4.5.1 The Sentaurus® TCAD software
Technology Computer-Aided Design (TCAD) simulations are a tool for semiconductor devices development and performance analysis. TCAD simulations discussed in this dissertation were performed using Sentaurus™ Workbench [199] within the Synopsys® (Synopsys, Inc., Mountain View, CA) framework.
The Sentaurus Structure Editor [200] is used to model a 2D TCAD device, defining the relevant geometry, materials, doping concentrations (or resistivity), doping profiles, contact regions. A TCAD device approximates a real device and continuous properties (e.g. doping profiles) are defined at a finite number of discrete points (or nodes) in space. At any point between these nodes, properties will be calculated by interpolation. The mesh can be user- defined though the declaration of a meshing strategy, which will have to be a compromise between results accuracy requiring finer meshes and simulation time constrains commanding coarser meshes.
This mesh-like grid structure of nodes is loaded into the Sentaurus Device (Sdevice) [201] simulation tool. In all semiconductor devices, charges (such as electrons and holes) and traps (dopants, defects, …) determine the electrostatic potential and, in turn, are themselves affected by the electrostatic potential. The electrostatic potential ϕ is solved everywhere in the device using the Poisson equation:
∇ ∙ (ε∇ϕ) = −q(p − n + ND− NA) − ρtrap (4.2)
where ε is the electrical permittivity, q is the electron charge, n and p are the electron and hole densities (units cm−3), ND and NA are the donors and acceptors doping concentrations (units cm−3), ρtrap is the charge density contributed by traps and fixed charges.
TCAD allows charge deposition at any location in a device. For subsequent drift and diffusion processes, carrier transport is governed by the continuity equations. For a semiconductor these are described in the form of charge conservation as:
�∇ ∙J���⃗= q�Rn net+ ∂n
∂t� for electrons −∇ ∙J���⃗= q�Rp net+∂p∂t� for holes
(4.3)
where J���⃗ and Jn ���⃗ are the current densities (units Acmp −2) for electrons and holes respectively, n and p are the electron and hole densities respectively, Rnet is the net recombination rate (units
s−1) is the net rate of recombination by all processes. These equations are solved iteratively,
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to satisfy predefined convergence criteria, or until a given number of user-defined iterations has been performed.
Depending on the device under investigation and the level of accuracy required, different transport models, each based on a different expression to compute the current densities, can be selected in Sdevice. For the simulations described in this dissertation, the drift-diffusion model was used. It considers the effect of thermal diffusion and the drift caused by the local electric field resulting from applied bias (if any) and electrostatic forces between carriers. It is the default carrier transport model and it is suitable for isothermal simulations of low-power density devices with long active regions.
Defects reduce charge collection by various generation–recombination processes. These are processes that exchange carriers between the conduction band and the valence band. Recombination through deep defect levels in the semiconductor energy gap is called Shockley– Read–Hall (SRH) recombination. An electron from the conduction band and a hole from the valence band combine at the trap level and their contribution to the signal is lost. The SRH lifetimes dependence on doping profiles is modelled in Sdevice through the Scharfetter relation. The Mobility model was declared in the Physics section of the Sdevice command file to implement an SRH doping-dependent process.
Traps and fixed charges are important parameters. They may enhance recombination and increase leakage current. The SRH model depends on traps implicitly but does not model them. It is left for the user to define their concentrations and characteristics.
Traps can be fixed charge traps, which are always completely occupied; acceptor traps, which are uncharged when unoccupied and carry the charge of one electron when occupied, donor traps, which are uncharged when unoccupied and carry the charge of one hole when occupied.
The specification of trap characteristics for a material or region in the TCAD device can be done using the Trap model in the Physics section. It allows for the parametrization of the trapped charge at the interfaces and of the point defects in the substrate, specifying the energy levels, the concentration as a function of the accumulated dose and the cross-section for electrons and holes.
Radiation incident on a semiconductor device triggers the generation of electron–hole pairs in silicon. With Sdevice, in the Physics section it is possible to model the carrier generation through the Gamma Radiation Model. The user can define a dose rate (𝑟𝑟𝑟𝑟𝑟𝑟/𝑠𝑠) and the irradiation duration.
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Alternatively, a Heavy Ion Model can be used. The model is used to represent a minimum ionising particle (MIP) incident on the device. The charge deposited by the particle along a track, or its linear energy transfer (LET) generation density (pairs/cm3), is a user-defined parameter, along with track length, incident location and direction, and lateral distribution.
Once environment variables (e.g. temperature) are set and the relevant physical models are activated (charge carrier mobility, avalanche effects, saturation of the electric field etc.), the electrical behaviour of the TCAD device is simulated by Sdevice. Currents, voltages and charge distributions and generations are computed at each mesh node based on the set of equations chosen to describe the carrier transport mechanisms, following the standard finite element analysis (FEA) scheme. Three main simulation types can be performed.
A voltage ramping simulation, in which the voltage applied to an electrical contact is ramped up (or down). This is used to simulate the measurement of the device I-V characteristic.
A small-signal AC analysis, in which small sinusoidal signals are super-imposed upon the direct-current bias voltage. From the device response, capacitances can be extracted. This is used to simulate the measurement of the device C-V characteristic.
A time-dependent simulation, in which the transient response of the TCAD device to incident particles is assessed. Either the Gamma Radiation Model or the Heavy Ion Model can be used.
Results simulated at each mesh node are examined by visualization with Sentaurus Visual (Svisual). This helps the study of field shapes and charge trajectories that are unknowable in experiment. Signals extracted from the electrodes can be displayed with the Sentaurus Inspect tool.
4.5.2 The Octa model
Using Sentaurus Structure Editor, 2D TCAD devices representative of the Octas bulk and epitaxial were created. For the latter, Figure 23 illustrates one of its n+ electrode along with its p+ guard ring. Figure 24 illustrates the simulated electric field for the same area.
The simulated representation of the space-charge distribution in Figure 23 shows that the depleted region is stretched outside the limits of the p-n junction due to the presence of charges in the silicon oxide layer. The depleted region depth for the Octa epitaxial was estimated to be approximately 3 μm, a value which is consistent with those reported for dosimeters based on p-n junctions operated without any external bias [117] and with values simulated for a similar epitaxial device presented in Aldosari et al. [202].
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The radiation damage of the pre-irradiated Octa bulk was considered by implementing the
Trap model. As reported in the literature, defects generated in a silicon substrate by a Co-60
gamma source can be effectively modelled by introducing interstitial CiOi complexes and VV divacancy centres in the substrate, as well as positive trapped charge at the interfaces with and within the silicon dioxide layers [203].
Following recommendations in Aldosari et al. [202] and references therein, a two-level radiation damage model was implemented for the silicon substrate (Table 5).
Following recommendations reported in the same references, a concentration of trapped charges at the Si-SiO2interfaces and within the SiO2 layers of C = 1012 1
cm2 and C = 107 1cm2
for the pre-irradiated Octa bulk and for the Octa epitaxial respectively was considered. The TCAD devices were validated against experimentally determined I-V and C-V characteristics, with doping concentrations and profiles tuned to fit the experimental results.
Table 5. Two-level radiation damage model. D is the dose in water in units of kGy [202].
Energy [eV] Type of defect Introduction rate [cm−1] Cross section [cm−2] Electrons Holes Ev+ 0.36 CiOi donor 1.826 × 1012× D 2.5 × 10−14 2.5 × 10−15
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Figure 23. Simulated representation of the space-charge distribution for an epitaxial device. The depletion region is stretched outside the limits of the p-n junction due to the presence of charges in silicon oxide layer. Distances are in microns. Brown area represents the SiO2 layer, grey areas represent the aluminium contact of the n+ electrode. The p+ guard ring is visible on the left.
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