pplied Physics Letters, Vol. 79, No. 8, pp. 1130–1132, 20 August 2001
©2001 American Institute of Physics. All rights reserved.

Measurement of piezoelectric field and tunneling times in strongly biased InGaN/GaN quantum wells

Y. D. Jho, J. S. Yahng, E. Oh,^a) and D. S. Kim^b)

Department of Physics, Seoul National University, Seoul 151-747, Korea

Received: 29 March 2001; accepted: 27 June 2001

We have measured both spectrum- and time-resolved photoluminescence (PL) of InGaN/GaN light-emitting diode structure as a function of an external bias. From spectrum-resolved PL, we observed regions of blueshift and redshift in peak PL energies. From the bias point at which redshift begins, which we attribute to the inversion of electric field due to full compensation of the piezoelectric field (PEF), we estimate PEF to be 2.1±0.2 MV/cm. From time-resolved PL, we found the carrier lifetimes to drastically decrease (2.5 ns–2 ps) with increasing reverse bias. We attribute this decrease to escape tunneling through tilted barriers. © 2001 American Institute of Physics.

Contents

• BODY OF ARTICLE
• REFERENCES
• FIGURES
• FOOTNOTES

Recently, InGaN/GaN quantum well systems have received considerable attention due to its optoelectronic applications as light emitting devices with spectral range from green to UV. From extensive investigation of this system, researchers have found a large piezoelectric field (PEF) in strained heterostructures of GaN based materials and have studied PEF both theoretically¹ and experimentally.^{2,3,4,5,6,7,8,9} Experimentally, one manifestation of PEF is the observed variations in transition energy, which has been explained by quantum confined Stark effect invoked by PEF.^3,4,5,8 Although existence of PEF in group III–N systems is well established, the reported PEF value has been scattered from 2.45 MV/cm (Ref. 2) to less than 1 MV/cm (Ref. 5) even with similar indium compositions of around 15%–20%. In the recombination lifetime, carrier localization in InGaN quantum well (QW) has been introduced to explain the lifetime dependence on detection photon energy, particularly in structures with relatively large indium composition.⁶ The increase of photoluminescence (PL) lifetime with the continuous increase of well width from 2 to 5.5 nm was explained by PEF-induced electron-hole separation.²

For GaAs-based QW systems, in the absence of PEF, the increase of PL lifetime with increasing field^10,11 was reported and various tunneling mechanisms such as escape tunneling through tilted barrier,^11,12 resonant tunneling,¹³ and phonon-assisted tunneling¹⁴ were extensively studied. In order to comprehend the consequences of the PEF present in InGaN QWs, it is useful to investigate the recombination energy and carrier lifetime as the external field completely compensates the PEF or even inverts the original field direction in QWs. Optical studies under complete compensation of the PEF with external field have not been reported to our knowledge, though the blueshift of the PL peak with increasing reverse voltage was studied.^3,6 In this letter, we have investigated the influence of the PEF and the escape tunneling on optical properties of InGaN/GaN QWs embedded in a p–i–n structure, both in spectral and time domain. The PEF strength was determined from the applied field at which the PEF is completely compensated. The spectral and temporal changes of PL emission were analyzed based on the variational method,^10,11,15 and the semiclassical tunneling model,^11,12,16 respectively.

The sample was grown on a c-plane sapphire substrate by metalorganic chemical vapor deposition. It consists of undoped GaN (1.5 µm), n-GaN (4 µm), five quantum wells of In_0.15Ga_0.85N (2.2 nm) and four barriers of GaN (10 nm), p-Al_0.1Ga_0.9N (30 nm), and p-GaN (0.2 µm). Time resolved and cw PL measurements were carried out varying the external bias from +2 to –22 V, using a streak camera with a 10 ps time resolution and a monochromator, respectively. In order to obtain a better time resolution, femtosecond pump–probe reflectance was measured in the range from –16 to –30 V. Above the cw breakdown voltage (~–23 V), an external field was applied in the form of a square-function pulse which was synchronized with the pump–probe detection scheme. The excitation source was a frequency-doubled Ti:sapphire laser, whose energy was fixed at 3.3 eV for PL and 3.1 eV for pump–probe measurements. The peak power density was estimated to be about 200 MW/cm² and the doubled pulse width was about 250 fs. All measurements were carried out at room temperature.

In Fig. 1, the schematic band diagrams of our sample structure are depicted, based on the actual material parameters. Conduction band potential is set to be zero at z = 0, and for a convenience sake, a 6:4 ratio between the conduction and valence band discontinuity was assumed. The direction of PEF is set opposite to the reverse external voltage as discussed in the previous studies.^2,3,4,5,6 With PEF, electron and hole wave functions corresponding to the lowest QW bound states are spatially separated as shown in Fig. 1(a). In Fig. 1(b) where the external field compensates the PEF in the well, the overlap of the electron and hole wave functions will increase and the carrier recombination may become easier. However, the increasing external field reduces the effective barrier width continuously and the tunneling time is significantly shorter than recombination time in the case of Fig. 1(b).

Figure 1.

Spectrum- and time-resolved PL spectra are shown in Figs. 2(a) and 2(b), respectively. The oscillations in the spectra of Fig. 2(a) are due to the Fabry–Pérot-type interference fringes between air-GaN and the GaN-sapphire interfaces. Time-resolved PL signals are spectrally integrated except for the scattered laser noise, which is rejected by a grating and slit pair. The PL peak was blueshifted with increasing reverse voltage due to the compensation of the PEF, and then redshifted with a further increase of the voltage. The redshift indicates that the net electric field in the InGaN well is inverted. In Fig. 2(b), we can clearly observe the drastic decrease of decay time with increasing reverse bias. In small external bias region, the main decay component of the order of nanosecond was mixed with a fast decay component comparable to the time resolution of the streak camera. The main decay component of the lifetime was decreased from 2.5 ns (at +2 V) to 10 ps (over –16 V). The fast initial decay, as observed for 0 V in Fig. 2(b), seems to be associated with the spectral integration of our signal and the variation of the PL decay time with respect to the photon energy.⁶

Figure 2.

Experimental PL peak energy and decay time are shown as filled squares in Figs. 3(a) and 3(b), respectively. The results were obtained after Gaussian fitting for PL peak energy and the exponential fitting for the main decay time, respectively. From variational method^10,11,15 incorporating the results of Poisson equation, the theoretical energy curve was obtained setting the value of PEF as a fitting parameter, where the most plausible value was about 2.1±0.2 MV/cm [dotted line in Fig. 3(a)]. The total electric field within the wells (barriers) E_w (E_b) was formulated by¹⁷

where V_bi, F_p, and V_a are the built-in potential, the piezoelectric field, and the applied voltage, respectively. L_w (L_b), N_w (N_b), and L_d represent the well (barrier) width, the number of wells (barriers), and the depletion width, respectively. The depletion width was obtained from the capacitance–voltage (C–V) measurement, considering the series combination of the capacitances in the intrinsic and doped regions.¹⁸ In the region of GaN layers, the PEF was neglected. To be self-consistent with the Poisson equation, the electric field in the depletion region linearly varies from zero to the maximum value,^18,19 which resulted in L_d/2 instead of L_d in Eqs. (1) and (2). If the electric field in the depletion layer was assumed to be constant and to have the same value with the electric field in the intrinsic region, PEF strength deduced would be 1.35 MV/cm and the theoretical curve [dotted line in Fig. 3(a)] would disagree with the experimental data. Therefore, our results show that when the depletion layer widths are of the same order or larger than the intrinsic region, the constant field assumption fails. The ratio between the conduction and the valence band offset energies was not a critical factor in determining the PEF and the ratios of 6:4, 4:1, and even 3:7 result in similar PL peak energy variation as long as the QW bound states exist. The bulk In_0.15Ga_0.85N energy was assumed to be 2.647 eV by including the gap fluctuation^8,20 and other material parameters were obtained from Ref. 9. Coulomb interaction between carriers was neglected in the calculations and the exciton binding energy was assumed to be constant at 30 meV.²¹

Figure 3.

The theoretical carrier lifetime is given by the recombination time _r calculated from overlap integral of the electron and hole wave functions, and the tunneling escape time _t:

(solid line) which is calculated from our theory is in good agreement with the experiments, as shown in Fig. 3(b). _r and _t each contains one fitting parameter; the recombination lifetime under flatband condition^10,11,15 and the carrier oscillation time within the well,^11,12 respectively. We note that, in disregard of potential fluctuations, 4:1 band offset ratio provides the best fit for the electron tunneling time. The carrier decay time change on three orders of magnitude is mostly due to the escape tunneling of electrons through the barriers. The well width which is smaller than the bulk exciton Bohr radius (~3.4 nm) keeps the wave function overlap within a limited change. The relatively large discrepancy between experiments and calculations in the pump–probe measurement range is not yet clearly understood. The continual decrease of PL intensity in Fig. 2(a), even in the small reverse bias region where the tunneling is not dominant [see Fig. 3(b)], can be attributed to the increase of leakage photocurrent, which will be described elsewhere together with the details of the calculations used in Fig. 3.

The electron effective mass of GaN is three times heavier than that of GaAs. In spite of the heavy mass and the thick barrier widths in our sample, we found that the tunneling time was comparable or even faster than in GaAs QW.^11,12 This efficient tunneling can be attributed to the strong applied field. For example, with a bias of –30 V, the applied field was about 2.5 MV/cm and the effective tunneling barrier width was of the order of 1 nm. Our work implies that the InGaN/GaN structure has potential applications for fast devices.

In summary, we performed cw and time-resolved PL measurements of an InGaN light-emitting diode structure over the large external bias range. We observed, the plateau region followed by a slight redshift in the plot of the PL peak energy versus voltage. We attributed the three orders of magnitude change in carrier lifetime as a function of bias mostly to tunneling effect. From these measurements combined with C–V measurements, we could accurately determine PEF to be 2.1±0.2 MV/cm in our In_0.15Ga_0.85N quantum wells.

This work was supported by MOST (the National Research Laboratory Program), KOSEF (the Center for Strongly Correlated Materials Research, and Grant No. 97-0702-03-01-3), and National Program for Tera-Level Nanodevices of the Ministry of Science and Technology as one of the 21 Century Frontier Programs. The sample used in this work was provided by Samsung Electronics.

REFERENCES

¹

F. Bernardini, V. Fiorentini, and D. Vanderbilt, Phys. Rev. B 56, R10024 (1997). First citation in article

²

P. Lefebvre, A. Morel, M Gallart, T. Taliercio, J. Allgre, B. Gil, H. Mathieu, B. Damilano, N. Grandjean, and J. Massies, Appl. Phys. Lett. 78, 1252 (2001). First citation in article

³

T. Takeuchi, C. Wetzel, S. Yamaguchi, H. Sakai, H. Amano, I. Akasaki, Y. Kaneko, S. Nakagawa, Y. Yamaoka, and N. Yamada, Appl. Phys. Lett. 73, 1691 (1998). First citation in article

⁴

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, Phys. Rev. B 57, R9435 (1998). First citation in article

⁵

C. Wetzel, T. Takeuchi, H. Amano, and I. Akasaki, Phys. Rev. B 61, 2159 (2000). First citation in article

⁶

S. F. Chichibu, T. Azuhata, T. Sota, T. Mukai, and S. Nakamura, Appl. Phys. Lett. 88, 5153 (2000), and references quoted therein. First citation in article

⁷

H. Kollmer, J. S. Im, S. Heppel, J. Off, F. Scholz, and A. Hangleiter, Appl. Phys. Lett. 74, 82 (1999). First citation in article

⁸

S. F. Chichibu, A. C. Abare, M. S. Minsky, S. Keller, S. B. Fleichser, J. E. Bowers, E. Hu, U. K. Mishra, L. A. Coldren, S. P. DenBarrs, and T. Sota, Appl. Phys. Lett. 73, 2006 (1998). First citation in article

⁹

T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, Jpn. J. Appl. Phys., Part 2 36, L382 (1997). First citation in article

¹⁰

H.-J. Polland, L. Schultheis, J. Kuhl, E. O. Göbel, and C. W. Tu, Phys. Rev. Lett. 55, 2610 (1985).  [MEDLINE] First citation in article

¹¹

K. Köhler, H.-J. Polland, L. Schultheis, and C. W. Tu, Phys. Rev. B 38, 5496 (1988). First citation in article

¹²

T. B. Norris, X. J. Song, W. J. Schaff, L. F. Eastman, G. Wicks, and G. A. Mourou, Appl. Phys. Lett. 54, 60 (1989).  [SPIN] First citation in article

¹³

K. Leo, J. Shah, E. O. Göbel, T. C. Damen, Köhler, and P. Ganser, Appl. Phys. Lett. 56, 2031 (1990).  [SPIN] First citation in article

¹⁴

D. Y. Oberli, J. Shah, T. C. Damen, J. M. Kuo, J. E. Henry, J. Lary, and S. M. Goodnick, Appl. Phys. Lett. 56, 1239 (1990).  [SPIN] First citation in article

¹⁵

G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, Phys. Rev. B 28, 3241 (1983). First citation in article

¹⁶

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Nonrelativistic Theory, 3rd ed. (Pergamon, New York, 1977), pp. 178–181. First citation in article

¹⁷

J. P. R. David, T. E. Sale, A. S. Pabla, P. J. Rodríguez-Gironés, J. Woodhead, R. Grey, G. J. Rees, P. N. Robson, M. S. Skolnick, and R. A. Hogg, Appl. Phys. Lett. 68, 820 (1996). First citation in article

¹⁸

See, e.g., S. M Sze, in Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981), pp. 74 and 118. First citation in article

¹⁹

H. S. Veloric and M. B. Prince, Bell Syst. Tech. J. 36, 975 (1957). First citation in article

²⁰

L. K. Teles, J. Furthüller, L. M. R. Scolfaro, J. R. Leite, and F. Bechstedt, Phys. Rev. B 63, 085204 (2001). First citation in article

²¹

G. Traetta, R. Cingolani, A. D. Carlo, F. D. Sala, and P. Lugli, Appl. Phys. Lett. 76, 1042 (2000). First citation in article

FIGURES

Full figure

Fig. 1. Schematic band diagrams of In_0.15Ga_0.85N/GaN QWs along the growth direction z, illustrating the origin of carrier recombination and the escape tunneling through barrier (a) in the absence of external field and (b) when the net electric field in the well is zero. The wave functions (thin solid lines) and the confined energies in the well (horizontal lines) were obtained from the variational calculation. V_ext, F_P, and L_W are the external voltage, piezoelectric field, and the well width, respectively. First citation in article

Full figure

Fig. 2. Room temperature PL spectra as a function of an external voltage (a) in the spectral domain and (b) in the time domain (spectrally integrated). The interval of each spectrum in (a) is 2 V. The hollow circles show the PL peak energies obtained from Gaussian fitting. First citation in article

Full figure

Fig. 3. (a) PL peak energy and (b) PL decay time (solid square) shown together with pump–probe decay time (open star) as a function of an external voltage. The line curves in (a) are from theoretical calculations, assuming the electric field E_d varies linearly (solid line) in the depletion width or is constant (dotted line). In (b), , _t, and _r represent the carrier lifetime, tunneling escape time, and recombination time, respectively. First citation in article

FOOTNOTES

^aElectronic mail: esoh@phya.snu.ac.kr

^bElectronic mail: denny@phya.snu.ac.kr

p: Issue Table of Contents
Go to: Previous Article | Next Article
Other formats: HTML (smaller files) | PDF (57 kB)