.BondLib.Electrical.Analog.Spice.Utilities.Cj

Information

The Spice-style junction capacitance computes both the depletion capacitance value and the diffusion capacitance value of a junction used in a bipolar transistor. Different Spice dialects vary in the formulae they use for this purpose. Many Spice dialects actually don't use a formula for the junction capacitance at all, but rather compute the electric charge stored in the junction directly, which is conceptually cleaner. However, that approach is computationally cumbersome, as it leads to an awkward algebraic loop [1]. Thus, we chose to compute the junction capacitance, and use a (physically incorrect) approximate non-linear capacitor model (just as in the case of the simpler Ebers-Moll model). The numerical error should remain small, as the time constants associated with temperature change are much larger than those associated with electrical phenomena.

This particular model uses the space charge formula advocated in [2]. Since:

f = der(q)

the space charge, q, was symbolically differentiated. In the differentiation, only electrical signals, i.e., the voltage, e, were considered time-varying. The temperature gradients were assumed to be negligible. This produced an equation of the form:

f = C(e)*der(e)

which is the formula that was used to compute the non-linear capacitance C(e) in the model.

Notice that the junction capacitance assumes the function of the usually drawn junction diode. However in Spice, the so-called junction diode only carries the capacitive current. It computes the diodic current mathematically, but passes this information on as a modulating signal to the two non-linear current sources. Thus, the entire diodic (Ohmic) current really flows through the two non-linear current sources, which truly are non-linear resistors.

To reflect the mathematical reality of the model, a capacitor symbol was used to represent the junction capacitance in the icon layer. However, to make the circuit diagram look more familiar to Spice users, a diode was drawn as a shadow over the capacitance. 

Parameters:

 Is:      Transport saturation current (default value = 1e-16 Amp)

 EG:      Energy gap for temperature effect on saturation current (default value = 1.11 Volt)

 N:       Current emission coefficient (default value = 1)

 XTI:     Saturation current temperature exponent (default value = 3)

 CJ:      Zero-bias depletion capacitance at reference temperature (default value = 0.5e-12 F)

 MJ:      Junction grading coefficient (default value = 0.333)

 VJ:      Built-in potential at reference temperature (default value = 0.75 Volt)

 XCJ:     Fraction of base-collector depletion capacitance connected to internal base node (default value = 1)

 FC:      Depletion capacitance factor for linearization (default value = 0.5)

 Tau:     Ideal transit time (default value = 1e-9 sec)

 GminDC:  Leakage conductance (default value = 1e-15 Mho)

 Area:    Relative area occupied by the diode (default value = 1)

 Level:   Transistor modeling level (Ebers-Moll = 1; Gummel-Poon = 2) (default value = 2)

 BE:      True if base-emitter junction (default value = true)

 EMin:    if x < EMin, the exp(x) function is linearized (default value = -100)

 EMax:    if x > EMax, the exp(x) function is linearized (default value = 40)

References:

  1. Cellier, F.E. (1991), Continuous System Modeling, Springer-Verlag, New York, pp. 224-225.
  2. Massobrio, G. and P. Antognetti (1993), Semiconductor Device Modeling with Spice, 2nd edition, McGraw Hill, New York, p.69.
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