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 grid point, the three sets of unknowns are solved. We note that, at the user’s discretion, AMPS requires the mesh to have adjustable grid spacing. As stated, after obtaining these three state variables as a function of x, band edges, recombination profiles electrical field, carrier populations, trapped charge, current densities, and any other data related to transport may be extracted.
First, AMPS measure the simple band diagram, built-in potential, electric field, trapped carrier populations, and free carrier populations found in a device if there is no bias (voltage or light) of any kind. These solutions obtained at thermodynamic equilibrium permit to “see what the device will look like.”
AMPS will then use such solutions obtained at thermodynamic equilibrium as starting presumptions for the iterative scheme that will contribute to the full characterization of a device structure under voltage, illumination, or both voltage and illumination bias. AMPS produce output, such as band diagram (which include quasi-Fermi levels), carrier populations, recombination profiles, currents, current-voltage (I-V) characteristics, and spectral response for device structures with different voltage, illumination or voltage and illumination bias [14–16].
Given the range of voltage bias in the window for specifying the conditions for voltage bias, this range of voltages applies to both the dark I-V and light I-V. If the user wishes to get a biased band diagram, he/she can open the selected biased window to give AMPS the value that must (1) lie in the voltage detailed in the previous window and (2) be constant with the previously selected voltage step.
The only distinction at the user input window between light and dark I-V is in the lighting process, the user has to check “light on.” AMPS received AM1.5 by default but the user may specify the photon flux and spectrum. A box called “light-x,” is provided as a neutral filter/concentrator. The absorption coefficient must be manually entered by the user. Yet AMPS provide the user with an alternative in the “Eopt” box to shift the absorption coefficient linearly. Because absorption coefficient information is not easy to obtain most of the time, this linear shift will help the user check the band gap adjustment. You can see details on the user interface.
If the user wishes to see the current produced at each wavelength, the “spectral response” box must be checked. With and without light bias, AMPS will always produce spectral response. The spectrum and the flux in the window of the spectrum determine the light bias. The user-defined spectrum, therefore, defines the range of the QE graph. Users can also adjust the frequency of the probe laser. At the defined voltage bias, AMPS will produce QE.
1.5 Automat for Simulation of Heterostructures (AFORS-HET)
A lot of different experimental approaches are used to analyze (thin film) heterojunction solar cells, varying from traditional techniques for the characterization of solar cell, such as current-voltage characteristics or quantum efficiency to more sophisticated ones, such as surface photovoltage, photo- and electroluminescence, impedance, capacitance/conductance, decay in photoconductance intensity modulated photocurrent spectroscopy or electrically detected magnetic resonance [17–20].
AFORS-HET allows these measures to be interpreted AFORS-HET simulates solar cells with heterojunction, as well as the observables of the related techniques of measurement. A visual framework enables all simulation information to be displayed, stored, and compared. It is possible to perform arbitrary variations of parameters, multi-dimensional parameter fitting and optimization.
AFORS-HET is used specifically to model heterojunction solar cells based on amorphous/crystalline Si with the TCO/a-Si:H(n, p)/c-Si(p, n)/ a-Si:H(p, n)/Al form where ultra-thin (5 nm) a-Si:H sheets of hydrogenated amorphous silicon are mounted on top of a thick (300 μm) crystalline wafer of Silicon. Up to 19.8% of experimental efficiencies have been found.
It is possible to model an arbitrary sequence of semiconducting layers, laying down the properties of corresponding layer and interface, i.e., the defect state distribution (DOS). Utilizing recombination statistics by Shockley-Read-Hall, semiconductor equations are solved in one dimension (1) for thermodynamic equilibrium, (2) for stable conditions under externally applied voltage or current and/or illumination, (3) for small extra sinusoidal externally applied voltage/illumination modulations, (4) for temporary conditions due to general external variations. It is, therefore, possible to determine the internal characteristics of the cell-like band diagrams, local rates of generation and recombination, local currents of the cell, current densities, and phase shifts. In addition, it is possible to simulate a range of characterization methods, i.e., I-V, transient, pulselength, wavelength, intensity, and voltage-dependent photovoltaic surface (TR-SPV, PD-SPV, WD-SPV, ID-SPV, VD-SPV), transient luminescence (TR-PEL, intTR-PEL), internal and external quantum efficiency (QE), impedance/admittance spectrum, spectral-resolved photo, and electroluminescence (PEL) [21–23].
External users can implement new characterization approaches and new numerical segments (open-source on request). To date, these numerical modules have been established: (a) modules for front contact: metal/ semiconductor Schottky- or Schottky-Bardeen- or metal/insulator/semiconductor contact; (b) modules for interface: no interface or drift diffusion or thermionic emission semiconductor/semiconductor heterojunction
