The intrinsic relationship between the kink-and-tail and box-shaped zinc diffusion profiles in n-GaSb

To analyze the characteristics of the Zn profiles, the Boltzmann–Matano method was used to determine the effective Zn diffusion coefficient (D_eff) as a function of concentration (C). Figure 2(a) shows the results for a kink-and-tail profile (pure Zn, 500 °C, 2 h) and a box profile (Ga-rich, 500 °C, 2 h). Figure 2(b) displays the best fits for the pure Zn and Ga-rich curves from figure 1(a). For the box-shaped profile, the function of D_eff∝C is a good fit for the main region (I), and D_eff∝C⁻² fits the near surface region (II, III). For the kink-and-tail-shaped profile, the three regions are fitted as follows: D_eff∝C is good fit for the tail region (I); D_eff∝C² is the best fit for the highest concentration region (III) and D_eff∝C⁻²fits the short transition region (II) around the kink point. Other profiles in our experiments showed similar trends.

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It is generally accepted that the dissociative [19] or kick-out mechanisms [12] can be used to explain Zn diffusion phenomena in III–V compound semiconductors; the difference between the mechanisms is whether Zn atoms move by occupying the group III vacancies or kicking out the group III atoms in the lattice. From our viewpoint, the mechanism that dominates is determined by the diffusion sources.

Under Ga-rich diffusion conditions, the native Ga vacancies on the surface of GaSb were occupied suppressing the escape of Ga atoms. Zn atoms can only move by kicking out Ga atoms; thus, the kick-out mechanism dominated. This process can be depicted as an interstitial Zn atom (Zn⁺_i) kicking out a lattice-located Ga atom (Ga⁰_Ga) to the interstitial state (I⁺_Ga), after which the Zn atom will become an ionized acceptor (Zn⁻_Ga) and a hole (h⁺) will be produced:

$$\begin{equation} {\rm Zn}_{\rm i}^ + + {\rm Ga}_{{\rm Ga}}^0 \rightleftharpoons {\rm Zn}_{{\rm Ga}}^ - ({\rm Zn}_{\rm s}^ - ) + {\rm I}_{{\rm Ga}}^ + + h^ + . \end{equation} \tag{ 1a }$$

The charge state of the interstitial Ga is considered to be singly ionized due to the low-Fermi level in p-GaSb (Zn doped). Using Fick's second law and mass action law, a simplified calculation method [20] was used to calculate the effective Zn diffusion coefficient (D_eff); it can be expressed as

$$\begin{equation} D_{{\rm eff}} = D_{{\rm sur}} {\rm (}C_x {\rm /}C_{{\rm sur}} {\rm ), i}{\rm .e}{\rm . }D_{{\rm eff}} \propto C, \end{equation} \tag{ 1b }$$

where D_sur and C_surare the surface Zn diffusion coefficient and concentration, respectively, and C_xis the Zn concentration at a depth of x.

Using the above analysis, we revealed that the kick-out diffusion process will behave as the function D_eff∝C if the interstitial Ga atom is singly ionized, which coincides with the main region of the box-shaped profile (figure 2(b)).

Under pure Zn conditions, we assumed that large amounts of Ga vacancies would be formed due to the escaping of Ga atoms from the surface in addition to the small amount of native Ga vacancies inside GaSb. We presumed that the Zn atoms move by occupying the Ga vacancies in priority because it is easier to occupy the existing Ga vacancies than to kick out the Ga atoms in the lattice. This dissociative diffusion process can be depicted as an interstitial Zn atom (Zn⁺_i) moving to occupy a Ga vacancy (V⁰_Ga) and becoming an ionized acceptor (Zn⁻_Ga); this reaction produces two holes (h⁺) according to the charge balance

$$\begin{equation} {\rm Zn}_{\rm i}^ + + {\rm V}_{{\rm Ga}}^0 \rightleftharpoons {\rm Zn}_{{\rm Ga}}^ - ({\rm Zn}_{\rm s}^ - ) + 2h^ + .\end{equation} \tag{ 2a }$$

Using the same calculation method as above, D_eff can be expressed as

$$\begin{equation} D_{{\rm eff}} = D_{{\rm sur}} {\rm (}C_x /C_{{\rm sur}} {\rm )}^2 {\rm , i}{\rm .e}{\rm . }D_{{\rm eff}} \propto C^2 . \end{equation} \tag{ 2b }$$

The above dissociative diffusion process forms the high-concentration diffusion front (figure 2(b)), and behaves as the function D_eff∝C² if the Ga vacancies are neutral, which coincides with the surface region of the kink-and-tail profiles.

Because we assumed that the Ga vacancies inside GaSb were mainly gained by Ga atoms escaping from the surface, with the deepening of diffusion, the concentration of vacancies decreases to a native thermal equilibrium value at the corresponding temperature. The lack of Ga vacancies restricts further diffusion of Zn atoms via the dissociative mechanism. Thus, we deduced that interstitial Zn atoms are forced to move by kicking out the Ga atoms in the lattice and occupying their positions in the tail region. A short transition region (II) between the surface (I) and the tail (III) regions reflects the comparative influence of the dissociative and the kick-out mechanisms. The analysis was corroborated because the tail region had nearly the same shape and relationship between D_eff and C as the box profile with the same diffusion temperature and duration (figure 2).

PL spectroscopy is a non-destructive technique for detecting various types of defects and impurities in semiconductors [21]. Here, we used this technology to further verify the similarity between the main region of the box profiles and the tail region of the kink-and-tail profiles. The PL spectra of the profiles in figure 2(b) with the samples at 13 K were measured at different etching depths from the surface, shown in figures 3(a) and (b).

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In the region beyond the diffusion depth (A6, B7), the PL spectrum exhibited a T-band transition at approximately 740 meV [22], which was the same as the n-GaSb substrates. In the main region of sample A (A3, A4) and the tail region of sample B (B5, B6), the PL spectra showed the same characteristics, which indicates that they have the same types of defects after diffusion, suggesting that the Zn diffuses via the same mechanism in both regions. The peak that develops as the depth increases at approximately 780 meV is related to excess Ga [23–26], indicating that the kick-out mechanism dominates in these regions because the dissociative diffusion process does not produce excess Ga; these data confirm that our previous hypothesis is reasonable. In the near-surface region of sample A (A1, A2) and the high-concentration surface region of sample B (B1–B4), the PL spectra exhibited a large peak at 740 meV and an extremely weak peak at 810 meV caused by excitonic transition. There was no 780 meV peak in the high-concentration surface region of the kink-and-tail profiles; this shows that there was no Ga excess, which demonstrates that Zn diffused via the dissociative mechanism in this region. The concentration of Zn atoms in the surface region (10¹⁹–10²⁰ cm⁻³) exceeded the native concentration of V_Ga (10¹⁷ cm⁻³), indicating that a large amount of Ga atoms in the GaSb crystals escaped from the surface. The box profiles were obtained under Ga-rich conditions, which restrained the escape of the Ga atoms. Thus, the dissociative mechanism only took effect in the very shallow region and was unable to form the high-Zn-concentration surface diffusion front.

Based on the above analysis, we can conclude that Zn moves through Ga vacancies in the surface region of the kink-and-tail profiles and the Ga vacancies are mainly produced through Ga escaping from GaSb wafers. Under pure Zn condition, Ga atoms can escape through their own sublattices, at the same time Ga atoms can easily occupy Sb vacancies (Ga_GaV_SbV_GaGa_Sb) [22, 27] and form antisite Ga atoms (Ga_Sb), those of which near the surface can also escape. Under Sb-rich conditions, Ga atoms can only escape through their own sublattices because the Sb vacancies on the GaSb surface are occupied. The escaping speed of Ga atoms under Sb-rich condition is lower than that of the pure Zn condition, which results in the shallow surface diffusion region (figure 1(a)). The existing Sb atoms do not affect the tail region of the kink-and-tail profiles, and the shapes of the tail region under pure Zn and Sb-rich conditions almost coincide if we cut off the surface region (figure 1(a)).

When the diffusion temperature was above 600 °C, the self-diffusion coefficient of Ga in GaSb became very large. If the Ga atoms were not present in the diffusion sources, the GaSb wafers melt (shown in the insets in figure 1(b)) due to the escape of large amounts of Ga atoms. The difference between the results from Ga-rich versus Sb-rich sources indirectly shows that Ga atoms diffuse more rapidly than Sb atoms, which is consistent with Bracht's results [28].