(Invited, Digital Presentation) Langmuir-Type Formulation for Atomic-Order Surface Reactions of Reactant Gases on Si (100) and Ge (100) Surfaces
Authors: Murota Junichi 
Published: February 2024

Accurate knowledge of atomically controlled processing for group IV semiconductors is very important for the fabrication of Si-based ultrasmall devices in ultralarge-scale integration [1]. In this review, the Langmuir-type formulation is performed for atomic-order surface reactions of reactant gases on group IV semiconductor (100) surface in ultraclean hot-wall low-pressure CVD.
Now, assuming that one reactant molecule M is adsorbed at one free surface site with partial decomposition of M, total site density n0 on the surface is given by

n
0 = Q
s + Q
Ms, (1)
where Q
s is density of free site; Q
Ms, the site density where M is adsorbed.
Then the surface adsorption velocity of Q
Ms is given by
dQ
Ms/dt = k
Ms
P
M
Q
s - k
-Ms
Q
Ms = k
Ms
P
M
n
0 - (k
Ms
P
M + k
-M) Q
Ms, (2)
where k
Ms and k
-Ms is adsorption and desorption rate constants of M, respectively; P
M, partial pressure of M. The integration of eq. (2) with Q
Ms = 0 at t =0 gives

Q
Ms= [k
Ms
P
M
n
0/(k
Ms
P
M + k
-Ms)]{1 - exp[ - (k
Ms
P
M + k
-Ms)t]}. (3)
The self-limited adsorption given by eq. (3) with fitted n
0 and k
Ms (k
-Ms = 0) fits the experimental data of CH4 on Si(100) at 500-600oC [2], SiH3CH3 on Si and Ge(100) at 450oC [3], B2H6 on hydrogen(H)-free Si (100) at 180oC [4], PH3 on Ge (100) at 300oC [5], SiH4 on H-free Ge (100) at 260oC [6]. It is mentioned that H-free surface is prepared by preheating at the higher temperature than around 400oC on Si (100) and 300oC on Ge (100) in Ar and at the higher temperature the self-limited amount is scarcely influenced even by H2 in the present condition.
In the case of NH3 at 400oC on H-terminated Si (100) [7] and SiH4 at 260oC on H-terminated Ge (100) [6], it is proposed that the NH3 or SiH4 molecules are physically adsorbed self-limitedly at H-terminated sites. Then, total site density n
H0 is given by

n
H0 = Q
Hs + Q
MHs + Q
HMR, (4)
where Q
Hs is the site density of H-terminated site; Q
HMs, the site density where M is adsorbed physically at H-terminated site; Q
HMR, the site density where physically adsorbed M at H-terminated site decomposes partially. If the relationship between Q
Hs and Q
HMs is Q
HMs=K
HM
Q
Hs with thermal equilibrium constant K
HM, the surface decomposition velocity of Q
HMR is given by
dQ
HMR/dt = k
HMR
Q
HMR = k
HMR
K
HM
P
M(n
H0 - Q
HMR), (5)
where k
HMR is partial decomposition rate constant of adsorbed M.
The integration of Eq. (5) with Q
HMR = 0 at t =0 gives

Q
HMR=n
H0(1 - exp { - [k
HMR
K
HM
P
M/(1 + K
HM
P
M)]t}). (6)
The H-terminated surface is composed of H-free and H-terminated sites. For fraction x of the H-terminated sites, total site density is n
0 (1 - x) + n
H0 x and the self-limited amount is given by Q
Ms (1 - x) + Q
HMR x.
The self-limited adsorption/reaction for NH3 at 400oC on H-terminated Si (100) surface and SiH4 at 260oC on H-terminated Ge (100) surface given by eqs. (3) and (6) with x, n
0, n
H0, k
Ms, K
HM and k
HMR fits the experimental data.
For the SiH4, SiH3CH3 or PH3 where total site density on the surface is equal to substrate surface atomic density n
SSA, it is assumed that the site is the pair site such as Si-Si, Si-Ge or Ge-Ge pair. For CH4, B2H6 or NH3 where the total site density is equal to 2n
SSA, it is proposed that the site is one bond of Si or Ge. In the PH3 on Si (100) [5], it is assumed that P atoms of maximum 2n
SSA are adsorbed with self-limited reaction rate constant of PH3 at the P occupied sites where PH3 molecules have been adsorbed at Si-Si pair sites [8].
These results demonstrate that the atomic level surface reactions of reactant gases in the practical low-pressure CVD are explained based on the modified Langmuir-type model.
References: [1] J. Murota et al., Jpn. J. Appl. Phys.,
45, 6767 (2006). [2] A. Izena et al., J. Cryst. Growth,
188, 131 (1998). [3] T. Takatsuka et al., Appl. Surf. Sci., 162-163, 156 (2000). [4] H. Tanno et al., Solid-State Electron.,
53, 877 (2009). [5] Y. Shimamune et al., Appl. Surf. Sci, 162–163, 390 (2000). [6] T. Watanabe et al., Jpn. J. App. Phys.,
36, 4042 (1997). [7] T. Watanabe et al., J. Electrochem. Soc.,
145,425 (1998). [8] J. Murota et al., ECS J. Solid State Sci. Technol., 10, 024005 (2021).