6.7. PROBLEMS 291
Calculate the collector current in the active mode with an applied emitter base bias of
0.5 V. What is the collector current when the base current is now increased by 20%?
Problem 6.3An Sinpntransistor at 300 K has an area of 1 mm^2 , base width of 1.0μm,
and doping ofNde=10^18 cm−^3 ,Nab=10^17 cm−^3 ,Ndc=10^16 cm−^3. The minority
carrier lifetimes areτE=10−^7 =τB;τC=10−^6 s. Calculate the collector current in the
active mode for (a)VBE=0.5V,(b)IE=2. 5 mA, and (c)IB=5μA. The base diffusion
coefficient isDb=20cm^2 s−^1.
Problem 6.4Annpnsilicon transistor is operated in the inverse active mode (i.e.,
collector-base is forward biased and emitter base is reverse biased). The doping
concentrations areNde=10^18 cm−^3 ;Nab=10^17 cm−^3 ,andNdc=10^16 cm−^3 .The
voltages areVBE=−2V,VBC= 0.6 V. Calculate and plot the minority carrier distribution
in the device. Also calculate the current in the collector and the emitter. The device
parameters are:Wb=1. 0 μm,τE=τB=τC=10−^7 s,Db=20cm^2 s−^1 ,De=
10 cm^2 s−^1 ,Dc=25cm^2 s−^1 ,A=1mm^2.
Problem 6.5Calculate the error made in the emitter efficiency expression (i.e., equation
6.4.7 versus equation 6.4.6) when one makes the approximation given in the text for tanh.
Obtain the error as a function of the ratio ofLbtoWbn.
Problem 6.6Plot the dependence of the base transport factor in a bipolar transistor as a
function ofWb/Lbover the range 10 −^2 ≤Wb/Lb≤ 10. Assume that the emitter
efficiency is unity. How does the common-emitter current gain vary over the same range of
Wb/Lb?
Problem 6.7In annpnbipolar transistor, calculate and plot the dependence of the emitter
efficiency on the ratio ofNab/Ndein the range 10 −^2 ≤Nab/Nde≤ 1. Calculate the
results for the cases: (a)De=Db,Le=Lb,Wb=Lb,and(b)
De=0. 2 Db,Le=0. 2 Lb,Wb=0. 1 Lb.
Problem 6.8In a uniformly dopednpnbipolar transistor, the following current values are
measured (see figure 6.6 for the current definitions):
IEn =1.2mA IEp=0.1mA
IC=InC =1.19 mA IRBE=0.1mA
Determine the parametersα, β, γefor the transistor.
Problem 6.9Consider annpnbipolar transistor at 300 K with the following parameters:
Nde=5× 1018 s; Nab=5× 1016 cm−^3 ; Ndc=10^15 cm−^3
De=10cm^2 s; Db=15cm^2 s; Dc=20cm^2 s
τE =10−^8 s; τB =10−^7 s; τC =10−^6 s
Wb=1. 0 μm; A=0.1mm^2
Calculate the emitter current and the collector current as well as the values ofα, γe,βfor
VBE=0.6V;VCE=5V.
