The role of wetting layer and QD-layers on the performance of 1.3 µm QD-VCSEL

Abstract

The purpose of this paper is to investigate the effect of the thickness of the wetting layer (WL) and the number of quantum dots (QDs) on the performance of 1.3 µm QD vertical-cavity surface-emitting lasers (QD-VCSELs) using self-consistent model based on rate equations and thermal conduction equations. QD-VCSELs' output power and modulation bandwidth rolled-over due to self-heating. Results demonstrate that at the same bias current, the maximum achievable 3-dB modulation bandwidth and output power are not achieved, and the point of maximum 3-dB modulation bandwidth occurred at lower currents. In addition, the larger wetting layer thickness and the greater number of QD layers modify the self-heating and enhance the efficiency and output characteristics of the laser where the rolled-over of the laser happens at higher bias currents. Furthermore, since wetting-layer thickness and the number of QD layers increase, the self-heating phenomenon is modified and the efficiency and output characteristics of the QD-VCSELs are improved by the output power rollover at higher bias currents.

Appendix A: rate equations

Here, the rate equations for the 1.3 µm QD-VCSELs are listed [15, 21]. The parameters of the rate equations are demonstrated in Table 1.

$$\frac{{{\text{d}}N_{B} }}{{{\text{d}}t}} = \frac{J}{qb} + \frac{1}{{t_{ewb} }}\frac{{g_{w} f_{w} }}{\frac{b}{n}}\left( {1 - f_{B} } \right) - \left( {\frac{1}{{t_{bw} }} + \frac{1}{{t_{rB} }}} \right)N_{B}$$

(A1)

$$\frac{{{\text{d}}f_{w} }}{{{\text{d}}t}} = \frac{{\left( {1 - f_{w} } \right)}}{{g_{w} }}\frac{{N_{B} b/n}}{{t_{bw} }} - \frac{{f_{w} }}{{t_{ebw} }} + \mathop \sum \limits_{i = 0}^{n2} \left[ {\frac{{2P_{i} \rho }}{{g_{w} }}Es_{iw} f_{i} \left( {1 - f_{w} } \right) - R_{wi} f_{w} \left( {1 - f_{i} } \right)} \right] - \frac{{f_{w} }}{{t_{rw} }}$$

(A2)

$$\frac{{{\text{d}}f_{2} }}{{{\text{d}}t}} = \frac{{g_{w} }}{{2p_{2} \rho }}R_{w2} f_{w} \left( {1 - f_{2} } \right) - Rs_{2w} f_{2} \left( {1 - f_{w} } \right) + \mathop \sum \limits_{i = 0}^{1} \left[ {\frac{{p_{i} }}{{p_{2} }}Es_{i2} f_{i} \left( {1 - f_{2} } \right) - R_{2i} f_{2} \left( {1 - f_{i} } \right)} \right] - \frac{{f_{2} }}{{t_{r2} }}$$

(A3)

$$\frac{{{\text{d}}f_{1} }}{{{\text{d}}t}} = \frac{{g_{w} }}{{2p_{1} \rho }}R_{w1} f_{w} \left( {1 - f_{1} } \right) - Es_{1w} f_{1} \left( {1 - f_{w} } \right) + \left[ {\frac{{p_{2} }}{{p_{1} }}R_{21} f_{2} \left( {1 - f_{1} } \right) - Es_{12} f_{1} \left( {1 - f_{2} } \right)} \right] + \left[ {\frac{{p_{0} }}{{p_{1} }}Es_{01} f_{0} \left( {1 - f_{1} } \right) - R_{10} f_{1} \left( {1 - f_{0} } \right)} \right] - \frac{{f_{1} }}{{t_{r1} }}$$

(A4)

$$\frac{{{\text{d}}f_{0} }}{{{\text{d}}t}} = \mathop \sum \limits_{i = 1}^{2n} \left[ {\frac{{p_{i} }}{{p_{0} }}R_{i0} f_{i} \left( {1 - f_{0} } \right) - Es_{0i} f_{0} \left( {1 - f_{i} } \right)} \right] + \left[ {\frac{{g_{w} }}{{2p_{0} \rho }}R_{w0} f_{w} \left( {1 - f_{0} } \right) - Es_{0w} f_{0} \left( {1 - f_{w} } \right)} \right] - \frac{{f_{0} }}{{t_{r0} }} - \frac{1}{{2p_{0} nS_{a} \rho }}\frac{{\upsilon_{g} g_{{{\text{max}}}} \left( {f_{0e} + f_{0h} - 1} \right)}}{1 + \varepsilon S}$$

(A5)