Appendix C GAIN Examples

In this appendix, the use of the GAIN program is demonstrated for ten material systems. Each section below contains an example of how GAIN is used with one of these material systems.

C.1. Material system #1: AlGaAs/ AlGaAs

This is a simulation of a five-layer laser structure that contains a single quantum well (QW), two separated confinement heterostructure (SCH) layers, and two cladding layers as shown in Fig. C.1.1.

Figure C.1.1. Energy band diagram for the simple quantum well structure

C.1.1. Calculation of material compositions and energy band edges.

The first step of the GAIN program is to calculate the material compositions and energy band edges of the each layer. The user is asked to enter the photoluminescence wavelength, thickness, and strain of the QW, SCH, and cladding layers. After these parameters are input, the GAIN program generates two output files: cbandeg.dat and vbandeg.dat, containing the material compositions, and the conduction band edges and valence band edges respectively. The detailed explanation is provided in Chapter 2 of this manual.

a) The input parameters to the GAIN program in this step islisted in Table. C.4.1.

Table C.4.1. Input parameters to the GAIN program in this step.

Layer	l (um)	Strain	Thickness (Ǻ)
QW (Al_xGa_1-xAs)	0.87	------	50
SCH (Al_xGa_1-xAs)	0.74	------	60
Cladding (Al_xGa_1-xAs)	0.58		100

b) The steps in using the GAIN program to calculate the material compositions and energy band edges are listed in Table C.1.2

Table C.1.2. steps to run the GAIN program for necessary parameters.

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

ENTER 1 FOR AlGaAs/AlGaAs

2 FOR InGaAsP/InGaAsP/InP

3 FOR InGaAs/InGaAsP/InP

4 FOR InGaAlAs/InGaAlAs/InP

5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

6 FOR InGaAs/AlGaAs/AlGaAs

7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(MATCHED GaAs)

8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

9 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/InP

10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(matched InP)

11 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/AlAsxSb1-x

12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs (dilute N)

13 FOR In(1-x)Ga(x)As(y)P(1-y)/GaAs

14 FOR EXIT, BACK TO MAIN PAGE!

INPUT THE LAYER # FOR GRIN STRUCTURE(STEP)

STEP N=

INPUT THE WELL WAVELENGTH (um)

0.87

INPUT THE BARRIER WAVELENGTH (um)

0.74

INPUT THE CLADDING WAVELENGTH (um)

0.58

BANDGAP ENERGY OF QUANTUM WELL= 1.42528735632184 eV

INPUT CLADDING, BARRIER,QUANTUM WELL WIDTH (A)

100 60 50

WRITE CONDUCTION BAND PARAMETERS INTO CBANDEG.DAT

WRITE VALENCE BAND PARAMETERS INTO VBANDEG.DAT

INPUT 1 FOR NEW CALCULATION

2 FOR EXIT

INPUT =?

ENTER 1 FOR AlGaAs/AlGaAs

2 FOR InGaAsP/InGaAsP/InP

3 FOR InGaAs/InGaAsP/InP

4 FOR InGaAlAs/InGaAlAs/InP

5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

6 FOR InGaAs/AlGaAs/AlGaAs

7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(MATCHED GaAs)

8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

9 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/InP

10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(matched InP)

11 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/AlAsxSb1-x

12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs (dilute N)

13 FOR In(1-x)Ga(x)As(y)P(1-y)/GaAs

14 FOR EXIT, BACK TO MAIN PAGE!

THIS PROGRAM STOP HERE!, BACK TO MAIN PAGE

c) The output files, cbandeg.dat and vbandeg.dat are explained in Table C.1.3.

Table C.1.3. Material compositions and band offsets:

a) cbandeg.dat for conduction band

************************************************************************

QW strain lattice constant

0.000000E+00 0.565311E-09

material compositions

layer thickness, Al conduction band edges

0.10000000E+03 0.56115438E+00 0.0000000 0.4632184 cladding layer

0.60000000E+02 0.20182492E+00 0.0000000 0.1627524 SCH layer

0.50000000E+02 0.10323627E-02 0.0000000 0.0000000 quantum well

0.60000000E+02 0.20182492E+00 0.0000000 0.1627524 SCH layer

0.10000000E+03 0.56115438E+00 0.0000000 0.4632184 cladding layer

************************************************************************

b) vbandeg.dat for valence band

**************************************************** ********************

QW strain lattice constant

0.000000E+00 0.565311E-09

material compositions

layer thickness, Al valence band edges

0.10000000E+03 0.56115438E+00 0.0000000 -0.2494253 cladding layer

0.60000000E+02 0.20182492E+00 0.0000000 -0.0876359 SCH layer

0.50000000E+02 0.10323627E-02 0.0000000 0.0000000 quantum well

0.60000000E+02 0.20182492E+00 0.0000000 -0.0876359 SCH layer

0.10000000E+03 0.56115438E+00 0.0000000 -0.2494253 cladding layer

************************************************************************

C.1.2. Energy level calculations

After the calculation of the material compositions and energy band edges, the GAIN program calculates energy levels in the conduction band and valence bands. The detailed explanations are discussed in Chapter 3 of this manual.

a) The steps of how to calculate the energy levels are shown in Table C.1.4.

Table C.4.4. Steps to calculate the energy levels

i) Steps to calculate the conduction band energy levels

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

INPUT THE NUMBER OF QUANTUM WELLS NUM=?

INPUT TOTAL LAYERS FOR STRUCTURE--N ODD

INPUT N=

INPUT THE LOWEST POTENTIAL LAYER(1st Q-WELL) IC= ?

INPUT THE SELECTED CENTER LAYER OF STRUCTURE ICR=

*******************************************************

INPUT I=1 FOR AlGaAs

I=2 FOR InGaAsP

I=3 FOR In1-xGaxAs/InGaAsP/InP

I=4 FOR InGaAlAs/InGaAlAs

I=5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

I=6 FOR InGaAs/AlGaAs/AlGaAs

I=7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(GaAs)

I=8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

I=9 FOR InzGa1-zAs/AlxGayIn1-x-yAs/InP

I=10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(InP)

I=11 FOR InzGa1-zAs/AlxGayIn1-x-yAs/AlAsxSb1-x

I=12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs

I=13 FOR InGaAs/In(1-y)Ga(x)As(y)P(1-y)/GaAs

INPUT I= ?

*******************************************************

ENERGY EIGENVALUE===> 0.639537366786E-01 ERROR= .4682221E-14

ENERGY EIGENVALUE===> 0.192116584232E+00 ERROR= .4043667E-14

ENERGY EIGENVALUE===> 0.241763368724E+00 ERROR= .2926458E-14

ENERGY EIGENVALUE===> 0.310657613785E+00 ERROR= .2317973E-14

ENERGY EIGENVALUE===> 0.426765405664E+00 ERROR= .1485678E-14

FOR CHECKING THE Schrodinger WAVE FUNCTION INPUT I==> 1

SKIP INPUT I==> 2

I=?

INPUT THE EIGENVALUE

EIGEN VALUE=

0.639537366786E-01

INPUT THE NAME OF OUTPUT FILE

cb1.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.82988859E-04

CONFINEMENT FACTOR OF 2 th LAYER = 0.95857126E-01

CONFINEMENT FACTOR OF 3 th LAYER = 0.80811977E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.95857126E-01

CONFINEMENT FACTOR OF 5 th LAYER = 0.82988859E-04

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

INPUT THE EIGENVALUE

EIGEN VALUE=

0.192116584232E+00

INPUT THE NAME OF OUTPUT FILE

cb2.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.66304726E-02

CONFINEMENT FACTOR OF 2 th LAYER = 0.39546197E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.19581511E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.39546197E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.66304726E-02

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

ii) Steps to calculate the heavy hole energy levels

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

INPUT THE NUMBER OF QUANTUM WELLS NUM=?

INPUT TOTAL LAYERS FOR STRUCTURE--N ODD

INPUT N=

INPUT THE HIGHEST POTENTIAL(1st Q-WELL) LAYER IC= ?

INPUT THE SELECTED CENTER OF THE STRUCTURE ICR=?

*******************************************************

INPUT I=1 FOR AlGaAs

I=2 FOR InGaAsP

I=3 FOR In(1-x)Ga(x)As/InGaAsP/InP

I=4 FOR InGaAlAs/InGaAlAs

I=5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

I=6 FOR InGaAs/AlGaAs/AlGaAs

I=7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(GaAs)

I=8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

I=9 FOR In(z)Ga(1-z)As/AlxGayIn1-x-yAs/InP

I=10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(InP)

I=11 FOR InzGa1-zAs/AlxGayIn1-x-yAs/AlAsxSb1-x

I=12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs

I=13 FOR InGaAs/In(1-x)Ga(x)As(y)P(1-y)/GaAs

INPUT I= ?

*******************************************************

DOES THE STRUCTURE STRAIN OR STRAIN-COMPENSATED?

IF STRAIN ONLY INPUT 1, STRAIN-COMPENSATED INPUT 2

INPUT SELECT = ?

ENERGY EIGENVALUE===> -0.238975151109E+00 ERROR= .3120685E-14

ENERGY EIGENVALUE===> -0.197312089899E+00 ERROR= .4405413E-14

ENERGY EIGENVALUE===> -0.166878855802E+00 ERROR= .2808856E-14

ENERGY EIGENVALUE===> -0.139814196248E+00 ERROR= .4012646E-14

ENERGY EIGENVALUE===> -0.111477421547E+00 ERROR= .3853459E-14

ENERGY EIGENVALUE===> -0.102378800292E+00 ERROR= .1062527E-14

ENERGY EIGENVALUE===> -0.681164844294E-01 ERROR= .2446502E-14

ENERGY EIGENVALUE===> -0.188139816633E-01 ERROR= .1912450E-14

FOR CHECKING THE Schrodinger WAVE FUNCTION INPUT I==> 1

SKIP INPUT I==> 2

I=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.188139816633E-01

INPUT THE NAME OF OUTPUT FILE

hh1.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.38718131E-06

CONFINEMENT FACTOR OF 2 th LAYER = 0.35292976E-01

CONFINEMENT FACTOR OF 3 th LAYER = 0.92941327E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.35292976E-01

CONFINEMENT FACTOR OF 5 th LAYER = 0.38718131E-06

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.681164844294E-01

INPUT THE NAME OF OUTPUT FILE

hh2.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.68925350E-04

CONFINEMENT FACTOR OF 2 th LAYER = 0.18086577E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.63813061E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.18086577E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.68925350E-04

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

iii) Steps to calculate the light hole energy levels

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

INPUT THE NUMBER OF QUANTUM WELLS NUM=?

INPUT TOTAL LAYERS FOR STRUCTURE--N ODD

INPUT N=

INPUT THE HIGHEST POTENTIAL(1st Q-WELL) LAYER IC= ?

INPUT THE SELECTED CENTER OF THE STRUCTURE ICR=?

*******************************************************

INPUT I=1 FOR AlGaAs

I=2 FOR InGaAsP

I=3 FOR In(1-x)Ga(x)As/InGaAsP/InP

I=4 FOR InGaAlAs/InGaAlAs

I=5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

I=6 FOR InGaAs/AlGaAs/AlGaAs

I=7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(GaAs)

I=8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

I=9 FOR In(z)Ga(1-z)As/AlxGayIn1-x-yAs/InP

I=10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(InP)

I=11 FOR InzGa1-zAs/AlxGayIn1-x-yAs/AlAsxSb1-x

I=12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs

I=13 FOR InGaAs/In(1-x)Ga(x)As(y)P(1-y)/GaAs

INPUT I= ?

*******************************************************

DOES THE STRUCTURE STRAIN OR STRAIN-COMPENSATED?

IF STRAIN ONLY INPUT 1, STRAIN-COMPENSATED INPUT 2

INPUT SELECT = ?

ENERGY EIGENVALUE===> -0.205954300457E+00 ERROR= .3173697E-14

ENERGY EIGENVALUE===> -0.149979763519E+00 ERROR= .2832057E-14

ENERGY EIGENVALUE===> -0.114996860133E+00 ERROR= .2360129E-14

ENERGY EIGENVALUE===> -0.415229761969E-01 ERROR= .2788797E-14

FOR CHECKING THE Schrodinger WAVE FUNCTION INPUT I==> 1

SKIP INPUT I==> 2

I=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.415229761969E-01

INPUT THE NAME OF OUTPUT FILE

lh1.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.38818584E-03

CONFINEMENT FACTOR OF 2 th LAYER = 0.12463156E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.74996051E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.12463156E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.38818584E-03

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.114996860133E+00

INPUT THE NAME OF OUTPUT FILE

lh2.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.13841264E-01

CONFINEMENT FACTOR OF 2 th LAYER = 0.41302518E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.14626712E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.41302518E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.13841264E-01

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

b) The main output file from this part of GAIN program is energy.dat, containing all the energy levels as shown in Table C.1.5. After the energy eigen values are calculated, the GAIN program asks the user whether he would like to check the wave envelope function or not. We suggest that the user check the wave envelope functions of the first and second energy levels for conduction and valence bands. The plots of the envelope functions are shown in Fig. C.1.2, Fig. C.1.3, Fig C.1.4.

Table C.1.5. output file energy.dat

CONDUCTION BAND ENERGY===> 0.639537366786E-01 ERROR= .4682221E-14

CONDUCTION BAND ENERGY===> 0.192116584232E+00 ERROR= .4043667E-14

CONDUCTION BAND ENERGY===> 0.241763368724E+00 ERROR= .2926458E-14

CONDUCTION BAND ENERGY===> 0.310657613785E+00 ERROR= .2317973E-14

CONDUCTION BAND ENERGY===> 0.426765405664E+00 ERROR= .1485678E-14

HEAVY HOLE ENERGY===> -0.238975151109E+00 ERROR= .3120685E-14

HEAVY HOLE ENERGY===> -0.197312089899E+00 ERROR= .4405413E-14

HEAVY HOLE ENERGY===> -0.166878855802E+00 ERROR= .2808856E-14

HEAVY HOLE ENERGY===> -0.139814196248E+00 ERROR= .4012646E-14

HEAVY HOLE ENERGY===> -0.111477421547E+00 ERROR= .3853459E-14

HEAVY HOLE ENERGY===> -0.102378800292E+00 ERROR= .1062527E-14

HEAVY HOLE ENERGY===> -0.681164844294E-01 ERROR= .2446502E-14

HEAVY HOLE ENERGY===> -0.188139816633E-01 ERROR= .1912450E-14

LIGHT HOLE ENERGY===> -0.205954300457E+00 ERROR= .3173697E-14

LIGHT HOLE ENERGY===> -0.149979763519E+00 ERROR= .2832057E-14

LIGHT HOLE ENERGY===> -0.114996860133E+00 ERROR= .2360129E-14

LIGHT HOLE ENERGY===> -0.415229761969E-01 ERROR= .2788797E-14


Fig. C.1.2. Wave envelop functions for energy levels in conduction band	Fig. C.1.3. Wave envelop functions for heavy hole energy levels

Fig. C.1.4. Wave envelop functions for light hole energy levels

C.1.3. Computation of Gain and Laser Characteristics

This is the last step of simulations using the GAIN program. With the previous calculated material composition, energy band edges, energy levels, and other parameters like material loss and Auger coefficient, the GAIN program can simulate the threshold current, threshold current density, slope efficiency, optical gain and mode gain as functions of wavelengths and photo energies, and L-I curve. The details are explained in Chapter 4 of the manual.

In this part of GAIN program, the input file needs to be constructed with the results of the previous steps and according to the laser design. In this example, single quantum well structure is used to simulate a three-QW laser. For the two-quantum-well laser with a ridge length of 750 µm and ridge width of 3 µm, the input file is shown in Table C.1.6. The detailed steps of simulations are listed in Table C.1.7. The main output files: L-I curve, optical gain as a function of the wavelength, and mode gain vs. current density are plotted in Fig. C.1.5, Fig. C.1.6, and Fig. C.1.7.

a) The input file:

Table C.1.6. Input file for gain and threshold current calculation

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c 1. Input the compositions, width of well, effective index c

c and lasing wavelength. c

c Ex: xx,xz,qy,xy,lx,n,lam c

c for different materials the following are the forms of inputs. c

c c

c w -- > well, b -- > barrier cxz and cxy for cladding. c

c c

c a. AlxGa1-xAs : xx (Al w) xz (Al b) qy (0) xy (0) c

c b. In1-xGaxAsyP1-y : xx (Ga w) xz (Ga b) qy (As w) xy (As b) c

c c. In1-xGaxAs/InGaAsP : xx (Ga w) xz (Ga b) qy (0) xy (As b) c

c d. AlxGayIn1-x-yAs/InP : xx (Ga w) xz (Ga b) qy (Al w) xy (Al b)c

c e. c

c f. InxGa1-xAs/AlGaAs : xx (In w) xz (0) qy (0) xy (Al b) c

c g. c

c h. AlyInxGa1-x-yAs/AlGaAs : xx (Al w) xz (al b) qy (In w) xz (0)c

c i. In1-xGaxAs/AlGaInAs : xx (In w) xz (0) qy (Al b) xy (Ga b) c

c j. In(y)Ga(1-y)As(x)N(1-x) :xx(As w),xz(As, b),qy(In w),xy(In b)c

c k. InGaAs/InGaAsP/GaAs: xx (In w), (0), xz(Ga w) xy (As b)

c 2. Input the energy gap,temperature, barrier band edges(both bands)

c Ex: eg,temp,ec,ev c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

0.10323627E-02 0.20182492E+00 0 0 6.0 3.50 0.82

1.42528735632184 298 0.1627524 0.0876359

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c 3. Input the ist level sub-band energy levels. c

c Ex: ec1,eh1,el1 c

c c

c 4. Input the material loss, reflectivities, number of quantum c

c wells and beta(for spontaneous emission). c

c Ex: alpha,r1,r2,mm,beta. c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

0.639537366786E-01 0.188139816633E-01 0.415229761969E-01 1 0.681164844294E-01 1

12.0d0 0.30 0.30 1 5.D-5

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c 5. Input the cavity length, ridge width, internal efficiency c

c Auger, strain(except AlGaAs,put 0) and confinement factor. c

c Ex: cl,cw,etha,ca,es,confine c

c c

c 6. Input the cladding composition and band edges. c

c Ex: cxz,cxy,ecc,evv c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

750.D-4 3D-4 0.96 1.00d-29 0.01 0.009834488

0.56115438E+00 0.0 0.4632184 0.2494253

b) The steps for these calculations mentioned are listed in Table C.1.7

Table C.1.7. The steps for the gain and threshold current density calculations

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

THE INPUT FILE NAME=

in1_sys1_new.tex

SELECT MATERIAL=?

1--AlGaAs

2--InGaAsP

3--In1-zGazAs/InGaAsP/InP

4-- InGaAlAs

5--GaInP/AlzGawIn1-z-wP/Al0.5In0.5P

6-- InxGa1-xAs/AlxGa1-xAs/AlGaAs

7--In1-xGaxAs/InGaAsP/GaxIn1-xP(X=0.51) MATCHED TO GaAs

8--AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

9--InzGa1-zAs/AlxGayIn1-x-yAs/InP

10-- InGaAlAs/InGaAlAs/AlAsSb

11--InzGa1-zAs/AlxGayIn1-x-yAs/AlAsSb

12--In(y)Ga(1-y)As(x)N(1-x)/GaAs

13--InGaAs/In(1-x)Ga(x)As(y)P(1-y)/GaAs

INPUT SELECTION

INPUT MODE = ? FOR TE--> MODE =1, FOR TM--> MODE =2

INPUT TE OR TM ?

IF EL1 BELOW EH1 THEN SELECT 1, OTHERWISE SELECT 2

SELECTION=?

**************************************************

CALCULATE THE EFFECTIVE MASS

**************************************************

FOR QUASI-FERMI LEVEL SELECT=1,

FOR READ EXISTING QUASI-FERMI LEVEL SELECT=2

SELECT=?

J(LEAKAGE)=0.537974D+00 A/cm^2 N=0.239674D+19 1/cm^3

J(LEAKAGE)=0.554846D+00 A/cm^2 N=0.241654D+19 1/cm^3

J(LEAKAGE)=0.572232D+00 A/cm^2 N=0.243634D+19 1/cm^3

J(LEAKAGE)=0.590147D+00 A/cm^2 N=0.245614D+19 1/cm^3

……….

J(LEAKAGE)=0.215349D+04 A/cm^2 N=0.788120D+19 1/cm^3

J(LEAKAGE)=0.221784D+04 A/cm^2 N=0.790100D+19 1/cm^3

J(LEAKAGE)=0.228410D+04 A/cm^2 N=0.792080D+19 1/cm^3

J(LEAKAGE)=0.235231D+04 A/cm^2 N=0.794060D+19 1/cm^3

J(LEAKAGE)=0.242253D+04 A/cm^2 N=0.796040D+19 1/cm^3

J(LEAKAGE)=0.249481D+04 A/cm^2 N=0.798020D+19 1/cm^3

J(LEAKAGE)=0.256922D+04 A/cm^2 N=0.800000D+19 1/cm^3

**************************************************

G(J) PARAMETERS FROM SINGLE WELL

Go=0.218113D+02 1/cm Jo=0.303353D+03 A/cm^2

G(N) PARAMETERS FROM SINGLE WELL

NGo=0.221783D+04 1/cm XNo=0.136717D+19 1/cm^3

Jtr=0.111597D+03 A/cm^2 NTR=0.502953D+18 1/cm^3

THE OPTIMUM NUMBER OF QUANTUM WELL FOLLOWS THE ARTICLE

BY McIlory et al. IEEE JQE-21 1985.

THE OPTIMUM NUMBER OF QUANTUM WELL Nopt = 2

INPUT Nopt(CAN BE DIFFERENT FROM ABOVE CALCULATION)=?

NUMBER OF QUANTUM WELL(MAY OR MAY NOT BE Nopt)=?

**************************************************

1ST CHECK USE SINGLE WELL TIMES # OF WELLS

**************************************************

2ND CHECK FOLLOWS FORMULA BY McIlory IN IEEE

JOURNAL OF QUANTUM ELECTRONIC QE-21 1985.

**************************************************

Gth= 28.0530 1/cm Nth=0.176316D+19 1/cm^3 IY= 85

1ST CHECK Jth= 806.35405951 A/cm^2

2ND CHECK Jth= 631.98567 A/cm^2

1ST CHECK Ith=0.181430D+02 mA NUMBER OF WELLS= 2

2ND CHECK Ith=0.142197D+02 mA

**************************************************

CALCULATE THE P-I RELATION

NDATA= 316

**************************************************

CALCULATE THE SLOPE: mW/mA Y=A+BX

CONSTANT A= -7.3929014 SLOPE B= 0.4074803

**************************************************

INPUT POWER PO FOR THE LINEWIDTH, PO=0 FOR STOP

INPUT PO= mW

INPUT 1 FOR THE DYNAMIC CALCULATION. 2 FOR SKIP

INPUT =

K-FACTOR= 0.35774 nS MAXIUM FREQ.= 24.8387 GHz

**************************************************

INPUT 1 FOR CALCULATE THE GAIN(E) RELATION.

INPUT 2 FOR CALCULATE THE LINEWIDTH ENHENCEMENT

FACTOR AND PHOTON ENERGY RELATION

INPUT 3 FOR EXIT THE PROGRAM

THE INPUT # IS

INPUT FERMILEVELS IN C-BAND, V-BAND, AND CARRIER DENSITY

0.139680787212E+00 -0.953800948086E-02 0.200075187970E+19

CALCULATE THE CONVOLUTION GAIN(E) COEFFICIENT

**************************************************

INPUT THE NAME FOR THE CONVOLUTION OPTICAL GAIN(LAMBDA)

COGLa.txt

**************************************************

INPUT THE NAME FOR THE CONVOLUTION MODE GAIN(LAMBDA)

CMGLa.txt

INPUT THE NAME FOR THE CONVOLUTION OPTICAL GAIN(E)

COGEa.txt

**************************************************

INPUT THE NAME FOR THE CONVOLUTION MODE GAIN(E)

CMGEa.txt

**************************************************

INPUT 1 FOR REPEAT THE G(E) CALCULATION

INPUT 2 FOR REPEAT THE ALPHA(E) CALCULATION

INPUT 3 FOR EXIT

**************************************************

INPUT 1 FOR CALCULATE THE GAIN(E) RELATION.

INPUT 2 FOR CALCULATE THE LINEWIDTH ENHENCEMENT

FACTOR AND PHOTON ENERGY RELATION

INPUT 3 FOR EXIT THE PROGRAM

THE INPUT # IS

INPUT FERMILEVELS IN C-BAND, V-BAND, AND CARRIER DENSITY

0.160216100041E+00 -0.259237429430E-02 0.251553884712E+19

CALCULATE THE CONVOLUTION GAIN(E) COEFFICIENT

**************************************************

INPUT THE NAME FOR THE CONVOLUTION OPTICAL GAIN(LAMBDA)

COGLb.txt

**************************************************

INPUT THE NAME FOR THE CONVOLUTION MODE GAIN(LAMBDA)

CMGLb.txt

INPUT THE NAME FOR THE CONVOLUTION OPTICAL GAIN(E)

COGEb.txt

**************************************************

INPUT THE NAME FOR THE CONVOLUTION MODE GAIN(E)

CMGEb.txt

**************************************************

INPUT 1 FOR REPEAT THE G(E) CALCULATION

INPUT 2 FOR REPEAT THE ALPHA(E) CALCULATION

INPUT 3 FOR EXIT

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

c) The Output characteristics of designed laser from step 5 are summarized in Table C.1.7.

Table C.1.7 Characteristics of the designed laser

Optimized number of QWs (Nopt)	2
Number of QWs	2
Slope efficiency (%)	40.75
Jth (A/cm^2)	806.35 - 1^st check, for matching threshold conditions 631.99 – 2^nd check, using McIlory method
Ith (mA)	18.14 - 1^st check, for matching threshold conditions 14.22 - 2^nd check, using McIlory method
Peak l at operating temperature (um)	0.819 um for carrier density of 2.0E18 /cm3 0.819 um for carrier density of 2.5E18 /cm3
Peak material gain (1/cm)	3619.36/cm for carrier density of 2.0E18 /cm3 4386.09 /cm for carrier density of 2.5E18 /cm3


Fig. C.1.5. L-I curve of the laser	Fig. C.1.6. Optical gain-l curve of the laser

Fig. C.1.7. Mode gain as a function of current density (J)

C.2 Material system #2: InGaAs/InGaAlAs/InP

This is a simulation of a seventeen-layer laser structure that contains four quantum wells (QW), two separated confinement heterostructure (SCH) layers, and two cladding layers as shown in Fig. C.2.1. This device is a real one for research purpose. We will see the characteristics of this device.

Figure C.2.2. Energy band diagram for the simple quantum well structure

C.2.1. Calculation of material compositions and energy band edges.

a) The input parameters to the GAIN program in this step are listed in Table. C.2.1.

Table C.2.1. Input parameters to the GAIN program in this step.

Layer	l (um)	Strain	Thickness (Ǻ)
QW (Ga_1-xIn_xAs_yP_1-y)	1.525	-0.012	60
SCH (Ga_1-xIn_xAs_yP_1-y)	1.28		50
Cladding (Ga_1-xIn_xAs_yP_1-y)	0.98		100

b) The steps in using the GAIN program to calculate the material compositions and energy band edges are listed in Table C.2.2

Table C.2.2. steps to run the GAIN program for necessary parameters.

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

ENTER 1 FOR AlGaAs/AlGaAs

2 FOR InGaAsP/InGaAsP/InP

3 FOR InGaAs/InGaAsP/InP

4 FOR InGaAlAs/InGaAlAs/InP

5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

6 FOR InGaAs/AlGaAs/AlGaAs

7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(MATCHED GaAs)

8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

9 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/InP

10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(matched InP)

11 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/AlAsxSb1-x

12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs (dilute N)

13 FOR In(1-x)Ga(x)As(y)P(1-y)/GaAs

14 FOR EXIT, BACK TO MAIN PAGE!

INPUT THE LAYER # FOR GRIN STRUCTURE(STEP)

STEP N=

INPUT THE WELL WAVELENGTH (um)

1.525

INPUT THE BARRIER WAVELENGTH (um)

1.28

INPUT THE CLADDING WAVELENGTH (um)

BANDGAP ENERGY OF QUANTUM WELL= 0.683804000019804

INPUT CLADDING, BARRIER,QUANTUM WELL WIDTH (A)

100 50 60

In1-xGaxAsyP1-y, in output read Ga first then AsIN OUTPUT READ Ga FIRST THEN As

FOR InGaAsP, only compress strain (~1.5%) available

INPUT EX

-0.012

FOR LATTICE MATCHED BARRIER SELECT --> 1

FOR STRAIN COMPENSATED SELECT -- 2

INPUT SELECTION===> ?

WRITE CONDUCTION BAND PARAMETERS INTO CBANDEG.DAT

WRITE VALENCE BAND PARAMETERS INTO VBANDEG.DAT

INPUT 1 FOR NEW CALCULATION, 2 FOR EXIT

I= ?

ENTER 1 FOR AlGaAs/AlGaAs

2 FOR InGaAsP/InGaAsP/InP

3 FOR InGaAs/InGaAsP/InP

4 FOR InGaAlAs/InGaAlAs/InP

5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

6 FOR InGaAs/AlGaAs/AlGaAs

7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(MATCHED GaAs)

8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

9 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/InP

10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(matched InP)

11 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/AlAsxSb1-x

12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs (dilute N)

13 FOR In(1-x)Ga(x)As(y)P(1-y)/GaAs

14 FOR EXIT, BACK TO MAIN PAGE!

THIS PROGRAM STOP HERE!, BACK TO MAIN PAGE

c) The output files, cbandeg.dat and vbandeg.dat are explained in Table C.2.3.

Table C.2.3. Material compositions and band offsets:

a) cbandeg.dat for conduction band

************************************************************************

QW strain lattice constant

-.120000E-01 0.593923E-09

material compositions

layer thickness, Ga Al conduction band edges

0.10000000E+03 0.50731155E-01 0.1116804 0.1763546 cladding layer

0.50000000E+02 0.25335652E+00 0.5501187 0.0606978 SCH layer

0.60000000E+02 0.10405969E+00 0.5965452 0.0481108 quantum well

0.50000000E+02 0.25335652E+00 0.5501187 0.0606978 SCH layer

0.10000000E+03 0.50731155E-01 0.1116804 0.1763546 cladding layer

************************************************************************

b) vbandeg.dat for valence band

**************************************************** ********************

QW strain lattice constant

-.120000E-01 0.593923E-09

material compositions

layer thickness, Ga Al valence band edges

0.10000000E+03 0.50731155E-01 0.1116804 -0.2758368 cladding layer

0.50000000E+02 0.25335652E+00 0.5501187 -0.0949375 SCH layer

0.60000000E+02 0.10405969E+00 0.5965452 -0.0240554 quantum well

0.50000000E+02 0.25335652E+00 0.5501187 -0.0949375 SCH layer

0.10000000E+03 0.50731155E-01 0.1116804 -0.2758368 cladding layer

************************************************************************

C.2.2. Energy level calculations

a) The steps of how to calculate the energy levels are shown in Table C.2.4.

Table C.2.4. Steps to calculate the energy levels

i) Steps to calculate the conduction band energy levels

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

INPUT THE NUMBER OF QUANTUM WELLS NUM=?

INPUT TOTAL LAYERS FOR STRUCTURE--N ODD

INPUT N=

INPUT THE LOWEST POTENTIAL LAYER(1st Q-WELL) IC= ?

INPUT THE SELECTED CENTER LAYER OF STRUCTURE ICR=

*******************************************************

INPUT I=1 FOR AlGaAs

I=2 FOR InGaAsP

I=3 FOR In1-xGaxAs/InGaAsP/InP

I=4 FOR InGaAlAs/InGaAlAs

I=5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

I=6 FOR InGaAs/AlGaAs/AlGaAs

I=7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(GaAs)

I=8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

I=9 FOR InzGa1-zAs/AlxGayIn1-x-yAs/InP

I=10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(InP)

I=11 FOR InzGa1-zAs/AlxGayIn1-x-yAs/AlAsxSb1-x

I=12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs

I=13 FOR InGaAs/In(1-y)Ga(x)As(y)P(1-y)/GaAs

INPUT I= ?

*******************************************************

ENERGY EIGENVALUE===> 0.670294366291E-01 ERROR= .3576162E-14

ENERGY EIGENVALUE===> 0.101465108959E+00 ERROR= .3081508E-14

ENERGY EIGENVALUE===> 0.155412249439E+00 ERROR= .2750090E-14

FOR CHECKING THE Schrodinger WAVE FUNCTION INPUT I==> 1

SKIP INPUT I==> 2

I=?

INPUT THE EIGENVALUE

EIGEN VALUE=

0.670294366291E-01

INPUT THE NAME OF OUTPUT FILE

cb1.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.11124994E-01

CONFINEMENT FACTOR OF 2 th LAYER = 0.18768431E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.60238139E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.18768431E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.11124994E-01

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

INPUT THE EIGENVALUE

EIGEN VALUE=

0.101465108959

INPUT THE NAME OF OUTPUT FILE

cb2.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.46526184E-01

CONFINEMENT FACTOR OF 2 th LAYER = 0.36258718E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.18177326E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.36258718E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.46526184E-01

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

ii) Steps to calculate the heavy hole energy levels

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

INPUT THE NUMBER OF QUANTUM WELLS NUM=?

INPUT TOTAL LAYERS FOR STRUCTURE--N ODD

INPUT N=

INPUT THE HIGHEST POTENTIAL(1st Q-WELL) LAYER IC= ?

INPUT THE SELECTED CENTER OF THE STRUCTURE ICR=?

*******************************************************

INPUT I=1 FOR AlGaAs

I=2 FOR InGaAsP

I=3 FOR In(1-x)Ga(x)As/InGaAsP/InP

I=4 FOR InGaAlAs/InGaAlAs

I=5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

I=6 FOR InGaAs/AlGaAs/AlGaAs

I=7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(GaAs)

I=8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

I=9 FOR In(z)Ga(1-z)As/AlxGayIn1-x-yAs/InP

I=10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(InP)

I=11 FOR InzGa1-zAs/AlxGayIn1-x-yAs/AlAsxSb1-x

I=12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs

I=13 FOR InGaAs/In(1-x)Ga(x)As(y)P(1-y)/GaAs

INPUT I= ?

*******************************************************

DOES THE STRUCTURE STRAIN OR STRAIN-COMPENSATED?

IF STRAIN ONLY INPUT 1, STRAIN-COMPENSATED INPUT 2

INPUT SELECT = ?

ENERGY EIGENVALUE===> -0.266289655713E+00 ERROR= .2082626E-14

ENERGY EIGENVALUE===> -0.220090610686E+00 ERROR= .2912430E-14

ENERGY EIGENVALUE===> -0.186287733747E+00 ERROR= .4671376E-14

ENERGY EIGENVALUE===> -0.140850401092E+00 ERROR= .8911599E-14

ENERGY EIGENVALUE===> -0.122228608502E+00 ERROR= .4338441E-14

ENERGY EIGENVALUE===> -0.101432618035E+00 ERROR= .1307382E-14

ENERGY EIGENVALUE===> -0.428488013474E-01 ERROR= .2038714E-14

ENERGY EIGENVALUE===> 0.509274076994E-02 ERROR= .2348418E-14

FOR CHECKING THE Schrodinger WAVE FUNCTION INPUT I==> 1

SKIP INPUT I==> 2

I=?

INPUT THE EIGENVALUE

EIGEN VALUE=

0.509274076994E-02

INPUT THE NAME OF OUTPUT FILE

hh1.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.43858757E-06

CONFINEMENT FACTOR OF 2 th LAYER = 0.19049653E-01

CONFINEMENT FACTOR OF 3 th LAYER = 0.96189982E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.19049653E-01

CONFINEMENT FACTOR OF 5 th LAYER = 0.43858757E-06

SELECT=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.428488013474E-01

INPUT THE NAME OF OUTPUT FILE

hh2.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.18387626E-04

CONFINEMENT FACTOR OF 2 th LAYER = 0.90457734E-01

CONFINEMENT FACTOR OF 3 th LAYER = 0.81904776E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.90457734E-01

CONFINEMENT FACTOR OF 5 th LAYER = 0.18387626E-04

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

iii) Steps to calculate the light hole energy levels

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

INPUT THE NUMBER OF QUANTUM WELLS NUM=?

INPUT TOTAL LAYERS FOR STRUCTURE--N ODD

INPUT N=

INPUT THE HIGHEST POTENTIAL(1st Q-WELL) LAYER IC= ?

INPUT THE SELECTED CENTER OF THE STRUCTURE ICR=?

*******************************************************

INPUT I=1 FOR AlGaAs

I=2 FOR InGaAsP

I=3 FOR In(1-x)Ga(x)As/InGaAsP/InP

I=4 FOR InGaAlAs/InGaAlAs

I=5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

I=6 FOR InGaAs/AlGaAs/AlGaAs

I=7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(GaAs)

I=8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

I=9 FOR In(z)Ga(1-z)As/AlxGayIn1-x-yAs/InP

I=10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(InP)

I=11 FOR InzGa1-zAs/AlxGayIn1-x-yAs/AlAsxSb1-x

I=12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs

I=13 FOR InGaAs/In(1-x)Ga(x)As(y)P(1-y)/GaAs

INPUT I= ?

*******************************************************

DOES THE STRUCTURE STRAIN OR STRAIN-COMPENSATED?

IF STRAIN ONLY INPUT 1, STRAIN-COMPENSATED INPUT 2

INPUT SELECT = ?

ENERGY EIGENVALUE===> -0.235564886491E+00 ERROR= .4251760E-14

ENERGY EIGENVALUE===> -0.159589791816E+00 ERROR= .2633269E-14

ENERGY EIGENVALUE===> -0.968705335737E-01 ERROR= .1268730E-14

FOR CHECKING THE Schrodinger WAVE FUNCTION INPUT I==> 1

SKIP INPUT I==> 2

I=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.968705335737E-01

INPUT THE NAME OF OUTPUT FILE

lh1.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.83034669E-02

CONFINEMENT FACTOR OF 2 th LAYER = 0.20626333E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.57086641E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.20626333E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.83034669E-02

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.159589791816E+00

INPUT THE NAME OF OUTPUT FILE

lh2.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.44635531E-01

CONFINEMENT FACTOR OF 2 th LAYER = 0.39731088E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.11610718E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.39731088E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.44635531E-01

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

b) The main output file from this part of GAIN program is energy.dat, containing all the energy levels as shown in Table C.2.5. After the energy eigen values are calculated, the GAIN program asks the user whether he would like to check the wave envelope function or not. We suggest that the user check the wave envelope functions of the first and second energy levels for conduction and valence bands. The plots of the envelope functions are shown in Fig. C.2.2, Fig. C.2.3, Fig C.2.4.

Table C.2.5 Output file energy.dat

CONDUCTION BAND ENERGY===> 0.670294366291E-01 ERROR= .3576162E-14

CONDUCTION BAND ENERGY===> 0.101465108959E+00 ERROR= .3081508E-14

CONDUCTION BAND ENERGY===> 0.155412249439E+00 ERROR= .2750090E-14

HEAVY HOLE ENERGY===> -0.266289655713E+00 ERROR= .2082626E-14

HEAVY HOLE ENERGY===> -0.220090610686E+00 ERROR= .2912430E-14

HEAVY HOLE ENERGY===> -0.186287733747E+00 ERROR= .4671376E-14

HEAVY HOLE ENERGY===> -0.140850401092E+00 ERROR= .8911599E-14

HEAVY HOLE ENERGY===> -0.122228608502E+00 ERROR= .4338441E-14

HEAVY HOLE ENERGY===> -0.101432618035E+00 ERROR= .1307382E-14

HEAVY HOLE ENERGY===> -0.428488013474E-01 ERROR= .2038714E-14

HEAVY HOLE ENERGY===> 0.509274076994E-02 ERROR= .2348418E-14

LIGHT HOLE ENERGY===> -0.235564886491E+00 ERROR= .4251760E-14

LIGHT HOLE ENERGY===> -0.159589791816E+00 ERROR= .2633269E-14

LIGHT HOLE ENERGY===> -0.968705335737E-01 ERROR= .1268730E-14


Fig. C.2.2. Wave envelop functions for energy levels in conduction band	Fig. C.2.3. Wave envelope functions for heavy hole energy levels. There is some rounding error with plot

Fig. C.2.4. Wave envelope functions for light hole energy levels

C.2.3 Computation of Gain and Laser Characteristics

This is the last step of simulations using the GAIN program. With the previous calculated material composition, energy band edges, energy levels, and other parameters like material loss and Auger coefficient, the GAIN program can simulate the threshold current, threshold current density, slope efficiency, optical gain and mode gain as functions of wavelengths and photon energies, and L-I curve. The details are explained in Chapter 4 of the manual.

In this part of GAIN program, the input file needs to be constructed with the results of the previous steps and according to the laser design. In this example, single quantum well structure is used to simulate a three-QW laser. For the three-quantum-well laser with a ridge length of 750 µm and ridge width of 3 µm, the input file is shown in Table C.2.6. The detailed steps of simulations are listed in Table C.2.7. The main output files: L-I curve, optical gain as a function of the wavelength, and mode gain vs. current density are plotted in Fig. C.2.5, Fig. C.2.6, and Fig. C.2.7.

a) The input file:

Table C.2.6. Input file for gain and threshold current calculation

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c 1. Input the compositions, width of well, effective index c

c and lasing wavelength. c

c Ex: xx,xz,qy,xy,lx,n,lam c

c for different materials the following are the forms of inputs. c

c c

c w -- > well, b -- > barrier cxz and cxy for cladding. c

c c

c a. AlxGa1-xAs : xx (Al w) xz (Al b) qy (0) xy (0) c

c b. In1-xGaxAsyP1-y : xx (Ga w) xz (Ga b) qy (As w) xy (As b) c

c c. In1-xGaxAs/InGaAsP : xx (Ga w) xz (Ga b) qy (0) xy (As b) c

c d. AlxGayIn1-x-yAs/InP : xx (Ga w) xz (Ga b) qy (Al w) xy (Al b)c

c e. c

c f. InxGa1-xAs/AlGaAs : xx (In w) xz (0) qy (0) xy (Al b) c

c g. c

c h. AlyInxGa1-x-yAs/AlGaAs : xx (Al w) xz (al b) qy (In w) xz (0)c

c i. In1-xGaxAs/AlGaInAs : xx (In w) xz (0) qy (Al b) xy (Ga b) c

c j. In(y)Ga(1-y)As(x)N(1-x) :xx(As w),xz(As, b),qy(In w),xy(In b)c

c k. InGaAs/InGaAsP/GaAs: xx (In w), (0), xz(Ga w) xy (As b)

c 2. Input the energy gap,temperature, barrier band edges(both bands)

c Ex: eg,temp,ec,ev c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

0.10405969 0.25335652 0.5965452 0.5501187 6.0 3.348741 1.31

0.94656 298 0.0606978 0.0949375

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c 3. Input the ist level sub-band energy levels. c

c Ex: ec1,eh1,el1 c

c c

c 4. Input the material loss, reflectivities, number of quantum c

c wells and beta(for spontaneous emission). c

c Ex: alpha,r1,r2,mm,beta. c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

0.0670294366291 -0.509274076994E-02 0.096870533574 0.101465108959 0.0428488013474 0.159589791816

12.0d0 0.30 0.30 1 5.D-5

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c 5. Input the cavity length, ridge width, internal efficiency c

c Auger, strain(except AlGaAs,put 0) and confinement factor. c

c Ex: cl,cw,etha,ca,es,confine c

c c

c 6. Input the cladding composition and band edges. c

c Ex: cxz,cxy,ecc,evv c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

750.D-4 3D-4 0.96 1.00d-29 0.000 0.009834488

0.050731155 0.1116804 0.1763546 0.2758368

b) The steps for these calculations mentioned are listed in Table C.2.7

Table C.2.7. The steps for the gain and threshold current density calculations

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

THE INPUT FILE NAME=

in1.tex

SELECT MATERIAL=?

1--AlGaAs

2--InGaAsP

3--In1-zGazAs/InGaAsP/InP

4-- InGaAlAs

5--GaInP/AlzGawIn1-z-wP/Al0.5In0.5P

6-- InxGa1-xAs/AlxGa1-xAs/AlGaAs

7--In1-xGaxAs/InGaAsP/GaxIn1-xP(X=0.51) MATCHED TO GaAs

8--AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

9--InzGa1-zAs/AlxGayIn1-x-yAs/InP

10-- InGaAlAs/InGaAlAs/AlAsSb

11--InzGa1-zAs/AlxGayIn1-x-yAs/AlAsSb

12--In(y)Ga(1-y)As(x)N(1-x)/GaAs

13--InGaAs/In(1-x)Ga(x)As(y)P(1-y)/GaAs

INPUT SELECTION

INPUT MODE = ? FOR TE--> MODE =1, FOR TM--> MODE =2

INPUT TE OR TM ?

IF EL1 BELOW EH1 THEN SELECT 1, OTHERWISE SELECT 2

SELECTION=?

**************************************************

CALCULATE THE EFFECTIVE MASS

**************************************************

FOR QUASI-FERMI LEVEL SELECT=1,

FOR READ EXISTING QUASI-FERMI LEVEL SELECT=2

SELECT=?

J(LEAKAGE)=0.522156D-01 A/cm^2 N=0.328772D+19 1/cm^3

J(LEAKAGE)=0.544163D-01 A/cm^2 N=0.330752D+19 1/cm^3

J(LEAKAGE)=0.567097D-01 A/cm^2 N=0.332732D+19 1/cm^3

J(LEAKAGE)=0.590996D-01 A/cm^2 N=0.334712D+19 1/cm^3

……….

J(LEAKAGE)=0.685423D+04 A/cm^2 N=0.788120D+19 1/cm^3

J(LEAKAGE)=0.689811D+04 A/cm^2 N=0.790100D+19 1/cm^3

J(LEAKAGE)=0.694207D+04 A/cm^2 N=0.792080D+19 1/cm^3

J(LEAKAGE)=0.698612D+04 A/cm^2 N=0.794060D+19 1/cm^3

J(LEAKAGE)=0.703024D+04 A/cm^2 N=0.796040D+19 1/cm^3

J(LEAKAGE)=0.707444D+04 A/cm^2 N=0.798020D+19 1/cm^3

J(LEAKAGE)=0.711872D+04 A/cm^2 N=0.800000D+19 1/cm^3

**************************************************

G(J) PARAMETERS FROM SINGLE WELL

Go=0.704410D+01 1/cm Jo=0.147036D+03 A/cm^2

G(N) PARAMETERS FROM SINGLE WELL

NGo=0.716265D+03 1/cm XNo=0.126817D+19 1/cm^3

Jtr=0.540917D+02 A/cm^2 NTR=0.466534D+18 1/cm^3

THE OPTIMUM NUMBER OF QUANTUM WELL FOLLOWS THE ARTICLE

BY McIlory et al. IEEE JQE-21 1985.

THE OPTIMUM NUMBER OF QUANTUM WELL Nopt = 4

INPUT Nopt(CAN BE DIFFERENT FROM ABOVE CALCULATION)=?

NUMBER OF QUANTUM WELL(MAY OR MAY NOT BE Nopt)=?

**************************************************

1ST CHECK USE SINGLE WELL TIMES # OF WELLS

**************************************************

2ND CHECK FOLLOWS FORMULA BY McIlory IN IEEE

JOURNAL OF QUANTUM ELECTRONIC QE-21 1985.

**************************************************

Gth= 28.0530 1/cm Nth=0.629724D+19 1/cm^3 IY= 314

1ST CHECK Jth= 5406.36686808 A/cm^2

2ND CHECK Jth= 612.65148 A/cm^2

1ST CHECK Ith=0.121643D+03 mA NUMBER OF WELLS= 4

2ND CHECK Ith=0.137847D+02 mA

**************************************************

CALCULATE THE P-I RELATION

NDATA= 87

**************************************************

CALCULATE THE SLOPE: mW/mA Y=A+BX

CONSTANT A= -32.6181898 SLOPE B= 0.2681463

**************************************************

INPUT POWER PO FOR THE LINEWIDTH, PO=0 FOR STOP

INPUT PO= mW

INPUT 1 FOR THE DYNAMIC CALCULATION. 2 FOR SKIP

INPUT =

K-FACTOR= 0.58163 nS MAXIUM FREQ.= 15.2773 GHz

**************************************************

INPUT 1 FOR CALCULATE THE GAIN(E) RELATION.

INPUT 2 FOR CALCULATE THE LINEWIDTH ENHENCEMENT

FACTOR AND PHOTONN ENERGY RELATION

INPUT 3 FOR EXIT THE PROGRAM

THE INPUT # IS

INPUT FERMILEVELS IN C-BAND, V-BAND, AND CARRIER DENSITY

0.117426601301 -0.161989946432E-01 0.209974937343E+19

CALCULATE THE CONVOLUTION GAIN(E) COEFFICIENT

**************************************************

INPUT THE NAME FOR THE CONVOLUTION OPTICAL GAIN(LAMBDA)

ol1.txt

**************************************************

INPUT THE NAME FOR THE CONVOLUTION MODE GAIN(LAMBDA)

ml1.txt

INPUT THE NAME FOR THE CONVOLUTION OPTICAL GAIN(E)

oe1.txt

**************************************************

INPUT THE NAME FOR THE CONVOLUTION MODE GAIN(E)

me1.txt

**************************************************

INPUT 1 FOR REPEAT THE G(E) CALCULATION

INPUT 2 FOR REPEAT THE ALPHA(E) CALCULATION

INPUT 3 FOR EXIT

**************************************************

INPUT 1 FOR CALCULATE THE GAIN(E) RELATION.

INPUT 2 FOR CALCULATE THE LINEWIDTH ENHENCEMENT

FACTOR AND PHOTONN ENERGY RELATION

INPUT 3 FOR EXIT THE PROGRAM

THE INPUT # IS

INPUT FERMILEVELS IN C-BAND, V-BAND, AND CARRIER DENSITY

0.138679340946 -0.441266076305E-02 0.301052631579E+19

CALCULATE THE CONVOLUTION GAIN(E) COEFFICIENT

**************************************************

INPUT THE NAME FOR THE CONVOLUTION OPTICAL GAIN(LAMBDA)

ol2.txt

**************************************************

INPUT THE NAME FOR THE CONVOLUTION MODE GAIN(LAMBDA)

ml2.txt

INPUT THE NAME FOR THE CONVOLUTION OPTICAL GAIN(E)

oe2.txt

**************************************************

INPUT THE NAME FOR THE CONVOLUTION MODE GAIN(E)

me2.txt

**************************************************

INPUT 1 FOR REPEAT THE G(E) CALCULATION

INPUT 2 FOR REPEAT THE ALPHA(E) CALCULATION

INPUT 3 FOR EXIT

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

c) The Output characteristics of designed laser from step 5 are summarized in Table C.2.7.

Table C.2.7 Characteristics of the designed laser

Optimized number of QWs (Nopt)	4
Number of QWs	4
Slope efficiency (%)	26.8
Jth (A/cm^2)	5406.4 - 1^st check, for matching threshold conditions 612.7 – 2^nd check, using McIlory method
Ith (mA)	121 mA - 1^st check, for matching threshold conditions 13.7 mA - 2^nd check, using McIlory method
Peak l at operating temperature (um)	1.21 um for carrier density of 2.0E19 /cm3 1.18 um for carrier density of 3.0E19 /cm3
Peak material gain (1/cm)	2362 /cm for carrier density of 2.0E19 /cm3 3360 /cm for carrier density of 3.0E19 /cm3

Fig. C.2.5. L-I curve of the laser

Fig. C.2.6. Optical gain-l curve of the laser

Fig. C.2.7. Mode gain as a function of current density (J)

C.3. Material system #3: InGaAs/InGaAsP/InP

This is a simulation of a five-layer laser structure that contains a single quantum well (QW), two separated confinement heterostructure (SCH) layers, and two cladding layers as shown in Fig. C.3.1.

Figure C.3.3. Energy band diagram for the simple quantum well structure

C.3.1. Calculation of material compositions and energy band edges.

a) The input parameters to the GAIN program in this step is listed in Table. C.3.1.

Table C.3.1. Input parameters to the GAIN program in this step.

Layer	l (um)	Strain	Thickness (Ǻ)
QW (InGaAs)	1.56	0.003507	100
SCH (In_1-xGa_xAs_yP_1-y)	1.21	0	100
Cladding (InP)	0.9185		1000

b) The steps in using the GAIN program to calculate the material compositions and energy band edges are listed in Table C.3.2

Table C.3.2. steps to run the GAIN program for necessary parameters.

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

ENTER 1 FOR AlGaAs/AlGaAs

2 FOR InGaAsP/InGaAsP/InP

3 FOR InGaAs/InGaAsP/InP

4 FOR InGaAlAs/InGaAlAs/InP

5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

6 FOR InGaAs/AlGaAs/AlGaAs

7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(MATCHED GaAs)

8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

9 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/InP

10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(matched InP)

11 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/AlAsxSb1-x

12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs (dilute N)

13 FOR In(1-x)Ga(x)As(y)P(1-y)/GaAs

14 FOR EXIT, BACK TO MAIN PAGE!

INPUT THE LAYER # FOR GRIN STRUCTURE(STEP)

STEP N=

INPUT THE WELL WAVELENGTH (um)

1.56

INPUT THE BARRIER WAVELENGTH (um)

1.21

INPUT THE CLADDING WAVELENGTH (um)

0.9185

BANDGAP ENERGY OF QUANTUM WELL= 0.79487179

INPUT CLADDING, BARRIER,QUANTUM WELL WIDTH (A)

1000 100 100

FOR BARRIER IS LATTICE MATCHED SELECT ==>1

FOR BARRIER IS STRAIN COMPENSATED SELECT ==> 2

SELECTION IS ===> ?

STRAIN FOR In1-xGaxAs= 3.507367375368143E-003

WRITE CONDUCION BAND PARAMETERS INTO CBANDEG.DAT

WRITE VALENCE BAND PARAMETERS INTO VBANDEG.DAT

INPUT 1 FOR NEW CALCULATION, 2 FOR EXIT

I =?

ENTER 1 FOR AlGaAs/AlGaAs

2 FOR InGaAsP/InGaAsP/InP

3 FOR InGaAs/InGaAsP/InP

4 FOR InGaAlAs/InGaAlAs/InP

5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

6 FOR InGaAs/AlGaAs/AlGaAs

7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(MATCHED GaAs)

8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

9 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/InP

10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(matched InP)

11 FOR InzGa1-zAs/AlyGaxIn1-x-yAs/AlAsxSb1-x

12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs (dilute N)

13 FOR In(1-x)Ga(x)As(y)P(1-y)/GaAs

14 FOR EXIT, BACK TO MAIN PAGE!

THIS PROGRAM STOP HERE!, BACK TO MAIN PAGE

c) The output files, cbandeg.dat and vbandeg.dat are explained in Table C.3.3.

Table C.3.3. Material compositions and band offsets:

a) cbandeg.dat for conduction band

************************************************************************

QW strain lattice constant

0.350737E-02 0.584822E-09

material compositions

layer thickness, Ga As conduction band edges

0.10000000E+04 0.00000000E+00 0.0000000 0.1998462 cladding layer

0.10000000E+03 0.21142234E+00 0.4603684 0.0827718 SCH layer

0.10000000E+03 0.51884522E+00 0.0000000 -0.0190298 quantum well

0.10000000E+03 0.21142234E+00 0.4603684 0.0827718 SCH layer

0.10000000E+04 0.00000000E+00 0.0000000 0.1998462 cladding layer

************************************************************************

b) vbandeg.dat for valence band

**************************************************** ********************

QW strain lattice constant

0.350737E-02 0.584822E-09

material compositions

layer thickness, Ga As valence band edges

0.10000000E+04 0.00000000E+00 0.0000000 -0.3552821 cladding layer

0.10000000E+03 0.21142234E+00 0.4603684 -0.1471498 SCH layer

0.10000000E+03 0.51884522E+00 0.0000000 0.0095149 quantum well

0.10000000E+03 0.21142234E+00 0.4603684 -0.1471498 SCH layer

0.10000000E+04 0.00000000E+00 0.0000000 -0.3552821 cladding layer

************************************************************************

C.3.2. Energy level calculations

a) The steps of how to calculate the energy levels are shown in Table C.3.4.

Table C.3.4. Steps to calculate the energy levels

i) Steps to calculate the conduction band energy levels

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

INPUT THE NUMBER OF QUANTUM WELLS NUM=?

INPUT TOTAL LAYERS FOR STRUCTURE--N ODD

INPUT N=

INPUT THE LOWEST POTENTIAL LAYER(1st Q-WELL) IC= ?

INPUT THE SELECTED CENTER LAYER OF STRUCTURE ICR=

*******************************************************

INPUT I=1 FOR AlGaAs

I=2 FOR InGaAsP

I=3 FOR In1-xGaxAs/InGaAsP/InP

I=4 FOR InGaAlAs/InGaAlAs

I=5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

I=6 FOR InGaAs/AlGaAs/AlGaAs

I=7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(GaAs)

I=8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

I=9 FOR InzGa1-zAs/AlxGayIn1-x-yAs/InP

I=10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(InP)

I=11 FOR InzGa1-zAs/AlxGayIn1-x-yAs/AlAsxSb1-x

I=12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs

I=13 FOR InGaAs/In(1-y)Ga(x)As(y)P(1-y)/GaAs

INPUT I= ?

*******************************************************

ENERGY EIGENVALUE===> 0.102677331562E-01 ERROR= .4838213E-14

ENERGY EIGENVALUE===> 0.829312203346E-01 ERROR= .3134953E-14

ENERGY EIGENVALUE===> 0.116110587122E+00 ERROR= .1700480E-14

ENERGY EIGENVALUE===> 0.137409592564E+00 ERROR= .2887171E-14

ENERGY EIGENVALUE===> 0.193078448219E+00 ERROR= .2186428E-14

FOR CHECKING THE Schrodinger WAVE FUNCTION INPUT I==> 1

SKIP INPUT I==> 2

I=?

INPUT THE EIGENVALUE

EIGEN VALUE=

0.0102677331562

INPUT THE NAME OF OUTPUT FILE

cb1.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.23125143E-04

CONFINEMENT FACTOR OF 2 th LAYER = 0.60295889E-01

CONFINEMENT FACTOR OF 3 th LAYER = 0.87936197E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.60295889E-01

CONFINEMENT FACTOR OF 5 th LAYER = 0.23125143E-04

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

INPUT THE EIGENVALUE

EIGEN VALUE=

0.0829312203346

INPUT THE NAME OF OUTPUT FILE

cb2.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.30920015E-02

CONFINEMENT FACTOR OF 2 th LAYER = 0.29765260E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.39851080E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.29765260E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.30920015E-02

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

ii) Steps to calculate the heavy hole energy levels

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

INPUT THE NUMBER OF QUANTUM WELLS NUM=?

INPUT TOTAL LAYERS FOR STRUCTURE--N ODD

INPUT N=

INPUT THE HIGHEST POTENTIAL(1st Q-WELL) LAYER IC= ?

INPUT THE SELECTED CENTER OF THE STRUCTURE ICR=?

*******************************************************

INPUT I=1 FOR AlGaAs

I=2 FOR InGaAsP

I=3 FOR In(1-x)Ga(x)As/InGaAsP/InP

I=4 FOR InGaAlAs/InGaAlAs

I=5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

I=6 FOR InGaAs/AlGaAs/AlGaAs

I=7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(GaAs)

I=8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

I=9 FOR In(z)Ga(1-z)As/AlxGayIn1-x-yAs/InP

I=10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(InP)

I=11 FOR InzGa1-zAs/AlxGayIn1-x-yAs/AlAsxSb1-x

I=12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs

I=13 FOR InGaAs/In(1-x)Ga(x)As(y)P(1-y)/GaAs

INPUT I= ?

*******************************************************

DOES THE STRUCTURE STRAIN OR STRAIN-COMPENSATED?

IF STRAIN ONLY INPUT 1, STRAIN-COMPENSATED INPUT 2

INPUT SELECT = ?

ENERGY EIGENVALUE===> -0.345448893969E+00 ERROR= .5479616E-14

ENERGY EIGENVALUE===> -0.313421614966E+00 ERROR= .4977968E-14

ENERGY EIGENVALUE===> -0.286023116439E+00 ERROR= .3741431E-14

ENERGY EIGENVALUE===> -0.265617316582E+00 ERROR= .4216452E-14

ENERGY EIGENVALUE===> -0.234960966106E+00 ERROR= .1892574E-14

ENERGY EIGENVALUE===> -0.220233112417E+00 ERROR= .3492980E-14

ENERGY EIGENVALUE===> -0.198687987806E+00 ERROR= .2194434E-14

ENERGY EIGENVALUE===> -0.182167124769E+00 ERROR= .5669799E-14

ENERGY EIGENVALUE===> -0.173478187551E+00 ERROR= .3761173E-14

ENERGY EIGENVALUE===> -0.156637644140E+00 ERROR= .4590558E-14

ENERGY EIGENVALUE===> -0.154444131718E+00 ERROR= .2538691E-14

ENERGY EIGENVALUE===> -0.127480216412E+00 ERROR= .2519639E-14

ENERGY EIGENVALUE===> -0.758643937665E-01 ERROR= .2498963E-14

ENERGY EIGENVALUE===> -0.356919987894E-01 ERROR= .2709770E-14

ENERGY EIGENVALUE===> -0.109370594171E-01 ERROR= .2119172E-14

FOR CHECKING THE Schrodinger WAVE FUNCTION INPUT I==> 1

SKIP INPUT I==> 2

I=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.0109370594171

INPUT THE NAME OF OUTPUT FILE

hh1.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.18195603E-12

CONFINEMENT FACTOR OF 2 th LAYER = 0.48861990E-02

CONFINEMENT FACTOR OF 3 th LAYER = 0.99022760E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.48861990E-02

CONFINEMENT FACTOR OF 5 th LAYER = 0.18195603E-12

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.0356919987894

INPUT THE NAME OF OUTPUT FILE

hh2.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.60477885E-11

CONFINEMENT FACTOR OF 2 th LAYER = 0.20535375E-01

CONFINEMENT FACTOR OF 3 th LAYER = 0.95892925E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.20535375E-01

CONFINEMENT FACTOR OF 5 th LAYER = 0.60477885E-11

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

iii) Steps to calculate the light hole energy levels

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

INPUT THE NUMBER OF QUANTUM WELLS NUM=?

INPUT TOTAL LAYERS FOR STRUCTURE--N ODD

INPUT N=

INPUT THE HIGHEST POTENTIAL(1st Q-WELL) LAYER IC= ?

INPUT THE SELECTED CENTER OF THE STRUCTURE ICR=?

*******************************************************

INPUT I=1 FOR AlGaAs

I=2 FOR InGaAsP

I=3 FOR In(1-x)Ga(x)As/InGaAsP/InP

I=4 FOR InGaAlAs/InGaAlAs

I=5 FOR GaInP/(AlGa)0.5In0.5P/AlInP

I=6 FOR InGaAs/AlGaAs/AlGaAs

I=7 FOR InGaAs/InGaAsP/Ga0.51In0.49P(GaAs)

I=8 FOR AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

I=9 FOR In(z)Ga(1-z)As/AlxGayIn1-x-yAs/InP

I=10 FOR InGaAlAs/InGaAlAs/AlAsxSb1-x(InP)

I=11 FOR InzGa1-zAs/AlxGayIn1-x-yAs/AlAsxSb1-x

I=12 FOR In(y)Ga(1-y)As(x)N(1-x)/GaAs

I=13 FOR InGaAs/In(1-x)Ga(x)As(y)P(1-y)/GaAs

INPUT I= ?

*******************************************************

DOES THE STRUCTURE STRAIN OR STRAIN-COMPENSATED?

IF STRAIN ONLY INPUT 1, STRAIN-COMPENSATED INPUT 2

INPUT SELECT = ?

ENERGY EIGENVALUE===> -0.324350665429E+00 ERROR= .2529748E-14

ENERGY EIGENVALUE===> -0.268485842580E+00 ERROR= .4118834E-14

ENERGY EIGENVALUE===> -0.200300476894E+00 ERROR= .3413517E-14

ENERGY EIGENVALUE===> -0.181133391050E+00 ERROR= .2018955E-14

ENERGY EIGENVALUE===> -0.116983827560E+00 ERROR= .3183911E-14

ENERGY EIGENVALUE===> -0.161551734944E-01 ERROR= .3222829E-14

FOR CHECKING THE Schrodinger WAVE FUNCTION INPUT I==> 1

SKIP INPUT I==> 2

I=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.0161551734944

INPUT THE NAME OF OUTPUT FILE

lh1.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.28197495E-05

CONFINEMENT FACTOR OF 2 th LAYER = 0.39958233E-01

CONFINEMENT FACTOR OF 3 th LAYER = 0.92007789E+00

CONFINEMENT FACTOR OF 4 th LAYER = 0.39958233E-01

CONFINEMENT FACTOR OF 5 th LAYER = 0.28197495E-05

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

INPUT THE EIGENVALUE

EIGEN VALUE=

-0.116983827560

INPUT THE NAME OF OUTPUT FILE

lh2.txt

CONFINEMENT FACTOR OF 1 th LAYER = 0.39043702E-03

CONFINEMENT FACTOR OF 2 th LAYER = 0.19969312E+00

CONFINEMENT FACTOR OF 3 th LAYER = 0.59983288E-01

CONFINEMENT FACTOR OF 4 th LAYER = 0.19969312E+00

CONFINEMENT FACTOR OF 5 th LAYER = 0.39043702E-03

INPUT NEW EIGENVALUE--> 1, BACK TO MAIN PAGE--> 2

SELECT=?

b) The main output file from this part of GAIN program is energy.dat, containing all the energy levels as shown in Table C.3.5. After the energy eigen values are calculated, the GAIN program asks the user whether he would like to check the wave envelope function or not. We suggest that the user check the wave envelope functions of the first and second energy levels for conduction and valence bands. The plots of the envelope functions are shown in Fig. C.3.2, Fig. C.3.3, Fig C.3.4.

Table C.3.5. output file energy.dat

CONDUCTION BAND ENERGY===> 0.132273196491E+00 ERROR= .1825400E-14

CONDUCTION BAND ENERGY===> 0.338026920933E+00 ERROR= .2075989E-14

CONDUCTION BAND ENERGY===> 0.438393858497E+00 ERROR= .1374688E-14

CONDUCTION BAND ENERGY===> 0.500546559386E+00 ERROR= .1783885E-14

HEAVY HOLE ENERGY===> -0.190388140560E+00 ERROR= .3376657E-14

HEAVY HOLE ENERGY===> -0.178205351549E+00 ERROR= .2794590E-14

HEAVY HOLE ENERGY===> -0.146868929570E+00 ERROR= .1933278E-14

HEAVY HOLE ENERGY===> -0.649012884792E-01 ERROR= .1722105E-14

HEAVY HOLE ENERGY===> -0.584031671619E-02 ERROR= .1782035E-14

LIGHT HOLE ENERGY===> -0.224692198534E+00 ERROR= .5190988E-14

LIGHT HOLE ENERGY===> -0.169366776608E+00 ERROR= .3378719E-14

LIGHT HOLE ENERGY===> -0.978425419323E-01 ERROR= .2045359E-14


Fig. C.3.2. Wave envelop functions for energy levels in conduction band	Fig. C.3.3. Wave envelop functions for heavy hole energy levels

Fig. C.3.4. Wave envelop functions for light hole energy levels

C.3.3. Computation of Gain and Laser Characteristics

In this part of GAIN program, the input file needs to be constructed with the results of the previous steps and according to the laser design. In this example, a tensile single-quantum-well laser with a ridge length of 750µm and ridge width of 3 µm, the input file is shown in Table C.3.6. The detailed steps of simulations are listed in Table C.3.7. The main output files: L-I curve, optical gain as a function of the wavelength, and mode gain vs. current density are plotted in Fig. C.3.5, Fig. C.3.6, and Fig. C.3.7.

a) The input file:

Table C.3.6. Input file for gain and threshold current calculation

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c 1. Input the compositions, width of well, effective index c

c and lasing wavelength. c

c Ex: xx,xz,qy,xy,lx,n,lam c

c for different materials the following are the forms of inputs. c

c c

c w -- > well, b -- > barrier cxz and cxy for cladding. c

c c

c a. AlxGa1-xAs : xx (Al w) xz (Al b) qy (0) xy (0) c

c b. In1-xGaxAsyP1-y : xx (Ga w) xz (Ga b) qy (As w) xy (As b) c

c c. In1-xGaxAs/InGaAsP : xx (Ga w) xz (Ga b) qy (0) xy (As b) c

c d. AlxGayIn1-x-yAs/InP : xx (Ga w) xz (Ga b) qy (Al w) xy (Al b)c

c e. c

c f. InxGa1-xAs/AlGaAs : xx (In w) xz (0) qy (0) xy (Al b) c

c g. c

c h. AlyInxGa1-x-yAs/AlGaAs : xx (Al w) xz (al b) qy (In w) xz (0)c

c i. In1-xGaxAs/AlGaInAs : xx (In w) xz (0) qy (Al b) xy (Ga b) c

c c

c 2. Input the energy gap,temperature, barrier band edges(both bands)c

c Ex: eg,temp,ec,ev c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

0.51884522 0.21142234 0.0 0.4603684 10.0 3.32 1.55

0.79487179 298 0.10718016 0.1566647

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c 3. Input the ist level sub-band energy levels. c

c Ex: ec1,eh1,el1 c

c c

c 4. Input the material loss, reflectivities, number of quantum c

c wells and beta(for spontaneous emission). c

c Ex: alpha,r1,r2,mm,beta. c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

0.0102677331562 0.0109370594171 0.0161551734944 0.0829312203346 0.0356919987894 0.116983827560

10.0d0 0.3000 0.300 1 5.D-5

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c 5. Input the cavity length, ridge width, internal efficiency c

c Auger, strain(except AlGaAs,put 0) and confinement factor. c

c Ex: cl,cw,etha,ca,es,confine c

c c

c 6. Input the cladding composition and band edges. c

c Ex: cxz,cxy,ecc,evv c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

500.D-4 3D-4 0.97 3.10d-29 0.0 0.018

0.00 0.00 0.218876 0.364797

b) The steps for these calculations mentioned are listed in Table C.3.7

Table C.3.7. The steps for the gain and threshold current density calculations

ENTER 1 FOR THE NECESSARY PARAMETERS

2 FOR THE ENERGY VALUES OF CONDUCTION BAND

3 FOR THE ENERGY VALUES OF HEAVY HOLE BAND

4 FOR THE ENERGY VALUES OF LIGHT HOLE BAND

5 FOR THE LASER G-J AND G(LAMBDA)

6 FOR RATE EQUATIONS(TWO SECTION MODEL INCLUDED)

7 FOR EXIT

THE INPUT FILE NAME=

in1.tex

SELECT MATERIAL=?

1--AlGaAs

2--InGaAsP

3--In1-zGazAs/InGaAsP/InP

4-- InGaAlAs

5--GaInP/AlzGawIn1-z-wP/Al0.5In0.5P

6-- InxGa1-xAs/AlxGa1-xAs/AlGaAs

7--In1-xGaxAs/InGaAsP/GaxIn1-xP(X=0.51) MATCHED TO GaAs

8--AlyInxGa1-x-yAs/AlzGa1-zAs/GaAs

9--InzGa1-zAs/AlxGayIn1-x-yAs/InP

10-- InGaAlAs/InGaAlAs/AlAsSb

11--InzGa1-zAs/AlxGayIn1-x-yAs/AlAsSb

12--In(y)Ga(1-y)As(x)N(1-x)/GaAs

13--InGaAs/In(1-x)Ga(x)As(y)P(1-y)/GaAs

INPUT SELECTION

INPUT MODE = ? FOR TE--> MODE =1, FOR TM--> MODE =2

INPUT TE OR TM ?

IF EL1 BELOW EH1 THEN SELECT 1, OTHERWISE SELECT 2

SELECTION=?

**************************************************

CALCULATE THE EFFECTIVE MASS

**************************************************

FOR QUASI-FERMI LEVEL SELECT=1,

FOR READ EXISTING QUASI-FERMI LEVEL SELECT=2

SELECT=?

J(LEAKAGE)=0.104958D+03 A/cm^2 N=0.328772D+19 1/cm^3

J(LEAKAGE)=0.108158D+03 A/cm^2 N=0.330752D+19 1/cm^3

J(LEAKAGE)=0.111439D+03 A/cm^2 N=0.332732D+19 1/cm^3

J(LEAKAGE)=0.114800D+03 A/cm^2 N=0.334712D+19 1/cm^3

……….

J(LEAKAGE)=0.245553D+05A/cm^2 N=0.788120D+19 1/cm^3

J(LEAKAGE)=0.246733D+05A/cm^2 N=0.790100D+19 1/cm^3

J(LEAKAGE)=0.247912D+05A/cm^2 N=0.792080D+19 1/cm^3

J(LEAKAGE)=0.249092D+05A/cm^2 N=0.794060D+19 1/cm^3

J(LEAKAGE)=0.250272D+05A/cm^2 N=0.796040D+19 1/cm^3

J(LEAKAGE)=0.251453D+05 A/cm^2 N=0.798020D+19 1/cm^3

J(LEAKAGE)=0.252633D+05 A/cm^2 N=0.800000D+19 1/cm^3

**************************************************

G(J) PARAMETERS FROM SINGLE WELL

Go=0.178866D+02 1/cm Jo=0.967184D+02 A/cm^2

G(N) PARAMETERS FROM SINGLE WELL

NGo=0.993699D+03 1/cm XNo=0.951378D+18 1/cm^3

Jtr=0.355807D+02 A/cm^2 NTR=0.349993D+18 1/cm^3

THE OPTIMUM NUMBER OF QUANTUM WELL FOLLOWS THE ARTICLE

BY McIlory et al. IEEE JQE-21 1985.

THE OPTIMUM NUMBER OF QUANTUM WELL Nopt =