Abstract:
A device and a method of forming a continuous polycrystalline Ge film having crystalline Ge islands is provided that includes depositing an amorphous Ge (a-Ge) layer on a substrate, oxidizing the top surface of the a-Ge layer to form a GeO x  layer, depositing a seed layer of Al on the GeO x  layer and catalyzing the Al seed layer, where Ge mass transport is generated from the underlying a-Ge layer to the Al seed layer through the GeO x  layer by thermal annealing, where a continuous polycrystalline Ge film having crystalline Ge islands is formed on the Al seed layer.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates to growth of semiconductor thin films. More particularly, the invention relates to deposition of continuous polycrystalline Ge films having crystalline Ge island growth with preferred orientation. 
       BACKGROUND OF THE INVENTION 
       [0002]    Low-temperature synthesis of polycrystalline germanium (poly-Ge) thin films is of great interest in thin-film photovoltaic and electronics applications. Low-temperature synthesis of polycrystalline semiconductor thin films (Si or Ge) on amorphous substrates has important applications in thin-film transistors and solar cells. Recently, (poly-Ge) thin films have been investigated as a low-cost substitute for single crystalline Ge substrates. Ge has good lattice matching with III-V semiconductors, and poly-Ge substrates have been shown to seed epitaxial growth of GaAs or Ge overlayers for polycrystalline single-junction or multijunction solar cell fabrication. Moreover, as-grown poly-Ge films can serve as building blocks for thin-film transistors, a key device in advanced large-area electronics, such as flexible displays. 
         [0003]    Metal-induced (e.g., Al, Ni) crystallization (MIC) of amorphous semiconductor films can form polycrystalline films at temperatures much lower than those required in the absence of a metal catalyst. Amorphous Ge (a-Ge) thin films crystallize at 150-250° C. when Ge is in direct contact with Al. This opens up the possibility of crystalline semiconductor deposition on flexible polymeric substrates, whereas a-Ge solid-phase crystallization requires temperatures significantly higher than 300° C. However, a-Ge/Al interfaces exhibit uncontrolled crystallization with growth of randomly oriented Ge nanocrystallites mixed into the Al layer. For many applications, preparation of a polycrystalline semiconductor layer on the surface of a large-area substrate with controlled crystallite size and crystallographic orientation is crucial, and this is difficult to achieve with existing methods. 
         [0004]    What is needed is a method of forming oriented crystalline Ge structures on thin films using low-temperature processing for use in thin-film photovoltaics, thin-film transistors and large-area electronics. 
       SUMMARY OF THE INVENTION 
       [0005]    To address the needs in the art, a device and a method of forming a continuous polycrystalline Ge film having crystalline Ge islands is provided that includes depositing an amorphous Ge (a-Ge) layer on a substrate, oxidizing the top surface of the a-Ge layer to form a GeO x  layer, depositing a seed layer of Al on the GeO x  layer and catalyzing the crystallization of Ge using the Al seed layer, such that Ge mass transport occurs from the underlying a-Ge layer to the Al seed layer surface through the GeO x  layer by thermal annealing, where a continuous polycrystalline Ge film having crystalline Ge islands is formed on the Al seed layer. 
         [0006]    According to one aspect of the invention, the a-Ge layer has a thickness in a range of 5 nm to 500 nm. 
         [0007]    In another aspect of the invention, the GeO x  layer includes 1&lt;x&lt;2. 
         [0008]    In a further aspect of the invention, the GeO x  layer is formed by passing ozone gas or ozone-containing gas mixture over the a-Ge layer, where a thickness of the GeO x  layer is controlled by the oxidation time and the pressure of the ozone. 
         [0009]    According to one aspect of the invention, bias-voltage stressing of the GeO x  layer controls the areal density of the crystalline Ge islands. In one aspect, the bias-voltage stressing includes applying an electric field between the Al seed layer and the underlying a-Ge layer, where the electric field has a strength of up to 2×10 7  V/cm. In another aspect, the bias-voltage stressing includes applying an electric field between the Al seed layer and the underlying a-Ge layer for a duration of up to 1 hour. 
         [0010]    According to another aspect of the invention, the thermal annealing includes using a temperature in a range of up to 300° C., and for a duration of up to 6 hrs. 
         [0011]    In yet another aspect of the invention, the Al seed layer includes a patterned layer. According to one aspect, the patterned layer includes a pattern of pads that have a cross length in a range of 1 μm to 500 μm. 
         [0012]    In a further aspect of the invention, the substrate can include a silicon wafer having a SiO 2  layer, glass, flexible anodized Al sheets, or flexible polyethylene terephthalate (PET). 
         [0013]    In yet another aspect of the invention, the crystalline Ge islands have a radius up to 150 μm. 
         [0014]    According to a further aspect of the invention, the thermal annealing includes annealing in environments that include of vacuum, hydrogen, nitrogen, or argon. 
         [0015]    According to one embodiment of the invention a crystalline Ge island nanostructure device is provided that includes an amorphous Ge (a-Ge) layer disposed on a substrate, a GeO x  layer disposed on a top of the amorphous Ge layer, a Al seed layer disposed on the GeO x  layer, and crystalline Ge islands formed on the Al seed layer, where Ge mass transport is generated from the underlying a-Ge layer to the Al seed layer through the GeO x  layer by thermal annealing, where a continuous polycrystalline Ge film having crystalline Ge islands is formed on the Al seed layer. 
         [0016]    In one aspect of the current embodiment, the a-Ge layer has a thickness in a range of 5 nm to 500 nm. 
         [0017]    In another aspect of the current embodiment, the GeO x  layer includes 1&lt;x&lt;2. 
         [0018]    In a further aspect of the current embodiment, the Al seed layer includes a patterned layer. In another aspect, the patterned layer includes a pattern of pads, where the pads have a cross length in a range of 1 μm to 500 μm. 
         [0019]    In yet another aspect of the current embodiment, the substrate can include a silicon wafer having a SiO 2  layer, glass, flexible anodized Al sheets, or flexible polyethylene terephthalate (PET). 
         [0020]    According to one aspect of the current embodiment, the crystalline Ge islands have a radius up to 150 μm. 
         [0021]    In another aspect of the invention, the Al seed layer has a thickness in a range of 2 nm to 400 nm. 
         [0022]    According to one aspect of the invention, the seed layer can be Al, Au or Ag. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]      FIGS. 1   a - 1   b  show SEM micrographs and Ge and Al Auger elemental maps, according to one embodiment of the invention. 
           [0024]      FIGS. 2   a - 2   b  show Ge surface coverage and the area fraction of Ge on Al, according to one embodiment of the invention. 
           [0025]      FIG. 3  shows bias-voltage induced dielectric breakdown of the GeO x  interfacial layers, according to one embodiment of the invention. 
           [0026]      FIGS. 4   a - 4   c  show SEM micrographs of how the density of nucleated Ge islands varies as a function of the biasing history, according to one embodiment of the invention. 
           [0027]      FIG. 5   a  shows the nucleation behavior for different interfacial layers after layer exchange annealing at 250° C., according to one embodiment of the invention. 
           [0028]      FIGS. 6   a - 6   c  show schematic drawings of the crystalline Ge island nucleation, according to one embodiment of the invention. 
           [0029]      FIGS. 7   a - 7   b  show graphs of the areal density of nucleated Ge islands vs. annealing time and Ge island growth after 200° C., 250° C. and 300° C. annealing, respectively, according to one embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0030]    The current invention includes Al-seeded layer exchange crystallization to form poly-Ge thin films with micron-sized grains and (111)-preferred orientation at 200° C. A sub-nm GeO x  (1&lt;x&lt;2) interfacial layer is intentionally interposed between the upper Al and the underlying a-Ge layer. The Al seed layer can have a thickness in a range of 2 nm to 400 nmm, and the a-Ge layer can have a thickness in a range of 5 nm to 500 nm, where the seed layer can be Al, Au or Ag. The interfacial layer, which can be engineered to provide relatively sparse, nanoscale fast-diffusion paths for Ge transport, controls the nucleation of (111)-oriented Ge crystallites on the Al film surface. During layer exchange crystallization, Ge atoms in the amorphous phase diffuse upwards, and crystalline Ge islands nucleate and grow laterally until completely covering the initially-overlying Al film. In one aspect, the crystalline Ge islands can have a radius up to 150 μm. The driving force is the reduction of free energy during the amorphous Ge to crystalline Ge phase transformation. In one aspect of the invention, the Al layer includes a patterned layer, where the patterned layer includes a pattern of pads that have a cross length in a range of 1 μm to 500 μm. According to different embodiments, the invention can be used with poly-Ge films in thin-film photovoltaics, thin-film transistors, and large-area electronics. 
         [0031]    According to one embodiment of the invention, amorphous germanium (a-Ge) and crystalline Al (c-Al) films are deposited in an electron-beam evaporation system with no intentional substrate heating. First, a-Ge thin films (100 nm thick for example) are thermally evaporated on SiO 2  substrates. Substrates such as a silicon wafer having a SiO 2  layer, glass, flexible anodized Al sheets, or flexible polyethylene terephthalate (PET) can be used. In one example, Si (100) wafers with a thermally oxidized SiO 2  film (100 nm thick for example) are used. In one aspect, a series of cleaning procedures are used to remove hydrocarbon and metal contaminants prior to a-Ge film deposition. These can include a sequence of isopropyl alcohol (IPA) rinse for 5 minutes, 4:1 H 2 SO 4 :H 2 O 2  dip cleaning at room temperature for 10 minutes, 5:1:1 H 2 O:H 2 O 2 :HCl dip cleaning at room temperature for 10 minutes, followed by drying in N 2  atmosphere. The sub-nm GeO x  interfacial layer can be prepared by flowing ozone gas or ozone-containing gas mixture over the as-deposited a-Ge film to oxidize the film surface without substrate heating, where a thickness of the GeO x  layer is controlled by the oxidation time and the pressure of the ozone. In one example, the GeO x  thickness and oxygen stoichiometry x is determined by the oxidation time, using an O 3  partial pressure fixed at 0.05 Torr. Oxidized samples are immediately transferred to the electron-beam evaporation system and used as the substrate for Al layer deposition. The thickness of blank Al films (for crystallization kinetics studies) and patterned Al pads (for bias stressing) can be 50 nm. 
         [0032]    In another embodiment of the invention, annealing can be carried out at temperatures up to 300° C. in ultra high vacuum, where the annealing time can be a duration of up to 6 hrs, and the annealing environments can include vacuum, hydrogen, nitrogen, or argon. 
         [0033]    According to one embodiment, bias-voltage stressing of the GeO x  layer controls the areal density of the crystalline Ge islands. In one aspect, the bias-voltage stressing includes applying an electric field between the Al layer and the a-Ge layer, where the electric field has a strength of up to 2×10 7  V/cm, and for a duration of up to 1 hour. In one example, a Ti layer and a 25 nm Pt layer are deposited sequentially as the back electrode prior to 100 nm a-Ge deposition, and Al films were patterned into 200 μm diameter circular pads. A computer-programmed voltage source (Keithley 230) can be applied a constant bias between the Al pad and the underlying Pt/Ti metal layers. The voltage drop across the GeO x  layer is defined by the applied bias. 
         [0034]    Layer exchange crystallization of a-Ge seeded by Al was directly observed by imaging Ge islands on the Al film surface with elemental contrast after annealing. During thermal annealing, Ge atoms diffuse upwards through the GeO x  interfacial layer to the Al surface, nucleate polycrystalline Ge islands on the Al surface and these overgrow laterally until impinging with one another, resulting in a distribution of Al and Ge elements on the sample surface prior to completion of a-Ge crystallization.  FIGS. 1   a - 1   b  show plan-view scanning electron microscopy (SEM) micrographs  100  for the samples annealed for 90 min and 3 h, respectively. The bright contrast regions in  FIG. 1   a  are Ge-rich, and the dark contrast regions in  FIG. 1   a  are Al-rich.  FIG. 1   b  shows near-complete Ge surface coverage after annealing for 3 h at 250° C. Given sufficiently long annealing time, crystalline Ge can substantially cover the original Al surface. 
         [0035]    SEM was used to characterize Ge surface coverage on the Al layer for all the annealed samples in the following example. Imaging the Ge surface distribution at various stages of crystallization allows one to independently measure the areal density and average area of Ge crystal islands as a function of annealing time. The size of Ge islands is correlated with the size of Ge grains within them. The islands are composed of multiple grains. The thickness of the Ge islands remains approximately constant as they grow laterally, which is indicated by the uniform thickness of as-crystallized Ge layers observed in cross-section TEM characterization.  FIGS. 2   a - 2   b  show Ge surface coverage SEM images  200 , where the GE surface coverage, or the area fraction of Ge on Al, increases after annealing at 250° C. for 15, 30, 45, 60, 90, 120, and 180 minutes. The SEM images, one displayed per sample, were from two sample batches: one batch with a thin GeO x  interfacial layer prepared by 35 s O 3 -oxidation, as shown in  FIG. 2   a ; and the other with a GeO x  layer prepared by 45 s O 3 -oxidation, as shown in  FIG. 2   b . The scale bar for all the SEM images  200  is 20 μm. Detailed analysis of the SEM images  200  indicates how Ge island nucleation and growth behave as a function of GeO x  layer characteristics and annealing temperatures at various stages of crystallization. 
         [0036]    The effects of local bias-voltage induced dielectric breakdown of the GeO x  layers are discussed, where local bias-voltage induced dielectric breakdown of the GeO x  layers provides a way to tune the density of nucleated Ge islands with an applied electrical field (see  FIG. 6   c ). As an example, Al pads (200 μm in diameter) were patterned on the a-Ge film with an O 3 -grown GeO x  layer. Then, 1.0V DC bias was applied to individual Al pads for different durations, e.g. 16 s and 140 s, with the sample annealed immediately thereafter at 200° C. for 20 minutes in vacuum to induce island nucleation. Statistically, there are two types of biasing history  300 , as shown in  FIG. 3 . Here, the solid-line curve represents one type of biasing history in which current spikes occur periodically (e.g. at times &lt;140 s) and the leakage current density gradually increases, an indication of accumulated damage in the GeO x  layer akin to soft dielectric breakdown. The dashed-line curve represents the other type of biasing history, where the current density remains low before the occurrence of any significant change in the current density, and then the bias is removed. The cumulative charge per area that flows across the GeO x  layers for both types of biasing experiments is on the order of 10 −2  C cm −2  and 10 −7  C cm −2 , respectively. The density of nucleated Ge islands varies significantly as a function of the biasing history, as indicated by the series of SEM micrographs  400  in  FIGS. 4   a - 4   c . DC bias stressing increases the density of defective sites in the GeO x  layer, and thus controls the areal density of Ge islands nucleated on the Al film surface. 
         [0037]    At various stages of crystallization, the areal density and average area of Ge crystal islands on the Al layer was measured and the results were compared to a proposed kinetic model for layer exchange crystallization. The images, which were collected from random locations on each sample, were analyzed with the software package Image. The bright contrast regions were marked and counted as crystallized Ge islands, in keeping with the contrast differences observed in  FIGS. 1   a - 1   b . Each data point is obtained by statistical analysis of the images collected from each sample.  FIG. 5   a  shows the nucleation behavior  500  for different interfacial layers (GeO x  grown by room temperature O 3 -oxidation for 35 s vs. 45 s) after layer exchange annealing at 250° C. There is an upper limit for the density of Ge islands, which saturates at 1.206×10 6  cm −2  for the GeO x  layer prepared by 35 s oxidation and 9.21×10 5  cm −2  for the layer prepared by 45 s oxidation after ˜30 min and ˜60 min anneals, respectively. It is assumed there is an existence of a fixed number of randomly distributed sites where Ge islands could possibly nucleate (the areal density of fast-diffusion paths through the GeO x  layer), characteristic of the a-Ge oxidation time. Maximum nucleus density was achieved prior to coalescence of most of the Ge islands and within 10&#39;s of minutes of annealing, which suggests a decaying nucleation rate with time. Ge island growth for the 35 s and 45 s samples with different maximum nucleus densities was also measured, as shown in  FIG. 5   b  and  FIG. 5   c . Below, a model for island nucleation, growth and coalescence is described, which will guide the subsequent analysis. 
         [0038]    For growth of individual Ge islands, two limiting cases are considered: 1) linear radial growth, characterized by transformation of Ge atoms in the amorphous phase to the crystalline phase at the island growth front and 2) Ge surface diffusion-limited growth, characterized by Ge surface atomic fluence that decreases with the island radius and the annealing time.  FIGS. 6   a - 6   c  schematically illustrate the nucleation  600 , where  FIG. 6   a  shows lateral growth and coalescence of disk-shaped crystalline Ge islands  602  on the surface of the Al layer  604  during annealing. As shown in  FIG. 6   b , microscopically, Ge atoms diffuse from the a-Ge layer  606 , shown disposed on a substrate  610  through the GeO x  layer  608  via a low areal density of fast-diffusion paths, become surface adsorbed adatoms along Al/Ge interface or on the Al surface, and contribute to the lateral growth of crystalline Ge islands. Upward diffusion of Ge atoms to Al film surface is likely through grain boundaries in the Al film.  FIG. 6   c  shows a patterned Al layer  612 , where the patterned layer includes a pattern of pads  614  that have a cross length in a range of 1 μm to 500 μm. 
         [0039]    When there is a transition between the two growth regimes, one expects a Ge island of radius r I  to initially grow radially at a constant rate v G  up to a threshold radius r T , with further growth being diffusion-limited. The subject model assumes that Ge islands nucleate with a cylindrical shape  602  (see  FIG. 6   a ) at a critical radius r e  and that the initial growth rate v G  is temperature dependent with an activation energy of Q G , which is related to the energy barrier for Ge atoms to migrate across the growth front. The diffusion-limited growth velocity is: 
         [0000]    
       
         
           
             
               
                 
                   
                     v 
                     = 
                     
                       
                         
                            
                           
                             r 
                             I 
                           
                         
                         
                            
                           t 
                         
                       
                       = 
                       
                         
                           D 
                           * 
                         
                         
                           
                             r 
                             I 
                           
                            
                           
                             ln 
                              
                             
                               ( 
                               
                                 
                                   r 
                                   I 
                                 
                                 / 
                                 
                                   r 
                                   e 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where r I  is the radius of island growth front, and r e  is the critical radius at which the Ge island nucleates initially. D* is defined as the effective diffusion coefficient, which is a measure of the surface or interface chemical diffusivity for Ge atoms diffusion on the Al film surface or along the Al/Ge interface. The growth of individual Ge islands can be described in the following compact form. Continuity of island growth velocity at r I =r T  is imposed to combine the two growth mechanisms, resulting in: 
         [0000]    
       
         
           
             
               
                 
                   v 
                   = 
                   
                     
                       
                          
                         
                           r 
                           I 
                         
                       
                       
                          
                         t 
                       
                     
                     = 
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   v 
                                   0 
                                 
                                  
                                 
                                   exp 
                                    
                                   
                                     ( 
                                     
                                       
                                         - 
                                         
                                           Q 
                                           G 
                                         
                                       
                                       / 
                                       kT 
                                     
                                     ) 
                                   
                                 
                               
                               , 
                               
                                 
                                   r 
                                   I 
                                 
                                 ≤ 
                                 
                                   r 
                                   T 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   D 
                                   * 
                                 
                                 
                                   
                                     r 
                                     I 
                                   
                                    
                                   
                                     ln 
                                      
                                     
                                       ( 
                                       
                                         
                                           r 
                                           I 
                                         
                                         / 
                                         
                                           r 
                                           e 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                               , 
                               
                                 
                                   r 
                                   I 
                                 
                                 &gt; 
                                 
                                   r 
                                   T 
                                 
                               
                               , 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    with the threshold radius r T  satisfying, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       D 
                       * 
                     
                     
                       
                         r 
                         T 
                       
                        
                       
                         ln 
                          
                         
                           ( 
                           
                             
                               r 
                               T 
                             
                             / 
                             
                               r 
                               e 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       v 
                       G 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    In the linear growth regime, v 0  is a temperature-independent pre-factor and Q G  is the activation energy for the temperature-dependent growth rate v G . At temperature T, the transition point to diffusion-limited growth will depend on the relative values of the constant growth rate v G  and the effective surface diffusion coefficient D*. The area fraction of Ge on Al, which is the degree of layer exchange crystallization f(t), is written as: 
         [0000]        f ( t )=1−exp(− A   e   /A )=1−exp(−∫ 0   t   {dot over (N)}   N (τ) Y (τ, t ) d τ),  (4)
 
         [0000]    where A is the sample surface area, A e  is the extended area, {dot over (N)} N  (τ) is the nucleation rate at time τ, and Y(τ,t) is the area of a Ge island that nucleates at timer and grows until time t. Here, it is assumed that growth rates of individual Ge islands involve the supply of Ge atoms from underneath the central region of nucleated Ge islands. 
         [0040]    Two methods were used to track the time dependence of the average area of the Ge islands, as a proxy measure of Ge island growth: (1) directly counting islands when there is no impingement, and (2) indirectly calculating the average area from the measured surface area fraction and the areal density of Ge islands nucleated on the film surface using Eq. (4) after coalescence of Ge islands begins. The integration in the exponential term of Eq. (4) is approximately equal to the product of the nucleation density and the average area of the Ge islands overgrowing the Al film. The second method is a good estimate because the nucleus density quickly saturates prior to coalescence of most Ge islands during annealing. The values from the direct measurements and the indirect calculations are identical when there is no coalescence. Furthermore, the second method considers the contribution of Ge island growth to an increase in the extended area that is calculated from Ge surface coverage in  FIG. 5   b , an important intermediate step for the growth kinetics analysis. Although the apparently fractal growth in  FIGS. 2   a - 2   b  and in reported Au/Ge crystallization indicates local anisotropy of the growth velocity, the assumption of isotropic radial growth of Ge islands is in reasonably good agreement with the measured data. As shown in  FIG. 5   c , the data points for the 35 s GeO x  layer exhibit a parabolic increase of average island area with time, indicating linear growth with a constant radial growth velocity. Data for the 45 s GeO x  layer exhibit a non-linear increase of the island area with time at later stages of annealing, indicating diffusion-limited growth. 
         [0041]    Interestingly, one of the two distinctive growth mechanisms appears to dominate after ˜60 min annealing, depending on the areal density of nucleated Ge islands as a result of using different interfacial layers. As the island density decreases, the average distance between neighboring Ge islands increases. Without coalescence considered, a Ge island should follow a transition from linear radial growth (e.g. atomic-transformation-limited) to surface diffusion-limited growth, consistent with the results shown in  FIG. 5   c  for the GeO x  layer prepared by 45 s O 3 -oxidation. However, if the poly-Ge islands begin to impinge on one-another, neighboring Ge islands impose geometric constraints on each island&#39;s lateral growth. If the average island separation is small enough, e.g. for the 35 s GeO x  samples, a substantial number of Ge islands coalesce prior to the transition to the diffusion-limited growth regime. The Ge surface area fraction on the Al layer continues to increase as displayed in  FIG. 5   b , while the extended area fraction increases in a parabolic fashion with time. The  FIG. 5   c  insets show the calculated growth velocities as a function of the Ge island radius based on the measured average area. When the sum of the radii of two neighboring Ge islands exceeds the average island separation, substantial island coalescence occurs and lateral growth is no longer the case for the majority of Ge islands, as indicated by the dashed line in the  FIG. 5   c  insets. The threshold radius (˜3 μm) extracted from the calculated growth velocities is comparable to the average distance between neighboring Ge islands for the 45 s GeO x  samples. This may explain why a small decrease in this average distance inhibits the transition to the diffusion-limited growth regime, when switching from the 45 s GeO x  samples to the 35 s GeO x  samples. 
         [0042]    In addition, the temperature dependence of Ge island nucleation and growth is discussed. The samples prepared by 35 s O 3 -oxidation are emphasized here, and the previous analysis is repeated for both 200° C. and 300° C. annealing. The measured data points are interpreted using the aforementioned model, with fitted parameters listed in Table 1. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 List of fitted parameters for the kinetics model of nanoscale nucleation and lateral growth of Ge islands in two dimensions. 
               
             
          
           
               
                   
                 Maximum 
                 Nucleation 
                   
                 Linear growth 
                 Diffusion-limited growth 
               
             
          
           
               
                 Sample and 
                 nucleus density, 
                 saturation time, 
                 Growth 
                 velocity, 
                 Effective diffusion 
                 Size of critical 
               
               
                 annealing condition 
                 N 0  [10 4  cm −2 ] 
                 τ N  [min] 
                 Mechanism 
                 v 0  [nm min −1 ] 
                 coefficient, D* [cm 2  s −1 ] 
                 nuclei, r e  [μm] 
               
               
                   
               
             
          
           
               
                 GeO x  by 35 s O 3     −     
                 117.7 ± 4.5  
                 11.5 
                 Linear growth 
                 51 ± 1 
                 Not applicable 
               
               
                 oxidation/250° C. 
               
             
          
           
               
                 GeO x  by 45 s O 3     −     
                 92.1 ± 4.2 
                 14.3 
                 Linear growth/ 
                 51 ± 1 
                 (2.13 ± 0.25) × 10 −11  [a] 
                 0.83 ± 0.01 
               
               
                 oxidation/250° C. 
                   
                   
                 diffusion-limited 
               
               
                 GeO x  by 35 s O 3     −     
                 79.1 ± 3.5 
                 τ→0 
                 Mostly 
                  7.9 ± 0.8 
                 (4.28 ± 0.17) × 10 −13  [a] 
                 2.0 ± 0.1 
               
               
                 oxidation/200° C. 
                   
                   
                 diffusion-limited 
               
             
          
           
               
                 GeO x  by 35 s O 3     −     
                 &gt;150 
                 Not applicable 
                 Linear growth 
                 400 ± 20 
                 Not applicable 
               
               
                 oxidation/300° C. 
               
               
                   
               
             
          
         
       
     
         [0043]    First, the maximum nucleus density N 0  and the nucleation saturation time τ N  are fitted from the measured nucleation kinetics for the various GeO x  interfacial layers and annealing conditions investigated. The linear growth velocity v 0  is estimated from the growth kinetics in the linear regime only. The effective diffusion coefficient D* and average size of island critical nuclei r e  are fitted to Eq. (2) from the growth kinetics data in the diffusion-limited regime. Finally, the threshold radius r T  is calculated from v 0 , D* and r e  using Eq. (3). The calculated curves for the density and average area of the Ge islands are least-squares fits to the model and are also plotted in  FIG. 5   a  and  FIGS. 7   a - 7   b  ( 700 ).  FIG. 7   a  shows the areal density of nucleated Ge islands vs. annealing time, with the maximum nucleus density equal to 7.91×10 5  cm −2  for 200° C. annealing and with the Avrami time constant τ N  close to zero. Lower annealing temperature reduces the probability of a certain nucleation site being active, decreasing the maximum nucleus density.  FIG. 7   b  shows Ge island growth after 200° C., 250° C. and 300° C. annealing. The growth at 300° C. exhibited linear growth kinetics at a constant radial island growth rate of 400±20 nm min −1 . The activation energy for the growth velocities is estimated to be 0.90±0.11 eV. On the other hand, the growth at 200° C. exhibited a strongly diffusion-limited mechanism, with the transition to surface diffusion-limited growth occurring at an early stage of annealing. 
         [0044]    Such a disparity in the growth mechanisms for 250° C. and 300° C. vs. 200° C. annealing indicates the temperature dependence of the threshold radius, characteristic of the transition. Both linear growth (e.g. Ge atom attachment to the island growth front) and Ge surface diffusion on the Al layer are thermally activated processes. Analysis of the data in  FIGS. 7   a - 7   b  indicates that when the annealing temperature decreases from 250° C. to 200° C., the constant growth rate, v G , reduces by a factor of ˜⅙, while the effective surface diffusion coefficient, D*, decreases by ˜2 orders of magnitude. The diffusion-limited growth velocity decreases much more strongly with temperature reduction, so that the threshold radius shifts to a smaller value for lower annealing temperatures. While the maximum nucleus density is also reduced at 200° C., the growth of Ge islands is strongly diffusion-limited. Such insights are critical in optimizing annealing temperatures and time to produce an efficient process of minimal thermal budget for device fabrication. Modeling Ge layer exchange crystallization as a simple one-step kinetic process, the natural assumption in the absence of the thorough mechanistic description provided in this work is inadequate to predict rates and design the metal-induced crystallization process. 
         [0045]    The present invention has now been described in accordance with several exemplary embodiments, which are intended to be illustrative in all aspects, rather than restrictive. Thus, the present invention is capable of many variations in detailed implementation, which may be derived from the description contained herein by a person of ordinary skill in the art. All such variations are considered to be within the scope and spirit of the present invention as defined by the following claims and their legal equivalents.