Abstract
Convective mass transfer phenomena become significant in sub-micrometre liquid phase epitaxial layer growth. An aqueous solution containing 0.01m K3Fe(CN)6+0.01m K4Fe(CN)6+1.0m KOH in a Plexiglass vessel was used to simulate the fluid motion and mass transfer condition in liquid phase epitaxy. The mass transfer phenomena between the liquid phase epitaxial system and electrochemical system at mass transfer limiting condition are equivalent. This was theoretically and experimentally verified. The influence of growth conditions, such as growth time (40 ms≤t≤300 s), solution depth (0.625 cm≤H≤1.25 cm), and solution kinematic viscosity (0.0104 cm2s−1≤v≤0.0161 cm2s−1), on the growth rate of the epi-layer were simulated by the electrochemical method. The dependence of simulated epi-layer thickness,L', on growth time,t, can be expressed asL'=αt β. Whent≤0.1 s, the convective mass transfer process predominates and β=0.9±0.2. Whent>0.1 s, the mass transfer rate is controlled by diffusion and β=0.5±0.05.
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Abbreviations
- A :
-
area of epi-layer or electrode (cm2)
- A d :
-
constant in Equations 4 and 5 (cm3 A−1 s−1)
- A c :
-
constant in Equations 12 and 13 (cm3 A−1 s−1)
- a :
-
constant in Equation 14 (-)
- C b :
-
bulk concentration in the LPE system (mol cm−3)
- C' b :
-
bulk concentration in the electrochemical system (mol cm−3)
- C i :
-
surface concentration in LPE system (mol cm−3)
- C s :
-
solid concentration of the epi-layer (mol cm−3)
- D :
-
diffusivity in the LPE system (cm2s−1)
- D' :
-
diffusivity in the electrochemical system (cm2 s−1)
- F :
-
Faraday number (C mol−1)
- H :
-
solution depth (cm)
- I :
-
electric current (A)
- i :
-
electric current density (A cm−2)
- k m :
-
convective mass transfer coefficient in the LPE system (cm s−1)
- k 'm :
-
convective mass transfer coefficient in the electrochemical system (cm s−1)
- L :
-
epi-layer thickness (cm)
- L' :
-
simulated epi-layer thickness by electrochemical method (cm)
- L d :
-
moving distance of slider (cm)
- L w :
-
well length in LPE and electrochemical system (L=0.587 cm) (cm)
- n :
-
number of charge transfer (equiv.mol−1)
- Re :
-
Reynolds number in the LPE system (VL w /v)
- Ré :
-
Reynolds number in the electrochemical system (VL w /v)
- Sc :
-
Schmidt number in the LPE system (v/D)
- Sć :
-
Schmidt number in the electrochemical system (v/D')
- Sh :
-
Sherwood number in the LPE system (k m x/D)
- S′h :
-
Sherwood number in the electrochemical system (k m x/D')
- t :
-
contact time of melt and substrate in LPE system or contact time of solution and electrode in electrochemical system (s)
- t a :
-
approximate contact time (s)
- V :
-
well moving velocity (cm s−1)
- W :
-
well width in LPE and electrochemical system (w=0.813 cm) (cm)
- x :
-
characteristic length (cm)
- y :
-
distance from the solid surface to the solution (cm)
- α:
-
constant in Equation 4
- β:
-
constant in Equation 14
- ν:
-
kinematic viscosity of solution (cm2 s−1)
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Chen, LJ., Hsueh, KL., Wan, CC. et al. Mass transfer rate measurement of short time liquid phase epitaxial growth using an electrochemical method. J Appl Electrochem 21, 998–1004 (1991). https://doi.org/10.1007/BF01077586
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DOI: https://doi.org/10.1007/BF01077586