Analog Simulation:SPICE Transistor models

SPICE Transistor models

The main problem when simulating electronic circuits lies in the modeling of semiconductor circuit elements, especially transistors. One tries to map as precisely as possible the real circuit to the computer in order to avoid a very cost-intensive redesign of the integrated circuit. For this purpose it is not sufficient to signify a BJT by its current gain only or a MOSFET by its threshold voltage, but a lot of model parameters have to be used in order to catch the static, dynamic, and temperature behavior of transistors. The manufacturing companies of transistors or integrated circuits provide model parameters of the transistors produced or used, respectively, so by calling a transistor model by its component name much hidden information is activated. It is unsatisfactory for the users to apply these models without knowing the physical meaning of the different model parameters. There are, of course, many references in which the transistor model parameters are explained in detail (e.g., [10.8]). It does not make sense to repeat here all the details of transistor modeling, and in order to convey a fundamental idea of the complex topic the following effects will be omitted:

• Temperature effects;

• Bulk resistance effects;

• Dynamic effects (all transistor capacitances are assumed 0).

The last assumption is justified by technological progress. Transistor capacitances are nowadays of the order of fF, the capacitances of the connection lines on a chip are at least of the same order of magnitude. Therefore the dynamic behavior, i.e., mainly the delay, for digital circuits is nearly totally determined by the connections.

The following discussion is restricted to the Bipolar Junction Transistor (BJT) and the Metal oxide Field Effect Transistor (MOSFET) because these transistors are most important for modern inte- grated circuits. BJT and MOSFET will be introduced by using default model parameters in the evaluation version of PSPICE [10.5]. Even in the first version of SPICE sensible default parameters were inserted in case the user did not or could not specify parameters and thus the elementary properties of the transistor were correctly simulated. For illustration purposes the large signal equivalent circuit using the default parameters is shown. From that the small signal equivalent circuit is derived by differentiation at the operating point, because the latter is important for analog circuit design. The influence of a selected model parameter on the static behavior of transistors will be discussed. Dealing with MOSFETs the industrial standard BSIM3v3-model will be discussed by its characteristics and by its small signal parameters.

Figure 10.8 shows the equivalent circuit for an npn transistor without capacitors and bulk resistances. Table 10.2 shows a list of respective static model parameters, SPICE names and SPICE default values [10.8]. The most important element in fig. 10.8 is the collector current source which is controlled by two diode currents:

describes the increase of the charge of majority carriers in the base zone resulting from high current injection with which a decrease of current gain for high currents is associated. For small voltages and currents (Q2 « 1) one finds Q1 ≈ 1 and QB ≈ 1.

A glimpse at the SPICE default values shows that apparently only a few parameters are necessary If the reverse current gain BR is neglected the simple large signal equivalent circuit for the active (forward) operation is found (fig. 10.9). Figure shows a circuit which allows determination of the family of characteristics IC = f (VCE) with IB as parameter.

The result is displayed in fig. 10.11. One can easily realize the forward current gain BF = 100 (SPICE default value) in the active region. Because of the default value BR = 1 for the reverse current gain the family of characteristics for negative collector emitter voltages are degenerated to a thick line.

Discussion of the Early Effect (Parameter VAF)

Figure 10.12 shows the equivalent circuit of an npn transistor in forward operation taking into account the Early voltage VAF of the BC diode.

Figure 10.13 shows the family of characteristics with VAF = 10 V. This low value was chosen in order to make the Early effect conspicuous. Usually transistors have Early voltages in the order of 80 ... 120 V. From fig. 10.13 one realizes that the extension of the spread family of characteristics intersect approximately at the point (−10 V, 0 A). The Early effect has to be taken into account when dealing with analog circuits as it causes the finite output resistance of a transistor.

Figure 10.14 shows the small signal equivalent circuit corresponding to fig. 10.12. For the operational point A it is found

These equations show the difference between the model parameter BF and the current gain βDC or βAC respectively. When taking the Early effect into account BF = βDC = βAC is only valid for small values of VCE. Table 10.3 shows the small signal parameters determined by PSPICE for the operating point IBA = 300 μA, VCEA = 5 V. Inserting the model parameters VT = 25.85 mV, VAF = 10 V, nF = 1, BF = 100 into the equation above, the numerical values of the small signal parameters in table 10.3 can be verified.

Consideration of low current effects and high current injection

Figure 10.15 shows the output family of characteristics of an npn transistor with the Early effect neglected but taking into account the high current injection (IKF = 10 mA). Comparing with fig.

one realizes that the current gain decreases

Fig. 10.14 Small signal equivalent circuit of the npn transistor (with Early effect) From fig. 10.12 and equation (10.4) there is found with increasing collector current. The condition will be discussed in detail by means of fig. 10.16 which shows the so called Gummel Plot.

source in fig. 10.10 was replaced by a voltage source with a voltage varying between 0.1 V and 1 V. The resulting base and collector current of the transistor are displayed on a logarithmic scale, the chosen model parameters for the transistor are two last parameters describe an extreme nonlinear diode which models the additional base current caused by recombination of carriers. The asymp- totes shown in fig. 10.16 result from equations (10.4) and (10.6). The following paragraph dis- cusses the current gain of the BJT which is not defined precisely.

From fig. 10.16 one observes that the model parameter BF (forward current gain) describes a constant relation between collector and base current only in a very restricted range which becomes even smaller for modern transistors. With higher collector currents the exponential character is lost owing to high current injection, with lower base currents the constant relation to the collector current is lost owing to recombination. Figure 10.17 shows the DC current gain β DC = iC/iB as a function of iC.

This diagram was generated by means of PROBE, the graphical output program of PSPICE, using the same analysis values as in fig. 10.16. The asymptotic approximations were taken from [10.8].

Figure 10.17 shows how doubtful it is to signify a BJT by a single value for the current gain. Table 10.4 shows the parameters for the operating point VBEA = 0.7 V, VCEA = 5 V. Figure 10.18 shows βDC and βAC as a function for iB of the transis- tor analyzed in fig. 10.16. The small signal current gain βAC is calculated according to equation (10.14) by differentiation of iC with respect to iB. The cursor signifies the values of β DC and βAC for the operating point, which are consistent with the values shown in table 10.4.

MOSFET

There are several MOSFET models to be called up in SPICE. The parameter LEVEL signifies the kind of model to be applied [10.8]:

• LEVEL = 1 (Default value) signifies the physical ‘first order model’ (SHICHMAN, HODGES);

• LEVEL = 2 signifies an extended physical model with additional equations and parameters mainly in order to take care of the effects caused by short channel length;

• LEVEL = 3 signifies a semi-empirical model with parameters determined by adaptation to measured values. It is almost as powerful as LEVEL 2 but needs up to 40 % less computer time;

• LEVEL = 4, 5, 6 signify today outdated inter- mediate versions of models for better simulation of submicron technology effects;

• LEVEL = 7 signifies the industrial standard model of today: BSIM3v3 model [10.3]. It is a physical model. By means of a pseudo- 2D description of the MOSFET the following effects can be taken into account:

– Reduction of threshold voltage;

– Non-uniform doping

– Reduction of carrier mobility caused by cross field

– Bulk effect

– Saturation of carrier velocity

– Drain induced lowering of barrier

– Channel length modulation

– Reduction of output resistance caused by ‘hot’ carriers

– Conduction in the region below threshold voltage

– Parasitic resistances at source and drain.

First, the ‘First Order Model’ (LEVEL = 1) will be discussed in its static behavior. Starting from the default model the influence of channel length modulation and bulk voltage will be shown by simulated characteristics. The simulation of characteristics serves also as access to the BSIM3v3 model which in its default version is simply called up by input of the parameter LEVEL = 7. In order to characterize a MOSFET geometry the parameters can be directly assigned to the single transistor, whereas the electrical parameters have to be listed in the model’s description. With this arrangement it is possible to characterize transistors with different geometries, but which are manufactured in the same process, by defining only one set of model parameters. Figure 10.19 serves as an explanation of the different geometrical parameters, which are used in the following equations. The parameters AD, AS, PD, PS are only necessary to determine capacitances [10.6]. As only static behavior will be discussed here they will not be taken into account any more.

Figure 10.20 shows the static large signal equivalent circuit of n-channel MOSFET. Table 10.5 lists the static parameter of the MOSFET model (LEVEL = 1).

The following equations describe the DC behavior of an n-channel MOSFET. For the p-channel MOSFET SPICE automatically alters the signs accordingly.

Default MOSFET

Figure 10.21 shows a circuit which serves for simulation of different characteristics. Figure 10.22 shows the family of characteristics. ID = f (VDS) of a default n-channel MOSFET, fig. 10.23 shows the control characteristic ID = f (VGS) and its differential quotient the linearity of which shows the quadratic character of the control characteristic.

Table 10.6 lists the model parameter of the default n-channel MOSFET from the OUTPUT file generated when simulating the circuit in fig. 10.21. Note that W = L = 100 μm is automatically set (default values).

The same characteristics as before will be dis- cussed in order to show the differences to the LEVEL 1 model. Figure 10.28 shows the output characteristics for VGS = 3 V and the differential output resistance. The latter is (when dealing with the BSIM3v3 model, according to [10.8]) deter- mined not only by channel length modulation but also by drain-induced lowering of barrier and bulk effect. The latter causes the exponential increase of

the output characteristic with higher drain currents and therefore the lowering of the output resistance. Figure 10.29 shows the control characteristic and the corresponding differential quotient which is now not linear. Therefore one does not find a purely quadratic control characteristic anylonger, as with the LEVEL 1 model. Figure 10.30 shows the influence of the bulk voltage on the drain cur- rent and the corresponding differential quotient

Table 10.10 lists operating point and small signal parameter values which are marked by the cursor in the characteristics discussed above. One finds satisfactory correspondence. The small signal behavior is also described by the small signal equivalent circuit shown in fig. 10.27 whereas the small signal parameters of the BSIM3v3 model are determined in a much more complicated way, as before.