Photo current - Spontaneous emission spectrum in light-emitting diodes

Chapter 3 Spontaneous emission spectrum in light-emitting diodes

3.6 Photo current

Furthermore, the photo-current measurement was used to investigate the absorption spectra of LEDs. Three AlGaInP LEDs with different wavelength

(red, yellow and yellow-green) were used. The wafer structure of the samples which has an n-type GaAs substrate, a 600-nm-thick n-type Al0.5In0.5P hole-blocking layer, a 600-nm-thick p-type Al0.5In0.5P electron-blocking layer, and a 11μm-thick p-type GaP current spreading layer. The emission wavelength and distributed Bragg reflector (DBR) for each sample was to adjust the structure of MQWs, as shown in Fig. 3.11, Fig. 3.12 and Fig. 313.

Figure 3.14 to figure 3.16 shows the photo-current spectrum under varying reverse bias (0V, -5V, -10V) and EL spectrum measured at 20mA. The photo current spectrum shows independent with reverse bias. It is indicated that the MQWs of the samples are in the depletion regions, thus, when laser excited the electron-hole pairs in MQWs, both electrons and holes will sweep out toward

n-type layer and p-type layer, respectively. At low energy tail, the photo current

spectrum shows similar feature with the EL spectrum. That is due to the optical joint density of state is a factor of the absorption spectrum and emission spectrum (Eq. 3.12 and Eq. 3.19). On the other hand, the increased of the photo current spectrum with interference can be attributed the existence of the DBR under n-type layer. Therefore, the penetrated laser form MQWs can be reflexed to MQWs and reabsorbed. The intensity of the reflection and the width can be simulated from the index of the sample structures, as shown in Fig. 3.17.

Moreover, both of the intensity of the photo current spectra decreased when Eg>2.3eV. The reason of the decrease of the intensity can be explained by the absorption of the GaP. As we assumed that the absorption spectrum of the MQWs is a step function, the absorption spectrum of GaP can be obtained from the dividing the step function and photo current spectrum, as shown in Fig. 3.18, Fig. 3.19 and Fig. 3.20. Despite the influence of the DBR and absorption of GaP, the photo current spectrum shows the same feature with the optical joint density

of states obtained from the EL spectrum. This result indicated that the

3.7 Conclusion

This work presents a model for describing the spectra of quantum wells.

The carrier temperature can be determined from the high-energy tail of the spectrum and the probability distribution function can be deduced by further numerical processing. This model was applied to an AlGaInP LED, and the measured carrier temperatures were found to be very close to the temperatures.

This finding is important evidence of the validity of the proposed model. Two methods are used to obtain the optical joint density of states of the samples. The optical joint density of states can be obtained by dividing the emission spectrum by the Boltzmann distribution function or measured by the photo current measurement.

Reference

[1] N. C. Chen, C. M. Lin, C. Shen, W. C. Lien, and T. Y. Lin, Opt. Express 16, 20759 (2008).

[2] B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics, (John Wiley &

Sons, 1991). P.593

[3] H. D. Summers, J. D. Thomson, P. M. Smowton, P. Blood, and M.

Hopkinson, Semicon. Sci. Tech., vol.16, p.140, (2001).

[4] P. Blood, E. D. Fletcher, P. J. Hulyer, and P. M. Smowton, Appl. Phys. Lett., vol.48, p.1111, (1986).

[5] P. Blood, A. I. Kucharska, J. P. Jacobs, and K. Griffiths, J. Appl. Phys., vol.70, p.1144, (1991).

[6] N. C. Chen, Y. N. Wang, C. Y. Tseng, and Y. K. Yang, Appl. Phys. Lett. 89, 101114 (2006).

[7] N. C. Chen, W. C. Lien, Y. K. Yang, C. Shen, Y. S. Wang, and J. F. Chen, J.

Appl. Phys. 106, 074514 (2009).

Fig. 3.1 Dispersion relation of electron-hole recombination and phonon emission

Fig. 3.2 Density of states in two-dimensional

Fig. 3.3 Theoretical emission spectrum in two-dimensional quantum structure

26 (E_g-E_g0 )/_Eg

-4 -2 0 2 4

P(Eg)

(hv-E_g0 )/_Eg

-4 -2 0 2 4

0.0 0.2 0.4 0.6 0.8 1.0

_Eg

Fig. 3.4 Theoretical emission spectrum of an LED

Fig. 3.5 Sample structure of an AlGaInP LED

Fig. 3.6 Power spectra of the LED measured at 10 mA, and the temperature ranges from 400 to 120 K

Fig. 3.7 Photon density spectra measured at 10 mA on a semi-log scale and the temperature ranges from 400K to 120K

2.0 2.1 2.2 2.3 2.4

slope= -37.714 = -(KT

j)^-1

T_j=307.65K

Spontaneous emission (a.u.)

Photon energy (eV) T_ambient=300K

Fig. 3.8 Junction temperature obtained from gradients of high-energy tails in an EL spectrum at 300K

Fig. 3.9 Dependences of junction temperatures on ambient temperatures obtained from gradients of high-energy tails

Fig. 3.10 Temperature dependence of optical joint densities of states from 400K to 120K

Fig. 3.11 Sample structure of the red LED

Fig. 3.12 Sample structure of the yellow LED

Fig. 3.13 Sample structure of the yellow-green LED

1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6

0.0 0.2 0.4 0.6 0.8 1.0

Photo cu rr en t (a .u.) EL i nten s it y (a.u.)

hv (eV)

0V -5V -10V EL

Fig. 3.14 Photo current spectrum and EL spectrum of the red LED

Fig. 3.15 Photo current spectrum and EL spectrum of the yellow LED

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7

Fig. 3.16 Photo current spectrum and EL spectrum of the yellow-green LED

Fig. 3.18 Absorption spectrum of GaP in red LED

1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

 (cm-1 )

absorption (a.u.)

Energy (eV)

0 1000 2000 3000 4000 5000 6000

Fig. 3.19 Absorption spectrum of GaP in yellow LED

1.8 2.0 2.2 2.4 2.6 2.8

absorpti on (a.u. )  ( cm

-1

)

Energy (eV)

0 1000 2000 3000 4000 5000 6000 7000 8000

Fig. 3.20 Absorption spectrum of GaP in yellow-green LED

Chapter 4 Optical joint density of states in InGaN/GaN multiple-quantum-well light-emitting diodes

4.1. Introduction

Because of the wide range of energy gaps in group-III nitride-based materials, InGaN/GaN-based multiple quantum wells (MQWs) have been used in a broad range of emission wavelengths, such as blue, green and yellow light-emitting diodes (LEDs) [1]. Although the number of applications of these devices has increased in the past decade, their special features still attract considerable attention. For example, despite their high dislocation density (typically in the range 10⁸-10¹⁰ cm^-2), their luminescence efficiency is peculiarly higher than expected [2]. Also, a large Stokes-like shift occurs between the emission peak and the absorption edge, and this shift correlates with indium content [3]. Many studies have confirmed that indium atoms are important to these phenomena [4]. Since localized states that result from self-organized In-rich regions are regarded as quantum dots [5] or quantum disks [6], electron-hole pairs are likely associated with the localized states rather than being transferred to threading dislocations that act as nonradiative centers [7,8].

Additionally, the quantum-confined Stark effect (QCSE) that is caused by the piezoelectric field has been found to have a large influence on the emission [9].

Because of a large lattice mismatch between GaN and InGaN, a strong strain-induced piezoelectric field tends to shift the quantum-confined level to lower energy [10]. However, the reasons for the blueshift of the emission peak with increasing current and the anomalous broadening of the full width at half

maximum (FWHM) are still under debate. Since both the photoluminescence (PL) and the electroluminescence (EL) peaks are at the absorption tail, some researchers have suggested that the blueshift results mainly from the band filling effect of the localized states that correspond to the formed In-rich regions [11].

Others have argued that the blueshift is related to the screening of the piezoelectric field by carriers [12]. Chichibu et al. [13] argued that the blueshift is a combined effect of band filling of localized states and screening of the QCSE. Notably, most related studies have used PL excitation (PLE) to obtain the absorption spectrum. However, the electrically injected carriers and the corresponding emission prevent the absorption spectrum from being obtained under large forward bias. Therefore, the band filling effect of localized states and the piezoelectric effect with a forward current are difficult to determine, and definitive explanations of the blueshift and anomalous increase in the FWHM are still unavailable. On the other hand, the reason of S-shift (redshift-blueshift-redshift) in InGaN/GaN LEDs with varying temperatures is also need more evidence. The explanation of the S-shift has been study for many decades [14,15]. The recombination mechanism of the InGaN LEDs in different temperature ranges can be explained as follows: (i) For T<50K, since radiative lifetime at the lowest temperature is fast and dominant the recombination process, carriers should recombination radiatively in quantum states before relax down into localized states. Thus, when temperature further increased, carriers relax into localized states and induce emission peak decreased. (ii) For 50K<T<150K, since carriers are recombined in localized states and the occupation of probability in each state by an electron-hole pair should obtained by Boltzmann distribution function. Thus, when temperature increased, the occupation of probability at higher states should increase and induce emission

peak increased. (iii) For T>150K, since temperature induced band gap shrinkage dominate the emission peak, the emission peak decrease with increasing temperature [16-19]. However, the research of these current and temperature induced peak shift has left many questions unanswered, more work must be done.

This work presents a method for determining the optical joint density of states of nitride-based LEDs using an EL spectrum instead of a PLE. The proposed method of extracting the optical joint density of states is to divide the EL spectrum by the Boltzmann distribution function, to determine the effect of current on the blueshift and the increase in the FWHM [20]. Similar methods, in the form of relations among spontaneous emission, absorption and gain spectra, have been extensively used in studying the details of InGaAsP, AlGaAs, InGaAs and GaAs laser diodes in various aspects [21-28]. Besides, the authors have successfully explained the carrier dynamics, the redshift of the edge emission, the junction temperature and the broadening of the emission spectrum of AlGaInP LEDs by using this method [29,30]. All of these successful precedents justify the method used in this paper. The samples investigated herein are commercial products that were grown on c-plane sapphire substrates by metal organic vapor deposition. Three InGaN/GaN-based light-emitting diodes with different emission wavelengths (violet, blue and green) were adopted. To obtain their spectra, the devices were placed on a heat sink and operated in pulsed mode with a frequency of 1000Hz and a duty cycle of 10% to diminish any possible effect of Joule heating. Thus, the junction temperatures of the measured devices were determined only by the environment, and the corresponding Boltzmann distribution functions are obtained from the ambient temperatures.

4.2 Current dependent of emission spectra

Figure 4.1 presents the normalized EL spectra of the samples under various currents at 300K. The peaks shifted to higher energy as the current increased, and the degree of shift was correlated with the indium content. From 10mA to 80mA, the blueshifts for the violet, blue and green LEDs were 0meV, 19meV and 37meV, respectively. The FWHM for the violet, blue and green LEDs were 89meV, 140meV and 160meV, respectively, indicating that the FWHM was strongly correlated with the indium content but weakly correlated with current density. Similar results concerning the blueshift and the increase in the FWHM have been observed in many studies, including those mentioned above.

To determine how localized states and piezoelectric field affect the spectrum under various currents, the optical joint densities of states of these devices are determined under various currents from the measured spectra. The spontaneous emission spectrum of an LED is [20,29,30]

 

^h ^e ^h ^KT

r    ^^ ... (4.1) where  h is the optical joint density of states, which is the density of allowable transition states that satisfy the k-selection rule, or equivalently, the density of states for electron-hole pairs, and e^^h^^KT is the Boltzmann distribution function, which describes the probability of occupation of each state by an electron-hole pair. Generally, the optical joint density of states has the same mathematical form as the electron (hole) density of states, except in that the effective mass of electron (hole) should be replaced by the reduced mass of electron-hole pairs [20]. Thus, when the optical joint density of states is obtained, the characteristics of the electron and hole densities of states are also obtained, and the optical joint density of states can easily be deduced from the spontaneous emission spectrum by merely dividing the emission spectrum by

the Boltzmann distribution function. Notably, such a method is preferable to PLE, since PLE obtains the optical joint density of states via an absorption spectrum, which cannot be obtained at large forward bias. Figure 4.2 shows the relative optical joint densities of states obtained from the EL spectra. All of these curves show two distinct regions – a low-energy tail and a high-energy region, where the density of states increases steeply with increasing energy. Since the low-energy tails of all of these samples are independent of current, the tails are attributed to the formation of localized states. In contrast, the steep increase of the density of states in the high-energy region indicates that these states correspond to the unlocalized states of the two-dimensional quantum structure [25], and its characteristics depend strongly on the samples. The violet LED yields the largest slope among these samples, and its density is independent of current; for blue and green LEDs, the curves of densities strongly depend on current, and their slopes increase with the current, as revealed by the linear fitted dashed lines. These dependences of density on both the sample and the current can be explained by the effect of the piezoelectric field and the screening of this field by carriers. The large amount of indium in the wells in blue and green LEDs makes the piezoelectric field therein wells significant. This field tilts the potential of the quantum well, as shown in Fig. 4.3(a), and electrons and holes in the same well should be spatially separated on opposite sides of the well. Thus, both the electron-hole wave-function overlap and the effective band gap of the well are decreased [32]. As the operating current was increased, the number of carriers in the wells increased, and the piezoelectric field drove the carriers to screen the field itself. Therefore, both the wave-function overlap and the band gap energy increased, as shown in Fig. 4.3(b). S. F. Chichibu et al. [33] and C. K.

Choi et al. [34] reported similar results. Their results reveal that the slope of the

absorption edge is determined by the piezoelectric field and can be screened by increasing the Si-doping concentrations in the barriers.

Since the slopes of the densities of states in the high-energy region depend on current, the blueshift of the spectra may be attributed to this phenomenon. To examine quantitatively this possibility, the densities of states of blue and green LEDs at various currents were approximated by the linear fitted dashed lines plotted in Fig. 4.2; then, the theoretical emission spectra were obtained by multiplying these fitted curves by the Boltzmann distribution function, as shown in Fig. 4.4. Figure 4.5 presents the blueshifts that were obtained from these theoretical spectra and from the experiment. The agreement between these two sets of data clearly demonstrates the proposed cause of the blueshift, and provides evidence of the screening of the piezoelectric field by carriers.

However, the FWHMs of the simulated spectra are lower than those obtained experimentally, as shown in Fig. 4.6. This discrepancy results from the linear approximations of the densities of states that wholly ignored the existence of localized states in the low-energy tails [5]. Although these localized states are known to be independent of current, as mentioned above, they still contribute appreciably to the emission spectra. In fact, the low-energy sides of the EL spectra are determined by the energy distribution of these localized states. Thus, as the indium content is increased, the low-energy tail should be further extended, and the corresponding FWHM of the emission spectrum should increase.

In summary, the optical joint densities of states of three InGaN/GaN-based LEDs with different emission wavelengths were determined at various currents.

The optical joint density of states has two distinct regions, a high-energy region, which corresponds to the unlocalized quantum well states and a low-energy tail,

which corresponds to the localized states. As the operating current is increased, the slope of the density of states at high-energy region increases with the screening of the piezoelectric field. This fact causes the peak of the EL spectrum to blue-shift with increasing current. The low-energy tail of the optical joint density of states determines the extension of the low-energy side of the EL spectrum, and this fact explains the anomalous increase in the FWHM of the emission of nitride-based LEDs. Furthermore, both of these effects are enhanced by increasing indium content, which relationship is responsible for the increase in blueshift and FWHM with the emission wavelength of the device.

4.3 Temperature dependent of emission spectra

Figure 4.7 presents the normalized PL spectrum of the sample with varying temperatures from 20K to 340K. Figure 4.8 shows the S-shaped variation with temperature. The peak energy shifts from 2.76eV to 2.75eV when temperature increased from 20K to 80K, and shifts to 2.76eV when temperature increased to 200K. The peak energy shifts to 2.744eV when temperature further increased to 340K.

To further understand the S-shaped shift of the emission peak under various temperatures, the optical joint densities of states of the sample are determined under various temperatures from the measured spectra. Figure 4.9 shows the relative optical joint densities of states obtained from the PL spectra with varying temperature. Similar to the optical joint densities of states obtained from the EL spectra, these curves also show two distinct regions – a low-energy tail and a high-energy region. According to the previous result, the low-energy tails are attributed to the formation of localized states and the steep increase of the density of states in the high-energy regions are attributed to the unlocalized states of the two-dimensional quantum structure. Here, the unlocalized states of the two-dimensional quantum structure can be linear fitted as shown in Fig. 4.10.

To further consider the effects of the emission peak by these two regions, the theoretical emission spectra of these two regions were obtained. The theoretical emission spectra of the two-dimensional quantum structure were obtained by using the fitted dish lines multiplying the Boltzmann distribution function, as shown in Fig. 4.11. On the other hand, the optical joint densities of states of localized states can be obtained by divided from the origin optical joint densities of states and linear fitted lines as shown in Fig. 4.12. The theoretical emission spectra of localized states were obtained by multiplying the Boltzmann distribution function, as shown in Fig. 4.13.

To further compare these two theoretical emission spectra with varying temperatures, the theoretical emission peak of the localized states shows S-shaped shift, however, the theoretical emission peak of the two-dimensional quantum structure shows only redshifts, as shown in Fig. 4.14. This result indicates that the S-shaped shift is mainly attributed to the localized states and can be explained by the delocalization of excitons out of potential minima. The emission spectrum corresponded to the quantum structure is only affected by the Varshni redshift of the band gap energy. Furthermore, when the temperature increased to 200K, the emission peak positions are contributed by both localized states and quantum structure and redshifts with temperature. The value of the shifts is smaller than the theoretical emission peak of the localized states, which indicated that the emission spectrum corresponded to the unlocalizated two-dimensional quantum structures become to dominate the PL emission peak.

In summary, the optical joint densities of states of a nitride-based LED were determined with varying temperatures. The optical joint density of states can be divided into two regions, a low-energy tail is attributed to the localized states and a high-energy tail is attributed to the unlocalized states of the two-dimensional quantum well. The theoretical emission spectra of the two

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