CN114662346B - Simulation prediction method for dislocation extension characteristics in semiconductor laser - Google Patents
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Abstract
The invention relates to the technical field of semiconductor lasers, and discloses a simulation prediction method for dislocation extension characteristics in a semiconductor laser, which comprises the following steps: establishing a dynamic control equation of dislocation extension of the semiconductor laser: establishing a structure model of the semiconductor laser; acquiring an elastic modulus and an external driving condition; carrying out dislocation simulation by using software, solving a variable rho in a dynamic control equation, and carrying out visual processing on a simulation result; carrying out actual dislocation verification under the same external driving condition, comparing the simulation result with the actual result, and modifying unknown parameters to re-simulate if the result is inconsistent until the simulation result is consistent with the actual result; and performing simulation prediction on the dislocation characteristics of the unknown semiconductor laser under the external driving condition by using the obtained dynamic control equation. The method disclosed by the invention can deeply understand the internal dislocation propagation mechanism, and can carry out calculation prediction and effective control on external conditions and the internal structure and material design of the device.
Description
Technical Field
The invention relates to the technical field of semiconductor lasers, in particular to a simulation prediction method for dislocation extension characteristics in a semiconductor laser.
Background
The semiconductor laser has the advantages of wide output wavelength range, simple structure, easy integration and the like, and can be widely applied to the fields of material processing, optical communication, medicine, laser sensing, military, aerospace and the like. The reliability is very important to the application, and as the application requirements are continuously expanded, the requirements on the reliability service life and the failure rate are continuously improved, the research on the reliability of the semiconductor laser is greatly concerned by people.
Research has found that dislocations are the major failure mode of semiconductor lasers, and it is therefore necessary to gain insight into the underlying mechanisms and properties of dislocations. However, the existing research on the dislocation in the semiconductor laser mainly focuses on observation of phenomena and analysis of reasons after failure, and a research report on a middle dynamic expansion process is lacked, and meanwhile, a simulation method for the dislocation expansion in the semiconductor laser on a macroscopic dimension is not available. The existing simulation method is mainly based on the physical first principle of atomic scale, molecular dynamics, dislocation dynamics and the like, the simulated solution has larger limitations on time and space scales and calculation cost, and the simulation requirement of a semiconductor laser, which has various heterogeneous materials and a complex structure, on the macroscopic scale cannot be met.
Disclosure of Invention
In order to solve the technical problems, the invention provides a simulation prediction method for dislocation extension characteristics in a semiconductor laser, so as to achieve the purposes of deeply knowing the internal extension mechanism of dislocation, and carrying out calculation prediction and effective control on external conditions and the internal structure and material design of a device.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a simulation prediction method for dislocation extension characteristics in a semiconductor laser comprises the following steps:
step one, establishing a dynamic control equation of dislocation expansion of the semiconductor laser:
wherein the content of the first and second substances,
wherein, the first and the second end of the pipe are connected with each other,
in order to be a diffusion term, the diffusion term,
is a drive term;
ρ is the dislocation density distribution to be determined, and is the coordinate (c) ((R))
) And time t;
is the proportionality coefficient of the diffusion term, C 11 ，C 12 And C 44 Is the elastic modulus of the semiconductor laser material, f: (
) As a dislocation driving source is (
) And a random function of time t;
is a function of the current, temperature and dislocation activation energy of the diffusion term;
is a function of the current, temperature and dislocation activation energy of the drive term; a. the 1 Is the applied temperature of the diffusion term, the current proportionality constant; a. the 2 Is the applied temperature of the driving term, the current proportionality constant; i is an applied current, I 0 Is a current normalization constant, n 1 Is a diffusion termCurrent acceleration factor, n 2 Is the current acceleration factor of the drive term, E 1 Is the activation energy of the diffusion term, E 2 Is the activation energy of the drive item; t is the temperature, T 0 K is the boltzmann constant for the reference temperature;
establishing a structural model of the semiconductor laser to be simulated, and giving initial simulation conditions t = 0;
step three, obtaining the elastic modulus C of the semiconductor laser material to be simulated 11 ，C 12 、C 44 And external driving conditions, including temperature T and current I;
step four, unknown parameters in the dynamic control equation
，A 1 ，A 2 ，n 1 ，n 2 ，E 1 ，E 2 Firstly, setting according to experience, and obtaining a dislocation driving source f (x, y, z, t) through a DLA (diffusion limited aggregation) process;
fifthly, carrying out dislocation simulation by using software, solving a variable rho in a dynamic control equation, and carrying out visualization processing on a simulation result;
sixthly, carrying out actual dislocation verification by using the semiconductor laser to be simulated under the same external driving condition, comparing the simulation result with the actual result, and modifying unknown parameters in the dynamic control equation if the simulation result does not meet the actual result
，A 1 ，A 2 ，n 1 ，n 2 ，E 1 ，E 2 Returning to the step four, and performing re-simulation until the simulation result is consistent with the actual result;
and seventhly, simulating and predicting the dislocation characteristics of the unknown semiconductor laser under the external driving condition by using the obtained dynamic control equation.
In the above scheme, in the second step, the simulated initial conditions are as follows: at an initial time t =0, the value ρ =1 at the selected dislocation start point (x, y, z) and the remaining position ρ = 0.
In the above scheme, in step four, the process of obtaining the dislocation driving source f (x, y, z, t) through the DLA process is as follows:
(1) randomly generating source points in a set region of the semiconductor laser, wherein the set region refers to a region with the largest stress in a semiconductor laser structure model;
(2) the source point makes random Brownian motion, and the direction of the source point wandering is defined according to the material lattice bonding direction of the semiconductor laser;
(3) judging whether the source point exceeds a set boundary, if so, ending the motion process, iterating for time t +1, and returning to the step (1); if not, continuing to move;
(4) the source point is condensed when meeting the set seed point, and if not, the step (2) is returned to continue to do random Brownian motion;
(5) substituting the condensed source point time and coordinate information into a dislocation driving source f (x, y, z, t) in a dynamic control equation;
(6) and (5) iterating time t +1, judging whether the time t reaches the set time, if not, continuing the step (1), and if so, ending the whole process.
Through the technical scheme, the method for simulating and predicting the dislocation propagation characteristic in the semiconductor laser, provided by the invention, has the following beneficial effects:
the invention establishes a set of dynamic control equations for describing the dislocation space-time evolution by analyzing factors and physical models influencing the dislocation motion characteristics, simulates the dynamic expansion process and random appearance of dislocations in the semiconductor laser, and quantifies the influence relationship of external driving conditions (temperature and current), device structures and material characteristics on the dislocation dynamic expansion characteristics, thereby deeply knowing the internal expansion mechanism of dislocations and carrying out calculation prediction and effective control on the external conditions and the internal structure and material design of devices.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below.
Fig. 1 is a schematic flow chart of a method for simulating and predicting dislocation propagation characteristics in a semiconductor laser according to an embodiment of the present invention;
FIG. 2 is a process algorithm for deriving the dislocation driving source f (x, y, z, t) by the DLA process;
FIG. 3 is a comparison of simulated and actual dislocation results for example 1 of the present invention, wherein (a) is the simulated dislocation result and (b) is the actual dislocation result;
FIG. 4 is a comparison of simulated and actual dislocation results for example 2 of the present invention, wherein (a) is the simulated dislocation result and (b) is the actual dislocation result.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
The invention provides a simulation prediction method of dislocation extension characteristics in a semiconductor laser, which comprises the following steps as shown in figure 1:
step one, establishing a dynamic control equation of dislocation expansion of the semiconductor laser according to the properties of dislocations in the semiconductor laser, wherein the dislocations have the following characteristics:
1. dislocation is an irreversible process and does not have time reversal invariance, and a dislocation motion equation is not of a fluctuation type and is supposed to be of a diffusion type;
2. dislocation motion is a thermally activated process, affected by temperature, current and activation energy;
3. the dislocation density can be propagated, annihilated and reacted with each other in the motion process, and the evolution of the dislocation density is the balance result of diffusion and chemical reaction;
4. dislocation motion is controlled by the structure of the device and the crystal orientation of the material, and the device has spatial anisotropy;
5. the appearance of dislocation propagation is random.
The dynamic control equation established from the above properties of dislocations in semiconductors is as follows:
wherein the content of the first and second substances,
wherein the content of the first and second substances,
in order to be a diffusion term, the diffusion term,
are the drive terms.
ρ is the dislocation density distribution to be determined, and is the coordinate (c) ((R))
) And time t;
is the proportionality coefficient of the diffusion term, C 11 ，C 12 And C 44 Is the elastic modulus of the semiconductor laser material, f: (
) As a dislocation driving source is (
) And a random function of time t;
is a function of the current, temperature and dislocation activation energy of the diffusion term;
is the current, temperature of the driving termDegree and dislocation activation energy; a. the 1 Is the applied temperature of the diffusion term, the current proportionality constant; a. the 2 Is the applied temperature of the driving term, the current proportionality constant; i is an applied current, I 0 Is a current normalization constant, n 1 Current acceleration factor, n, being a diffusion term 2 Is the current acceleration factor of the drive term, E 1 Is the activation energy of a diffusion term, E 2 Is the activation energy of the drive item; t is temperature, T 0 K is the boltzmann constant for the reference temperature;
in this embodiment, the unit and value of each parameter are shown in table 1.
TABLE 1 description of the parameters
| (symbol) | Unit of | Value taking | Remarks for |
| ρ | |||
| 1/m 2 | To obtain the variable by simulation | ||
| C 11 | GPa | 118.8+1.4x | Given material Al x Ga 1-x As determined (known) |
| C 12 | GPa | 53.8+3.2x | Given material Al x Ga 1-x As determined (known) |
| C 44 | GPa | 59.4-0.5x | Given material Al x Ga 1-x As determined (known) |
 |
m 3 s/kg | 10 -11 | Calibrated by experiment (unknown) |
f( |
1/m 2 s | Determined by the DLA Process (unknown) | |
 |
NA | 2.50x10 -4 | Calibrated by experiment (unknown) |
 |
NA | 2.50x10 -4 | Calibrated by experiment (unknown) |
| A 1 | NA | 10 -9 | Calibrated by experiment (unknown) |
| A 2 | NA | 10 -9 | Calibrated by experiment (unknown) |
| I | mA | 10 | External input parameter (known) |
| I 0 | |
1 | Constant (known) |
| n 1 | NA | 2 | Obtained by experiment (unknown) |
| n 2 | NA | 2 | Obtained by experiment (unknown) |
| E 1 | eV | 1 | Obtained by experiment (unknown) |
| E 2 | eV | 1 | Obtained by experiment (unknown) |
| T | k | 373.15 | External input parameter (known) |
| T 0 | k | 298.15 | Setting parameters (known) |
| k | eV/K | 8.617x10 -5 | Constant (known) |
And step two, establishing a structural model of the semiconductor laser to be simulated, and giving initial conditions of simulation, namely, when the initial time t =0, the value rho =1 at the selected dislocation starting point (x, y, z), and the rest position rho = 0. The dislocation starting point is generally chosen at the edge of mesa where defects easily occur.
Step three, obtaining the elastic modulus C of the semiconductor laser material to be simulated 11 ，C 12 、C 44 And external driving conditions including temperature T and current I.
Step four, unknown parameters in the dynamic control equation
，A 1 ，A 2 ，n 1 ，n 2 ，E 1 ，E 2 The dislocation driving source f (x, y, z, t) is obtained through the DLA process.
The above equation establishes the material property (C) 11 ，C 12 ，C 44 ) Influence relationship of external influence factors on dislocation dynamic expansion, and diffusion term of spatial second partial derivative of spatial anisotropy of dislocation expansion (
) The random occurrence of dislocations appears as a dislocation drive source in the equation (
Function of time and space).
Dislocation driving source
Having randomness satisfies the following algorithm:
considering the propagation of dislocations as random walk (anisotropic quasi-brownian motion, defined by the above-mentioned dynamic control equation), it is considered that strain accumulates to some extent and attaches to some previously formed point defect to form a defect chain, and this process is according to DLA, as shown in fig. 2, and the specific algorithm is as follows:
(1) randomly generating source points in a set region of a semiconductor laser; the setting area is an area with large internal stress of the selected device and is generally near an internal oxide layer;
(2) the source point makes random Brownian motion, and the direction of the source point wandering is defined according to the material lattice bonding direction of the semiconductor laser;
(3) judging whether the source point exceeds a set boundary (namely the whole semiconductor laser), if so, ending the motion process, iterating for time t + 1, and returning to the step (1); if not, continuing to move;
(4) the source point is condensed when meeting the set seed point, and if not, the step (2) is returned to continue to do random Brownian motion;
(5) substituting the condensed source point time and coordinate information into a dislocation driving source f (x, y, z, t) in a dynamic control equation;
(6) and (5) iterating time t + 1, judging whether the time t reaches the set time, if not, continuing the step (1), and if so, ending the whole process.
And fifthly, performing dislocation simulation by using software, solving a variable rho in the dynamic control equation, and performing visual processing on a simulation result.
Sixthly, carrying out actual dislocation verification by using the semiconductor laser to be simulated under the same external driving condition, scanning the actual dislocation condition by adopting a TEM (transmission electron microscope), comparing the simulation result with the actual result, and modifying unknown parameters in the dynamic control equation if the result does not meet the actual result
，A 1 ，A 2 ，n 1 ，n 2 ，E 1 ，E 2 And returning to the step four, and re-simulating until the simulation result is consistent with the actual result.
And seventhly, simulating and predicting the dislocation characteristics of the unknown semiconductor laser under the external driving condition by using the obtained dynamic control equation.
Example 1
The embodiment of the invention uses GaAs/Al 0.3 Ga 0.7 Taking an oxidized VCSEL semiconductor laser formed by two As materials As an example, parameter values in the equation are shown in table 1, 300 grids with the size of a two-dimensional plane are set during simulation, and the lower left corner of the two-dimensional plane is provided with 300X 300 gridsFor the origin of coordinates (0, 0), the simulation is performed by dividing the space into grids, i.e., dividing the picture into 300 × 300 grids.
The initial conditions for the simulation were: at initial time t =0, at a selected dislocation starting point, i.e. (a) in fig. 3,
=1, and the rest positions
=0。
The area set in the DLA simulation process step (1) is shown as the area in the box in (a) in fig. 3, and the coordinate range is: x =200~250, y =200~250,
=1。
obtained by DLA
The term is introduced into the dynamic control equation to obtain
Then will be
The visualization processing is performed, the obtained simulation result is shown in fig. 3 (a), and the TEM electron microscope scanning actual dislocation picture is shown in fig. 3 (b), so that the simulation result is similar to the appearance of the actual dislocation.
Example 2
The embodiment of the invention uses GaAs/Al 0.3 Ga 0.7 As two materials form an oxidized VCSEL semiconductor laser As an example, the parameter values in the equation are shown in table 1, the size of a two-dimensional plane is set to 300 × 300 grids during simulation, the lower left corner is the origin of coordinates (0, 0), and the space division grid is solved during simulation, that is, a picture is divided into 300 × 300 grids.
The initial conditions for the simulation were: initial time t =0At selected dislocation starting points, i.e., the dot positions in (a) of fig. 4,
=1, and the rest positions
=0。
The area set in the DLA simulation process step (1) is shown as the area in the box in (a) in fig. 4, and the coordinate range is: x = 280-290, y = 30-120,
=1。
obtained by DLA
The term is introduced into the dynamic control equation to obtain
Then will be
The simulation result obtained by the visualization processing is shown in fig. 4 (a), and the actual dislocation picture scanned by the TEM electron microscope is shown in fig. 4 (b), which shows that the simulation result is similar to the appearance of the actual dislocation.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (2)
1. A simulation prediction method for dislocation extension characteristics in a semiconductor laser is characterized by comprising the following steps:
step one, establishing a dynamic control equation of dislocation expansion of the semiconductor laser:
wherein the content of the first and second substances,
wherein the content of the first and second substances,
in order to be a diffusion term, the diffusion term,
is a drive term;
ρ is the dislocation density distribution to be determined, and is the coordinate (c) ((R))
) And time t;
is the proportionality coefficient of the diffusion term, C 11 ，C 12 And C 44 Is the elastic modulus of the semiconductor laser material, f: (
) As a dislocation driving source is (
) And a random function of time t;
is a function of the current, temperature and dislocation activation energy of the diffusion term;
is a function of the current, temperature and dislocation activation energy of the drive term; a. the 1 Is the applied temperature of the diffusion term, the current proportionality constant; a. the 2 Is the applied temperature of the driving term, the current proportionality constant; i is an applied current, I 0 Is a current normalization constant, n 1 Current acceleration factor, n, being a diffusion term 2 Is the current acceleration factor of the drive term, E 1 Is the activation energy of the diffusion term, E 2 Is the activation energy of the drive item; t is the temperature, T 0 K is the boltzmann constant for the reference temperature;
establishing a structural model of the semiconductor laser to be simulated, and giving simulated initial conditions;
step three, obtaining the elastic modulus C of the semiconductor laser material to be simulated 11 ，C 12 、C 44 And external driving conditions, including temperature T and current I;
step four, unknown parameters in the dynamic control equation
，A 1 ，A 2 ，n 1 ，n 2 ，E 1 ，E 2 Setting according to experience, and obtaining a dislocation driving source f (x, y, z, t) through a DLA process, wherein the DLA process is a diffusion-limited agglomeration process;
fifthly, carrying out dislocation simulation by using software, solving a variable rho in a dynamic control equation, and carrying out visual processing on a simulation result;
sixthly, carrying out actual dislocation verification by using the semiconductor laser to be simulated under the same external driving condition, comparing the simulation result with the actual result, and modifying unknown parameters in the dynamic control equation if the simulation result does not meet the actual result
，A 1 ，A 2 ，n 1 ，n 2 ，E 1 ，E 2 Returning to the step four, and performing re-simulation until the simulation result is consistent with the actual result;
step seven, simulating and predicting the dislocation characteristics of the unknown semiconductor laser under the external driving condition by using the obtained dynamic control equation;
the process of obtaining the dislocation driving source f (x, y, z, t) by the DLA process in step four is as follows:
(1) randomly generating source points in a set region of the semiconductor laser, wherein the set region refers to a region with the largest stress in a semiconductor laser structure model;
(2) the source point makes random Brownian motion, and the direction of the source point wandering is defined according to the material lattice bonding direction of the semiconductor laser;
(3) judging whether the source point exceeds a set boundary, if so, ending the motion process, iterating for time t +1, and returning to the step (1); if not, continuing to move;
(4) the source point is condensed when meeting the set seed point, and if not, the step (2) is returned to continue to do random Brownian motion;
(5) substituting the condensed source point time and coordinate information into a dislocation driving source f (x, y, z, t) in a dynamic control equation;
(6) and (5) iterating time t +1, judging whether the time t reaches the set time, if not, continuing the step (1), and if so, ending the whole process.
2. A method as claimed in claim 1, wherein in step two, the initial conditions for simulation are: at an initial time t =0, the value ρ =1 at the selected dislocation start point (x, y, z) and the remaining position ρ = 0.
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