† Corresponding author. E-mail:
Project supported by the National Key R&D Program of China (Grant Nos. 2016YFB0400803 and 2016YFB0401801), the National Natural Science Foundation of China (Grant Nos. 61674138, 61674139, 61604145, 61574135, 61574134, 61474142, 61474110, 61377020, and 61376089), the Science Challenge Project, China (Grant No. TZ2016003), and the Beijing Municipal Science and Technology Project, China (Grant No. Z161100002116037).
Performances of blue and green laser diodes (LDs) with different u-InGaN upper waveguides (UWGs) are investigated theoretically by using LASTIP. It is found that the slope efficiency (SE) of blue LD decreases due to great optical loss when the indium content of u-InGaN UWG is more than 0.02, although its leakage current decreases obviously. Meanwhile the SE of the green LD increases when the indium content of u-InGaN UWG is varied from 0 to 0.05, which is attributed to the reduction of leakage current and the small increase of optical loss. Therefore, a new blue LD structure with In0.05Ga0.95N lower waveguide (LWG) is designed to reduce the optical loss, and its slope efficiency is improved significantly.
GaN-based laser diodes (LDs) have attracted much attention due to their wide applications in high-density optical storage and small portable projectors.[1–7] Compared with the traditional LD structure proposed by Nakamura,[7,8] the optical characteristics, especially the optical field distribution, could be improved by using a complex upper waveguide (UWG) with an unintentionally-doped InGaN (u-InGaN) interlayer.[9–11] To meet the demands of practical application, both optical and electrical characteristics should be studied carefully. In particular, the slope efficiency (SE) of GaN-based LD is necessary to be further investigated, which determines the electro-optic conversion efficiency and the possibility of its commercialization, although there is some research on the different influences of u-InGaN UWG on the slope efficiencies (SEs) for the blue and green LDs, including theoretical analyses and experimental research of the slope efficiency of GaN-based LDs.[12,13]
In this work, the u-InxGa1−xN (0 ≤ x ≤ 0.05) layer is designed to be the UWG and the effects of u-InGaN UWG on the optical and electrical characteristics for blue and green LDs are investigated based on the theoretical calculations using the two-dimension simulator LASTIP. In particular, the different influences of u-InGaN UWG on the slope efficiency (SE) are studied systematically. The results are considered to be useful for the practical LD structure design and will be beneficial to improving the performances of GaN-based blue and green LDs.
The device structure of GaN-based blue and green laser diodes is shown in Fig.
The optical and electrical characteristics of the GaN-based blue and green LDs are theoretically simulated by LASTIP (Crosslight Software Inc.). It is a powerful calculation software for semiconductor laser diodes in two dimensions, in which the Poisson’s equation and the current continuity equations are solved by using the finite element method.[14,15] During our calculation, both the p-type and n-type electrodes are set to be an ideal ohmic contact, and only 25% of the theoretical value[16] of the polarization field is applied. The absorption coefficients of the n-type and p-type layers are set to be 5 cm−1 and 50 cm−1, respectively, except for the heavily Mg-doped Al0.2Ga0.8N electron blocking layer (EBL) and the heavily Mg-doped GaN (p++-GaN) contact layer whose absorption coefficients are taken as 100 cm−1. In addition, the refractive indexes of the InGaN-based and AlGaN-based materials are obtained by using an approximate method as follows:
The optical characteristics of blue and green LDs with different u-InGaN UWG are investigated. As shown in Fig.
It is also noted that the optical loss of blue LDs is greater than that of green LDs. It can be seen that the FWHM of blue LDs is larger than 200 nm, and smaller than that of green LDs. It means that comparing to green LDs, the proportion of optical field in the p-type area and the optical loss of blue LDs would increase more severely when the center of the optical field is pushed towards to the p-type area. According to our calculation, for the green LDs, the proportion of optical field in the electron blocking layer increases from 18.6% to 23.8%. However, for the blue LDs, the proportion of optical field in the electron blocking layer increases from 22.0% to 38.1%. That is why the optical loss of blue LDs is larger than that of green LDs.
The threshold current and output light power of blue and green LDs are shown in Figs.
![]() | Fig. 3. (color online) Variations of (a) threshold current and (b) output light power with the indium content of u-InGaN UWG under an injecting current of 120 mA for blue and green LDs. |
It is noted that for the blue and green LDs, the tendencies of threshold current and indium content of UWG are different. It is known that the threshold current is proportional to the optical confinement factor and inversely proportional to the optical loss. In Figs.
It is noted that the output light power of blue LDs decreases when the indium content of u-InGaN UWG is over 0.03, although the corresponding threshold current decreases. Meanwhile, the output light power of green LDs is improved as the indium content of u-InGaN UWG increases from 0 to 0.01, although the corresponding threshold current rises obviously. These two phenomena suggest that the slope efficiency has been changed when the indium content of u-InGaN UWG varies from 0 to 0.05. As shown in Fig.
![]() | Fig. 4. (color online) Variations of slope efficiencies of blue and green LDs with indium content of u-InGaN UWG. |
![]() | Fig. 5. (color online) Variations of percentages of electron leakage current for the blue and green LDs with indium content of u-InGaN UWG. |
In Fig.
It can be surmised that the different influences on the slope efficiency between the blue and green LDs are caused by the different refractive index contrasts between the active region and the waveguide layer for the blue and green LDs. Specifically, the refractive index contrast between InGaN and AlGaN materials would be narrowed when the lasing wave length increases from blue to green. It means that the optical confinement would be weakened when the indium content of u-InGaN UWG is the same, thus less optical field would be distributed in UWG and optical loss is small compared with scenarios of the blue LDs, which can be observed in Figs.
Based on the discussion above, to reduce the optical loss of blue LDs, using an InGaN LWG layer should be a good method, which improves the slope efficiency by pushing the optical field towards the n-type area. Therefore, compared with the blue LD with u-In0.02Ga0.98N UWG (named LD2) whose slope efficiency is the biggest, another blue LD structure, named LD2-5, is also simulated. The UWG layer of LD2-5 is u-In0.02Ga0.98N (the same as for the LD2), but the LWG layer is taken as In0.05Ga0.95N, whose indium content is much higher than that of GaN LWG in LD2. The optical field distributions of LD2 and LD2-5 are shown in Fig.
Different effects of u-InxGa1−xN (0 ≤ x ≤ 0.05) upper waveguide on optical and electrical characteristics of blue and green LDs are studied by using LASTIP. It is found that due to the different optical confinements in the blue and green LDs, the dominant factors that affect the slope efficiency are different when the indium content of u-InGaN UWG varies from 0 to 0.05. For the blue LDs, the slope efficiency is mainly affected by the percentage of electron leakage current first and subsequently by the optical loss. Nevertheless, for the green LDs, the dominant factor is always the percentage of electron leakage current.
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