The Bipolar Transistor

• Switching Time:

• We analyze the case in which the transistor is initially on, V ₀ > V _BE(on) and in the forward-active mode, and then turns off at t=0.
• This situation is similar to the diode case, which occurs in 2 phases.
• Phase I:
• The base charge is removed, turning the transistor off.
• The base-emitter voltage remains relatively constant.
• Phase II:
• The base-emitter voltage drops to zero.
• The junction capacitances are discharged.

The Bipolar Transistor

• Switching Time, Phase I:
• Before time t = 0, the excess minority carrier change in the base equals:

• I _C is expressed by the following formula:

• We can assume that the base-emitter voltage remains constant and is ~= V _BE(on) .
• The space charge of the be and bc junctions is constant over this interval.

 

• The length of this interval is defined by the time it takes to remove the base charge.
• The base current that accomplishes this is:

The Bipolar Transistor

• Switching Time, Phase I:
• This current actually serves two purposes:
• To sustain the recombination in the base .
• To remove the base charge.

 

• Solving for Q _F (t) by taking the initial condition for Q _F into account:

 

• The time to remove the excess charge, e.g. when Q _F = 0.

The Bipolar Transistor

• Switching Time, Phase I:
• The recombination current in (1) is often small compared to I _B and can be ignored.
• Therefore, we can assume all base current is used to remove base-charge yielding:

• Note that C _D is the large-signal equivalent capacitance defined over the range delta V.
• Therefore, if recombination is ignored, it is a simple RC.

 

• Switching Time, Phase II:
• Once the transistor is off, the rest of the transient is devoted to discharging the junction capacitances to 0 volts.

• This first-order RC time const. gives time to reach 90% of the final value.

The Bipolar Transistor

• Example:

• First compute the initial values of the currents.
• Since V _CE is 2V, the transistor is in forward-active.
• The base current is:

• After switching the input, the base current changes direction:

The Bipolar Transistor

• Example:
• The time to remove the base charge is:

• Alternatively, using the simplified expression:

 

• The circuit behaves like an RC-equivalent network during the space-charge removal.

 

• In order to compute the time constant, it is necessary to first linearize the junction capacitances over the voltage range of interest.

The Bipolar Transistor

• Example:
• The collector voltage (2V) remains fixed during the switch, so C _bc can be modeled as a grounded capacitor.
• The V _be decreases from 0.75 to 0 V while V _bc increases from 1.25 to 2 V.
• Therefore, K _eq(be) :

• And K _eq(bc) is 0.68 .
• The value of t _depl is:

• This is quite a bit larger than the base-charge removal period.

The Bipolar Transistor

• Example:
• Spice validation:

• During the removal of the base charge, the collector current rapidly decreases.
• Then the transistor goes into cut-off and the base-emitter voltage decays.

The Actual Bipolar Transistor

• Second Order Effects, The Early Voltage:
• In the analysis of forward-active, we stated that the base-collector junction was reverse-biased and had no effect on the collector current.

• This held true because we ignored the width of the depletion region in computing the width of the base region, e.g. we set W = W _B .
• It becomes more important to consider this as W is reduced.

 

• Furthermore, increasing the collector base voltage, increases the reverse bias and the width of the depletion regions.

 

• This reduces the base width and reduces the forward transit time t _F and raises the collector current.

 

• Therefore, collector current increases as a function of collector voltage.

The Actual Bipolar Transistor

• Second Order Effects, The Early Voltage:

• The point of intersection to the V _CE -axis of all extrapolated curves is the early voltage, V _A , which varies in integrated circuits from 15 to 100 V.
• The inverse of the early voltage is analogous to the channel-length modulation parameter , l , in MOS transistors.
• It is accounted for as:

The Actual Bipolar Transistor

• Second Order Effects, Breakdown Voltages:
• The mechanism of avalanche breakdown in a pn -junction was described previously.
• Breakdown can occur at the be and bc junctions in bipolar transistors, which limits the voltages that can be applied to a device.

 

• The breakdown voltages depend on the configuration and are commonly expressed as:
• BV _CBO : Common base configuration breakdown voltage (10s of V).
• V _CE0 : Common emitter configuration.
• BV _EBO : Base-emitter breakdown voltage (6-8Vs).

The Actual Bipolar Transistor

• Second Order Effects, Parasitic Resistances:

 

• The collector resistance consists of three components: r _C1 , r _C2 and r _C3 .
• r _C3 tends to be the dominant component.

 

• It is reduced from 1k W to 20 W in advanced processes using n ⁺ to create a deep collector .

The Actual Bipolar Transistor

• Second Order Effects, Parasitic Resistances
• The value of r _B ranges from 50 to 500 W s.
• Unfortunately, it varies with collector current due to current crowding .
• This effect varies the distance between the active base region and the base contact.

 

• These resistances play a more significant role for higher collector currents.
• The R _s cause voltage drops that reduce the voltages on internal device terminals, and therefore, device currents.

 

• In order to obtain simulation results that reflect the hardware, these resistances need to be carefully modeled or reduced.

 

• Increasing the emitter area and providing multiple base and emitter terminals are methods of reducing their effect.

The Actual Bipolar Transistor

• Second Order Effects, b _F Variations
• Our ideal model predicts b _F as a constant, which it is not:

• For intermediate value of V _BE , the value of b _F is constant.

 

• However:
• At low V _BE values:
• The recombination of carriers in the be depletion region increases base current and reduces gain.

The Actual Bipolar Transistor

• Second Order Effects, b _F Variations
• At high V _BE values:
• The injected minority carrier density in the base approaches the majority density, and the hole current from base to emitter increases significantly, reducing collector current.

 

• The Kirk effect (or base stretching into the collector region) also reduces gain at high injection levels.

 

• These effects can be modeled by modulating the emission coefficient n in the base and collector currents:

• For example, the high injection effect is modeled by modifying n from the standard value of 1 to 2 .

Bipolar SPICE Models

• Early versions of SPICE supported two separate models:
• Ebers-Moll (E-M).
• Gummel-Poon (G-P).

 

• These have been merged into modified Gummel-Poon .
• This model incorporates extensions to handle the high-bias conditions.
• The complete SPICE model is shown below:

Bipolar SPICE Models

• Under normal operating conditions, the values of the current sources are given by the modified Ebers-Moll equations:

• The model superimposes the forward and reverse-operation conditions.

 

• The base-width modulation factor is incorporated in the collector current through the early voltage, V _A .

Bipolar SPICE Models

• This model does not take into account second-order effects occurring at low current levels or high injection levels.
• Use the Gummel-Poon model.

 

• Q _BE and Q _BC represent the combined effects of the depletion and base charge for the be and the bc junctions.

Bipolar SPICE Models

Parameter Name	Symbol	SPICE name	Units	Default Value
Transport Saturation Current	IS	IS	A	1.0E-016
Maximum Forward Current Gain	bF	BF	-	100
Forward Current-Emission Coeff.	nF	NF	-	1
Forward Early Voltage	VAF	VAF	V	inf
Maximum Reverse Current Gain	bF	BR	-	1
Reverse Current-Emission Coef	nR	NR	-	1
Reverse Early Voltage	VAR	VAR	V	inf
Corner for Forward Beta High-Current Roll-off (1)	IKF	IKF	A	inf
be Junction Leakage Sat. Current (1)		ISE	A	1.0E-13
be Junction Leakage Emission Coeff. (low-current condition) (1)		NE	-	1.5
Corner for Reverse Beta High Current Roll-off (1)	IKR	IKR	A	inf
bc Junction Leakage Sat. Current (1)		NC	A	1.0E-13
bc Junction Leakage Emission Coeff. (low-current condition) (1)		NC	-	2
Ideal Forward Transit Time	tF	TF	sec	0
Ideal Reverse Transit Time	tR	TR	sec	0

Bipolar SPICE Models

Parameter Name	Symbol	SPICE name	Units	Default Value
Emitter Resistance	rE	RE	Ohms	0
Collector Resistance	rC	RC	Ohms	0
Zero-Bias Base Resistance	rB	RB	Ohms	0
Minimum Base Resistance		RBM	Ohms	RB
Current where RB fall halfway to RBM		IRB	A	inf
Zero-Bias be-Junction Capacitance	Cbe0	CJE	F	0
be-Junction Grading Coeff.	mbe	MJE	-	0.33
be-Junction Built-in Voltage	fbe	VJE	V	0.75
Zero-Bias bc-Junction Capacitance	Cbc0	CJC	F	0
bc-Junction Grading Coeff.	mbc	MJC	-	0.33
bc-Junction Built-in Voltage	fbc	VJC	V	0.75
Zero-Bias Collector-Substrate Cap.	Ccs0	CJS	F	0
cs-Junction Grading Coeff.	mcs	MJS	-	0
cs-Junction Built-in Voltage	fcs	VJS	V	0.75

• (1): Gummel-Poon Model Parameter

Bipolar SPICE Models

• There is only one individual transistor parameters for bipolar (unlike MOS).
• AREA factor: Determines how many bipolar junction transistors (of type MODNAME) are put in parallel.

 

• This is rarely used.
• More commonly, a different model is specified for every possible device dimension used in the design.
• This is acceptable since, unlike MOS, there are usually only a couple different size devices used.

• A 1.0 m m process bipolar transistor model: