6.7. PROBLEMS 295
Problem 6.27Consider anpnSi-BJT at 300 K with the following parameters:
Nde =10^18 cm−^3
Nab =10^17 cm−^3
Ndc =10^16 cm−^3
Db =30.0cm^2 s−^1
Lb =10. 0 μm
Wb =1. 0 μm
De =10cm^2 s−^1
Le =10. 0 μm
Emitter thickness = 1. 0 μm
Device area = 4. 0 × 10 −^6 cm^2
Calculate the emitter efficiency and gainβwhen the EBJ is forward biased at 1.0 V and the
BCJ is reverse biased at 5.0 V. Calculate the output conductance of the device defined by
go=
ΔIC
ΔVCB
Problem 6.28An important advance in Si bipolar transistors is the use of polysilicon
emitters. If a normal ohmic contact is made to an emitter, the injected minority density
goes to zero at the ohmic contact boundary. In polysilicon emitters, heavily doped
polysilicon forms the contact to the emitter. The minority density does not go to zero at the
polysilicon contact, but decreases to zero well inside it. This allows one to have very thin
emitter contacts for high-speed operation. Discuss the disadvantage of such a contact over
a normal ohmic contact in a thin emitter. (Consider the emitter efficiency and how it is
affected by a thin emitter by using the discussions in chapter 5 on the narrowp-ndiode.)
Problem 6.29Consider annpnBJT with a base width of 0.5μm and base doping of
1017 cm−^3. The hole mobility is 200 cm^2 /V·s. An emitter stripe of 25 μm× 100 μmis
placed to form the EBJ. If a base current of 100μA passes in the device and the EBJ is
forward biased at 0.7 V at the edge of the emitter,estimatethevalueoftheforwardbiasof
theEBJatthemiddleoftheemitter. Discuss the possible problems that the biasing
difference could cause. (Assume that the base current is flowing through an area 100 μm
× 0. 5 μm.)
Problem 6.30From our discussions of narrowp-ndiodes, the importance of the boundary
conditions imposed on the injected minority charge at the contact is quite obvious. We
have used the condition that the minority charge density goes to zero at the contact. This is
a reasonable approximation for the metal contact. One approach to defining the boundary
conditions at any interface is through the concept of a recombination velocity. The
recombination velocityvrecomis defined via the relation (say, for holes as minority charge)
Jp|boundary=evrecomδp|boundary
