1. Introduction

Injection luminescence spectra of superbright blue and green light-emitting diodes (LEDs) based on InGaN/AlGaN/GaN heterostructures were studied in [1] [2] [3] [4] [5]. It was interesting to study the breakdown luminescence in the same structures hoping to receive some additional information on the parameters which influence on the properties of effective LEDs.

Avalanche breakdown luminescence in GaN was studied previously in cases of i-n- and MIS - diodes [6] [7] [8] [9]. It was shown that at reverse bias, electrons are tunneling from metal to the n-side of the junction and at sufficiently high voltage cause impact ionization and avalanche breakdown.

There is a high electric field in the active layer of the blue InGaN/AlGaN/GaN LEDs as it was concluded from the spectral and capacitance measurements [3] [4] [5]. The high doping of the p-side and a thin active layer distinguish these LEDs from the previous [6] [7] [8] [9] [10] ones. In this paper we describe breakdown luminescence spectra of blue LEDs and analyze electrical and luminescence properties of InGaN/AlGaN/GaN structures at reverse bias.

2. Experimental results

We have studied the LEDs based on the InGaN/AlGaN/GaN structures with a thin layer - quantum well InGaN - described in [1] [2]. Blue LEDs with known parameters of the injection luminescence spectra [2] [3] [4] were chosen for measurements. Reverse current-voltage and capacitance-voltage curves of a blue diode (N 3) are shown in Figure 1 and Figure 2.

Figure 1
figure 1

Reverse current-voltage curves of a blue diode (N3); 1 - T=77 K, 2 - T=300 K, 3 - EJ=dV/d(lnJ), T=300 K.

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Figure 2
figure 2

Reverse capacitance-voltage curves of a blue diode (N3).

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The main part of the curves at |V|< 10 V can be approximated by two exponents:

$${\text{J}}\,{{\sim}}\,{\text{exp}}\left( {\left. {\text{e}} \right|\,{\text{V/}}{{\text{E}}_{\text{J}}}} \right),$$
(1)

with a parameter EJ = 0.86◊0.90 eV changing near |V| = 5◊6 V. The change in the slopes of derivatives dV/d(lnJ) is shown in Figure 1. The reverse current-voltage characteristics of the green LEDs differed from the blue ones (see Figure 3), according to lower electric fields in the structures [2] [3] [4]. The values of Ej were almost independent on the temperature (T = 80◊300 K). This behavior is attributed to a tunnel component of the current. It is to be noted that some changes in the J(V) characteristics near |V| = 5◊6 V were seen by other authors [10] [11] but they did not pay attention to these facts.

Figure 3
figure 3

Reverse current-voltage derivative for blue and green LEDs.

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The impact ionization begins at higher voltages |V|> 8◊10 V as can be concluded from a minimum of C(V) curves (a maximum of the curves 1/C2 = f(V) is seen in Figure 1. The luminescence could be detected at a threshold of about Vth ≈ −11 V. We have measured the luminescence spectra at the currents |J|< 5 mA which were not destructive for the blue diodes. The luminescence - radiative recombination - indicated a creation of the minority carriers as a result of the impact ionization. The luminescence was visually non homogeneous because of microplasma mechanism of breakdown current.

The breakdown luminescence spectra for three LEDs are shown in Figure 4. The injection luminescence spectra are also shown. The intensity of the breakdown luminescence is 6–7 orders of magnitude lower than of the injection ones, as indicated on the ordinate axes.

Figure 4
figure 4

Avalanche breakdown luminescence spectra of blue InGaN/AlGaN/GaN LED’s; J = − 4 mA, room temperature.

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The broad band of luminescence is seen in the region 1.7◊3.5 eV. The high energy edges of the spectra are at energy 3.4 eV, approximately equal to the gap Eg of GaN at the room temperature. A shoulder at 3.2 eV corresponds to the energy of Eg−ΔEA, where ΔEA - ionization energy of Mg-acceptor. The maxima in the range of 2.6◊2.8 eV correspond to the maxima of injection luminescence spectra. The broad maxima in the range 2.2◊2.3 eV correspond to the well known “yellow band” in n-GaN connected with donor-acceptor pairs and/or double donor radiative recombination [12]. The charged impurity distribution in the lower doped p-type side of the structure was determined from dynamical capacitance measurements (see the method in [11]). From C(V) curves a model distribution of charges, electric fields and an energy diagram of the structures at reverse bias was deduced as shown in Figure 5. The charge concentration on the p-side of the space charge region of the heterojunction is (1◊2) · 1018 cm−3 (a width of 11 nm), on the n-side - of 1 · 1019 cm−3 (a width of 1.5 nm), there are compensated quasi-neutral layers (10◊11 nm) adjacent to the active layer (2.5◊4 nm). It is necessary to introduce into the model charged walls on the heterointerfaces to describe the capacity measurements. The electric field in the active layer InGaN is quite high - of E ≈ 107 V/cm, the fields in the adjacent layers - of E ≈ 2◊4·106 V/cm.

Figure 5
figure 5

The energy diagram (a), the model distribution of charge (b) and electric field (c) of the structure at the reverse bias.

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3. Discussion.

The tunnel component of the reverse current can be described by the theory of the J(V) characteristics of highly doped abrupt p-n-junctions in the direct-bandgap semiconductors [13]:

$${\text{J}}\,{{\sim}}\,\left( {{\text{V - }}{{\text{V}}_{\text{k}}}} \right){\text{exp}}\left( {{\text{B}}\left( {\left. {\text{e}} \right|\,\left. {\,{\text{V}}} \right|{\text{/2}}{{\text{E}}_{\text{g}}}} \right)} \right),B = \left( {{{\pi /}}{{\text{2}}^{{\text{3/2}}}}} \right)\left( {2{{\text{m}}_{{\text{cv}}}}^{\text{*}}/{h^2}} \right)\left( {{E_g}^{3/2}/{\text{e}}{\bf{E}}} \right);{{\text{m}}_{{\text{cv}}}}^*{{\text{m}}_{\text{v}}}^*/\left( {{{\text{m}}_{\text{c}}}^* + {{\text{m}}_{\text{v}}}^*} \right);$$
(2)

where Vk is a contact potential, Eg - effective energy gap, mc*, mv* - effective masses. Taking the parameters mc*=0.22m0; mv*=0.54 m0, Eg=3.4 eV, we have estimated the electric field in the active region: E ≈ 2·107 V/cm (at the experimental values of Vk = 3.2 eV, EJ = 0.86◊0.9 eV), see Figure 1.

The threshold for impact ionization can be connected with the effective concentration of charged impurities in the p-n-junction by the empirical equation [14]:

$$\left| {{{\text{V}}_{{\text{th}}}}} \right| = 60{\left( {{{\text{E}}_{\text{g}}}/1.1} \right)^{3/2}}{\left( {{\text{N/1}}{{\text{0}}^{16}}} \right)^{ - 3/4}}.$$
(3)

Taking the parameters Eg = 3.4 eV, |Vth|= 11.5 V, we receive from this equation a value of N ≈ NA ≈ 1·1018 cm−3. This value is in accordance with the analysis of capacitance measurements and an evaluation of electric field distribution [3] [5].

The impact ionization is due to electrons tunneling from valence band of the p-side of the structure through the active region of InGaN, subsequent drift in the electric field to the adjacent quasi-neutral and charged n-layer of the structure and receiving an energy of about 3Eg sufficient for impact ionization.

The impact ionization coefficient of the electrons can be assumed great in comparison with that of holes, αn>>αp. In order to evaluate αn the mean-free paths of hot electrons λfr and effective phonon energies kθ are to be estimated taking into account additional high energy extreme in the conduction band. The next extreme between L and M points are at 5.5 eV and the next Γ valley is at 5.6 eV (see Figure 6).

Figure 6
figure 6

The energy bands involved in the five-band k·p calculation. [16]

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It seems that the changes in the slopes near |V| = 5◊6 V are connected with a probability of high energy electrons to get into Γ-point extreme with high effective masses. The problem of hot electrons in GaN is far from clear.

We can describe the results assuming that the electron-hole pairs are divided by the electric field in the time of W/Vt ≈ 10−13 ◊ 10−14 s (Vt ≈2 · 107 cm/s) and only a small part of the electrons can come to the external boundary of the space charge n-region. If the radiative lifetimes are of 10−9 s, only a small part of the pairs can recombine radiatively in the structure. So we can understand why the efficiency of the breakdown luminescence is very low.

The spectral maxima in the region of 2.2◊2.3 eV connected with donor-acceptor pairs and/or double donor radiative recombination were seen in the n-GaN [12] [15]. This is an evidence that the most part of radiative recombination is due to electrons created near the n-side of the structure. This recombination is caused by some structural defects; high electric fields and impact ionization are concentrated near defects.

The shoulder at 3.2 eV can be described by optical transitions connected with Mg-acceptors. It means that part of the holes created by impact ionization can recombine with electrons in the conduction band on the p-side of the structure.

4. Conclusions

1. Avalanche breakdown luminescence spectra were detected in blue LEDs based on the InGaN/AlGaN/GaN p-n-heterostructures at reverse voltages about 11◊12 V ≈ 3Eg with an intensity of about 6 orders of magnitude lower than injection luminescence spectra. The high energy edge of the spectra corresponds to energy gap of GaN, Eg.=3.4 eV.

2. There are high electric fields in the active InGaN layers of the InGaN/AlGaN/GaN heterostructures, up to 107 V/cm. In the adjacent compensated layers the fields are of (2◊4)106 V/cm. Tunnel component of the current dominates at reverse bias < 10 V; tunneling electrons initiate impact ionization at reverse bias ≈ 3Eg. Special points in current-voltage characteristics near V = - (5◊6) V are connected with higher energy extreme in the conduction band of GaN.

3. A low efficiency of the breakdown luminescence can be understood because of the division of electrons and holes by high electric fields. Broad luminescence band (2.14◊3.4 eV) corresponds to the recombination of carriers mostly on the external boundaries of the space charge regions.