Designs of blue and green light-emitting diodes based on type-II InGaN-ZnGeN₂ quantum wells Free

The ternary compound InGaN has been implemented in InGaN quantum wells (QWs) with GaN barriers for active regions in current commercial light-emitting diodes (LEDs) and laser diode emitters that are emitting in the visible spectral range.^1–8 One of the major challenges in InGaN QWs-based optoelectronic devices lies in the low radiative efficiency or optical gain due to charge separation, resulting from the existence of large polarizations in III-nitride semiconductor materials grown along the C-plane orientation. The detrimental effects from the band bending and charge separation become more severe for InGaN QWs emitting in the green and longer wavelength region, in which higher In content and wider QW width are required. Recently, several approaches based on the concept of large overlap QW designs have been proposed to reduce the charge separation by using novel QW structures such as (1) a staggered InGaN QW,^9–13 (2) a strain-compensated InGaN-AlGaN QW,^14,15 (3) a type-II InGaN-GaNAs QW,^16,17 (4) an InGaN-delta-InN QW,¹⁸ and (5) InGaN QW with delta-AlGaN layer.^19,20 Additional efforts have focused on the development of InGaN QW LEDs and laser diodes grown along non-polar and semi-polar planes^21,22 to remove or reduce the effects from the internal polarizations in polar structures. Note that in these QW structure designs, the layered materials all use III-nitride compound semiconductors (GaN, InN, and AlN) and their alloys.

The II-IV-nitrides ZnGeN₂, ZnSiN₂, and ZnSnN₂ form a family of semiconductors related to the III-nitrides. This family is derived, in principle, from the III-nitrides by replacing every two group III atoms by an ordered pair composed of one group II atom and one group IV atom.^23–30 The resulting orthorhombic structure is closely related to the wurtzite structure of the III-nitrides, with distortions of the bond angles of less than a couple of degrees. The Zn-IV-nitrides span the visible-, or infrared-, to ultraviolet wavelength range in band gaps and hence could be of potential interest as optical emitters in this wavelength range. The band gap of ZnGeN₂ has recently been theoretically predicted²³ and experimentally measured,^24–26 to be within a few percents of the band gap of GaN. In addition, the lattice constants of ZnGeN₂ and GaN match to within 1%.²⁵ More recently, the theoretical studies based on first principle calculations indicate a large band offset between GaN and ZnGeN₂ (ΔE_c = 1.4 eV; ΔE_v = 1.5 eV), which allows the formation of a type-II heterostructure.³¹ ZnGeN₂ is the only material discovered so far that has the closest lattice-match, a similar bandgap, and a large band offset with GaN.

In this paper, we focus on the designs of type-II InGaN-ZnGeN₂ QW structures for both blue-emitting and green-emitting LED applications. Different design protocols are compared between blue and green emitting type-II QWs. By inserting a thin layer of ZnGeN₂ in the conventional type-I InGaN QW, the band structure is significantly modified. The type-II QW has the advantages of (1) enhancing the electron-hole wave function overlap significantly due to the confinement of holes in the ZnGeN₂ layer as well as the shift of the electron wave function toward the center of the QW and (2) extending the emission wavelength into the longer wavelength range with the use of low In-content InGaN. Although GaN/ZnGeN₂ heterostructures have not been experimentally tried yet, it is promising to grow this heterostructure due to the following reasons: (1) The lattice parameters and energy band gap of ZnGeN₂ have been verified by both theory and experiments. (2) The experimental growth conditions such as growth temperature for ZnGeN₂ are close to that of GaN,^25,26,32 which is also expected from their similar energy band gap. Thus, it is feasible and promising to grow GaN or InGaN/ZnGeN₂ heterostructures. Simulation studies based on a self-consistent 6-band k·p method of the proposed type-II InGaN-ZnGeN₂ QW indicate the enhancements of 6.1–7.2 times for the spontaneous emission radiative recombination rate in the blue wavelength region, and 4.6–4.9 times in the green wavelength region, as compared to that of the type I InGaN QW emitting at the same wavelength regions.

Heterostructures, in which electrons and holes have their lowest energies in different materials, are called “type II.” The concept of the type-II InGaN-ZnGeN₂ QW design is proposed to address the charge separation issue in the conventional type-I InGaN QW due to the band bending from the strong spontaneous and piezoelectric fields in the QW. The spontaneous polarization field in III-nitride materials arises from the non-ideal internal cell parameters (c/a) of the wurtzite III-N [0001]-oriented materials. The piezoelectric polarization in an InGaN-based QW arises due to the lattice-mismatch-induced strain in the material. As one of the group II-IV-nitride materials, ZnGeN₂ has a similar crystal structure, lattice constant, and energy band gap as GaN, which enable the promise to form InGaN-ZnGeN₂ heterostructures. Due to the large band offset between GaN and ZnGeN₂, the insertion of a thin layer of ZnGeN₂ into the InGaN QW allows (i) the shift of the electron wave function and (ii) a strong hole confinement within the ZnGeN₂ layer, which leads to a significant enhancement of the electron-hole wave function overlap and thus to an enhancement of the spontaneous emission recombination rate. Figure 1 shows the schematics of (a) a conventional In_xGa_1−xN QW and (b) a type-II In_yGa_1−yN-ZnGeN₂-In_zGa_1−zN QW. For the conventional InGaN QW with uniform In content, a reasonable QW thickness with an appropriate In content was selected for the design of blue and green emission wavelengths. For the type-II QW designs, the InGaN QW thickness was kept the same as that of the conventional QW, and a thin layer of ZnGeN₂ was inserted in the InGaN QW to form a type-II heterostructure. The position and thickness of the ZnGeN₂ layer and the In content in the type-II QW are the important parameters for achieving maximum overlap of the electron and hole wave functions while maintaining an emission wavelength similar to that of the conventional QW. Due to the large band offset between InGaN and ZnGeN₂, the electron wave function in the conduction band is spread and penetrates to the GaN barrier region. In order to better confine the electron wave function, a thin AlGaN layer with a large bandgap is inserted between the InGaN sublayer and the GaN barrier.

In this study, the self-consistent 6-band k·p method was used to perform the band structure calculations, which take into account the effect of strain, the valence band mixing, and the spontaneous and piezoelectric polarizations, as well as the carrier screening effect. The detailed description of the method was presented in Ref. 14. The material parameters of III-nitrides for the band structure calculations are obtained from Refs. 33 and 34, which are summarized in the table in Ref. 14. The material parameters of ZnGeN₂ are obtained from Refs. 23 and 31. The parameter of the spontaneous polarization of ZnGeN₂ is from Ref. 35.

Figure 2 shows the energy band diagrams of (a) a conventional type-I 30 Å In_0.19Ga_0.81N QW and (b) an asymmetric type-II 23 Å In_0.16Ga_0.84N/3 Å ZnGeN₂/7 Å In_0.16Ga_0.84N/15 Å Al_0.2Ga_0.8N QW. Both QWs are designed with peak emission wavelengths at λ ∼ 485 nm. In the conventional InGaN QW, the strong electrostatic field causes the energy band bending for both conduction and valence bands in QW, which leads to a separation of the electron and hole wave functions and thus reduces the electron-hole wave function overlap (Γ_{e_hh}),^36–40 as shown in Fig. 2(a). The type-II QW design, as shown in Fig. 2(b), leads to improved performance due to the following mechanisms: (i) a strong hole confinement in the ZnGeN₂ layer due to a large band offset between InGaN and ZnGeN₂ and (ii) the extra confinement of the electron wave function due to the thin AlGaN barrier layer. Overall, the electron-hole wave function overlap (Γ_{e_hh}) of the type-II QW is enhanced by 2.93 times, from 13.9% for the conventional type I QW to 40.7%.

In addition, the deep hole confinement in the ZnGeN₂ layer allows the use of a much lower In content in the InGaN QW. Here, we are able to reduce the In content from 19% in the conventional type I InGaN QW to 16% in the type-II QW design. The reduced In-content in the InGaN layer leads to (i) the suppression of a large fraction of the band bending, which helps to shift the wave functions to the center of the QW and (ii) the improvement of the InGaN QW quality by use of a higher growth temperature for the lower In-content incorporation. Separately, the purpose of the thin layer of low Al-content AlGaN between the InGaN QW and GaN barrier is to serve as a large bandgap barrier for a better confinement of the electrons in the conduction band.

The spontaneous emission spectra of the conventional type-I 30 Å In_0.19Ga_0.81N QW (dashed lines) and the type-II 30 Å In_0.16Ga_0.84N/3 Å ZnGeN₂ QW (solid lines) were calculated at carrier density of n = 1−5 × 10¹⁸cm⁻³, as shown in Fig. 3. Note that the step size of the photon energy used in the calculations of the spontaneous emission spectra was 0.01 eV. From the comparison, we observe a significant enhancement of the spontaneous emission for each carrier density. For the case of n = 5 × 10¹⁸cm⁻³, the type-II QW (1.24 × 10²⁷s⁻¹cm⁻³ eV⁻¹) shows ∼4 times enhancement of the peak spontaneous emission spectra as compared to that of the conventional one (0.31 × 10²⁷s⁻¹cm⁻³ eV⁻¹). As the carrier density increases, we observe an obvious blue shift of the spontaneous emission spectrum peak for the type-I InGaN QW, due to the carrier screening effect. For the type-II QW, the blue shift of the spontaneous emission spectrum peak with an increase in carrier density is much suppressed, mainly due to the reduced band bending. Figure 4 plots the spontaneous emission radiative recombination rate (R_sp) for both type-I and type-II QWs as a function of the carrier density up to 5 × 10¹⁸ cm⁻³. The R_sp is obtained by integrating the spontaneous emission spectra over the photon energy. The type-II QW design shows an enhancement of 6.1–7.2 times as compared to that of the type-I QW.

A similar concept of a type-II InGaN-ZnGeN₂ structure has been implemented to design a green-emitting QW. Figure 5 shows the energy band diagrams of (a) a conventional type-I 30 Å In_0.23Ga_0.77N QW and (b) a type-II 20 Å In_0.1Ga_0.9N/5 Å ZnGeN₂/10 Å In_0.1Ga_0.9N/15 Å Al_0.25Ga_0.75N QW. Both QWs were designed as active regions with emission wavelength at λ ∼ 530 nm. In the type-I InGaN QW, a relatively high In-content of 23% was used to achieve the green emission, which leads to a strong band bending and a low electron-hole wave function overlap of 11.2%. In the type-II QW design, the ZnGeN₂ layer strongly confines the hole wave function, and the electron wave function is shifted to the InGaN layer due to the large band offset between the InGaN and ZnGeN₂ as well as to the AlGaN barrier layer. These effects lead to an enhanced electron-hole wave function overlap of 26.2%. Note that a very low In content of 10% is used in the type-II green emitting QW design which is experimentally favorable for obtaining high material quality.

Figure 6 plots the spontaneous emission spectra of the type-I 30 Å In_0.23Ga_0.77N QW (dashed lines) and type-II 20 Å In_0.1Ga_0.9N/5 Å ZnGeN₂/10 Å In_0.1Ga_0.9N/15 Å Al_0.25Ga_0.75N QW (solid lines) at carrier densities n = 1–5 × 10¹⁸cm⁻³. The peak spontaneous emission intensity shows a significant enhancement for the type-II QW as compared to that of the conventional one over this entire range of carrier density. At n = 5 × 10¹⁸ cm⁻³, the peak spontaneous emission of the type-II QW is 0.96 × 10²⁷ s⁻¹cm⁻³ eV⁻¹, which is ∼5.6 times of the type-I QW (0.17 × 10²⁷ s⁻¹cm⁻³ eV⁻¹). The enhancement of the spontaneous emission radiative recombination rate for the type-II QW is a consequence of its improved electron-hole wave function overlap. Similar to the blue-emitting QW designs, we observe an obvious blue shift of the peak spontaneous emission wavelength for the type-I QW as the increase of the carrier density. The peak spontaneous emission wavelength of the type-II QW shows much less blue shift.

The spontaneous emission radiative recombination rate (R_sp) as a function of carrier density for both the type-I In_0.23Ga_0.77N QW (dashed line) and the type-II In_0.1Ga_0.9N-ZnGeN₂-Al_0.25Ga_0.75N QW (solid line) is shown in Fig. 7. As the carrier density increases, the spontaneous emission radiative recombination rates for both type-I and type-II QWs show monotonic increases. The R_sp for the type-II QW is enhanced by 4.6–4.9 times as compared to that of the conventional QW.

From the design studies of type-II InGaN-ZnGeN₂ QW LEDs emitting in blue and green wavelength regions, we found that the thickness of the ZnGeN₂ layer plays an important role for determining the emission wavelength due to the strong hole confinement in this layer. In addition, the position of the ZnGeN₂ within the InGaN QW is also important for the optimization process to achieve a maximal electron-hole wavefunction overlap. Different from the conventional InGaN QW design, in which either higher In content or thicker QW is required to extend the emission wavelength to longer wavelength region, the design of the type-II InGaN-ZnGeN₂ QW has more degrees of freedom. More importantly, it is possible to extend QW emission wavelength even using lower In content, which is experimentally preferable.

It is worth noting that in this study, we have not taken into account the potential advantage from the improved material quality in the type-II QWs due to the use of lower-In content InGaN. We expect that the nonradiative recombination will be suppressed in the novel type-II InGaN-ZnGeN₂ QWs, which further enhances the LED efficiencies.

In summary, type-II InGaN-ZnGeN₂ QWs are analyzed as improved active regions for LEDs emitting in the blue and green wavelength regions. The insertion of the lattice-matched ZnGeN₂ layer within the InGaN QW forms a type-II structure, which shifts the electron and hole wave functions and leads to a significant enhancement of the electron-hole wave function overlap. This effect in turn enhances the spontaneous emission radiative recombination rate in InGaN QW LEDs. In addition, due to the large band offset between InGaN and ZnGeN₂, the strong hole confinement in the ZnGeN₂ layer leads to a red shift of the transition wavelength between the conduction and valence bands, and thus requires lower In content to achieve the same emission wavelength as compared to the conventional type-I InGaN QW. The use of the type-II InGaN-ZnGeN₂ QW designs can potentially achieve high performance green/yellow/red LEDs without using QWs and with high In content. The novel heterostructures based on the combination of the III-nitrides and the II-IV-nitrides have great promise to advance the optoelectronic properties of the next-generation LEDs and laser diodes.

The authors acknowledge the support from the National Science Foundation (DMREF-1533957).