Download Exam 2 Study Problems

ENEE 313, Exam 2 Practice Questions
Part I
1. Give the expression for drift current and explain what it is.
2. Give the expression for diffusion current and explain what it is.
3. Give the expression for electron mobility and explain what it is.
Part II:
1) If the electron concentration in a semiconductor is found to be: n(x) = Nd exp(x/Ln),
provide an expression for the diffusion current density. Nd and Ln are constants.
Part III (30pts):
A n1-n2 junction is formed by doping two different sides of a Si bar with ND1 and ND2,
respectively as shown in Figure 1.
1) Derive an expression starting from the current equation, for the built-in potential of
this structure at equilibrium (current equals zero) in terms the doping and the thermal
voltage.
2) If ND1 < ND2, then show the direction of the built in electric field.
3) Does this structure pass current in both directions, or does it rectify. Explain your
answer in a sentence or two. Use terms like built in potential and conductivity.
ND1
ND2
Figure 1
Part IV (30 pts).
1. A silicon bar of length L and cross section area A is uniformly doped with a constant
donor of concentration ND. If a voltage V is applied across the length L of the bar. Give
an expression for the current in going into the bar in terms of given dimensions and
appropriate physical parameters. Is the current drift or diffusion, why? (You can use
approximations here like neglecting ni if you can justify it.)
2. The entire bar is now doped again uniformly with doping NA which is 100 times
greater than ND. Now give an expression for the current going into the bar. (You can use
approximations here like neglecting ni if you can justify it.)
Part V. (40 pts.)
A diode is composed of an abrupt PN junction with ND = 1.0 x 1016/cm3 and NA = 1.0 x
1017/cm3. The diode is very long so you can assume the ends are at x =positive and
negative infinity.
1. Without doing any calculations, tell me if current at the junction is due mostly to holes
or electron, give their approximate ratio and explain why?
2. Starting with the current and continuity equations, derive an expression for the
minority carrier current in the N quasi-neutral region of the PN junction.
3. Without doing any more derivations, but by symmetry arguments only, provide an
expression for the minority carrier current in the P quasi neutral region.
4. If there is no recombination or generation in the depletion region, mathematically show
that the electron and hole currents must be constant in this region.
5. Describe in words and provide a sketch of where the capacitors in the PN junction
come from.
Part VI (35pts.): The following questions refer to the material with band structure given
by the two equations below. (G gives the gap. CB and VB represent conduction and
valence bands, respectively.)
E(k) = Ak2 + G (CB)
E(k) = -Bk2
(VB)
1) Provide a simple criterion for the minimum frequency of the light that is capable
generating electron-hole pairs in this material in terms of the above band structure. (Hint,
use the bandgap G).
2) If the scattering rate for both electrons and holes is 1/τ, find the electron and hole
mobilities in terms of the band structure parameters above. (Hint from the band structure
obtain the effective masses for electrons and holes, and then use that in the expression for
mobility)
3) What is the intrinsic carrier concentration for this material in terms of the above band
parameters. (Hint, use the expression that relates bandgap to intrinsic carrier
concentration)
4) If a voltage VA is applied across a bar of length D made of this intrinsic material, and
the bar has cross-section area A, give an expression for the current into and out of the bar.
5) If the material is now doped with ND donors and NA acceptors, and NA >> ND >> ni ,
Is this material N-type or P-type, why? Is there a net charge on this material or is it
neutral, why?
6) Give an expression for the current IA through the doped bar if the bar has cross
sectional area A, length D, and voltage applied VA.
Part VII (33pts).
A silicon PN junction diode is doped with 1017/cm3 donors and 1018/cm3 acceptors. The
diode has a cross-section area of 100um x 100um. (um=micron).
1. Sketch a generic current vs. voltage curve for a PN junction doide for forward
and reverse bias. Indicate the value of the voltage where the PN junction starts to
turn on strongly on the curve.
2. What is the built-in voltage for this PN junction?
3. What are the two types of capacitors associated with a PN junction diode?
Describe in words physically what gives rise to these capacitors?
4. For the circuit in Figure 1 below, VDC = 5.0V, and VAC = 1.0sin(ωt), write an
expression for the output voltage as a function of the angular frequency ω. The
output voltage is between the diode and ground. (Hint, calculate and use the
appropriate capacitance from the previous question. Also, neglect diode reverse
bias current.)
Vout