Perovskite Materials for Energy and Environmental Applications. Группа авторов

is followed on the basis of the flowchart in Figure 1.2 [3, 8–12]:

      1 The ASA program has a built-in parser to run through the input file. After one statement is read, the appropriate part of the program is invoked.

      2 The first part of an input file always consists of statements thatDefine the simulated device, i.e. the layers, including their width and the grid.Set electrical parameters of the material, e.g., the valance tail slope parameters Nv0, Evo. These parameters are set for every electrical layer.Set optical parameters, e.g., the refractive index and extinction coefficient of the layers.Set calculation and model settings, e.g., if the Newton method is to be used.

      3 After this initialization, the calculations are started with “solve.”The program generates the grid according to the definition earlier in the input file. The arrays of the simulated device are allocated and filled with the (initial) values defined by the given (electrical) parameters. When the defect pool model is selected, the defect density NDB(x) is calculated.If it is not read from external file, the program calculates the generation rate in the device using the GENPRO1, GENPRO2, or GENPRO3 module.One of the five simulation modes can be selected by a “solve” statement:(a) equil: in this mode, the electron, hole densities and the matching potential are calculated in thermodynamic equilibrium. These calculations are automatically carried out before mode 2.(b) jv: the current-voltage characteristics of the simulated device are computed, by using the Poisson and continuity equations. A selection can be made between the Newton and Gummel method. The calculations can be carried out with or without carriers generation by illumination.(c) cv: the capacitance-voltage characteristics of the simulated device are calculated. It is calculated by using mode 2 to find the currents at an applied voltage of and , which gives rise to a difference in charge density Δρ(x). By calculating the difference in surface charge at the front and back contacts, Δσ is also found. These define the capacitance at voltage V.(d) sr: the spectral response (i.e. the external quantum efficiency EQE) is calculated by using mode 2 and the generation rate profile calculated by one of the optical models. The EQE is defined by ΔI/(qΔnphoton), where Δnphoton is the differential number of photons between the (optional) bias spectrum S and the bias spectrum plus a monochromatic probe light S + Δnphoton.(e) rt: the reflection and transmission are calculated. This is carried out by module GENPRO1 (no scattering included).

      4 The desired program output can finally be saved to particular files using the “print” statement.

Figure 1.2 Flowchart showing steps for calculation using ASA adapted from [3].

1.4 Analysis of Microelectronic and Photonic Structures (AMPS)

      AMPS is a computer-based program in one-dimensional designed to simulate physics of transport in solid-state semiconductor devices. This applies the first principles of continuity equations and Poisson’s equations method to examine transport behavior of electronic and optoelectronic semiconductor device based structures. Such architectures of device can consist of or incorporate amorphous or crystalline, polycrystalline materials. AMPS numerically solve the three controlling equations for semiconductor devices (the Poisson equation, the equations of electron continuity, and the hole continuity) short of having any a-priori statements regarding the processes of regulation of transport in such devices. AMPS can be used with this general and precise numerical treatment to study various device structures, including the following [13]:

       Solar cells having P-n and p-i-n structures and detectors with homojunction and heterojunction;

       Homojunction and heterojunction of microelectronic structures of p-n, p-i-n, n-i-n and p-i-p;

       Designs of solar cells with multijunction;

       Microelectronic multi-junction structures;

       Structures for detectors with graded composition and solar cells;

       Microelectronic structures graded in composition;

       New microelectronic, photovoltaic and optoelectronic devices;

       Optional back layered Schottky barrier devices.

Information, such as J-V characteristics, can be achieved in the dark and under illumination using the solutions given by an AMPS simulation software. These can be measured as a temperature variable. Collection efficiencies can also be obtained for solar cell, as well as detector designs as a function of light bias, voltage, and temperature. Additionally, significant information, like electric field concentrations, free and trapped carrier populations, profiles of recombination, and current densities of individual carriers, can be found from the AMPS program as a function of position. AMPS can be used to evaluate transport in different types of device structures that may include amorphous, crystalline, or polycrystalline layers or combinations of these. AMPS is intended to analyze, model, and optimize microelectronic, photovoltaic, or optoelectronic device architectures.

      AMPS incorporate the following:

       a contact treatment allowing thermionic emission, as well as recombination happening at contacts of the device;

       a generalized gap state model for bulk or interface distribution of density of states;

       both recombination processes, i.e., band-to-band recombination process and Shockley-Read-Hall recombination phenomenon;

       a model for recombination that instead of using the frequently-applied single recombination level method calculates Shockley-Read-Hall recombination transport with any inputted general gap state distribution;

       Fermi-Dirac statistics instead of Boltzmann statistics only;

       gap state concentrations calculated with real statistics for temperature instead of frequently used T = 0K method;

       a model for trapped charge, which accounts for charge in any inputted overall gap state distribution;

       a model for gap state, allowing energy variation of capture cross-section;

       distribution of gap states whose properties change with position;

       spatial variation of carrier mobility;

       spatial variation of electron and hole affinities;

       different mobility gaps and optical gaps;

       calculation of characteristics of the device as a function of temperature and also with or without illumination in both forward and reverse bias;

       analysis of device structures made-up utilizing single crystalline, multicrystalline, or amorphous materials or all three.

The transport physics of device can be described in three controlling equations when modeling microelectronic and optoelectronic devices: the equation of Poisson, the equation of continuity for free holes, and the continuity equation for free electrons. So evaluating transport properties turn out to be a challenge to overcome with solving three coupled nonlinear differential equations, each having two boundary conditions associated with it. In AMPS, these three equations together with the suitable boundary conditions are concurrently tackled, so as to achieve a set of three unknown state variables at each device level: the electrostatic potential, the quasi-Fermi level of the hole, and the quasi-Fermi level of the electron. The carrier quantities, currents, fields, and so on, can thus be determined from these three state variables. To ascertain these state variables, the computer uses the method of finite differences and also the Newton-Raphson methodology. Iteratively, the Newton-Raphson Method calculates the roots of a function or roots of a set of functions if these roots are given a suitable initial supposition. Through AMPS, the one-dimensional structure being studied is separated into sections by a network of grid points. Then for each