Origin of the anomalous temperature evolution of photoluminescence peak energy in degenerate InN nanocolumns

Pai-Chun Wei; Surojit Chattopadhyay; Fang-Sheng Lin; Chih-Ming Hsu; Shyankay Jou; Jr-Tai Chen; Ping-Jung Huang; Hsu-Cheng Hsu; Han-Chang Shih; Kuei-Hsien Chen; Li-Chyong Chen

doi:10.1364/OE.17.011690

1. Introduction

The complexity of the indium nitride (InN) material reflects in the large number of publications, each year, attempting to provide a conclusion to the related unresolved issues. The controversy on its inherent intrinsic band gap (E_G) [1–4] and possible origins attributed to it is just one example [5,6]. A closer look at the variation of E_G under varied physical conditions reveal events which are similar in complexity to that of E_G itself. For example, InN does not necessarily obey the conventional trend of lowering of E_G at elevated temperatures [3,7–9]. The observation of a blue shift of the photoluminescence (PL) peak (E_PL) with increasing temperature is in stark contrast with the conventional semiconductor behaviour. However, common trends of red shift [4,9,10] or near invariance [4,9] of the band edge with increasing temperature has also been observed. To propose a unified model to explain such scattered observations of E_PL variation with temperature, Shen et al. [9] proposed a model involving surface electron accumulation due to severe band bending in the InN nanorods. However, the trend of temperature dependent E_PL variation or the absence of it, were also observed for thin film samples [3,7] whose curvature-less surface does not support a spatial charge separation as strong as in nanostructures. Moreover, experimental determination of the density of surface electrons and the extent of resultant band bending is not straightforward [11]. In this report we attempt to provide a more direct and experimentally viable classification of InN material, based on their carrier concentrations (n), which demonstrate the whole range of E_PL(T) variation irrespective of nanostructure or thin film sample geometry. The analysis centers on the variation of electron effective mass with temperature that is plausible given the non-parabolic conduction band in degenerate InN unlike conventional non-degenerate semiconductors.

2. Experimental details

InN nanocolumns were grown on (0001) sapphire substrates by the gas source molecular beam epitaxy (GS-MBE) [12]. Metallic indium (99.9999% purity) was evaporated from a conventional Kundsen cell (K-cell) while nitrogen was supplied from the highly volatile hydrazoic acid (HN₃) [12] during the growth processes. In this study, samples with different carrier densities were achieved by controlling the III/V ratios and incorporating an In pre-deposition layer. Samples S1-S4 was grown using a lower III/V ratio compared to samples S5-S8. In this study, an In pre-deposition layer (~10 nm thick, grown at 550°C) was used to release the strain and assist in the surface migration of adatoms while growing good quality InN on the lattice mismatched sapphire substrates. InN nano-column structures were grown with (S1-S4) and without (S5-S8) the In pre-deposition buffer layer by the same MBE system. The morphologies and structures of InN products were characterized using field emission scanning electron microscopy (FESEM) (JEOL 6700) and high-resolution transmission electron microscopy (HR-TEM, JEOL 2000 FX). The emission properties of the InN samples were studied by conventional PL [12] spectroscopy with 532 nm excitation.

3. Results and discussion

Figure 1 shows a composite image of the InN nanocolumn samples depicting a combined morphology (Fig. 1(a), (b)) and structural (Fig. 1(c), (d)) information. The thickness (length) of the nanocolumn layer is ~800 nm, the diameter and density of the nanocolumns is about 200 nm and ~10⁹ cm⁻², respectively.

Fig. 1 Representative images of vertically quasi-aligned InN nanocolumns; (a) Cross sectional scanning electron microscope (SEM) image, (b) Top view SEM, (c) Cross-sectional high resolution transmission electron microscope (HRTEM) image, and (d) HRTEM image of a selected area from (c). Inset in (d) shows the selected area electron diffraction (SAED) of the wurtzite InN nanocolumns.

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PL measurements (Fig. 2(a) ) demonstrate E_PL as low as 0.71 eV (S1) and blue shifting to 0.81 eV (S8). The relative symmetry of the PL line shape, in S1-S4, is partially lifted, for the samples S5-S8, with a concomitant broadening of the line width resulting in a blue shift of the peak [13].

Fig. 2 (a) Experimental PL spectra (dashed lines), at 20 K, of InN nanocolumns prepared with and without In pre-deposition layer as described in the text. The spectra are vertically shifted for clarity. Fitting results (according to Eq. (6)) are shown by the solid lines for each spectrum. (b) The FWHM of the PL peak as a function of temperature for samples S1-S8. (c) Variation of optical bandgap in InN samples as a function of carrier concentration. InN thin film’s bandgap data collected from literature (□ [14],◊ [15]) and nanocolumns data (E_PL at 20 K) from this work (●) are shown in the same plot. Theoretical variation of InN band gap as a function of carrier concentration is shown for reference assuming (—) parabolic (m* = 0.07 m₀) and (—) non parabolic (see Eq. (2)) conduction band edge.

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However, independent of E_PL, all the samples showed a widening of the full width at half maximum (FWHM) of the PL peak with increase in measurement temperature (Fig. 2(b)). The carrier concentration, n, in the InN sample is related empirically to the FWHM by [14]

\log (FWHM) = 0.50737 \log (n) - 7.5988

Using Eq. (1), the ‘n’ in the InN nanocolumns can be roughly estimated between 4.1 × 10¹⁸ (for S1) and 1.8×10¹⁹ cm⁻³ (for S8), increasing with the blue shift of E_PL (Fig. 2(a)). In order to verify the acceptability of the ‘n’ value estimated using Eq. (1), the observed E_PL at 20K has been plotted as a function of ‘n’ in the light of existing literature data [14,15] and theoretical predictions assuming non-parabolic [14–16] conduction band (E_c) edge (Fig. 2(c)). The non-parabolic conduction band edge is given by

E_{C} (k) = E_{G} + \frac{ℏ^{2} k^{2}}{2 m_{0}} + \frac{1}{2} (\sqrt{E_{G}^{2} + 4 E_{P} \frac{ℏ^{2} k^{2}}{2 m_{0}}} - E_{G})

where E_P is a fitting parameter. For degenerate InN studied here, an extraordinarily good match has been observed between the experimental data and the non-parabolic theoretical fit that supports the acceptance of the ‘n’ values estimated using Eq. (1). Fitting procedures yielded an intrinsic bandgap, E_G = 0.653 eV, and E_P = 12.5 eV. We could now classify the samples, S1-S8, more realistically as a function of ‘n’. The blue shift observed in Fig. 2(a) can now be attributed to the Burstein-Moss (BM) shift.

In contrast to the usual FWHM broadening with temperature (Fig. 2(b)), E_PL(T) shows distinctive evolution (Fig. 3(a) ) depending on ‘n’. In this case, for samples with low (< 5 × 10¹⁸ cm⁻³) and high (> 6 × 10¹⁸ cm⁻³) ‘n’ values, E_PL shows a conventional red shift and an anomalous blue shift, respectively, with increasing temperature (Fig. 3(a)). Interestingly however, there appears an undefined boundary between these two regimes of ‘n’ values (n~5.2 × 10¹⁸ cm⁻³) where the E_PL(T) remain nearly invariant. Such temperature independent E_PL is not new in InN [4,9]. Shen et al. [9] nicely explained the E_PL(T) evolution, as observed in this work, with the help of surface carrier accumulation in InN nanorods. However, the phenomenon could be observed in thin films also [3,7] as shown in Fig. 3(a), where the surface charge accumulation is comparatively less. Moreover, the maximum temperature coefficient of E_PL (dE_PL/dT), ~ ± 0.13 meV/K (Fig. 3(a)), appears to be the same in case of nanorods as well as films which differs in the extent of band bending. Hence there appears a more fundamental explanation to this effect.

Fig. 3 (a) Plot of PL peak energies as a function of temperature for samples S1-S8 (hollow symbols) from this study, and from published references (Thin film (♦ [3,4]), nanorods (● [9], ■ [10])). Estimated carrier concentration values (in units of cm⁻³) are marked for each sample (S1-S8). (b) The schematic of a band diagram according to Eq. (3), showing the electron and hole quasi-Fermi level movement with temperature.

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We begin an analysis of the results with a distinction between E_G and E_PL. Mathematically, we could express this as (Fig. 3(b)),

E_{P L} (n, T) = E_{G} (n, T) + E_{F n} (n, T) - E_{F p} (n, T)

where E_Fn and E_Fp are the electron and hole quasi-Fermi levels measured from bottom of conduction band and top of valence band, respectively. The variation of E_PL, at constant ‘n’, with temperature can then be written as

\frac{d E_{P L}}{d T} = \frac{d E_{G}}{d T} + \frac{d E_{F n}}{d T} - \frac{d E_{F p}}{d T}

The first term on the right hand side of Eq. (4) represent the conventional red shift in band gap with increasing temperature through lattice dilation as governed by the Varshni equation [17]. The temperature derivatives of the E_Fn have an inverse dependence with the effective mass and can be approximated as [18]

\frac{d E_{F n}}{d T} ~ \frac{d}{d T} [\frac{ℏ^{2}}{2 m_{d} (T)} {(3 π^{2} n (T))}^{\frac{2}{3}}]

where both the effective mass, m_d [19], and n, are functions of temperature theoretically. In degenerate semiconductors the variation of n with T was previously considered insignificant [20]. However, due to the confirmation of a non-parabolic conduction band edge for the degenerate InN, we have considered a temperature dependence of the effective mass. Actually this has been indicated with reference to GaAs [13], InSb [21] and PbTe [22]. Effective mass can reduce by 10-15% over a temperature increment of 280 K, and such change is also supported in literature [23]. Under such a situation we may expect a shift of E_Fn, say from E_Fn1 to E_Fn2 (Fig. 3(b)) as temperature is increased, which we will show later.

The last part on the right hand side in Eq. (3) involves the movement of E_Fp with temperature. The shift of E_Fp, say from E_Fp1 to E_Fp2 as temperature is increased (Fig. 3(b)), is small but may not be ignored given the small band gap in InN.

The net temperature dependence of the shift in bandgap is thus a competition between the lattice dilation $(\frac{d E_{G}}{d T})$ on one hand and the sum $(\frac{d E_{F n}}{d T} - \frac{d E_{F p}}{d T})$ on the other. The former results in a red shift whereas the latter yields a blue shift of the band gap with increasing temperature. The effective temperature evolution depends on the magnitude of these two terms. At low n (<5 × 10¹⁸ cm⁻³ in this case), the lattice dilation dominates and hence an overall red shift with increasing temperature has been observed. This is reasonable since at low ‘n’ the band filling effect to push E_Fn up is insignificant or absent. Literature reports of high quality InN (n~3 × 10¹⁷ cm⁻³) [10] always show the conventional red shift with increasing temperature (Fig. 3(a)). On the contrary, at high n (>6 × 10¹⁸ cm⁻³ in this case), the thermal response of InN is governed by electronic rather than phononic interactions. The sum $(\frac{d E_{F n}}{d T} - \frac{d E_{F p}}{d T})$ dominates, resulting in an overall blue shift of the E_PL.

To confirm this, the intensity (I) and shape of the PL bands for samples S1-S8, at each temperature, were fitted according to the following expression [24]

I (ℏ ω) ~ {[ℏ ω - E_{G} (n)]}^{\frac{γ}{2}} f (ℏ ω - E_{G} (n) - E_{F n})

where

ℏ ω

is the photon energy, E_G(n) is a ‘n’-dependent band gap that approaches the intrinsic band gap E_G at vanishing ‘n’, f is the Fermi-Dirac function, and γ is a parameter (2 ≤ γ ≤ 4, for InN) involving the relaxation of the momentum conservation law in interband transitions. For the sake of simplicity in fitting we ignored the E_Fp in Eq. (3) to arrive at Eq. (6). The fitting is excellent for the main PL feature of all the samples (Fig. 2(a)) barring the high energy tail for S7 and S8. There may be an additional weak PL component around 930 meV probably due to some disorder-localized states prevalent in highly defective (n > 10¹⁹ cm⁻³) samples S7 and S8 [25].

The fitting results are shown in Fig. 4(a) . Clearly E_F _n was invariant with temperature for samples with low ‘n’ (S1-S3). However, for samples with higher ‘n’ (S5-S8), there was a marked blue shift of E_Fn with temperature. This confirmed our initial conjecture. A simplified band diagram, showing the changes in E_PL, E_G, and E_Fn with temperature, is shown in Fig. 4(b) and (c) for low and high values of ‘n’, respectively. Quantitatively, for sample S8, even if the conventional red shift of E_G(T) with T is around ~40 meV, the blue shift of E_Fn is nearly ~70 meV, resulting in a net ~30 meV blue shift of the E_PL with temperature (Fig. 3(a)). The actual net shift of E_PL will also involve any shift of E_Fp with T, however small it may be. However, for intermediate n~5.2 × 10¹⁸ cm⁻³ in this work, the competing shifts of E_G(T) and E_Fn(T) are comparable and the temperature invariance of E_PL was observed.

Fig. 4 (a) Variation of the quasi-Fermi level, E_Fn, with temperature, obtained by fitting the temperature dependent photoluminescence spectra for each sample (S1-S8) according to Eq. (6). Schematic band diagram showing the change in the intrinsic bandgap (ΔE_G), defined as the separation between the conduction band minima and valence band maxima, and the quasi-Fermi level $Δ E_{F n} = E_{F n 2} - E_{F n 1}$ with temperature for (b) low and (c) high carrier density InN nanocolumn. The optical bandgap, E_PL, is also shown.

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4. Conclusion

In conclusion, temperature evolution of optical bandgap in indium nitride nanocolumns has been explained in the light of their carrier density. The shift in the optical bandgap depends on two competing factors, (i) the separation of conduction band edge minima and valence band edge maxima that red shifts with temperature, and (ii) the shift of the quasi-Fermi level that either remain invariant or blue shifts with temperature. When carrier density is < 5 × 10¹⁸ cm⁻³ the former dominates, whereas for carrier density > 6 × 10¹⁸ cm⁻³ the latter dominates and a net red or blue shift, respectively, was observed in the optical bandgap with increasing temperature. However, the shift of the hole quasi-Fermi level should also be considered for a complete understanding of the temperature evolution of the E_PL. In a set of InN samples it would be possible to predict the relative temperature evolution, red or blue, of the E_PL if their carrier concentrations are known. Thermal response of bulk carrier density seems to be more fundamental in specifying the temperature evolution of E_PL, in InN thin film or nanostructures.

Acknowledgement

The authors would like to thank National Taiwan University, Academia Sinica, Ministry of Education and National Science Council in Taiwan as well as the US AFOSR-AOARD for financial supports.

References and links

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Origin of the anomalous temperature evolution of photoluminescence peak energy in degenerate InN nanocolumns

Abstract

1. Introduction

2. Experimental details

3. Results and discussion

4. Conclusion

Acknowledgement

References and links

Cited By

Figures (4)

Equations (6)

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