VE320 Homework 7 - Solved

Exercise 7.1
(a)   A Schottky barrier diode formed on n-type silicon has a doping concentration ofNd = 5 × 1015 cm−3 and a barrier height of ϕB0 = 0.65 V. Determine the builtin potential barrier Vbi.

(b)  If the doping concentration changes to Nd = 1016 cm−3, determine the values of ϕB0 and Vbi. Do these values increase, decrease, or remain the same?

(c)   Repeat part (b) if the doping concentration is Nd = 1015 cm−3.

Exercise 7.2
For a p type semiconductor in contact with a metal, when does it form a Schottky contact, and when does it form an Ohmic contact? Please draw the energy band diagram for each case, and explain using your own words

Exercise 7.3
A pn junction diode and a Schottky diode each have cross-sectional areas of A = 8 × 10−4 cm2. The reverse saturation current densities at T = 300 K for the pn junction diode and Schottky diode are 8×10−13 A/cm2 and 6×10−9 A/cm2, respectively. Determine the required forward-bias voltage in each diode to yields currents of (a) 150µA

(b)   700µA

(c)    1.2 mA

Exercise 7.4
A metal, with a work function ϕm = 4.2 V, is deposited on an n-type silicon semiconductor with χs = 4.0 V and Eg = 1.12eV. Assume no interface states exist at the junction. Let T = 300 K.

(a)   Sketch the energy-band diagram for zero bias for the case when no space chargeregion exists at the junction.

(b)  Determine Nd so that the condition in part (a) is satisfied.

(c)   What is the potential barrier height seen by electrons in the metal moving into thesemiconductor?

Exercise 7.5
A metal-semiconductor junction is formed between a metal with a work function of 4.3eV and p-type silicon with an electron affinity of 4.0eV. The acceptor doping concentration in the silicon is Na = 5 × 1016 cm−3. Assume T = 300 K.

(a)  Sketch the thermal equilibrium energy-band diagram.

(b) Determine the height of the Schottky barrier.

(c) Sketch the energy-band diagram with an applied reverse-biased voltage of VR = 3 V.

(d) Sketch the energy-band diagram with an applied forward-bias voltage of Va = 0.25 V

Exercise 7.6
The dc charge distributions of four ideal MOS capacitors are shown in Figure P10.1.

For each case:

(a)  Is the semiconductor n or p type?

(b)  Is the device biased in the accumulation, depletion, or inversion mode?(c) Draw the energyband diagram in the semiconductor region.

Figure 1: Figure for Problem 7.6

Exercise 7.7
(a)   Consider an n+polysilicon-silicon dioxide-n-type silicon MOS structure. Let Nd = 4 × 1015 cm−3. Calculate the ideal flat-band voltage for tox = 20 nm = 200˚A

(b)  Considering the results of part (a), determine the shift in flat-band voltage for (i)   cm−2 and (ii) .

(c) Repeat parts (a) and (b) for an oxide thickness of tox = 12 nm = 120˚A.

Exercise 7.8
Consider an n+polysilicon gate on silicon dioxide with a p-type silicon substrate doped to Na = 3 × 1016 cm−3. Assume 10 cm−2. Determine the required oxide thickness such that the threshold voltage is VTN = +0.65 V. Please provide the process of derivation.

Exercise 7.9
Draw the C-V curves of a MOS capacitor with n-type Si as the substrate, at low frequency and high frequency, respectively. Explain why they are different.