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A reverse-biased voltage is applied to either device in the vertical configuration of two light-emitting diodes (LEDs) grown on patterned and flat Si (110) substrates with weak and strong quantum-confined Stark effects (QCSEs), respectively, in the InGaN/GaN quantum wells for independently controlling the applied voltage across and the injection current into the p-i-n junction in the lateral configuration of LED operation. The results show that more carrier supply is needed in the LED of weaker QCSE to produce a carrier screening effect for balancing the potential tilt in increasing the forward-biased voltage, when compared with the LED of stronger QCSE. The small spectral shift range in increasing injection current in the LED of weaker QCSE is attributed not only to the weaker QCSE, but also to its smaller device resistance such that a given increment of applied voltage leads to a larger increment of injection current. From a viewpoint of practical application in LED operation, by applying a reverse-biased voltage in the vertical configuration, the applied voltage and injection current in the lateral configuration can be independently controlled by adjusting the vertical voltage for keeping the emission spectral peak fixed.
© 2014 Optical Society of America
1. Introduction
Due to its hexagonal crystal structure, the quantum-confined Stark effect (QCSE) can be observed in an InGaN/GaN quantum-well (QW) of a c-plane light-emitting diode (LED) [1–5]. The QCSE is formed through the combination of a few electric fields built in a QW, including the strain-induced piezoelectric field, the spontaneous polarization field, and the space-charge induced field in a p-i-n junction [6–9]. In a Ga-face, c-plane InGaN/GaN QW LED structure, the piezoelectric and spontaneous polarization fields are oriented from p-GaN toward n-GaN. Without an applied voltage, the space-charge induced field is oriented in the opposite direction. Among the three fields, the dominating piezoelectric field, which is at the order of 1 MV/cm, leads to a net electric field in a QW pointing from p-GaN toward n-GaN in an LED [4]. The electric field in the QW leads to a potential tilt for spatially separating the electron and hole wave functions such that the radiative recombination rate is reduced and the effective band-gap energy is decreased for red-shifting the emission spectrum. In the operation of an LED, the applied forward-biased voltage reduces the space-charge induced field such that the net field is increased for further tilting the QW potential and hence further reducing the effective band gap (emission spectrum red shift). On the other hand, the injected carriers can generate a screening effect of the electric field in the QW for reducing the tilt of its potential, leading to the widely observed blue shift of LED emission spectrum with increasing injection current [10]. In such an LED, the QCSE screening effect (possibly plus the band-filling effect) by carrier injection dominates over the effect of applied-voltage induced potential tilt in determining the emission spectrum variation of an LED. Although the blue-shift behavior in injecting current has been widely observed in LED operation, the interplay between the applied forward-biased voltage and injection current for controlling the QCSE in an InGaN/GaN QW of an LED has not been investigated yet. Since the QCSE is a crucial factor in optimizing LED operation, the understanding of the individual effects of applied forward-biased voltage and injection current is important for controlling the QCSE in an LED. In particular, the role of device resistance, which relates the applied voltage and injection current, of an LED in controlling the QCSE needs to be clarified. From a viewpoint of practical application, the QCSE controls the emission spectrum of an LED. How we can independently adjust the applied voltage and injection current in LED operation for maintaining the emission spectrum is an important issue.
In this paper, we use two on-Si-substrate LEDs of different strain conditions to study the interplay between the applied voltage and injection current. Because of the advantages of low cost, large wafer size, high thermal and electrical conductivities, and potential for integrating with electrical circuits, the growth of a GaN-based LED structure on Si substrate has attracted much research attention. To fabricate LEDs on Si substrate, various methods have been used for compensating or releasing the thermal stress in the nitride epitaxial layer induced during sample cooling down from the high growth temperature [11], including the use of specially designed AlGaN or AlN buffer and AlN/GaN superlattice inter-layers [12–14]. Based on those methods, crack-free LEDs have been fabricated. In this study, with the conducting substrate of Si, besides the application of a forward-biased voltage in the lateral configuration (in the operation of a conventional LED), we can apply a reverse-biased voltage in the vertical configuration across the whole epitaxial layer and the substrate for independently controlling the p-i-n junction voltage and injection current such that the effects of applied voltage and injection current on the QCSE can be observed separately. In other words, by applying the reverse-biased voltage in the vertical configuration, we can independently adjust the applied voltage and injection current in the lateral configuration for controlling the LED emission spectrum. In section 2 of this paper, the procedures of LED sample fabrication are described. The characterization results of the two LED samples are presented in section 3. Then, the discussions about the individual effects of applied voltage and injection current on LED output spectral shifts are made in section 4. Finally, the conclusions are drawn in section 5.
2. Fabrication of light-emitting diodes
LED samples A and B are grown on patterned and flat p-type Si (110) substrate, respectively [15]. In sample A, one-dimensional periodic trenches with 16, 6, 10, and 25 μm in period, trench width, ridge width, and trench depth, respectively, are fabricated along the <1-10> direction (a-axis) on Si (110) substrate for lateral overgrowth of GaN. With such a trench pattern, the thermal stress due to the thermal mismatch between Si and GaN along the m-axis can be reduced because of the decreased contact area at the nitride/Si interface. Also, the small lattice mismatch along the m-axis (only −1.65% between GaN [1-100] and Si [001]) can help in reducing the dislocation density in the nitride epitaxial layer. Although the lattice mismatch along the a-axis is large (17%), the lateral growth over the trenches can bend the formed dislocations such that the dislocation density near the top surface can be reduced. Meanwhile, after coalesced overgrowth, the buried trenches can produce strong scattering for reducing the light intensity entering the Si substrate such that the optical loss caused by Si substrate absorption can be minimized.
On either the patterned or flat Si (110) substrate, a strain-compensation structure and then an InGaN/GaN QW LED structure are grown. The details of the growth conditions, epitaxial structures, and LED process procedures have been published in [15]. Here, a brief description is given. The strain-compensation structure includes (1) a totally 360 nm temperature-graded AlN buffer layer with five steps of AlN growth at 1100, 1000, 900, 800, and 700 °C of 72 nm in the thickness of each step, (2) a structure of 20-nm AlN sandwiched by two 430-nm GaN layers, and (3) a four-period GaN (250 nm)/AlN (20 nm) interlayer structure and a five-period interlayer structure of the same supperlattices are separated by a 430-nm GaN layer. The InGaN/GaN QW LED structure includes a 1-μm n-GaN layer, a five-period InGaN/GaN QW structure, a 20-nm p-AlGaN layer, and a 120-nm p-GaN layer. The epitaxial surface of sample A is crack-free. However, certain cracks are formed on sample B [15]. Standard lateral LEDs with a mesa dimension of 300 μm x 400 μm are fabricated. Figure 1 shows the epitaxial structure of either LED sample. Here, the trench pattern on the Si (110) substrate for sample A is not shown. By depositing a contact of Ni (10 nm)/Au (50 nm) on the bottom side of the Si substrate, a vertical LED configuration can be obtained by applying a voltage between the p-GaN layer and the Si substrate.
Fig. 1 Schematic drawing of the LED structure of both samples on Si (110) substrate and the operation circuit with the lateral and vertical applied voltages Vb and Vc, respectively. A current meter is connected to the p-contact for measuring the injection current. The buried trenches on Si (110) substrate in sample A are not shown in the figure.
3. Characterization results of light-emitting diodes
Figure 2 shows the output spectra of samples A and B at 70 mA in injection current with the lateral (curves A-L and B-L) and vertical (curves A-V and B-V) operation configurations. In the lateral (vertical) operation configuration, the circuit of the vertical (lateral) configuration is open. Here, one can see that the output spectra of sample B are shorter than those of sample A by a few nm in both lateral and vertical configurations. Also, the output spectra in the vertical configuration are slightly longer than those in the lateral configuration for both samples. It is noted that at a fixed injection current, the applied forward-biased voltage in the vertical configuration is expected to be significantly higher than that in the lateral configuration. The small difference in output spectrum peak between the lateral and vertical configurations in either sample shown in Fig. 2 indicates that the voltage drops across the p-i-n junctions in the two operation configurations are about the same. Figure 3 shows the relations between the injection current and applied forward-biased voltage (I-V curves) when samples A and B are individually operated in the lateral and vertical configurations. The device resistance levels of samples A and B in the lateral configuration (labeled by A-L and B-L) are 25.4 and 31.6 Ω, respectively. Those of samples A and B in the vertical configuration (labeled by A-V and B-V) are 117.2 and 118.2 Ω (in the voltage range between 11 and 15 V), respectively. The turn-on voltages of the two samples in both operation configurations are all around 3 V. No significant current leakage is observed in either sample under either operation condition. The large resistance levels in the vertical LED configuration are attributed to the use of the AlN layers in the strain compensation structure and the large thickness of this structure. Figure 4 shows the output intensities as functions of injection current of the two LED samples in the two operation configurations. One can see that in either sample A or B, the lateral operation configuration leads to slightly higher output intensity, when compared with the vertical operation configuration. Figure 5 shows the peak energy variations of output spectra with injection current of the two LED samples in the two operation configurations. Except the slight red shift at high injection current in the A-V case, the spectral peak energies blue shift with increasing injection current due to the QCSE screening effect in all cases. Because of the strain relaxation through the formation of the periodic trenches in sample A, the QCSE in this sample (or the blue-shift range in Fig. 5) is significantly smaller than that in sample B. In either sample A or B, the vertical configuration results in a slightly smaller blue-shift range. In the A-V case, the maximum blue-shift range when the injection current increases from 1 to 70 mA is only ~2.5 meV.
Fig. 2 Output spectra of samples A and B at 70 mA in injection current with the lateral (curves A-L and B-L) and vertical (curves A-V and B-V) operation configurations.
Fig. 3 Relations between the applied voltage and injection current (I-V curves) when samples A and B are operated in the lateral (curves A-L and B-L) and vertical (curves A-V and B-V) configurations.
Fig. 4 LED output intensities as functions of injection current when samples A and B are operated in the lateral (curves A-L and B-L) and vertical (curves A-V and B-V) configurations.
Fig. 5 Peak energy variations of output spectra with injection current when samples A and B are operated in the lateral (curves A-L and B-L) and vertical (curves A-V and B-V) configurations.
To confirm the difference of QCSE strength between the two samples, in Fig. 6, we show the variations of photoluminescence (PL) spectral peak energy with reverse-biased voltage in the lateral operation configuration of the two samples. The PL measurement results are obtained with the excitation of a HeCd laser (1 mW in power) at 325 nm at room temperature. Because the electric field in a QW, which is dominated by the strain-induced piezoelectric field, is oriented from the p-type layer toward the n-type layer, the application of a reverse-biased voltage can reduce the potential tilt in the QW such that the PL spectral peak blue-shifts with increasing reverse-biased voltage. In Fig. 6, the blue-shift ranges of PL spectral peak as the applied voltage varies from 0 to −6 V are 8 and 25 meV in samples A and B, respectively. Such results clearly confirm that the QCSE in sample B is significantly stronger than that in sample A.
Fig. 6 Variations of PL spectral peak energy with reverse-biased voltage in the lateral operation configuration of samples A and B.
To study the interplay between applied voltage and injection current, we arrange the circuit as shown in Fig. 1 for either sample. Here, two voltage sources are used to provide a forward bias (Vb) in the lateral operation configuration and a reverse bias (Vc) in the vertical configuration. A current meter is inserted right above the p-contact of the device for monitoring the variation of injection current (Ib) into the active region of the device with increasing Vc values while Vb is fixed. First, for either sample, four Vb values are selected to generate the injection currents, Ib, at 10, 30, 50, and 70 mA when Vc is 0. The four Vb values for generating Ib of 10, 30, 50, and 70 mA in sample A (B) are 3.48, 4.02, 4.53, and 5.02 (3.47, 4.21, 4.82, and 5.37) V, respectively. Figure 7 shows the device output intensities as functions of reverse-biased voltage, Vc, in various cases when Vb levels are fixed at the labeled values. In each case, the output intensity decreases with increasing Vc, even down to the zero level. The variation trend is caused by the decreasing injection current as Vc increases. This behavior can be used for the output intensity modulation of an LED for communication application. Figure 8 shows the peak energy variations of the device output spectra with the monitored injection current, Ib, in various cases of fixed Vb values (as labeled). For comparison, the curves A-L and B-L in Fig. 5 are repeated in Fig. 8. Here, one can see that in either sample A or B, the emission spectrum blue shifts with increasing Ib for a fixed Vb and red shifts with increasing Vb for a fixed Ib.
Fig. 7 Device output intensities as functions of the reverse-biased voltage, Vc, in various cases when Vb levels are fixed at the labeled values.
Fig. 8 Peak energy variations of the device output spectra with the monitored injection current, Ib, in various cases of fixed Vb values (as labeled). For comparison, the curves A-L and B-L in Fig. 5 are repeated here.
4. Discussions
Figure 9 shows the relations between Ib and Vb of samples A and B when the peak energies of output spectra are fixed at 2.6525, 2.6575, and 2.6625 eV. The curves here are obtained through first fitting each set of data points in Fig. 8 by an equation of y = a + bln(x + c) with optimization parameters a, b, and c. The fitting curves are shown as the continuous lines in Fig. 8. In Fig. 9, one can read the required injection current for keeping the device emission wavelength unchanged in varying the applied voltage. It is noted that the curves in Fig. 9 are different from the I-V curves in Fig. 3, in which a current source with floating voltage is used for driving the device. In Fig. 9, instead, with the application of Vc, the applied voltage across and injection current into the p-i-n junction can be independently controlled. It is noted that by considering more values of spectral peak energy, we can draw more curves in Fig. 9 similar to those already shown such that a data point can be found at any (Vb, Ib) coordinate within the LED operation range. In this situation, we can read the shift range of spectral peak in varying the applied voltage (injection current) when the injection current (applied voltage) is fixed. It is also noted that along the variation of each curve in Fig. 9, the applied reverse-biased voltage in the vertical configuration, Vc, is varied. In other words, for a given applied voltage, Vb, the injection current, Ib, can be changed by adjusting Vc with the emission spectral peak energy being fixed.
Fig. 9 Relations between injection current, Ib, and applied voltage, Vb, of samples A and B when the peak energies of output spectra are fixed at 2.6525, 2.6575, and 2.6625 eV.
Based on the curves in Fig. 9, we can estimate the required carrier density in a QW to generate a strong enough QCSE-screening effect for compensating the potential tilt (emission red shift) due to the applied forward-biased voltage. Here, generally the curve slopes of sample B (stronger QCSE) are smaller than those of sample A (weaker QCSE), implying that the intrinsically smaller QW potential tilt in sample A requires a larger injection current or a higher QW carrier density for compensating the potential tilt caused by the applied forward-biased voltage, when compared with sample B. This behavior can be attributed to the larger separation between the electron and hole wave functions in a QW of a larger potential tilt for producing a stronger screening effect, when compared with that in a QW of a smaller potential tilt. It is noted that the discussion here is based on the reasonable assumption that the QW emission mainly originates from its effective band edge. Using the curves of 2.6625 eV for emission spectral peaks in Fig. 9 as examples, in sample A, when the applied voltage increases from 3.48 to 5.02 V, an extra injection current of 42 mA is needed for balancing the potential tilt caused by the increased applied voltage. By assuming the uniform distribution of injection current over the mesa of 300 μm x 400 μm in dimension, we need to supply an extra carrier density of 4.37 x 1019 cm−2 per sec into each QW for balancing the increment of the electric field of 1.03 MV/cm in each QW of sample A (3 nm in QW width). In other words, to maintain the emission peak energy at 2.6625 eV in sample A, an extra carrier density of 4.24 x 1013 cm−2 per sec is required per unit electric field increment (in V/cm). On the other hand, in sample B, when the applied voltage increases from 4.21 to 5.37 V, an injection current of 22 mA needs to be added for balancing the potential tilt caused by the increased applied voltage. In other words, to maintain the emission peak energy at 2.6625 eV in sample B, an extra carrier density of 2.97 x 1013 cm−2 per sec is required per unit electric field increment (in V/cm). Therefore, more carrier supply is needed in sample A for balancing the potential tilt trend in increasing the forward-biased voltage, when compared with sample B. Hence, in Fig. 5, the significantly smaller spectral shift range in sample A (curve A-L), when compared with sample B (curve B-L), is attributed not only to the weaker QCSE in sample A, but also to its smaller device resistance (see Fig. 3) such that a given increment of applied voltage leads to a larger increment of injection current. Therefore, besides its heating effect for changing emission spectrum, the device resistance is an important factor in controlling the emission spectral shift in LED operation through the carrier supply in varying the applied voltage.
5. Conclusions
In summary, we have first compared the operation behaviors in the lateral and vertical configurations of two LEDs on patterned and flat Si (110) substrates with weak and strong QCSEs, respectively, in the InGaN/GaN QWs. Then, a reverse-biased voltage was applied to either LED device in the vertical configuration for independently controlling the applied voltage across and the injection current into the p-i-n junction in the lateral configuration of LED operation. The results showed that more carrier supply was needed in the LED of weaker QCSE to produce carrier screening effect for balancing the potential tilt in increasing the forward-biased voltage, when compared with the LED of stronger QCSE. The smaller spectral shift range in increasing injection current in the LED of weaker QCSE was attributed not only to the weaker QCSE, but also to its smaller device resistance such that a given increment of applied voltage led to a larger increment of injection current. From a viewpoint of practical application in LED operation, by applying a reverse-biased voltage in the vertical configuration, the applied voltage and injection current in the lateral configuration can be independently controlled by adjusting the reverse-biased voltage in the vertical configuration for keeping the QCSE unchanged and hence the emission spectral peak fixed.
Acknowledgments
This research was supported by National Science Council, Taiwan under the grants of NSC 102-2221-E-002-204-MY3, NSC 102-2120-M-002-006, NSC 101-2622-E-002-002-CC2, and NSC 102-2221-E-002-199, by the Excellent Research Projects of National Taiwan University (102R890951 and 102R890952), and by US Air Force Scientific Research Office under the contract of AOARD-13-4143.
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