Bipolar Fundamentals
VBE Emitter Base V CB Collector SC
1E-1
IC0
1E-2 1E-3
IB 0
IC
Ec Ev
IB
Current (A)
IC IB
Ec Ev x
1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 0.4
-WE
0
W
B
Base current = holes injected current holes injected from base into emitter. Collector curre
ECE 230B, HW-#5, Winter 2012
1.
Apply constant-field scaling rules to the long-channel currents, Eq. (3.19) for the
linear region, and Eq. (3.23) for the saturation region, and show that they behave as
indicated in Table 4.1.
Solution:
Under the scaling t
ECE230A Fall 2009
Solution for Quiz #3
1. A semiconductor is doped with acceptors (Na) and donors (Nd). (a) Assuming the degeneracy factor is 2 for donors and 4 for acceptors. Nd > Na, p0, and Nd is 75% ionized, find the approximate electron concentration
ihtJ
Final, ECE230B, Winter 2412
zo
Assume Si, room temperature, and complete ionization.
V4
.
(10 pts) Consider an MOS capacitor with SiOz on n-type Si of No = 3x1016 cm-3.
(a) Sketch the C-V curve (high frequency).
(b) lf the Si bands bend down by 0.1 V
ECE 230B Quiz-1 (Winter 2010)
Assume silicon, room temperature, complete ionization. Consider an abrupt n+-p junction with p-type doping of Na = 1017 cm-3. (a) What is the built-in potential? (b ) If both contacts are 0.1 cm away from the junction, estima
ECE 230B, HW-1, Winter 2010 Solutions 1. 3-D Gauss law is obtained after a volume integration of 3-D Poissons equation and takes the form of Q S E dS = si , where the LHS is an integral of the normal electric field over a closed surface S, and Q is the ne
ECE230A Fall 2009
Solution for Quiz #2
1. For the 1-D InGaAs/InAlAs superlattice, the effective mass for InGaAs and InAlAs are denoted as m1 and m2, respectively. (a) Find the general solution of the Schordinger equation in regions I and II. (b) Write the
ECE230A Fall 2009
Solution for Homework #2
1. For the Kronig Penny model, show that (a) v (b) 0 at the band edge.
d 2 a 2 cos(ka) = dk 2 cos( a ) cos( a ) a sin( a ) p a 2 where = 2mE = h 2m h
(c) Find the effective mass assuming P=3/2, ka=, and a=3/2. In
ECE230A Fall 2009
Solution for Homework #3
1. The intrinsic carrier concentration at room temperature (300K) for Ge and Si is 2.3x1013 cm-3and 1.1x1010 cm-1, respectively. The bandgap energy Eg,Ge=0.67 eV, Eg,Si = 1.1 eV. (a) Find the intrinsic concentrat
ECE230A Fall 2009
Solution for Homework #1
1. Provide a photograph of yourself and a brief self-instruction (3~4 sentences about your background, current status and study/research interest) 2. Many III-V compound semiconductors such as GaAs and InP have t
ECE 230B, HW-1, Winter 2012
1.
Use the density of states, N(E), derived in Section 2.1.1.2 to evaluate the average kinetic
energy of electrons in the conduction band:
K.E.
( E Ec ) N ( E ) f ( E )dE
Ec
Ec
.
N ( E ) f ( E )dE
(a) For a non-degenerate semic
ECE 230B, HW-3, Winter 2012
Solutions
+
1.
Sketch the C-V curve (high frequency) of an MOS capacitor consisting of n poly gate on
n-type Si doped to N d =1016 cm-3. Calculate and show the flatband voltage on the C-V.
Draw the band diagram for V g =0. Give
ECE 230B, HW-#4, Winter 2010 1. Apply constant-field scaling rules to the long-channel currents, Eq. (3.23) for the linear region, and Eq. (3.28) for the saturation region, and show that they behave as indicated in Table 4.1. 2. Apply constant-field scali
ECE 230B, HW-#3, Winter 2010 1. Consider an n-channel MOSFET with 20 nm thick gate oxide and uniform p-type substrate doping of 1017 cm-3. The gate work function is that of n+ Si. (a) What is the threshold voltage? Sketch the band diagram at threshold con
ECE 230B, HW-#4, Winter 2010 1. Apply constant-field scaling rules to the long-channel currents, Eq. (3.19) for the linear region, and Eq. (3.23) for the saturation region, and show that they behave as indicated in Table 4.1. Solution: Under the scaling t
ECE 230B, HW-#3, Winter 2010 1. Consider an n-channel MOSFET with 20 nm thick gate oxide and uniform p-type substrate doping of 1017 cm-3. The gate work function is that of n+ Si. (a) What is the threshold voltage? Sketch the band diagram at threshold con
ECE 222B, Winter 2010 Homework Set 4: Problems 1 and 2 are due Tuesday, Feb 17th. 1. We wish to determine what fraction of light in glass (for simplicity, let the permittivity of the glass be g = 20 ), incident from the left upon an air gap with width is
ECE 222B, Winter 2010 Homework Set 4 Solutions 1. We wish to determine what fraction of light in glass (for simplicity, let the permittivity of the glass be g = 20 ), incident from the left upon an air gap with width is transmitted across the gap into an
ECE 222B, Winter 2010 Solution to Homework Set 5 1. Problem 8-2, Balanis Solution: Calculate a number of guide parameters given the dimensions a = 0.02286 m and b = 0.1016 m, and relative permittivity r = 2.56. It follows that the speed of light in the wa
ECE 222B, Winter 2010 Homework Set 6, Due March 11th 1. Assume that you are given a dielectric covered ground plane as shown in Figure 8-30 of Balanis. Assume that the height of the dielectric covering is h, the dielectric permittivity is d , and the perm
ECE 222B, Winter 2010 Solutions for Homework Set 6 1. Assume that you are given a dielectric covered ground plane as shown in Figure 8-30 of Balanis. Assume that the height of the dielectric covering is h, the dielectric permittivity is d , and the permea
MOSFET Scaling
Device scaling: Simplified design goals/guidelines for shrinking device dimensions to achieve density and performance gains, and power reduction in VLSI. reduction in VLSI. Issues: Short-channel effect, Power density, Switching delay, Relia
ECE 230B, HW-1, Winter 2010 1. 3-D Gauss law is obtained after a volume integration of 3-D Poissons equation and takes the form of Q S E dS = si , where the LHS is an integral of the normal electric field over a closed surface S, and Q is the net charge e
ECE 230B, HW-2, Winter 2010 1. When the gate voltage greatly exceeds the threshold for strong inversion, a first-order solution of s(Vg) can be obtained from the coupled equations, Eqs. (2.195) and (2.182), by keeping only the inversion charge term. Show
ECE 230B, HW-2, Winter 2010 Solutions 1. When the gate voltage greatly exceeds the threshold for strong inversion, a first-order solution of s(Vg) can be obtained from the coupled equations, Eqs. (2.195) and (2.182), by keeping only the inversion charge t
ECE 230B Midterm (Winter 2010)
Assume silicon, room temperature, complete ionization. 1. (20 pts) An abrupt p-n junction with Nd = 1018 cm-3 and Na = 1017 cm-3 is forward biased at 0.5 V. (a) Draw the band diagram. Label the Fermi levels and indicate wher
ECE 230B Quiz-2 (Winter 2010)
Assume silicon, room temperature, complete ionization. Consider the design of a 100 nm (channel length) nMOSFET. Assume a gate oxide thickness of 3 nm. (a) What substrate doping (assume uniform) is needed for control of short
ECE 230B, HW-#4, Winter 2012
1.
Consider an n-channel MOSFET with 20 nm thick gate oxide and uniform p-type
substrate doping of 1017 cm-3. The gate work function is that of n+ Si.
(a)
What is the threshold voltage? Sketch the band diagram at threshold
con
ECE 230B, HW-2, Winter 2012
1.
Assume silicon, room temperature, complete ionization. An abrupt p-n junction with N a =
N d = 1017 cm-3 is reversed biased at 2.0 V.
(a) Draw the band diagram. Label the Fermi levels and indicate where the voltage
appears.