389
Bipolar Junction Transistor Compact Models
where:
C jE0 is the EB-junction capacitance per unit area at V B′E′ = 0
m jE is the doping gradient coefficient
f BE is the EB-junction built-in potential that depends on the
base doping concentration N B and emitter doping concentration, N E
We can show from Equation 2.109
φ BE
kT
B E
i
v
N N
n
=
ln
2
(11.36)
where:
N B = N a (acceptor concentration)
N E = N d (donor concentration) for npn-BJTs.
Similarly, the CB-junction capacitance due to V BC is given by
C V
C
V
JC
BC
jC
B C
BC
mjC
( )= + (
)
′ ′
0
1
φ
(11.37)
where:
C jC0 is the CB-junction capacitance per unit area at V B′C′ = 0
f BC is the CB built-in potential that depends on base doping concentration N B and collector doping concentration, N C
and is given by
φ BC
B C
i
v
N N
n
=
kT ln
2
(11.38)
where:
N B = N a (acceptor concentration)
N C = N d (donor concentration) for npn-BJTs
• Effect of diffusion capacitances: The transition of injected minority carrier charge determines the speed of the transistor. The
injected minority carriers from the emitter diffuse through the
(1) EB-junction space-charge region, (2) neutral base region, and
(3) CB-junction space-charge region. Thus, we consider three diffusion capacitances for forward injection and three for reverse
injection.
Let us consider the capacitance effect due to the injected charge
in the EB space-charge layer as shown in Figure 11.17. Let us define
Q E , Q BE , Q B , and Q BC as the components of the total diffusion charge
Q DE in the emitter, EB-junction space-charge layer, neutral base,
and CB-junction depletion regions, respectively. If τ Fdc is the total
Bipolar Junction Transistor Compact Models
where:
C jE0 is the EB-junction capacitance per unit area at V B′E′ = 0
m jE is the doping gradient coefficient
f BE is the EB-junction built-in potential that depends on the
base doping concentration N B and emitter doping concentration, N E
We can show from Equation 2.109
φ BE
kT
B E
i
v
N N
n
=
ln
2
(11.36)
where:
N B = N a (acceptor concentration)
N E = N d (donor concentration) for npn-BJTs.
Similarly, the CB-junction capacitance due to V BC is given by
C V
C
V
JC
BC
jC
B C
BC
mjC
( )= + (
)
′ ′
0
1
φ
(11.37)
where:
C jC0 is the CB-junction capacitance per unit area at V B′C′ = 0
f BC is the CB built-in potential that depends on base doping concentration N B and collector doping concentration, N C
and is given by
φ BC
B C
i
v
N N
n
=
kT ln
2
(11.38)
where:
N B = N a (acceptor concentration)
N C = N d (donor concentration) for npn-BJTs
• Effect of diffusion capacitances: The transition of injected minority carrier charge determines the speed of the transistor. The
injected minority carriers from the emitter diffuse through the
(1) EB-junction space-charge region, (2) neutral base region, and
(3) CB-junction space-charge region. Thus, we consider three diffusion capacitances for forward injection and three for reverse
injection.
Let us consider the capacitance effect due to the injected charge
in the EB space-charge layer as shown in Figure 11.17. Let us define
Q E , Q BE , Q B , and Q BC as the components of the total diffusion charge
Q DE in the emitter, EB-junction space-charge layer, neutral base,
and CB-junction depletion regions, respectively. If τ Fdc is the total