Reference no: EM131007924

Comment: I need solution as step and explanation Every thing because i have to understand every thing in solution so i need answer with explanation and details

Remember :

Work should be detailed so that student can understand

Part -1:

1. a) Describe the concept of energy bands of semiconductors and draw the energy band diagram for intrinsic semiconductor for two temperatures: 0K and T>0K.

b) Explain the difference between intrinsic and extrinsic semiconductors. State the mass action law for semiconductors.

c) Calculate and compare the resistivity of intrinsic and extrinsic silicon if the latter is doped by boron to concentration of 1.5 x 10¹⁶ cm^-3. The mobility of electrons is 0.15 m²V^-1s^-1 and that of holes, 0.05 m²V^-1s^-1. Is the extrinsic silicon p or n-type semiconductor?

2. a) Draw a fully labelled band diagram for a pn junction with no applied voltage. Calculate the built-in potential if the doping concentration on the n- type side is 2x1017 cm^-3 and on the p-type side 5x10¹⁵ cm^-3 at 300K.

b) Calculate the value of the total depletion width for the case of ND and NA doping concentration given in a). Is the depletion width wider on the n- or p- type side of the junction and why?

3. a) Draw a labelled cross-section of an n-channel MOSFET.

b) Derive an expression for drain current (ID) below pinch-off, as a function of the gate (VG) and drain voltage (VD), the capacitance per unit area of the gate (Co) and channel length (L) and width (W). Explain the meaning of pinch- off.

c) State the difference between enhancement and depletion types of MOSFET. Sketch the symbols and transfer characteristics of these two types of devices for p- and n- channel transistors.

4. a) Describe the advantages and disadvantages of the CMOS inverter compared to the equivalent circuit produced in nMOS technology.

b) Illustrate your answer in a) by plotting transfer and current characteristics for CMOS and nMOSFET inverters.

c) Discuss with circuit diagrams, how CMOS can be used to replicate nMOS logic and how this leads to the concept of Domino Logic.

Part -2:

1. a) State the de Broglie hypothesis and explain the variation of energy versus wave vector for electrons in a crystal lattice.

b) If the density of available states in the conduction and valence bands are 2.8 x 10¹⁹ cm^-3 and 1.04 x 10¹⁹ cm^-3 respectively, calculate the energy bandgap using the intrinsic carrier concentration of ni = 1.45 x 10¹⁰ cm^-3. Comment on the type of material based on the calculated energy bandgap value.

c) Calculate the resistivity of the material in b) if the mobilities for electrons and holes are 0.15 m²V^-1s^-1 and 0.05 m²V^-1s^-1 respectively. Compare the obtained value with the resistivity of the silicon doped by phosphorus to 1 x 10¹⁷ cm^-3. Explain why the conductivity is improved in the latter case.

2. a) Draw an energy band diagram for a p-type silicon MOS capacitor in accumulation, depletion and inversion. Show the Fermi level and indicate the surface potential. Explain the physical interpretation of the diagram.

b) Calculate the value of surface potential at the onset of the inversion condition and also the value for threshold voltage (VT) for such a device. The silicon semiconductor is boron doped to 2 x 10¹⁶ cm^-3, and the thickness of the silicon oxide is 10 nm. Assume an ideal MOS capacitor.

c) Explain why the capacitance in inversion for this device differs when measured at high (1 MHz) and low (1 kHz) frequency.

3. a) Derive the equation for the drain current (ID) as a function of gate bias (VG) for a 18 MOS transistor in the sub-threshold regime, as shown below:

I_D ∝ exp(qV_G/mkT).

Is the current flow in this regime due to drift or diffusion of carriers and why? Illustrate by the use of an energy band diagram.

b) Use the above equation to find the sub-threshold slope factor (m) and hence explain how the threshold voltage can be engineered through the differential capacitances of the semiconductor and gate oxide.

4. a) Describe the principles involved in the design and layout of CMOS NOR and NAND gates.

b) Draw and label a possible layout for a CMOS NOR gate.

c) Calculate the sizes of all transistors in two-input NOR and two-input NAND gates for a process technology with the gate length L = 0.5 μm. The aspect ratio (W/L) of a minimum-size symmetric inverter is W/L = 1.5. State clearly the design principles used in your solution. Comment on the issues concerning the use of NOR versus NAND gates, in CMOS integrated circuit design.

Part -3:

1. a) Explain the concept of energy (E) versus wave vector (k) diagram for a free electron.

b) Develop, for a semiconductor, the idea of bands of closely spaced energy levels separated by an energy gap.

c) Describe with the brief statement the meaning of ‘p' and ‘n' type of semiconductors.

d) Calculate the values of Fermi potential at a temperature of 300 K for p- and n-type semiconductor regions doped to 5x10¹⁷ cm^-3 and 2x10¹⁶ cm^-3 respectively.

e)  Calculate the built-in potential at a temperature of 300 K for a pn-junction fabricated from semiconductors in d).

f) Is depletion width wider on p- or n-type side of the junction in e)? Illustrate with the aid of a diagram.

2. a) Draw and explain an energy band diagram for an MOS capacitor in 8 inversion.

b) Derive an expression for the threshold voltage for a p-type MOS structure in 10 terms of dimensions of the dielectric (t_ox), the relative permittivity of gate (ε_ox) and substrate (ε_s) materials and substrate doping concentration (N_A):

V_T = (ε_s/ε_ox).t_ox √(2qN_A(2Φ_F)/ε₀ε_s) + 2Φ_F.

c) Calculate the threshold voltage for a p-type MOS structure if the gate oxide thickness is 4 nm, and the substrate doping concentration is 1x10¹⁷ cm^-3. Assume an ideal MOS capacitor and use the simplified formula derived in b) without taking into account oxide charges and work function difference.

d) Comment on the value of threshold voltage obtained in c) if the thickness of the gate oxide decreases and substrate doping concentration increases.

3. a) Describe briefly the fabrication of a p-channel MOSFET in an n-well.

b) Develop an expression for the current flowing down the channel of an n- MOSFET in terms of the gate and threshold voltages, in the linear region:

I_D = μC_oW/L[(V_G -V_T)V_D -V_D²/2] .

Define the device constant in the expression above.

c) Design a symmetric CMOS inverter and deduce the aspect ratios 10 (width/length) for p- and n-MOSFET transistor for this case. Assume the mobilities of electrons and holes of μ_n = 545 cm²/Vs and μ_p = 130 cm²/Vs respectively, the threshold voltages for p- and n-MOSFETs equal to VTn = |VTp| = 0.7 V, and V_DD = 5 V.

d) Is CMOS a ratioless or ratioed logic circuit? Explain your reasoning with the aid of diagrams.

4. a) Draw the circuit diagrams for a two input NAND and a two input NOR gate made in CMOS technology and explain their operation.

b) Describe the principles involved in the design of CMOS NOR and NAND logic gates.

b) Draw and label a possible layout for a CMOS NOR gate.

c) Calculate the sizes of all transistors in two-input NOR and two-input NAND gates for a process technology with the gate length L = 0.5 μm. The aspect ratio (W/L) of a minimum-size symmetric inverter is W/L = 2.

State clearly the design principles used in your solution.

Comment on the issues concerning the use of NOR versus NAND gates in CMOS integrated circuit design.

Part -4:

1. a) De Broglie hypothesis implies the wave-particle duality for an electron. State this relation and explain significance of each term.

b) Derive and illustrate with the aid of a diagram the kinetic energy versus wave vector for free electron.

c) Why do the boundaries of a single crystal solid give rise to the formation of 8 separate energy levels at Π/a, where a is the lattice constant. Redraw the energy versus wave vector diagram in b) to include the effect of the finate boundaries.

d) Explain the formation of an energy gap by considering the potential and kinetic energy of electrons in a semiconductor lattice.

e) Design the doping concentration level of phosphorus ions to obtain the 5 conductivity of extrinsic silicon to 200 (Ωm)^-1. Assume the mobility of electrons of 0.15 m²V^-1s^-1.

f) Determine the position of Fermi level (in eV) from the conduction band edge for doping concentration calculated in e). Is this n- or p-type semiconductor? Assume room temperature (300 K).

2. a) Develop an expression for the current flowing down the channel of an n-MOSFET (Metal Oxide Semiconductor Field Effect Transistor) in terms of the gate (VG) and threshold (VT) voltages, in the saturation region (above ‘pinch off'):

I = μC_oW/2L(V_G-V_T)²

b) Define the device constant in the equation in a). Which parameters can a designer vary and why?

c) Explain the meaning of the ‘pinch-off' condition with the aid of a labelled cross-section of an n-MOSFET showing the channel and other regions.

d) The n-MOSFET in (a) is to be used to fabricate a complementary metal 10 oxide semiconductor (CMOS) inverter. Design its aspect ratio (W/L)n to obtain a symmetric CMOS inverter. Assume the mobilities of electrons and holes of μ_n = 545 cm²/Vs and μ_p = 130 cm²/Vs respectively, the threshold voltages for p- and n-MOSFETs equal to V_Tn = |V_Tp| = 0.8 V, V_DD = 3 V, and aspect ratio for p-MOSFET (W/L)p = 8.

e) State the two parameters, which govern the speed of CMOS inverters. 

3. a) Explain briefly the operation of a CMOS inverter. State its main advantages and disadvantages.

b) Sketch the transfer characteristic of a CMOS inverter and illustrate the regimes of operation of referring n- and p-MOSFET transistors.

c) A two-input NOR gate is to be made in CMOS technology. Draw the circuit diagram and describe the principles involved in its design.

d) Design the aspect ratio (W/L)p for p-MOSFETs for the circuit in c) so that the CMOS NOR gate has symmetric transfer characteristic.

Assume VDD = 3 V, threshold voltages of n- and p-MOSFETs equal, with V_Tn = V_Tp = 0.3V, (W/L)n = 2 for n-MOSFETs, and ratio of electron and hole mobilities μ_n / μ_n = 2.5.

Show clearly all your working.

4. a) Draw a sequence of circuit diagrams, starting from a pseudo-nMOS inverter, to develop the concept of domino logic.

b) State key disadvantage of a pseudo-nMOS inverter and compare its 8 operation to a CMOS inverter. Illustrate your reasoning by the aid of voltage transfer characteristic graph.

What kind of applications a pseudo-nMOS inverter is suited for?

c) Illustrate a two single-input domino CMOS logic gates connected in cascade and draw the voltage waveforms during the evaluation phase. Explain briefly its operation.

d) Describe the principles involved in the design of dynamic logic circuits.

Part -5:

1. a) Describe with two brief statements the meaning of ‘p' and ‘n' type semiconductors.

b) State the mass action law for semiconductors and explain the significance of each term.

c) Design the doping concentration level of boron ions to obtain the conductivity of extrinsic silicon of 100 (?m)^-1. Assume the mobility of holes is 0.05 m²/ Vs.

d) Determine the position of the Fermi level (in eV) from the valence band edge for the semiconductor in c). Is this an n- or p-type semiconductor?

e) Draw an energy band diagram for a pn junction under the zero bias condition. Label the band edges, the extrinsic and intrinsic Fermi levels.

f) You are asked to design an abrupt or step pn junction, with depletion region width of 0.2 μ_m, entirely on the n-type side of the junction. Assume the built-in potential across the junction, V_bi = 0.7 V.

i) What is the doping concentration of the n-type semiconductor that would meet this requirement?

ii) Explain how the depletion width would change if the doping concentration calculated in i) doubles. State the value of the depletion width (in μ_m).

iii) Illustrate, with the aid of a diagram, the space distribution of charge across the junction for the two scenarios given in i) and ii).

2. a) Draw an energy band diagram for a MOS capacitor in inversion. Show the Fermi level and indicate the surface potential. Explain the surface field effect.

b) Derive an expression for the threshold voltage of an ideal p-type MOS capacitor in terms of the thickness of the dielectric (t_ox), the relative permittivity of the gate (ε_ox) and the substrate (ε_s) materials, and the substrate doping concentration (N_A):

V_T = (ε_s/ε_ox).t_ox √(2qN_A(2Φ_F)/ε₀ε_s) + 2Φ_F.

The MOS capacitor discussed in b) is to be designed so the threshold voltage

i) What is the gate oxide thickness for the MOS capacitor that would provide the required threshold voltage?
Assume a p-substrate doping concentration of 1x10¹⁶ cm^-3 and an ideal MOS capacitor.

ii) Comment on the gate oxide thickness if the doping concentration increases 10x.

Sketch the high frequency (1 MHz) and low frequency (1 kHz) capacitance voltage characteristics of a MOS capacitor. Label the accumulation, depletion and inversion regions on the characteristics. Explain why the capacitance in inversion for this device differs when measured at high and low frequencies.

Briefly describe the fabrication of a p-channel MOSFET in an n-well.

b) Develop an expression for the current flowing in the channel of an n-MOSFET in terms of the gate, drain and threshold voltages, in the linear region:

I_D = μC_oW/L[(V_G -V_T)V_D -V_D²/2] .

where the symbols have their usual meanings. Define the device constant in the expression above.

c) State the difference between the enhancement and the depletion types of 5 MOSFETs. Sketch the symbols and transfer characteristics of these two types of devices for p- and n-channel transistors.

d) You are asked to design a CMOS inverter with a threshold voltage of 1.2 V. The inverter threshold voltage refers to the point on the inverter transfer characteristic where the transition from logic 1 to logic 0 (and vice versa) occurs, and where you would expect that both n- and p-channel MOSFETs work in their saturation regions.

Assume a power rail V_DD = 3 V, threshold voltages of n- and p-MOSFETs are V_Tn = 0.7 V, V_Tp = -0.8 V respectively, (W/L)n = 2 for the n-MOSFET, electron mobility μ_n = 545 cm²/V_s and hole mobility μ_p = 130 cm²/V_s.

i) What is the aspect ratio (W/L)p for p-MOSFET that would meet this requirement?

ii) Comment on the solution in i). Is this an optimal design solution?

e) State the two key parameters which govern the speed of CMOS inverters.

Part -6:

1. a) The De Broglie hypothesis implies the wave-particle duality for an electron. State this relation and explain the significance of each term.

b) Derive and illustrate with the aid of a diagram, the kinetic energy versus wave vector for a free electron.

c) Explain the formation of an energy gap by considering the potential and kinetic energy of electrons in a semiconductor lattice.

d) The doping concentrations of p- and n-type silicon are 5x10¹⁷ cm^-3 and 1x10¹⁶ cm^-3 respectively. Assume a temperature of 300 K.

i) Calculate values of the Fermi potential for p- and n-type silicon.

ii) Calculate the built-in potential for a pn-junction fabricated from these p- and n-type semiconductors.

iii) Calculate the depletion width for the pn-junction in ii).

iv) If the pn-junction is to be designed so that its depletion width is entirely on p-type side of the junction, comment on how doping concentrations above need to be changed.

e) Draw an energy band diagram for the pn junction in d) under the zero bias condition. Label the band edges, the extrinsic and intrinsic Fermi levels.

2. a) Develop an expression for the current flowing down the channel of an 10 n-MOSFET in terms of the gate (V_G) and threshold (V_T) voltages, in the saturation region (above ‘pinch off'):

I = μC_oW/2L(V_G-V_T)²

b) Define the device constant in the equation in (a). What parameters designer can vary and why?

c) Explain the meaning of the ‘pinch-off' condition with the aid of a labelled cross-section of an n-MOSFET showing the channel and other regions.

d) You are asked to design a symmetric complementary metal oxide semiconductor (CMOS) inverter.

Assume the mobilities of electrons and holes of μ_n = 545 cm²/Vs and μ_p = 130 cm²/Vs respectively, the threshold voltages for p- and n-MOSFETs equal to V_Tn = |V_Tp| = 0.7 V, V_DD = 5 V, and aspect ratio for p-MOSFET (W/L)_p = 8.

i) What is the minimum aspect ratio (W/L)n for an n-MOSFET which would meet this requirement?

ii) Is the CMOS inverter a ratioless or ratioed logic circuit? Explain your reasoning with the aid of diagrams.

3. a) Draw a plan view (layout) of a CMOS inverter including polysilicon and aluminium lines, contacts and implants.

b) State the two key parameters, which govern the speed of CMOS inverters.

c) Describe the principles involved in the design of CMOS NOR logic gates.

d) You are asked to design two-input NOR and two-input NAND gates for a process technology with the gate length L = 0.5 μm. The aspect ratio (W/L) of a minimum-size symmetric inverter is W/L = 1.5.

i) What is the width/length (W/L) of n- and p-MOSFETs used in the design?

ii) Comment on the issues concerning the use of NOR versus NAND gates in CMOS integrated circuit design.

e) Sketch two single-input domino CMOS logic gates connected in cascade. Draw the voltage waveforms during the evaluation phase. Explain briefly the circuit operation.