28
Growth of Germanium, Silicon, and Ge–Si Heterostructured Nanowires
         
C
in

C
0(NW)
, as
CC Ce e
dkT
µ
kT
in NW

-=
Ê
Ë
Á
Á
ˆ
¯
˜
˜
-
Ê
Ë
Á
Á
ˆ
¯
˜
˜
0
4
1
()
W
D
a
. (2.3)


For a constant diameter and at a constant temperature T
1
an increase


 µ/kT, and therefore an increase in the growth
v/b, is plotted to

       
in the temperature section. As the temperature decreases toward

          
in Fig. 2.2a. Therefore, for the same input partial pressure, the
      
must increase as the temperature is increased as depicted for the
case of T
2
< T
1
in Fig. 2.2b. On the other hand, as the temperature



growth rate must decrease as shown for the case of T
3
> T
1
in Fig. 2.2b.
         
        
rate on temperature and pressure, as discussed in the forthcoming
sections.

put the analysis in the context of the three processes commonly

    
R
1

through the Au particle, R
2

solid interface, R
3
, limited by nucleation of step ledges.
28
R
2
is not



29
The VLS Growth Mechanism


rate is not fast enough compared with its sidewall deposition growth
rate for comparable high aspect ratio NW growth.
28,29
       R
1
resembles an
   
4
    
interface and R
3
      

      R
3
   
        R
1
  
interface (both are area normalized), and the growth proceeds
        
µ


at otherwise constant temperature and pressure, µ
s
increases and
µ


case, R
3
R
1
decreases by a reduction of

4
decomposition and incorporation at the


4
partial pressure increases, R
1

R
3
increases leading to a higher growth rate, as we will discuss in the
Pressure Effects section. From this, we conclude that during steady
state NW growth, it is misleading to isolate either R
1
or R
3
as the

growth. For a constant diameter and pressure, if the temperature
µ

decreases but the temperature-dependent reaction
R
1
and similarly at
R
3
leading to higher growth rates
with temperature.


complexities and misinterpretations which can arise in the growth


        
         
   
30
  
adatom mean free paths
31

        
        
32,33
   
30
Growth of Germanium, Silicon, and Ge–Si Heterostructured Nanowires
group III materials is generally orders of magnitude higher than
     
34
The eutectic growth nanoparticle
comprises therefore of Au-group III composition. Since the mean


nanoparticle can be limited by the complex interplay between these
two growth precursors.
31
As such, a high growth temperature can



temperatures.
30
We state therefore that pulling the growth conditions
largely away from those that produce uniform NW morphologies,


misinterpretation of experimental data. Care must be exercised


presence of contaminants or low pressures and/or temperatures,

2.3 Size Effects in Nanowire Growth

of NWs are dependent on the size of the metal nanoparticle.

D
D
µ
kT
µ
kT kT d
=-
0
1
4a

. (2.4)
 µ
0
is the supersaturation of the semiconductor material
           
          
     
First, as the diameter of the NW decreases the magnitude of the
right hand term increases, and this corresponds to a reduction in



few nanometers eliminates the supersaturation condition in the
growing nanoparticle such that NW growth ceases below a minimal
critical diameter, d
c


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