Please do and/or note the following:

• Do all seven problems.

• Unless you show work in the derivations and solutions you will get no credit for the answers;

obviously copied answers from study partners, etc., will also receive no credit.

• **Make a copy of your homework before you turn it in **as it may not be returned before

the fourth midterm exam on November 30, although solutions will be posted.

Problem #1

i) A silicon pnp BJT with NE = 5 x 1017/cm3, NB = 1017/cm3, NC = 5 x 1014/cm3, and WB = 3 μm is in

thermal equilibrium at 300K. Please note that by WB (metallurgical base width) we mean the portion of

the base that is neutral (0 to xB) plus the portions of the EBJ and CBJ depletion regions that lie in the ntype

base (in other words, the as-fabricated base width).

a) sketch the energy band diagram for the device, properly positioning the Fermi level (hint: with

respect to Efi) in the three device regions (E,B,C)

b) find Vbi for both the EBJ and CBJ

c) find the depletion region widths (the parts that lie in the n-type base) for both the EBJ and CBJ

d) sketch the electrostatic potential, setting V=0 in the emitter region

e) sketch the electric field, calculating Emax in the EBJ and CBJ

f) roughly sketch (no numbers) the charge density as a function of position inside the BJT

g) determine xB

h) calculate the net potential difference between the collector and emitter

ii) Now let the BJT be biased as follows: VEB = 0.5V, and VCB = -2V.

a) sketch the energy diagram for the device, properly positioning the Fermi level (hint: with respect

to Efi) in the three device regions (E,B,C)

b) superimposed on the respective sketches completed in parts i)d),i)e),and i)f) above, sketch the

electrostatic potential, electric field, and charge density as a function of position inside the BJT.

Your sketches may be very rough (we are interested in qualitative change, not numbers here).

Problem #2

The base and emitter of a silicon npn bipolar junction transistor are uniformly doped at impurity

concentrations of NB = 1016/cm3, NE = 1018/cm3. A forward-biased VBE = 0.610V is applied. The neutral

base width is xB = 2 μm and the minority carrier diffusion length in the base is LB = 10 μm.

a) Calculate the excess minority carrier concentration in the base a: i) x=0 and b) x=xB/2.

b) Determine the ratio of the actual minority carrier concentration at x=xB/2 to that of the ideal

case of a liner minority carrier distribution.

Problem #3

An npn silicon BJT at T=300K has uniform dopings of NE = 1019/cm3, NB = 1017/cm3, and NC =

1016/cm3. The transistor is operating in inverse active mode with VBE = -2V and VBC = 0.565V. a)

Sketch the minority carrier distribution through the device and find the minority carrier concentrations at

x = xB and x’’=0; b) If the metallurgical base width is 1.2μm, determine the neutral base width.

Problem #4

A silicon npn transistor at T=300K has an area of 10-3 cm2; a neutral base width of 1 μm; doping

concentrations of NE = 1018/cm3, NB = 1017/cm3, NC = 1016/cm3; DB = 20 cm2/s, τB0 = τE0 = 10-7 s, and

τC0 = 10-6 s. Assuming that the transistor is biased in the forward active region, and the recombination

factor is unity, calculate the collector current for: a) VBE = 0.5V (you may need to estimate); b) IE = 1.5

mA; c) IB = 2 μA.

Problem #5

Consider an npn silicon BJT at T=300K with the following parameters: DB = 25 cm2/s, DE = 10 cm2/s,

τB0 = 10-7 s, τE0 = 5 x 10-8 s, NB = 1016/cm3, xE = 0.5μm. The recombination factor has been determined

to be 0.998. We need a common emitter current gain of β = 120. Letting αT = γ, determine the minimum

neutral base width and the minimum emitter doping to achieve this specification.

Problem #6

An npn silicon BJT at 300K has NB = 1017/cm3, NC = 1016/cm3, metallurgical base width of 1.1 μm, DB =

20 cm2/s, and base-emitter cross-sectional area of = 10-4 cm2. The transistor is biased forward active

with VBE = 0.6V. Determine:

a) The change in neutral base width as VCB changes from 1 to 5V.

b) The corresponding change in collector current.

c) Estimate the Early voltage.

d) Find the output resistance.

Problem #7

A high voltage silicon npn BJT is t be designed such that the uniform base doping is NB = 1016 /cm3 and

the common-emitter current gain is 50. The breakdown voltage is to be at least 60V. Determine the

maximum collector doping and the minimum collector length to support this voltage. Let n=3.