EE212Spring2010HMW4

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EE212-SemiconductorDevicesandModeling

Spring2010-2011

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Homework IV (not to be collected)

Photodiodes, Solar Cells, LEDs

1.

a) Find the current, I, flowing through the following Si sample at T=500 K, if Vb = 0.5 V. Thesample is uniformly doped with donors at a density ofND=5x10

14cm-3, and acceptor doping

density is zero. The electric-field in the sample is constant between x=0 (where V=Vb) and x=L

(where V=0). Ignore the contribution of the holes to conductivity.

The temperature dependence of the low-field electron mobility in the above Si sample can be

approximated as

(cm2/V-sec) where T is the temperature in Kelvin.

b) Find the current, I, flowing through the above sample at T=300 K, if Vb= 30 V. Ignore the

contribution of holes to conductivity.

c) The above Si sample is used in the following configuration todetect light at T=300 K. Assume that the recombination

lifetimes, n=p= 1 sec and 300 K hole mobility is 400 cm2/V-

sec in the sample. Find the output voltage (Vout) under uniform

and continuous illumination of the sample, if 5x1019

electron-

hole pairs/cm3 are created optically every second (gop=5x1019

EHP/(cm3-sec)).You must derive the equation for steady-state

excess carrier concentrations starting from the balance between

generation and recombination (assume low level excitation).

Do not ignore the contribution of excess holes to conductivity.

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2. Which of the following statements is/are correct?

i) a nonzero current may flow through a short circuited p-n junction under illumination

ii) the open circuit voltage of a p-n junction under illumination depends on the energy bandgap of the

semiconductor

iii) a diode is typically used as a photo detector in the forward bias region

a) only i and iii b) only i and ii c) only i d) all of them e) only ii and iii

3. Consider the following biased p-n junction at steady-state. Under a bias voltage of V, as shown

below, the hole concentration at the edge of the depletion region in the n side is p neqV/kT

where pn is

the equilibrium hole concentration at the n-side. The excess carrier concentrations at the ohmic

contacts are zero. The junction cross-sectional area is A.

a) Ignore recombination and derive the expression for the hole diffusion current in the n-side and the

electron diffusion current in the p-side under dark conditions (no optical excitation) in terms of

equilibrium minority carrier concentrations and the other necessary parameters. Assume that W n >Ln , and the diode is illuminated with an optical excitation

rate of gop. Ignore optical excitation and recombination in the depletion region and derive the

expressions for the total current (I) and the photocurrent (IL) flowing through the junction under

illumination. Your result must reflect the above assumptions. Start from the continuity equation

or minority carrier diffusion equations, clearly show complete work, explain what you are doing

qualitatively (with words), and define the additional parameters used in your derivation.

4. A light source is incident on a long Si pn junction diode and generates an optical current density

of Jop = 25 mA/cm

2

. Calculate the induced open circuit voltage.

ND=1018

/cm3

NA=3x1016

/cm3 n=p=10

-7s Dn=18 cm

2/s Dp=6 cm

2/s

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Bipolar Junction Transistor (BJT)

5. The following figure displays the carrier and current flows in a BJT. Name the numbered (1-5)

flows and exchanges. Draw arrows pointing the current directions on the figure. What is theoperation (bias) region for this transistor?

6. Which one of the following does not belong to the three mechanisms for the base current of a

forward biased pnp transitor?

a) Electrons lost to recombination are supplied by the base contactb) Electrons injected into the collector junction are supplied by the generation in the basec) Electrons injected into the forward biased emitter junction are supplied by the base contactd) Thermally generated electrons in the collector are swept into the base by the reverse biased

collector junction

7. Fill in the blanks for the following sentences and drawings:

The two operational functions of transistors that form the basis for many electronics circuit

applications are . and .

For bipolar-transistors, a small control .is used to achieve large changes in the device ,

achieving amplification.

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In a good transistor the . current will be very small since emitter current is essentially

majority carrier current, and the ............... current is almost equal to the emitter current.

The proportionality factor between the majority carrier emitter current and collector current is called..

The ratio of the majority carrier emitter current and the total emitter current is called

.

Ratio of collector to emitter current is ..

Ratio of collector to base current is ..

Ratio of majority carrier lifetime to the base transit time is ..

In an npn BJT Emitter injects electrons into base region, almost all of them travel across narrow base

and are removed by .

Write the corresponding transistor operation regions on the graph

Base Transit Time places an upper limit on transistor operating .

The goal of biasing is to establish the . of the transistor.

The diffusion capacitance is directly proportional to the .. current and .... time.

Base-.. junction diode breakdown voltage is greater than base- junction diode

breakdown voltage.

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8. For the following questions, answer in one or two sentences.

(i) Why is the emitter doped more heavily than the base?(ii)The base width is small is often stated in device analysis. What is it being compared

with?

(iii)For a PNP device, indicate the voltage polarity (+ or -) for the following:

Region VEB VCB

Active

Saturation

9. An n-p-n BJT is biased in the forward active region (BE junction is forward biased and BC

junction is reverse biased) with IE=1 mA. The base transport factor of this BJT is equal to 0.98 and

the emitter injection efficiency is 0.95 . Ignore the contribution of thermally generated minority

carriers around the B-C depletion region to the terminal currents and find the collector and base

currents of this BJT.

10. Fill in the blanks of the following table to show whether the noted change in a BJT increases

(), decreases () orhas no significant effect (-) on the given BJT parameter.Change

Increase Base Width

Increase electron

recombination lifetime in

the base

Increase base doping

Increase Emitter Doping

Decrease Base doping

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11. Consider a p-n-p BJT biased with the following arrangement. Complete the sketch of the energy

band diagram of this BJT in the position range 0 - 4m.

Base Thickness= 2 m, NAEmitter= 10.NDbase , NDBase=10.NAcollector

EB Junction Contact Potential= 0.9 V, B-C Junction Contact Potential= 0.7 V

E- B Junction Total Depletion Layer Width= 0.1 m,

B-C Junction Total Depletion Layer Width = 0.4 m

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12. Ebers-Moll equations for npn transistor is given as

(a) Write down Ebers-Moll equations for a pnp transistor.

iE =

iB =

iC =

(b) Consider the following circuits constructed using the same BJT. Find base-to-collector current

amplification factorF of the transistor. VT = kT/q = 25mV.

p n p

E B C

0.65 V

19.6 mA

p n p

E B C

0.5 V

0.243 mA

p n p

E B C

-1 V

-2x10-

A

-1 V

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(c) Assume for a specific biasing circuit, the transistor operates at the boundary between forward

active mode and saturation mode. Draw the equivalent circuit for the transistor at the given

operating point.

(d) Employing the simplified equivalent circuit of part c), or working directly with the Ebers Moll

equations, obtain an expression for VEC at the specified operating point. Your answer should be in

terms of IB and Ebers-Moll parameters.

13.

14. The parameters of the BJT shown in the figure are as follows: F=0.99, R=0.2. The collector

current is IC=1mA and VT=25mV.

(a)Calculate the base current if the voltage between the collector and the emitter is VCE=0.1V.You can make reasonable approximations to simplify your calculations.What is the operation

region of the transistor?

(b)Repeat part (a) if the collector current is kept constant but VCE is increased to 0.3V. You canmake reasonable approximations to simplify your calculations

(c)By comparing the base current and the collector current values comment on whether thetransistor in part (a) or part (b) is biased closer to the boundary of the operation region found

in part (a).

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15.

16. A pnp BJT is connected to a DC current source (I1) and a DC voltage source (VCC).

Assume F=20=5R. Ignore the Early effect. Sketch ICC versus VCC for -5V

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17. IB-VBE characteristic of the npn BJT used in the following circuit is given below. Emitter injection

efficiency and base transport factor of the BJT are both equal to 0.995. Contribution of the thermally

generated minority carriers around the B-C depletion region to base current is negligible.

a) Find the collector current and collector-emitter voltage of the BJT in the following circuit, and plot theIC-VCE characteristic of the BJT on the provided graph. Mark the Q-point (operating point) (as Q) of the

BJT on the IC-VCE characteristic. Also show the boundary point (as B) between forward saturation and

forward active regions on the IC-VCE characteristic assuming that BJT enters saturation region when

VCE=0.8 V. Assume that the collector current is independent of VCB in the forward active region.

Do not attempt to use the transport (Ebers-Moll) equations. You are expected to plot the IC-VCE

characteristic corresponding to the IB flowing in the following circuit.

b) Find the value ofRC required to put the BJT on the boundary between the forward saturation andforward active regions under the same VBB (0.75 V) and VCC (5 V).

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18.

(a)Derive expressions for the i-v characteristics of the transistors shown in figures (a) and (b), interms of Is, F, and R.

(b)When the two transistors in figures (a) and (b) are identical, and the currents are made equalto a value I, it is found that the voltage v is 0.7 V for the diode in (a) and 0.6 V for the diodein (b). Find F /R.

(c)Assume that the ratio F/R is obtained for an n+pn+ transistor(emitter doping density=collector doping density). What does this ratio imply about the transistor geometry?

(d)For the transistor circuit shown below, find expressions for iE and i in terms of v, Is, Rand

F. Find the ratio of the two currents (i / iE). Assume v>>0 and F >>R.

19. The BJT in the following figure has a floating Base connection. Derive the relationship between

IE and VEC starting from the Ebers-Moll Model equations.

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20. Consider the pnp BJT pictured in the figure. Let WE be the quasineutral width of the emitter and

assume excess minority carrier concentration (nE)=0 at the metallic emitter contact (x`=WE). Also

assume that pB=0 at the base-collector junction (x=WB). The emitter doping (NE) is 100 times

greater than the base doping (NB).

a) The emitter width (WE) is 0.1 times the base width (WB). Assume that both the emitterand the base widths are much shorter than the carrier diffusion lengths Ln and Lp.

i) Sketch the minority carrier distribution on emitter and base regions for forward activemode operation of the BJT.

ii) Find the emitter injection efficiency.iii) What is the base transport factor based on the above assumption?

b) Assume that both the emitter and the base widths are much wider than thediffusion lengths.i) Sketch the minority carrier distribution on emitter and base regions for forward active

mode operation of the BJT.

ii) Find the emitter injection efficiency.

iii) What is the base transport factor based on the above assumption?

21. Consider an n-p-n BJT with the E-B junction forward biased and VCB= 0V. Ignore recombination

in the base and find the expressions for the total excess electron charge in the base (Qn) and diffusion

capacitance (CD) in terms of VBE, equilibrium electron concentration in the base (nbo) and the othernecessary parameters.

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22. Consider the following Si n-p-n bipolar junction transistor. The E-B and B-C depletion regions

are shown on the figure with the charge due to ionized impurities.

Diffusion coefficient of holes in emitter= 4 cm2/sec

Diffusion coefficient of electrons in base= 8 cm2/sec

Hole recombination lifetime in emitter= 2.95x10-9 sec

Electron recombination lifetime in base= 1x10-6 sec

A (E-B Junction cross-sectional area)=1x10-4 cm2 , kT/q=VT= 25 mV, ni= 1x1010 cm-3

a) What is the region of operation for the BJT. Why?b) How does this device operates as a controlled current source (Ic controlled by VBE) ? Explain

in every detail only with words .

c) Use kT/q=VT= 25 mV, ni= 1x1010 cm-3for the plotsrequested in this part.

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i) Plot the total hole concentration in the emitter. Note that y-axis is in log scale.

ii) Ignore recombination in the base and plot the total electron concentration in the base(your plot must reflect zero recombination in the base). Use linearly scaled y-axis

and label the values of n on the y-axis at the indicated (three) locations.

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d) Ignore recombination in the E-B depletion region. Derive the expression for the emittercurrent in terms of ni, NA , ND , VBE , WB , Lp , Dn , Dp and other necessary parameters.

Calculate the emitter current. Show complete work and simplify your expression noting that

VBE >>VT. You do not need to derive the expressions for the excess carrier distributions in the

emitter and base.

e) Calculate the emitter injection efficiency.f) Ignore recombination in the base and the thermally generated minority carriers in/around the

B-C depletion region and find the collector current.

g) Ignore recombination in the base and the thermally generated minority carriers in/around theB-C depletion region and find the base current.

h) Estimate the saturation current Is of the BJT using your answer to part (f) and the simplifiedexpression for the collector current in terms of Is.

i) Ignore recombination in the base and estimate the new collector current if VCB is increasedand WB is decreased to 1x10

-4cm (VBE is not changed). Clearly explain your reasoning.

j) Explain a mechanism that establishes an upper limit for VCB?

23. Answer the following questions for a p+np bipolar transistor at room temperature, assume that the

BJT is operating in the forward active region. Dp = 5 cm2s-

1,Dn = 10cm

2s-

1, WE = 500 nm; A = 25

m2, NAE = 1019 cm-3, NDB = 10

17cm-3,NAC = 1016cm-3.

i) What should the base width WB be for a current gain F of 100? Neglect depletion region widths.

ii) What is the emitter-base p-n diode saturation current IES?

iii) What is the EB voltage for a collector current of I C = 100 A?

iv) What is the base diffusion capacitance CD for IC = 100 A?

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EE212Spring2010HMW4