### Categorized |Design Considerations, IGBT, Power Design, Power Devices

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Posted on 11 March 2020

# Semiconductor Models

This article looks at semiconductor models used in electric circuit simulation. Before starting to look for suitable models, the following question must always be answered: What properties does my model have to have to meet the simulation task at hand?

• Analysis of the circuit operating principle: Ideal switch models
• Determination of losses and temperatures: Static models and state models
• Examination of individual switching processes: Physical model of semiconductor and behavior models

### Static semiconductor models

Static models are switch models to which a static characteristic can be assigned. Triggering is done via logic signals. These models are suitable for analyzing circuit operating principles and calculating losses in low-frequency circuits (e.g. line rectifiers). The forward characteristic of a semiconductor is typically:

• Line approximation
• Exponential function (with series resistance)
• Tables with deposited measuring points

### State models

The online simulation tool SemiSel can be used to perform simple power dissipation and temperature calculations. If necessary, however, state models can simply be generated using the data provided in the datasheets. These models use static characteristics and equations or "look-up tables" for switching losses and switching times. They are suitable for all simulation tools that are compatible with state graphs , , . These models are not suitable for examining switching processes; they have ideal switching edges, which is why no parasitic inductances may be factored into the simulation circuit.

Figure 1. Semiconductor modeling using state models; a) State description; b) Electric equivalent circuit

A model such as this comprises an "ideal" switch with a logic drive signal ("Gate"=1/0 in Figure 1), for which the power dissipation is calculated in 4 different states. In the example shown, the states (shown as circles) are given as IGBT switching states. If a transition (line) applies, e.g. if the signal "Gate = 1" is set, the marked, active state moves to the next state. In the example here, the marker would move from "Blocking" to "Turn-on". During this state, switching losses are caused; here, turn-on losses for the IGBT and turn-off losses for the diode. After a delay time ton, the marker moves to the next state - "Conducting" - where conducting losses occur. These losses are continuously calculated from the circuit current and the on-state voltage of the IGBT. The on-state voltage can be stored in the form of a characteristic or using a line approximation or assigned to the component. If the driver signal is set to "0", the component goes over to "Turn-off" state, in which turn-off losses occur. After a delay time toff, the IGBT goes back to the original state - "Blocking" - where the conducting losses of the diode are calculated. This completes the switching cycle. The switching losses can likewise be stored as a characteristic and read out for the current switching parameters. For simple cases, the equations for switching energies given in "IGBT and Diode Switching Loss Calculation" are used, since the junction temperature and DC link voltage dependencies are not available in the datasheet as characteristics.

Figure 2. Example of dependency of switching losses on IC, Tj, and VCC

Current sources in the thermal equivalent circuits can then be fed with the calculated losses (Figure 3). The resistances correspond with the Rth values of the thermal impedances. The capacitances are calculated from Cth = t/Rth. The temperature is then fed back to the switching parameters and affects the switching losses and on-state voltage of the models. For the PWM inverter, it suffices to calculate the losses and temperatures for one IGBT and one diode; this is owing to the symmetry here.

Figure 3. Thermal equivalent circuit and example of calculated temperature characteristic of a PWM inverter with 2 Hz output frequency

### Physical models of semiconductor and behavior models

Both model types claim to provide a realistic picture of the switching behavior in dependence of the driver and load conditions. They are highly suitable for investigating individual switching processes. Owing to the differences in time scale (some 10-9s for a single switching process ↔ heating in 100s), these models are not suitable for simulating heat build-up. Even just a few periods of a converter output frequency require substantial calculation time.

While physical models draw upon equations used in semiconductor physics, behavior models describe the semiconductors more like a blackbox would. Combined forms are feasible for use in any increments. For the physics-based semiconductor models, the main problem lies in the fact that the parameters are difficult to obtain, meaning that these models are ultimately not very practical for users. They do, however, offer the advantage that they provide valid results across a broad operating range. Behavior models are more easily parameterized with datasheet values and measured switching processes; one shortcoming here, however, is that they are often applicable to a limited range only. Both models, however, confirm that switching behavior is essentially determined by parasitic elements (LS) in the semiconductor environment. The merit of the given model can therefore only be assessed on the basis of how easily elements of the packaging can be included in the model.

An example of a behavior model is shown in Figure 4 . The static behavior is simulated using two characteristics: saturation characteristic and the transfer characteristic. The saturation characteristic is assigned to diode D1 and causes the voltage drop VCE = f(IC). The transfer characteristic controls the current source parallel to D2 in dependence of the applied gate voltage. The current in the IGBT rises and falls in line with the charge and discharge of the gate-emitter capacitance CGE via the gate. The most important element when modeling the dynamic behavior is the non-linear Miller capacitance which ensures feedback of the collector-emitter voltage to the gate.

Figure 4. Example of an IGBT behavior model with equivalent circuit elements 

The models can be optimized for certain operating points to ensure that they correctly model switching times and losses. They do not, however, sufficiently describe the switching properties for any given switching condition to malfunction/failure, meaning that the amount of time and work that goes into producing these models is by no means justified. What is more, no adapted models exist for latest-generation Trench IGBT, despite the fact that the switching behavior of these components differs greatly from that of the predecessor NPT-IGBT generation.

References:

 SIMPLORER® www.ansoft.com
 PLECS® www.plexim.com
 Wintrich, A.: "Verhaltensmodellierung von Leistungshalbleitern für den rechnergestützten Entwurf leistungselektronischer Schaltungen", diss., TU Chemnitz, 1996; http://archiv.tu-chemnitz.de/pub/1998/0023/data/inhalt.htm

IGBT and Diode Switching Loss Calculation

Power Module Junction Temperature Calculation

Thermal Modeling of Power Module Cooling Systems

Modeling of Temperature Dependence of Power Semiconductor I-V Curves

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## One Response

1. Lutz Zacharias says:

Der Stil des Verfassers (welcher mir im Übrigen nicht gänzlich unbekannt erscheint...), bringt die im Beitrag behandelte komplexe Thematik, sehr gut aufbereitet + sehr anschaulich an das Fachpublikum.

Vielen Dank.

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