Aaasa

Homework 1

Date assigned: 09/15/2015

Date due: 09/22/2015 (MIDNIGHT)

Problem 1

Consider a wafer of radius wr as shown in Figure 1. Assume square dies on the wafer

with side dimension de.

a. Calculate the number of useful dies (“physically intact”) on the wafer in terms of

wr and de.

b. What is the minimum ratio wr/de for which at least one useful die is obtained.

c. Plot the number of useful dies as a function of the ratio wr/de. Make sure that the

limits of wr/de are correct as obtained in answer (b) above.

d. Assume that the wafer has a defect density of Dd per unit area. Calculate the wafer

yield,

Y.

Note that the wafer yield is defined as Y = (no. of physically intact dies on the

wafer) × (die yield). To compute Y, you have to use the results from part (a)

above.

Square die

Edge dimension = de

Only solid colored dies are

physically intact. Shaded

portion is useless.

Figure 1: The wafer radius is wr. Shaded dies are useful. To find answer to part (a),

calculate how much area is wasted in the shaded portion.

Problem 2

Consider the ID-Vd characteristics of the transistor for Vgs > VT. That is, the transistor is in

ON condition.

a. Compute the resistance of the transistor as (∂ID/∂Vd)-1 for linear and saturation

regimes of transport.

b. Qualitatively plot the resistance as a function of Vds and Vgs on two separate plots.

Your answer must be presented in a tabular format as below.

Linear operation

Transistor resistance =

Qualitative plot of transistor resistance

versus Vds.

Qualitative plot of transistor resistance

versus Vgs.

Saturation operation

Transistor resistance =

Qualitative plot of transistor resistance

versus Vds.

Qualitative plot of transistor resistance

versus Vgs.

Problem 3

Consider the ID-Vg characteristics of the transistor.

a. Derive the transistor trans-conductance gm = ∂ID/∂Vg for Vgs < VT. Recall: for Vgs

< VT, transistor current varies exponentially with Vgs-VT. Note that the dependence...