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The Monte Carlo Simulation Coupled with Poisson Equation Applied to the Study of a Diode base of
Hg0.8Cd0.2Te
H. Moughli, A. Belghachi, A. Bouida, A. Hasni, L. Varani
To cite this version:
H. Moughli, A. Belghachi, A. Bouida, A. Hasni, L. Varani. The Monte Carlo Simulation Coupled with
Poisson Equation Applied to the Study of a Diode base of Hg0.8Cd0.2Te. Energy Procedia, Elsevier,
2013, 36, pp.50-56. �10.1016/j.egypro.2013.07.007�. �hal-02450419�
Energy Procedia 36 ( 2013 ) 50 – 56
1876-6102 © 2013 The Authors. Published by Elsevier Ltd.
Selection and/or peer-review under responsibility of the TerraGreen Academy doi: 10.1016/j.egypro.2013.07.007
The Monte Carlo Simulation Coupled With Poisson Equation Applied to the study of a Diode base of Hg
0.8Cd
0.2Te H.MOUGHLI
(*),A.BELGHACHI
(*),A.BOUIDA
(*),A.HASNI
(*),L.VARANI
(**)(*)Laboratory physics and semiconductor devices, Bechar University.Po.Box No. 417, 08000 Bechar, Algeria.
(**)Institut d’Electronique du Sud, UMR CNRS 5214, Université Montpellier II, c.c.084, place Bataillon, 34095 Montpellier Cedex 5, France.
E. mail: moughlihassane@yahoo.fr
Abstract
We propose in the present work a numerical solution employed to treat the coupled Monte Carlo method and Poisson equations. This technique is capable of capturing some important features of semiconductor devices.
Numerical results are presented for one-dimensional Hg0.8Cd0.2Te n nn structure, the presence of velocity overshoot has been observed and it is recognized that the fluctuation of velocity and energy term plays an important role in the simulation of semiconductor devices.
Keyword: Transport of carrier, Monte Carlo method, Poisson equation, semiconductor, n+ nn+ structure
1. Introduction
The main purpose of the simulation ofsemiconductordevices is to provide validation tools for the design of new structures. It provides an analysis of the various results it returns, to extract the physical parameters of components to optimize performance, while avoiding to use the technological achievements of pre-testing components, achievements that require resources significant and costly, both hardware and time[1].
For further integration, the size of the components is shrunk to the micron meter. However, simulation models valid for large components are no longer for submicron components due to the occurrence of significant events they are not taken into account.
The Monte Carlo method is used to resolve these issues. Emits, instead of solving directly the macroscopic equations that describe the operation of components, as is the case with drift-diffusion model or hydrodynamic, Monte Carlo method simulates statistically the behavior of circulating particles in these components. This does not have only a microscopic view of the function of the components, but also a better understanding of the phenomena that control it. However, due to the statistical nature of this model, it is necessary to monitor a large number of particles for a period time; this method takes extra calculations time.
Our aim therefore couple in one hand, the section on monitoring particle (Monte Carlo) and secondly, the Poisson equation to monitor the charge density distribution in the case of a one-dimensional n + n n + diode.The method presented is applied to an Hg0.8Cd2Te diode.
This material is used at 77 K for the photo detection of the wavelengths in the infrared window of 8 -14 μm, which corresponds to a narrow gap, typically from about 100meV. Under such conditions, the processes of impact ionization are favored, and corninencent to influence the current-voltage characteristic from a threshold electric field around 200 V / cm. In fact, it is expected that electrical disturbances similar to those induced by a microwave field are able to disrupt the electronic behavior of the material and, in fact, 2interfere with the photo detection.
2- Monte Carlo simulation
The algorithm for the simulation can be divided essentially into two parts:
-The first part, which manages the movement of particles subject to the electric field.
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Open access under CC BY-NC-ND license.
H. Moughli et al. / Energy Procedia 36 ( 2013 ) 50 – 56 51
-The second, which is to update, taking in mind the movement of particles, electric fields in the nodes, and involves solving a Poisson equation
2-1 -Part Monte Carlo:
The simulation by the Monte Carlo method is now one of the most used techniques to study the physical function of electronic components, and provides the ability to reproduce the various microscopic phenomena occurring in the sensitive semiconductor materials [4].
The general idea of Monte Carlo Simulation (MCS) in modern simulators is to study the dynamics of charge carriers during their movement in semiconductor materials. This movement generally comprises two stages:
* The movement under the influence of external forces, that is to say free range
* the reaction of the carrier to physical interactions in the material or diffusion (scattering) [5].
The principle of this method lies in the behavior of individual electrons subjected to an electric field, in the real space and the momentum space, for the:
1) We are associate to each carrier that we simulate the trajectory, an initial wave vector k and an initial position.
2) We used the process "self-ff scattering". It is to establish a distribution of time according to a law whose expression is simplified by the introduction of an interaction dummy null effect known as "self-ff scattering"[2]. ].
Knowledge of the state of the electron is carried out during regularly separated periods of time.
3)At each step we know, for each carrier its wave vector and the position at time t when the measurement is beginning. Then for a remarkable "p" carrier we know that:
K pt)r p t)E pt) E K p) 4)We do a free flightduration ∆t,so we have:
5)We are looking if there was an interaction during the time interval ∆Tby pulling a random number:
-If there is no interaction, the state of the carrier does not change.
- If there was interaction, we set the interaction at time t+∆t and we are lookingΔt after the scattering by drawing another random number, its state is now defined by
[5.6]:
1.2. art updating
Knowing the position of each particle we determine the charge density in the entire structure then we solve the Poisson equation (3).
(3) This, is discredited by the finite difference method as follows (4) [3]
(4)
Then we Calculates the resulting potentials using a resolution methods associated with partial differential equations using a direct method known as FACR (Fourier Analysis and Cyclic Reduction [1]), or relaxation method such as SOR (Successive Over Relaxation) or Multigrid [1, -1].Once the potential is known, the electric field is derived by the finite difference method(4):
(5)
The field at a point depends on the fields of neighboring points.
The simulation algorithm is a sequence of iterations of these two parts, one after the other.
The time loop is executed for a number of time steps until steady state is reached .I. 4. General Algorithm:
Monte Carlo simulation thus begins with initial values (electrostatic potential, energies and speed of the carriers) is close to their final values. Then the different sequences carried over to the flowchart in Figure (1) to loop are performed by the Monte Carlo simulation. After a number of iterations, the system reaches equilibrium where all equations Boltzmann, Schrödinger (along the y axis) and 1D Poisson are self- consistent. The flow of carriers is then conservative.
b) Study of a structure n+n n+ weakVoltage (DIODE):
As part of the application of Monte Carlo transport model to real devices, we simulated the case of a device one-dimensional diode
n
+n n
+ in Hg0.8Cd0.2Te n. This diode made from Hg0.8Cd0.2Te n of0.6 μm with a symmetrical doping profile. Its interior region is 0.2 μm wide with a concentration of 1013cm-3The emitter and collector are symmetrical with a width of 0.2 μm each, and a concentration ofn 5.41013cm-3. All this is illustrated in Figure (2). Note that all the simulation is made at a constant temperature of 77°K.n+ 5.41013
n 1013
n+ 5.41013 0.2 μm 0.2 μm 0.2 μm
Figure (2) : Schéma de la structure de la diode n
+nn
+à étudié.
In our simulation of this system, we use the following boundary conditions n+ junction on the left side (cathode)is grounded (polarized with a voltage VL= 0V), and applying a positive voltage to the anode (n++ junction on theright side) of 0.01 V (VR =0.01V),so that electrons are injected from the left end of
H. Moughli et al. / Energy Procedia 36 ( 2013 ) 50 – 56 53
the terminal (cathode) move to the far right (anode). We assume that the ohmic contact and ideal, in such a way as to preserve charge neutrality and thermal equilibrium at the contacts.
4-Results and discuss:
Figure (3) represents the electron density in the structure. We note that it is almost constant in the area n+
(
ND=
5.41013cm-3) with a slight excess in contact with a defect in the injector and collector contact.These variations result from the boundary conditions, and indicate the existence of a current diffusive nature .At the of border of then+n Junction of the cathode on the left, we see the establishment of a zone of space charge due to a depletion of electrons from the n+
side and an electron injection from n+ to n zone n creating a zone of accumulation. The same phenomenon exists in the n+n junction of the anode and n as the region is very thin, it is entirely accumulation.
The electron density is an order of superior greater than the initial density, which means, the density of impurity atoms.
The field distribution depends very little of the region of dopingn.
Figure (3) Profile of the electron density in the diode
Figure (4) and figure (5) represent the electric field and the potential change in the structure respectively.
In the limits of the n-layer, we have a repulsive field that opposes the diffusion of electrons from the contact, the field distribution in the vicinity of the two n+n junction’s coffespond well in areas of space charge and the field varies almost linearly in the n+ zone.
0,0 0,1 0,2 0,3 0,4 0,5 0,6
0,00E+000 1,00E+013 2,00E+013 3,00E+013 4,00E+013 5,00E+013 6,00E+013
Densité
position v=0.01 v=0.014
0.0 0.1 0.2 0.3 0.4 0.5 0.6 -15
-10 -5 0 5 10
champ éléctrique
position
v=0.014 v=0.01
Figure (4):
Profile of the electric field in the diode
0.0 0.1 0.2 0.3 0.4 0.5 0.6
-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016
potentiel
position
v=0.01 v=0.014
Figure (5): Profile of the electrostatic potential in the diode
H. Moughli et al. / Energy Procedia 36 ( 2013 ) 50 – 56 55
Knowing the kinetic energy, speed and position of each electron at each moment, we can plote the average kinetic energy and the drift velocity of electrons throughout the structure. The kinetic energy of electrons figure (6) is constant in the n+ region and is gr
.
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0 10 20 30 40 50 60
Energie
position
v=0.01 v=0.014
Figure (6) : Profile of energy in the diode
Also the velocity in figure (7), is low in the n+ region and increases greatly at the beginning of the n region then becomes constant (velocity of saturation or steady state). In the n+ anode side the speed decreases rapidly.
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.014 0.015 0.016 0.017 0.018 0.019 0.020 0.021 0.022 0.023 0.024
vitesse
position
v=0.01 v=0.014
Figure (7): Evolution of the velocity in the diode
At the front of the n region, the interactions are due to experienced by the electrons acoustic phonons scattering and the interaction probability is very low.
From a certain position, the most energetic electrons have reached energy of about 35meV and begin to emit polar optical phonons. Once the electron energy is becoming increasingly important, the issue of polar phonons then leads to a velocity distribution increasingly anisotropic, this explains the decrease in
average velocity.
Conclusion
In this paper, we presented: The design of an algorithm for the simulation of one-dimensional systems and the calculation of stationary profiles of a diode n+n n+ based onHgCdTe.
Note that the results obtained by Monte Carlo simulation coupled with Poisson equation preliminary results and original.
Acknowledgements
This work was performed as part of a project CMEP (11/832) between Laboratory of semiconductor devices physics, University of Bechar and Institution for electronics southeast University of Montpellier.
That mew very grateful.
References
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