# Wetting layer evolution and its temperature dependence during self-assembly of InAs/GaAs quantum dots

- Hongyi Zhang
^{1}, - Yonghai Chen
^{1}Email author, - Guanyu Zhou
^{1}, - Chenguang Tang
^{1}and - Zhanguo Wang
^{1}

**7**:600

https://doi.org/10.1186/1556-276X-7-600

© Zhang et al.; licensee Springer. 2012

**Received: **7 September 2012

**Accepted: **10 October 2012

**Published: **30 October 2012

## Abstract

For InAs/GaAs(001) quantum dot (QD) system, the wetting layer (WL) evolution and its temperature dependence were studied using reflectance difference spectroscopy and were analyzed with a rate equation model. WL thicknesses showed a monotonic increase at relatively low growth temperatures but showed an initial increase and then decrease at higher temperatures, which were unexpected from a thermodynamic understanding. By adopting a rate equation model, the temperature dependence of QD formation rate was assigned as the origin of different WL evolutions. A brief discussion on the indium desorption was given. Those results gave hints of the kinetic aspects of QD self-assembly.

### Keywords

Quantum dots Stranski-Krastanov growth mode Wetting layer Desorption Growth kinetics 81.07.Ta 81.05.Ea 68.08.Bc 78,67,Hc 68.35.Rh## Background

Epitaxial semiconductor quantum dots (QDs) have attracted much attention because of their application potential in novel optoelectronic devices [1–3]. They are usually fabricated utilizing the lattice mismatch between the epitaxial layer and substrate or the Stranski-Krastanov (SK) growth mode. It can be described as follows: for small coverage, two-dimensional (2D) layer-by-layer growth and pseudomorphic formation of wetting layer (WL) take place. When the WL reaches a certain critical thickness (CT), a 2D to three-dimensional (3D) transition starts, and QDs form on the substrate*.* QDs with high homogeneity in their size and shape are highly advantageous in applications. Basically, the WL configuration would also influence the optical properties of QDs and the performance of QD-based devices [4–7]. A controllable growth of QDs with desired properties requires a comprehensive understanding on the growth process. Therefore, it is necessary to have a clear understanding of the WL evolution during the QD self-assembly.

The commonly accepted thermodynamic understanding of the SK mode describes the QD formation on top of a WL of a certain thickness. However, it is not accurate in real situations. It has been reported that in the Ge/Si QD system, the WL thickness decreases after QD formation [8–10]. It is interpreted in the regime of kinetically controlled QD formation and growth. Since material transfer from WL to QDs sustains the QD formation and growth, a large material consumption rate by QD formation may induce the observed WL erosion [8, 9]. As for InAs/GaAs system, a step erosion of WL has also been observed after QD formation [11, 12]. Until now, there is no complete description of the WL evolution and its growth condition dependence. In our previous work, reflectance difference spectroscopy (RDS) was used to study the WLs in self-assembled nanostructures. Due to its sensitivity, heavy hole (HH)- and light hole (LH)-related transition energies before and after QD formation can be directly obtained from the resonant structures in the spectra [13–16]. In this paper, we studied the WL evolution and its temperature dependence based on RDS measurements. We found that, generally, there were two kinds of WL evolution, with deposition depending on growth temperatures. They were well explained in the regime of temperature dependence of QD growth rate with a rate equation model. The concave-up style of evolution was considered as a clear evidence for a non-zero QD growth rate when the WL thickness was smaller than the CT. We also gave a simple discussion on indium desorption during self-assembly. All of these results showed the kinetic aspects of WL evolution in the SK growth.

## Methods

Six InAs/GaAs(001) QD samples with different growth temperatures (from 490°C to 540°C, with an increment of 10°C) were grown in our Riber-32p molecular beam epitaxy (MBE) system. A 100-nm GaAs buffer layer was firstly deposited on 2-in semi-insulating GaAs substrates at 600°C. A nominal InAs amount of 2.0 monolayer (ML) (1.9 ML for the sample grown at 510°C) was then deposited with a calibrated rate of 0.1 ML/s at a controlled substrate temperature. A gradually changed InAs amount was achieved by stopping the substrate rotation. This method was widely used in studying the QD growth dynamics and to fabricate QD samples with low areal density [8, 10, 13, 17]. The effective indium flux and real deposition amount could be calibrated based on the cosine law for certain configurations of the MBE source beam [18]. Growth interruption (GI) of 10 s was introduced after InAs layer deposition. A 100-nm GaAs capping layer was then grown at 600°C. Details of the sample growth processes can be found in another study [16]. For further spectroscopy measurements, the samples were cut into 16 pieces along the direction corresponding to which the InAs amount increased gradually. To evaluate the WL information, the relative reflectance difference in the sample surface plane, i.e., $r/r=2\left({r}_{\left[110\right]}-{r}_{\left[11-0\right]}\right)/\left({r}_{\left[110\right]}+{r}_{\left[11-0\right]}\right)$, was measured with the RDS technique in ambient conditions. The setup of our RDS was reported elsewhere [19].

## Results and discussion

*θ*is the WL thickness,

*t*

_{ c }is the time of the 2D growth stage, and

*G*is the InAs deposition rate. The indium desorption rate is presumed to be proportional to the InAs amount in WL, and

*τ*

_{ des }represents the desorption time constant. The indium desorption process is generally considered as thermally activated [23, 24];

*τ*

_{ des }can be written as ${\tau}_{\mathit{\text{des}}}=\frac{1}{{\nu}_{0}}\text{exp}\left(\frac{{E}_{\mathit{\text{des}}}}{kT}\right)$, where

*v*

_{0}is a pre-exponential factor and

*E*

_{ des }is the activation energy of the indium desorption process. By solving Equation 1, the WL thickness versus growth time can be written as follows:

*F*

_{ QD }is used to represent the InAs consumption rate by the QD formation and growth [25].

*F*

_{ QD }is determined by the instability of WL and the material diffusion from WL to QDs [26]. The diffusion rate can be written as

*D*

_{ In }= (2

*k*

_{ B }

*T*/

*h*) exp (−

*E*

_{ dif }/

*k*

_{ B }

*T*), [26] where

*k*

_{ B }is Boltzmann's constant,

*h*is Planck's constant,

*T*is the substrate temperature and

*E*

_{ dif }is the energy barrier. In previous works, for a WL thickness of

*θ*, the instability of WL is commonly considered as (

*θ*−

*θ*

_{ c }). The driving force of QD growth, which is known as ‘superstress’, is defined as

*ξ*= (

*θ*−

*θ*

_{ c }) /

*θ*

_{ c }[27]. However, it is not suitable in describing our experimental results. The concave-up style of evolution shown in the upper panel of Figure 1b means a non-zero QD growth rate when the WL thickness is slightly below the CT, or else, the WL thickness would not reduce below the CT in the presence of sufficient InAs supply. A non-stopping QD formation when the WL thickness is smaller than the CT is also documented in previous experiments [28–30]. Hence, the unstable part of WL is written as (

*θ*−

*αθ*

_{ c }), (0 <

*α*< 1); correspondingly, the superstress is written as

*ξ*= (

*θ*−

*αθ*

_{ c }) /

*αθ*

_{ c }(0 <

*α*< 1). The QD formation and growth rate

*γ*is considered to be exponentially dependent on the superstress or

*γ*=

*b*exp (

*βξ*), where

*b*and

*β*were constant parameters [31, 32]. Consequently,

*F*

_{ QD }can be written as follows:

*dθ*/

*dt*< 0) resulted from the temperature dependence of QD formation rate,

*F*

_{ QD }. WL thickness would suffer a decrease if the deposition rate is not large enough to sustain the QD growth at the beginning of the 3D evolution stage.

*F*

_{ QD }then drops correspondingly according to its dependence on the superstress. It takes some time for the WL thickness to be stable to a certain value, for which the material deposition and the QD growth reach a balance. The bigger the deposition rate is, the thicker the stabilized WL. However, if the QD formation rate for the critical WL thickness is lower than the corresponding deposition rate, e.g., a lower growth temperature, WL thickness would keep on increasing after QD formation, which is the case in Figure 2a.

*G*= 0 in Equations 2 and 3 and calculate with the WL thicknesses after deposition as initial values. The simulation results of WL evolution at different temperatures are shown in Figure 3a. One could see that the main features are well reproduced compared with the experimental results. The WL thickness shows a monotonic increase if the temperature is set at 490°C but shows a concave-up evolution for temperatures of 520°C and 540°C. According to the discussion above, we know that the slowed down increase observed at lower temperature is because of the deposition rate dependence of the equilibrium WL thickness. For higher growth temperatures, the elevated QD formation rate at the beginning of the 3D growth stage led to WL erosion, which corresponds to the decrease of WL thickness on those non-rotating samples. WL thickness increases again with the deposition rate when the growth reaches equilibrium. It should also be noted that the simple equations do not reproduce the experimental results quantitatively because of their semi-empirical nature and the use of some adjustable parameters.

We would like to comment on a special feature of those non-rotating samples. The material deposition rate changes gradually at different positions of a sample, which leads to the same behavior of deposition amount for a given growth time. Considering a weak dependence of the CT on deposition rate, one would expect that it takes different times at those positions of the sample to enter the 3D growth stage. The 2D growth time *t*_{
2D
} can be calculated respectively from Equation 2 by taking *θ* = *θ*_{
c
}. One then obtains the 3D growth time *t*_{
3D
} = *t*_{
InAs
} − *t*_{
2D
}. The inset of Figure 3a shows the 3D growth time with deposition rates. It should be noticed that at some positions, they have very small values. Apparently, a near-zero 3D growth time cannot ensure an equilibrium quantum dot growth nor provide a steady-state WL thickness. It leads to stronger kinetic control characters on those samples.

where *t*_{
InAs
} is the InAs deposition time and *t*_{
GI
} is the GI time. The kinetic parameter of indium desorption, *E*_{
des
}, and *ν*_{
0
}, can be extracted from Equation 5 and Figure 1b. We adopt the WL thicknesses of the first four pieces of each sample with effective InAs deposition amounts of 1.14, 1.24, 1.34, and 1.45 ML to fit *E*_{
des
} and *ν*_{
0
}, respectively. The obtained *E*_{
des
} = 3.68 eV and *ν*_{
0
} are around 5.5 × 10^{22}. The activation energy is close to previously reported InAs decomposition energy and indium desorption activation energy from InGaAs [23, 33]. We notice that the fitting *ν*_{
0
} is such a big number; *ν*_{
0
} stands for the attempt frequency of desorption, which is commonly known with the order of 10^{12} to 10^{14} s^{−1} for desorption from metal and semiconductor surfaces. Such a big transition frequency obtained here is also reported by other groups in investigating the InAs/GaAs QD desorption [33] or As desorption from GaAs surface [34]. It is considered as physically achievable and could explain several characteristic features in InAs MBE growth [34]. The inset of Figure 3b shows the temperature dependence of the desorption life time (*τ*_{
des
}) for samples with different InAs deposition amounts based on the fitting results. The time constants show a weak dependence on the indium flux but strongly decrease with increasing temperature; *τ*_{
des
} decreases from 1,063 s at 490°C to 35 s at 540°C for samples with a deposition amount of 1.45 ML. The same strong dependence is also mentioned elsewhere [35]. Those time constants could be used to estimate the degree of desorption during the growth of InAs/GaAs(001) QDs at a certain temperature.

## Conclusions

In conclusion, two kinds of WL evolution process of InAs/GaAs(001) QD system have been discussed based on RDS measurements and a rate equation model. They were well understood in the regime of material balance of WL growth/consumption and temperature dependence of QD formation. The concave-up style of evolution is also an evidence of a non-zero QD growth rate when the WL thickness was slightly lower than the critical value. We also gave a brief discussion on the indium desorption process during growth. Those results helped us in understanding the kinetically controlled QD growth process.

## Declarations

### Acknowledgments

The work was supported by the National Natural Science Foundation of China (no. 60990313), the 973 program (2012CB921304, 2012CB619306), and the 863 program (2011AA 03A 101).

## Authors’ Affiliations

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