the liquid catalyst drop is squeezed (at this specific moment) by the rear SiNW/catalyst interface into an elliptic shape. Details of the in-situ real-time observation are available in Ref. [9]. It is also interesting to estimate the stretching or squeezing force experienced by the in-plane SiNWs during growth, when they develop under condition deviating from the balance condition of Z ¼1. Since the liquid catalyst drop favors always a spherical shape with lc ¼dc to minimize the exposed surface energy, we assume in a simplified situation that the strain energy of the liquid catalyst drop manifests itself mainly in terms of the change of the total exposed surface energy of the liquid catalyst drop, that is Estr ¼ sIn ð2d2c þ 4dc lc Þ,
ð5Þ
with sIn being the average surface and interface energy of the liquid In catalyst drop. Then, the pressure exerted on the SiNW/catalyst interface, due to the deformation of catalyst drop, can be written as 1 dEstr 4sIn ddc ddc lc p¼ 2 ¼ þ þ1 : ð6Þ fdc dlc dlc dc fdc dlc Since the volume of the catalyst drop can be considered as a constant V ¼ d2c lc , the deviations in the width and the length of the liquid catalyst drop are correlated as ddc dc ¼ : dlc 2lc Combining Eqs. (6) and (7), we obtain 2sIn dc 2sIn 1 ¼ 1=3 ðr 2=3 r 1=3 Þ: p¼ fdc lc fV
ð7Þ
ð8Þ
So, the pressure or stress exerted at the SiNW end (the SiNW/ catalyst interface), being positive for compressive and negative for tensile, is related to the deformation ratio defined as rdc/lc, and
75 Diameter of the In catalyst drop 50
100 nm p ~ (r 2/3 − r −1/3)
250 nm Pressure on SiNW (MPa)
1048
25
500 nm
0
-25
-50
Tension strain (η<1)
Compression strain (>1)
-75 0.8
1.0 Deformation ratio r = dc/lc
1.2
Fig. 5. Stress or pressure on the SiNWs/catalyst interface, as a function of the deformation ratio r dc/lc, guided by catalyst drops of different diameters.
scales up in general inversely with the mean size of catalyst drop V 1/3. In Fig. 5, we plot this pressure as a function of r, which according to our in-situ SEM observation could assume usually a range of at least 0.7–1.3 under different balance conditions. For a catalyst drop of around several hundreds nanometers, this pressure increases monotonically with Z and can easily reach a few tens of MPa. It is worthy to note that, when the compressive stress will be usually released by frequent direction-changing of the catalyst drop and lead to bending SiNWs as discussed before, the tensile strain introduced in the SiNWs during growth can be kept in the nanowires by their contact to the solid substrate. The conductivity, carrier mobility or structural properties of the SiNWs channels can be affected and modulated by this non-trivial strain of the SiNW (which scales up inversely to the size of catalyst). Further investigations of these aspects are still needed.
4. Summary In this paper, we have investigated the unique interfaces coupling behaviors in the IPSLS process and highlighted their impacts on the morphological and structural properties of the in-plane SiNWs. We have studied in detail the balance condition between the front absorption and rear deposition interfaces, and the deformation of the liquid catalyst drop in response to the interface interplay. We also establish a model to estimate the stress or strain that could be introduced in the SiNWs when guided by a deformed catalyst drop. These results help to establish a comprehensive understanding of this new IPSLS process and lay a basis for their various SiNWs-based device applications. References [1] S. Volker, V.W. Joerg, S. Stephan, G. Ulrich, Adv. Mater. 21 (25–26) (2009) 2681. [2] Y. Cui, Z. Zhong, D. Wang, W.U. Wang, C.M. Lieber, Nano Lett. 3 (2003) 149. [3] Y. Huang, X. Duan, Q. Wei, C.M. Lieber, Science 291 (5504) (2001) 630. [4] M. Dovrat, N. Arad, X.H. Zhang, S.T. Lee, A. Sa’ar, Phys. Rev. B 75 (20) (2007). [5] J.F. Qi, A.M. Belcher, J.M. White, Appl. Phys. Lett. 82 (16) (2003) 2616. [6] L. Yu, P. Roca i Cabarrocas, Phys. Rev. B 81 (2010) 085323. [7] L. Yu, P. Roca i Cabarrocas, Phys. Rev. B: Condens. Matter Mater. Phys. 80 (8) (2009) 085313. [8] L. Yu, M. Oudwan, O. Moustapha, F. Franck, P. Roca i Cabarrocas, Appl. Phys. Lett. 95 (11) (2009) 113106.
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