Appendix C Examples for Each Material System. 69

Chapter 1 Introduction

The GAIN program is a software program that is used to calculate the gain and r elated parameters in semiconductor quantum well laser structures. This tool can be used mainly in optoelectronics and photonics fields. It is free and runs under DOS and Windows based platforms.

The software works for thirteen material systems most of which are used to make semiconductor quantum well lasers, find the band offsets and energy levels in both conduction and valence bands, and calculate the gain curves with respect to wavelength and current density. The program uses one-dimensional analysis in computations, and gives fast and practically accurate results.

This software was developed by Dr. Tso-min Chou in the Department of Electrical Engineering at Southern Methodist University, Dallas, TX. One can find similar commercial software that serves for similar purposes. However, the GAIN program is very powerful 1-D analysis software. Since it was developed, the GAIN program has been extensively used and there is enough experience to verify that it produces fairly good results as 1-D analysis software. Although it is so, we do not give any warranty to your calculations. You might take the results from this software as a comparison, validation, or double check for your results. Please provide us feedback by sending your comments and/or comparison of your own calculations to those by GAIN program.

The contributions in preparing this User’s Manual by the members of the Photonics Group at SMU are greatly appreciated.

Chapter 2 Computation of Material Composition and Band Edges

This chapter includes the introduction of the input parameters for each material system and the output files generated by running the material system. The given example is for 1.55um single quantum well strain compensated SCH structure. For a better reading of this manual, the following conventions are used for giving the example of running the program. The Italic style is for the output screen from the screen of the program. The user’s typing starts with a “>” to indicate the user’s input.

2.1 Input Parameters for Each Material System

There are four major kinds of input parameters (I, II, III, and IV) for each material system. The following paragraph explains each input parameters:

I) # For GRIN STRUCTURE (STEP) N=:

This is the number of the layers except for the quantum well. For example, the simple SCH quantum well structure has the “N” which equals to 2. For the graded index SCH structure with single quantum well that can have 10 steps between the quantum part and cladding part, we then need to give N equaling to 11. N-1 does not include the cladding layer. Figure 2.1.1 shows the different conduction band structure of the simple and graded index SCH.

Figure 2.1.1 Different SCH structure for band edge profile

II) WELL, BARRIER AND CLADDING WAVELENGTH:

The wavelength range differs with the material system. We give the wavelength range for each material system layer in appendix A. The QW wavelength has the highest wavelength, then barrier wavelength and then cladding because of the band gap difference for different layers. The wavelength in the QW is related to the desired lasing wavelength. However, the input wavelength is approximated according to the bulk material’s energy band gap. If the user know the composition for quantum well, barrier and cladding layer, the appendix A provides the formula to calculate the wavelength. The wavelength in um can be obtained from 1.24/energy band gap.

III) CLADDING, BARRIER, and QUANTUM WELL WIDTH:

Users can input the desired width value in am-strong Å. If the GRINSCH and multiple quantum wells structure is for the desired structure, the user needs to be aware of the input value for the barrier width. The program divides the input barrier width over N-1 as the barrier width between the quantum wells.

IV) INPUT STRAIN:

From the strain constant (e) [1],

(2.1)

where a_q , a_b are lattice constants of the quantum well and barrier layers, respectively. From energy band semiconductor structure, figure 2.1.2, we know that the value of tensile strain is positive for a_q< a_b, and compressive strain has a negative value for a_q> a_b. (2.1) is good for the unstrained barrier and the barrier is lattice matched to the substrate. In (2.1), we can always put a_q as the strain layer and a_b for unstrain layer, which is usually lattice match to the substrate, to calculate the strain. For example, if we put strain in the barrier, we will have the barrier lattice as a_q and substrate lattice as a_b.

The other definition is often used for the strain constant

(2.2)

where a_u is the unstrained layer and usually lattice match to substrate, a_s is the strained layer

For this definition, a_s > a_u is compressive strain. We will get the positive strain constant. Similarly, if a_s < a_u, which is tensile strain, we will get the negative strain constant. However, for the Gain program, we use the equation (2.1) for the definition of the strain constant.

Figure 2.2.2 Energy band semiconductor structure. The conduction V_c and valence V_hh, V_lh potentials for a semiconductor structure with quantum-well, barrier and cladding layers. Notation: d_h: hydrostatic potential, d_s:shear potential, E_g: energy band gap for quantum well, E_gb: energy band gap for barrier, DV_c^b: conduction band offsets for the barrier, DV_c^c: conduction band offsets for the cladding, DV_v^b: valence band offsets for the barrier, DV_v^c: valence band offsets for the cladding.

Different material systems may have slightly different input parameters and procedures. The only big variation is for material system #10, which does not need the wavelength and width input parameters. So a list of input parameters and steps for each material system is shown in Table 2.1 based on the order that they appear in program screen.