3.1 Spectra at room temperature

The luminescence spectra of some LEDs at the room temperature (RT) and J=10 mA are given in Figure 1. The violet-blue and blue LEDs have spectral maxima ω_max = 2.58-2.75 eV, and the green LEDs in the ω_max = 2.38-2.45eV range dependent on the active layer In content (x=0.20-0.25 for the blue and 0.42-0.44 for the green LEDs). The LEDs span the entire visible short wavelength spectrum Reference Nakamura, Senoh, Iwasa, Nagahama, Yamada and Mukai[1] [2]. The spectra of a blue diode at various currents are shown in Figure 2. The exponential decay on both sides of the peak are unchanged over the range of currents plotted (J = 0.3-20 mA). The long wavelength side of the peak is described by an exponent:

Figure 1. Room temperature spectra of blue and green InGaN/AlGaN/GaN LEDs, J=10 mA (Arrows show E_max).

Figure 2. Room temperature spectra of blue InGaN/AlGaN/GaN LED #3 over the current range J = 0.3-20 mA.

The parameter E₀ varied in different diodes between E₀ = 42-50 meV > kT, and was independent of temperature. The short wavelength side of the peak is described to first approximation by the formula:

with a temperature dependent parameter equal to E₁ = 31-34 meV at RT.

3.2 Temperature dependence of spectra

The temperature dependence of spectra at T = 200-300 K for one of blue diodes is shown in Figure 3. The temperature, measured by a termocouple attached to the plastic cap of the LED, was current dependent above 1mA as a result of Joule heating. Therefore measurements were taken at J = 1 mA, where such heating was negligible. The data are bunched roughly in two groups in this temperature interval. The high energy side of the spectra are changing according to (2), the parameter E₁ being approximately proprtional to T.

Figure 3. Temperature dependent spectra of blue LED #2 at 1mA.

3.3 Interference structrure

A distinct structure on the spectra could be detected when measurements were done at a spectral resolution better than 1meV. This structure was better resolved when a Gaussian or hyperbolic fitting function is substracted from experimental curves, or if the derivatives of spectra were analysed (see Figure 4). The structure is nearly periodical. This can be understood if the light interference is taken into account. The period of the spectral structure is of the order of several nm. If the interference is localized in a layer having thickness t and a refractive index n, then

Figure 4. Two Gaussian approximation of a blue LED #3 spectrum at RT, J = 10 mA. The lower curve is the difference between the experimental data and the sum of the two Gaussians.

The n-GaN layer of the structure is t = 5.0 ± 0.5 μm. The values of the refractive index n and its dispersion (1 + (λ/n)(dn/dλ)) calculated from (3) for different blue LEDs were 2.48, 2.73, and 3.03. These values correspond to the known refractive index of GaN n = 2.5 to within the limits of the above analysis.

3.4 Dependence of intensity versus current

The integrated radiation intensity of the spectrum was proportional to the intensity at the peak I_max and the full width at half-maximum D(ω)_1/2. The D(ω)_1/2 values for the blue (D(ω)_1/2 = 0.12 - 0.13 eV) and green (D(ω)_1/2=0.15-0.16 eV) LEDs were current independent. We therefore were able to determine the current dependence of integrated intensity by merely measuring I_max.

The current dependence I_max(J) was different for blue and green LEDs (see Figure 5 and Figure 6). The linear dependence I_max(J) ~ J is seen in the current range 1 mA < J < 10 mA. For J > 10mA, Joule heating overrides the dependence. The intensity dropps dramatically at currents below 1 mA in the blue diodes, following a I_max(J) ~ J^4-5 dependence at RT (see also Figure 2). At lower temperature, the transition between the two regimes occurs at lower current levels (J < 0.1 mA). The green diodes had no such temperature dependence (see Figure 6a).

Figure 5a. Current dependence of I_max at RT for blue LED #5.

Figure 5b. RT J-V curve of blue LED #5.

Figure 6a. Current dependence of I_max at RT for green LED #3.

Figure 6b. RT J-V curve of green LED #3.

The difference in efficiency corresponds to the different J-V characteristics of blue and green diodes (see Figure 5 and Figure 6). The low temperature J(V) of the blue diodes was exponential:

with E_J = 130-140 meV independent of temperature. This can be caused by a tunnel “excess” current which is common for thin p-n-junctions with high electric fields in the space charge region. At higher currents the curve flattens and can be described by a temperature dependent exponent. In this regime, series resistance R_s is limiting the current:

where U is the p-n-junction potential. The green diodes had higher series resistance and the J(V) curve had no tunnel component.

3.5 Tunnel radiative recombination

Tunneling effects in blue LEDs were detected also in the low current EL spectra (see Figure 7). A wide spectral band is seen on the low energy side of the specta with its maximum moving nearly equal to the voltage ω_max ≈ V ≈ U. Analogous spectra were studied in highly doped GaAs, InP and GaSb narrow p-n junctions Reference Yunovich and Ormont[8] Reference Stuchebnikov and Yunovich[9]. It was shown that optical transitions between the tails in the density of states at the band gap edges are caused both by the high electric field at the junction and the fluctuating fields of charge impurities. Now we can conclude that such a situation occurs in GaN based structures characterized by narrow space charge regions and a thin 2D active layer.

Figure 7. Low current RT spectra of blue LED #2 showing tunnel radiative recombination.

4.1 Energy diagram

Let us analyze the energy diagram of a multilayered structure at forward bias (see Figure 8). There are three main current components in the space charge regions: tunneling, injection and recombination, and only injection and recombination currents in the 2D active layer. The tunneling component can dominate at low currents in highly doped junctions with thin space charge regions. The larger part of the space charge corresponds to the p-Al_0.1Ga_0.9N:Mg (~100 nm) layer. The space charge width is lower for blue diodes as determined by preliminary capacitance measurements which give values of 25 nm for the blue and 40 nm for green LEDs. We conclude that the difference between the two LED groups is differing concentrations of charge impurities in the p-regions. Tunneling dominates at low currents in blue LEDs. The main part of this component is non-raditive recombination, but another part is the tunnel radiative recombination. Injection and recombination in space charge p-region dominate in green LEDs at low currents. Effective radiative recombination is achieved when both carrier types are injected to the active QW layer. At high currents some of the voltage will drop across the adjacent layers, and some recombination will occur there. This produces the maximum of the quantum efficiency at a given current density. It means that the charge distribution in InGaN/AlGaN/GaN heterostructures is very important for optimizing the efficiency.

Figure 8. Energy diagram of a InGaN/AlGaN/GaN heterostucture under forward bias.

4.2 A model approximation of the main spectral band

The effective energy gap of a doped QW can be estimated by taking into account the dependence of E_g(x,T) for InGaN, shifts of QW levels for electrons and holes (ΔE_1c, ΔE_1v), shifts due to deformations ΔE_P, and shifts due to impurity band tails ΔE_A,D:

An estimation of E_g(x,T) was made by taking data from a review Reference Morkoc, Strite, Gao, Lin, Sverdlov and Burns[10]. The parameters ΔE_1c+ΔE_1v were approximated using standard formulae for levels in rectangular quantum wells Reference Herman[11] and approximate effective masses in InGaN. A model of joint 2D-density of states suggested in Reference Cingolani, Stolz and Ploog[6] and used in Reference Vardanyan and Yunovich[7] to analyze spectra of GaAs/AlGaAs MQWs can be applied to fit the spectral band by the equations:

with f_c(hω,kT,F_n) and (1 − f_v(hω,kT,F_p)) representing the Fermi functions for states near the effective band edges. One of the fits is shown in Figure 3. The fit is quite successful and the number of parameters is not so high. The parameter E₀ depends on the roughness of interfaces, strains, alloy inhomogenities and Coulombic impurity fields.

The exponential decay on the high energy side is described by the exponents

We would like tod iscuss the parameters of this fit in the future.