6.7. PROBLEMS 293
Problem 6.16Consider annpnsilicon bipolar transistor in which
Wb=2. 0 μm,Le=Lb=10. 0 μm, andDe=Db=10cm^2 s−^1. Assume that
Nab=10^16 cm−^3. What is the emitter injection efficiency forNde=10^18 , 1019 and 1020
cm−^3 when (a) bandgap narrowing is neglected, (b) bandgap narrowing is included?
Problem 6.17A siliconnpnbipolar transistor is to be designed so that the emitter
injection efficiency at 300 K isγe= 0.995. The base width is 0.5μmand
Le=10Wb,De=Db,andNde=10^19 cm−^3. Calculate the base doping required with
and without bandgap narrowing effects.
Problem 6.18Consider a GaAs/AlGaAs HBT in which an injector efficiency of 0.999 is
required at 300 K. The emitter and base doping are both 1018 cm−^3. The base width is 0.1
μm. The carrier diffusion coefficients areDb=60cm^2 s, andDe=20cm^2 s. The carrier
lifetimes areτB=τE=10−^8 s. Calculate the Al fraction needed in the emitter of the
HBT.
Problem 6.19Due to the high base doping possible, the base of an HBT can be very
narrow. Consider a GaAs/AlGaAs HBT where the GaAs base is 500A. The minority ̊
charge diffusion coefficient is 100 cm^2 /V·s in the base. Calculate the base transit time
limited cutoff frequency of this device.
Problem 6.20Consider ann-p-nbipolar transistor where the base is graded from
Al 0. 04 Ga 0. 96 As at the emitter end to GaAs at the collector end. The emitter material is
Al 0. 22 Ga 0. 78 AsanditisgradedtoAl 0. 04 Ga 0. 96 As at the base.
(a) Sketch the detailed band diagram of the HBT in equilibrium, and under forward active
bias. What is the quasi-electric field,Equasi,B, in the base?
(b) Solve the drift-diffusion equation to obtain an expression for the base minority carrier
concentration,n(x), in terms of the total currentJC,Equasi,B,andWB. Assumeμ=
1000 cm^2 /Vs.
Problem 6.21Due to an error during growth, the emitter-base grade in the transistor
shown in the figure 6.25 below was started after the emitter n-type dopant cell shutter was
opened. As a result, there was a thin n-type GaAs region between the p-type base and the
grade.
- Construct the equilibrium band diagram of this structure taking into account quasi-
electric and electrostatic fields. What is theβof this transistor at zero emitter-base
bias?
- Now, the transistor is operated under high-injection conditions. If an emitter-base
bias of 1V is applied, how will theβbe affected? Draw field and potential profiles to
explain your result.
