GaP multiquantum wells

Journal of Luminescence 133 (2013) 125–128

Contents lists available at SciVerse ScienceDirect

Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin

Double-scaled disorder in Ga(N,As,P)/GaP multiquantum wells C. Karcher a,n, K. Jandieri a, B. Kunert b, R. Fritz a, K. Volz a, W. Stolz a, F. Gebhard a, S.D. Baranovskii a, W. Heimbrodt a a b

Department of Physics and Material Sciences Center, Philipps University Marburg, D-35032 Marburg, Germany NAsPIII/V GmbH, Am Knechtacker 19, D-35041 Marburg, Germany

a r t i c l e i n f o

abstract

Available online 12 October 2011

The compositional dependence of the properties of metastable Ga(N,As,P) has been characterized optically by means of temperature dependent absorptive and emissive techniques. By assuming a twoscaled disorder within the alloy caused by microscopic composition fluctuations on the one hand and a fluctuation of strain fields or the well width on the other hand, Monte Carlo simulations of the carrier dynamics are in good agreement with the experimental findings. The compositional dependence further reveals an increase of disorder with decreasing nitrogen content. & 2011 Elsevier B.V. All rights reserved.

Keywords: Quaternary nitride alloys Photoluminescence Disorder Multiquantum wells Stokes shift Monte-Carlo-simulation

1. Introduction The quaternary Ga(N,As,P) semiconductor alloy has been introduced to enable a monolithic integration of a III–V semiconductor into a silicon substrate. The incorporation of both phosphorous and nitrogen into the GaAs host enables a controlled way of band gap tailoring and a reduction of the lattice mismatch below three percent. Nitrogen in particular strongly decreases the band gap of GaAs [1], which could be empirically understood by a band anticrossing interaction (BAC) between the localized nitrogen states and the extended conduction band of the host [2]. Apart from that strong red shift in band gap energy it has been shown that the incorporation of nitrogen into the III–V host introduces a huge amount of strongly localized states within the band gap caused by disorder [3,4] in the system. This can be observed by a non-monotonous emission energy shift with rising temperature, the so called s-shape accompanied by a peaking line width of the emission during that energetic development [3]. Such a behavior was predicted by Baranovskii et al. [5], who introduced a model in which excitons were able to travel through the spatially localized states by hopping transport. However, it has been recently shown [6] that this model with a single-scale disorder cannot be applied to the quaternary Ga(N,As,P) multiquantum well (MQW) structures. As suggested by Kazlauskas et al. [7], a second scale of disorder has to be introduced to enable a satisfactory agreement between experiment and simulation. A possible candidate as a source of that second scale of disorder is

n

Corresponding author. Tel.: þ49 6421 28 22118. E-mail addresses: [email protected], [email protected] (C. Karcher). 0022-2313/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2011.10.002

the well width fluctuation of the Ga(N,As,P) layer [6] caused by microscopic strain fields [8] induced by the incorporation of nitrogen. The goal of this paper is to examine the influence of the amount of incorporated nitrogen on both disorder scales and well morphology, enabling a further clarification of the origin of the second scale of disorder.

2. Material and methods Two Ga(N,As,P)/GaP triple QW structures with varying phosphorous and nitrogen content and similar well widths were examined in this study. The structures have been grown on (001)-oriented GaP substrate by metalorganic vapor phase epitaxy (MOVPE). A detailed description of the growth conditions can be found in Ref. [9]. The Ga(N,As,P) layers were grown pseudomorphically between 100 nm GaP barriers. An overview of the concentration and thickness of the layers are given in Table 1. Both P and N contents within the samples were determined by simulating high-resolution X-ray diffraction patterns. The estimated errors are 70.5% N and 72.7% P. By reducing the phosphorous content with increasing nitrogen content the macroscopic mismatch is kept around 2.6% compressive mismatch in both layer compositions, which has been verified by XRD measurements [16]. The well widths were determined by taking the mean width observed in transmission electron microscopy (TEM), with a fluctuation of 71 nm. The morphology of the Ga(N,As,P) layers was investigated by high resolution TEM. Fig. 1 shows a cross section of the investigated Ga(N,As,P) layers containing 2% and 4% N. A clear

126

C. Karcher et al. / Journal of Luminescence 133 (2013) 125–128

Table 1 Composition and layer thickness d of the Ga(N,As,P) MQWs. N (%)

P (%)

d (nm)

2 4

16 5

6.3 6.4

5.7nm

of the sample was measured by means of a standard setup consisting of a 1.25 m grating spectrometer and a liquid-nitrogen cooled Germanium detector. The detection wavelength of the spectrometer was set onto the low energy emission of the sample while the excitation energy was varied by tuning the Ti:sapphire laser. Further a mechanical chopper was used to force a non-zero frequency onto the signal, thereby being able to amplify the photoluminescence by standard lock-in technique. The sample was placed in a microcryostat in which temperatures from 10 K up to room temperature were applied.

6.5nm 3. Experimental

2% Nitrogen

4% Nitrogen Fig. 1. High resolution TEM [010] micrographs of layers containing 2% (top) and 4% (bottom) of nitrogen surrounded by GaP barriers.

2% Nitrogen

100nm

Fig. 2. Strain-contrast (202) TEM micrograph of a layer containing 2% of nitrogen surrounded by GaP barriers.

fluctuation in the layer thickness of about 1 nm can be identified, which confirms the existence of a second source of disorder with a lateral scale of about 50–100 nm. Furthermore the strain in the sample containing 2% N has been investigated by TEM (see Fig. 2). In between the laterally rather homogeneous GaP barriers, a distinct lateral strain-contrast fluctuation within the Ga(N,As,P) layers at a scale of 10–50 nm can be identified. This can be another source of the second scale of disorder in the quaternary system. It is interesting to note that three disorder phenomena are caused by the same origin, namely the incorporation of nitrogen. The electronic perturbation causes the short range microscopic potential fluctuation. The respective strain fluctuation causes the strain fields which can be observed in Fig. 2. These strain fields eventually lead to well width fluctuations observed in Fig. 1. It has been shown that the ternary Ga(As,P) host shows no signs of pronounced disorder, as both just a weak band bowing [10] of less than 0.3 eV and a monotonous emission energy shift [11] with respect to temperature could be observed in the alloy range up to 20% of phosphorous. Because of that we solely focus onto the nitrogen content and the well morphology of the samples in the following results and discussion. The samples were characterized by photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopy as well as contactless electromodulated reflectance (CER) spectroscopy. Details regarding the PL and CER setup can be found in Ref. [6]. By using a Spectra-Physics Model 3900S CW Ti:sapphire laser which is able to emit light with a photon energy varying from 1.1 to 1.7 eV, photoluminescence excitation measurements were performed. The laser was partly coupled out through a glass windows and both the wavelength and the power of the exciting light was monitored by using an Ocean Optics HR 4000 Spectrometer and a Coherent LabMAX Powermeter, respectively. The PL

100

10K

2% Nitrogen Intensity (arb. units)

6.4nm

10-1 200K 290K

10-2

100

10K

4% Nitrogen

Intensity (arb. units)

5.8nm

Fig. 3 shows the temperature dependent PL results of both samples in the range from 10 to 290 K. As the samples are MQW structures, they were excited by directly generating carriers within the quantum wells at an excitation energy of 1.70 eV, which is well below the indirect band gap of the barrier material GaP of 2.27 eV [12] at room temperature. Hence the PL is originating exclusively from electron–heavy hole recombination between the ground states of the conduction and valence band wells. One of the most prominent features is the difference in emission energy between the samples of about 120 meV at room temperature. This difference is a combined effect of decreased P content and increased N content. Both factors push the band gap of the structure containing more N towards lower energy by means of decreased Ga(As,P) alloy band gap and an enhanced band anticrossing interaction between the localized N states and the ternary host, respectively. Apart from that difference in emission energy, the line width of the sample containing 2% N is significantly larger than the line

10-1 120K

10-2 290K

10-3

1.1

1.2

1.3 Energy (eV)

1.4

1.5

Fig. 3. Temperature dependent photoluminescence spectra of the sample containing 2% (top) and 4% N (bottom), respectively.

C. Karcher et al. / Journal of Luminescence 133 (2013) 125–128

width of the sample containing 4% N, already indicating a larger amount of disorder within the material. Another feature which is clearly visible in both series of spectra is a complex temperature dependence of the peak emission. This non-monotonous dependence resembles the afore mentioned s-shape and is a characteristic feature in the optical properties of heavily disordered semiconductors. In order to get insight into the energetic distribution of states accounting for the observed PL, temperature dependent PLE measurements were performed (see Fig. 4). Although heavily broadened, a clear shoulder within the spectra can be identified and assigned to the band gap of the structure. The energetic progress of the band gap with regards to the temperature is clearly monotonous. To verify these results, additional CER spectra were measured, which yielded the same information and are not presented here. Instead of the term band gap we will refer to this energy which separates the localized from the extended states as the mobility edge [13,14] from now on. Fig. 5 shows a roundup of the main spectral features of both samples, i.e. the energy of the mobility edge and the energy of the peak emission plotted against the temperature. The spectral features of the mobility edge of the sample containing 4% N were taken from the results presented in Ref. [6]. As can easily be seen, both samples qualitatively yield the same features, i.e. a rather large Stokes shift at low temperatures and an s-shape in the peak

10K

2% Nitrogen

PL intensity (arb. units)

90K

160K

210K

Detection @1.44eV

1.45

1.50

1.60 1.55 Excitation energy (eV)

1.65

1.70

Fig. 4. Temperature dependent photoluminescence excitation spectrum of the sample containing 2% N.

2% Nitrogen

4% Nitrogen

1.6

Energy (eV)

Mobility edge Emission 1.5

127

emission energy. However, the energies of the observed features change when adding more nitrogen. As already discussed, both the energy of the mobility edge and the emission is decreased due to the mentioned effects. Apart from that, both the Stokes shift at low temperatures and the temperature at which the s-shape occurs decrease as well by about 20 meV and 80 K, respectively. Both features indicate a lowered disorder within the system containing more nitrogen. This seems to be surprising at first sight. Therefore we will compare the experimental findings with a full theoretical description of the observed behavior in the next section which will enable an exact quantification of the amount of disorder existing in both compositions.

4. Theory As already pointed out in Introduction, a model containing a single spatial scale of disorder and a respective exponential energy distribution of localized states does not suffice to satisfyingly simulate the experimental findings for any of the two compositions. Due to the failure of the single-scaled approach and because of the discovered morphologic features of the layers, a second scale of disorder based on fluctuations within the well width was introduced. A detailed description of the theoretical approach can be found in Ref. [6]. We use this double-scaled disorder to simulate the experimental findings by means of Monte-Carlo simulations. The energies of both scales are extracted from the temperature dependent emission spectra, i.e. the inverse of the logarithmic slope b ¼ e1 of the low-temperature PL spectra in 0 their low energy part and the thermal energy E0 of the peaking Stokes shift. Table 2 displays the extracted values of both energetic scales as well as the parameters used for the Monte-Carlo simulations, where N0 is the total number of trapping sites including Nnr nonradiative centers, a is their localization length, n0 is the attemptto-escape frequency, and t0 is the lifetime of the excitons with respect to radiative recombination. The latter were estimated by simulating the low-temperature PL spectra and the temperature dependent integrated photoluminescence intensities. This set of parameters enables an almost perfect simulation of the experimental findings regarding the Stokes shift and the line width of the observed temperature dependent emission. Fig. 6 shows a comparison between the simulated and the experimental emission data. Apart from the given parameters a temperature and energy dependent transition probability x for the transition of excitons between areas with different well widths was added to the model. Details of this approach can be again found in Ref. [6, section III C]. The congruency of theory and experiment in both compositions nicely emphasizes the validity of the two-scaled approach. As already expected from the spectral features of the emission in Fig. 3 and quantified by extracting the slope of the lowtemperature emission and the thermal energy of the s-shape occurrence, the disorder within the compound drops with increasing nitrogen content.

1.4 Table 2 Characteristic energies of the short ranged (E0) and long ranged (e0 ) disorder extracted from the experimentally observed emission features and parameters for the Monte-Carlo simulation extracted from the temperature dependent PL.

Mobility edge Emission

1.3 0

100 200 Temperature (K)

300 0

100 200 Temperature (K)

300

Fig. 5. Temperature dependent energy of the mobility edge, i.e. the band gap, and the peak emission of both compositions.

N (%) 2 4

E0 (meV) 15 10

e0 (meV) 50 40

N 0 a2 0.5 0.5

n0 t0

N nr =N 0 3

5  10 5  103

0.013 0.030

128

C. Karcher et al. / Journal of Luminescence 133 (2013) 125–128

2% Nitrogen

4% Nitrogen

140

FWHM (meV)

Strokes shift (meV)

120 100

fluctuations change the confinement energy of the e1-hh1 QW transition around 50 meV, which corresponds to the predicted long-scaled disorder (see Table 2). However, in order to verify the discrepancy of the long-ranged disorder in both samples, a sophisticated statistical analysis of the experimentally observed height modulation has to be performed.

80

5. Conclusion

60 40 20

Exp. Sim.

Exp. Sim.

200

Exp. Sim.

Exp. Sim.

50 100 150 200 250 0 Temperature (K)

50 100 150 200 250 Temperature (K)

160 120 80 40 0

Fig. 6. Comparison between simulation and experiment with respect to Stokes shift (top) and line width (bottom) of the temperature dependent emission.

When considering the short-ranged atomic disorder within the system, this trend appears to be counterintuitive at first glance, contradicting simple causality principles. However, as described theoretically in Ref. [15], the compositional dependence of the disorder scale E0 can be derived by the following expression:  4 @Ec 3 E0 C x2 ð1xÞ2 mn , ð1Þ @x where @Ec =@x is the dependence of the conduction band edge Ec with respect to the incorporated nitrogen fraction x, and mn is the effective electron mass. As empirically described by the BAC model, Ec is given by  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1 ð2Þ Ec ðxÞ ¼ ðEG þ EN Þ ðEG EN Þ2 þ4V 2 x , 2 where EG is the conduction band edge of the ternary Ga(As,P) host, EN is the energy of the isolated N state, and V is the coupling parameter between the states of the isovalent impurity and the conduction band of the host. For the considered nitrogen fractions, @Ec =@x can thus be approximated by x0:5 . Inserting this dependence into Eq. (1), one obtains an energy scale of the compositional disorder almost independent of the nitrogen content x. One further has to take into account that EG , EN, V cannot be considered as constant parameters when changing the phosphorous content. Hence, by using the approach suggested in Ref. [16] to determine the values of EG , EN and V and further taking into account the dependence of the effective mass on the nitrogen content x derived from the BAC model [17], one can show that E0 significantly decreases with increasing nitrogen content, agreeing with the experimental observations. In Ref. [6] a long-ranged layer height disorder caused by height fluctuations was suggested. Such features were clearly identified in both samples (see Fig. 1) in the range from 5.5 to 7.4 nm. These

Two Ga(N,As,P)/GaP triple QW structures containing different amounts of nitrogen and phosphorous were studied experimentally and theoretically. The temperature dependent spectral features reveal a high amount of disorder in the system which dominates the emissive behavior at low temperatures. A comparison of the Stokes shift and line width in both compositions highlights a drastic reduction of the disorder upon increasing nitrogen content. To quantify this reduction, a theoretical model with two energy scales of disorder potentials, which relate to two spatial length scales, was applied to model the experimental findings. The extracted disorder scales show a reduction of both the shortranged atomic and the long-ranged disorder. The second scale is either caused by strain-field or well width fluctuations. In order to explain the reduction in short-range disorder, an estimation of the compositional dependence of the atomic disorder scale was done, which is in agreement with the experimentally observed reduction of disorder. High resolution TEM micrographs further backed up the source of the second scale of disorder by uncovering height fluctuations from 5.5 to 7.4 nm at a comparably large lateral scale of 50– 100 nm. Due to a lack of sufficient micrographs a reliable statistical verification by means of a full statistical analysis of the fluctuation was not feasible.

Acknowledgements Financial support of the Fonds der Chemischen Industrie, of the Deutsche Forschungsgemeinschaft and the Federal Ministry of Education and Research is gratefully acknowledged. References [1] M. Weyers, M. Sato, H. Ando, Jpn. J. Appl. Phys. 31 (1992) L853. [2] W. Shan, W. Walukiewicz, J.W. Ager, E.E. Haller, J.F. Geisz, D.J. Friedman, J.M. Olson, S.R. Kurtz, Phys. Rev. Lett. 82 (1999) 1221. ¨ [3] H. Gruning, K. Kohary, S.D. Baranovskii, O. Rubel, P.J. Klar, A. Ramakrishnan, ¨ G. Ebbinghaus, P. Thomas, W. Heimbrodt, W. Stolz, W. Ruhle, Phys. Status Solidi (c) 1 (2004) 109. [4] J. Teubert, P.J. Klar, W. Heimbrodt, K. Volz, W. Stolz, P. Thomas, G. Leibiger, V. Gottschalch, Appl. Phys. Lett. 84 (2004) 747. [5] S.D. Baranovskii, R. Eichmann, P. Thomas, Phys. Rev. B 58 (1998) 13081. [6] C. Karcher, K. Jandieri, B. Kunert, R. Fritz, M. Zimprich, K. Volz, W. Stolz, F. Gebhard, S.D. Baranovskii, W. Heimbrodt, Phys. Rev. B 82 (2010) 245309. [7] K. Kazlauskas, G. Tamulaitis, A. Zukauskas, M.A. Khan, J.W. Yang, J. Zhang, G. Simin, M.S. Shur, R. Gaska, Appl. Phys. Lett. 83 (2003) 3722. [8] I. Nemeth, T. Torunski, B. Kunert, W. Stolz, K. Volz, J. Appl. Phys. 101 (2007) 123524. [9] B. Kunert, K. Volz, J. Koch, W. Stolz, J. Cryst. Growth 298 (2007) 121 (Thirteenth International Conference on Metal Organic Vapor Phase Epitaxy (ICMOVPE XIII)). [10] H.C. Marciniak, D.B. Wittry, J. Appl. Phys. 46 (1975) 4823. [11] A.H. Herzog, W.O. Groves, M.G. Craford, J. Appl. Phys. 40 (1969) 1830. ¨ [12] R.G. Humphreys, U. Rossler, M. Cardona, Phys. Rev. B 18 (1978) 5590. [13] N.F. Mott, Adv. Phys. 16 (1967) 49. [14] M.H. Cohen, H. Fritzsche, S.R. Ovshinsky, Phys. Rev. Lett. 22 (1969) 1065. [15] S.D. Baranovskii, A.L. Efros, Sov. Phys. Semicond. 12 (1978) 1328. [16] B. Kunert, K. Volz, J. Koch, W. Stolz, Appl. Phys. Lett. 88 (2006) 182108. [17] J. Wu, W. Shan, W. Walukiewicz, Semicond. Sci. Technol. 17 (2002) 860.