Instructions: Answer all 5 questions (total 100 marks), showing all your work. The marks are distributed as indicated. You must show all of your work (explanations and calculations) leading to your answer. This includes justifying the choice of the equation(s) that you use. (It is not sufficient to have the correct answer, you need to show how you obtained it.) Failure to show your work will result in zero marks being awarded for the question (or relevant part of the question).

How to submit: When you have completed the assignment, please do the following:

(i) Create a .pdffile of your worked solutions for all of the questions.

(ii) Submit both your .pdf solutions into the coursework submission link on Moodle.

Dependence of carrier mobility in silicon on the dopant concentration

1.   Starting from Boltzmann’s relations, do the following:

a)   Derive an expression for the intrinsic carrier density, ni, of silicon.                         [3 marks]

b)   Using the formula from Q1(a), calculate the intrinsic carrier density of silicon for temperatures of 77K (liquid nitrogen) and 25⁰C (room temperature).        Express your answer in units of cm-3 . (Note: For this problem, you may ignore the temperature dependence of the material parameters.)

c)   Explain the significance of the intrinsic carrier density on the diode leakage current, supporting your answer with equations .

d)   Describe the impact of temperature on the sensitivity of a reverse-biased photodiode. At what bias will the signal to noise ratio be the highest?

2.   Consider avalanche breakdown in a reverse-biased diode and do the following:

a)   If the avalanche breakdown process is dominated by hole multiplication,     explain how this process works. Support your explanation with a sketch the

avalanche process on an energy band diagram of the diode.                                   [6 marks]

b)   Identify the physical process responsible for the hole multiplication and    explain its operation using an energy -vs- momentum (E-vs-k) diagram. Be

sure to explain the role of energy and momentum conservation.                           [6 marks]

c)   Link the E-vs-k diagram (Q3b) and the diode band diagram (Q3a) descriptions

of the avalanche process by labelling the specific carriers in both diagrams .        [3 marks]

3.   Consider a diode, whose current-voltage performance at room temperature (T = 300K) is shown in Table Q2.

Table Q2: Typical current-voltage characteristics of a 1N4003 pn diode for Q2 for T = 25 oC.

Do the following:

a)   Make a semilogarithmic plot of the I-V data in Table 2.1

b)   Transform the diode equation I = I0 {exp () − 1} into an expression suitable for plotting a fit to the plot of the I-V data in Q2(a), showing any assumptions you make.

c)   Determine the values of the unknown coefficients I0 and n.

d)   Show that the assumptions you made are valid for the data analysed.

e)   Calculate the diode’s dynamic resistance at a forward bias current of 100mA.

4.   Consider a forward biased silicon pn diode with a junction area of A = 1.00x10-2 cm2,

operating at I = 200 mA at 25⁰C. The bases have thicknesses and doping densities of: Wp = 2.5 m; Na = 2.00x1018 cm-3

Wn = 300.0 m; Nd = 2.00x1017 cm-3

Showing and justifying all work, do the following:

a)   Calculate the minority carrier diffusion lengths and determine whether each    of the bases is “long” or “short” . (Use the data provided, choosing the mobility and carrier lifetime appropriate for the total doping concentrations.)

b)   Write the correct expression for the diode I-V characteristics, including that of the saturation current. (Assume that the diode is “ideal” .)

c)   Calculate the reverse saturation current, I0 . (Express your answer in A.)

d)   Calculate the built-in barrier height of the diode.

e)   Sketch the minority carrier distributions, labelling the key features.

f)    Calculate the minority carrier distributions at the edge of the depletion region. [4 marks]

g)   Calculate the fraction of the total current that is injected into the n-base.            [4 marks]

5.   Design a high efficiency (n > 85%) p-i-n photodetector to detect a 10 Gb/s optical signal from a 50 m diameter optical fibre. It will be used at room temperature

(25⁰C) with an amplifier with a 75 input impedance.

For your design, you may assume the following:

• the maximum p- and n-type doping densities are Na = 5x1019 cm-3 and Nd = 2x1018 cm-3;

• the diode is fabricated on a heavily doped (Na or Nd = 2x1018 cm-3 ) InP substrate (500 m thick), but you must choose its doping type;

• the electron and hole minority carrier lifetimes are n = p = 10 ns;

• the electron and hole mobilities are n = 1000 cm2V- 1s- 1 and p = 100 cm2V-1s- 1 ;

• the carrier saturation velocity is vsat = 107 cm/s;

• the p-contact resistivity is pc = 5x10-6 cm2  but n-contact resistivity can be neglected;

• the relative permittivity of the semiconductor is s/s = 12.6;

• the absorption coefficient of the semiconductor is = 104 cm-1 at the signal wavelength;

• the diode is anti-reflection coated (R ~ 0).

Your design should:

a)   Demonstrate that the absorption efficiency (n) is > 85%.

b)   Calculate the value of the required matching resistor.

c)   Demonstrate that the RC time constant and carrier transit time are both 30 ps or shorter.

d)   Sketch the diode structure and specify the photodetector dimensions and the thicknesses and doping (type and concentration) of all semiconductor layers (including the substrate).