*Applet Worksheet**(Open-Circuit PN Junction Virtual Lab)*

Built-in voltage V_{0}= V_{T}ln(N_{d}N_{a}/n_{i}^{2});Thermal voltage V_{T}= kT/q = 25.9 meV at 300 K;Depletion width We_{dep}= [(2_{s}/q)(1/N_{a}+ 1/N_{d}) V_{0}]^{1/2}, whereDielectric permittivity of Siee_{s}= 11.7_{0}= 1.04x10^{-12}F/cm;Assume n_{i}= 10^{10}/cm^{3}at 300 K for Si;x_{n}= W_{dep}*N_{a}/(N_{a}+N_{d});x_{p}= W_{dep}*N_{d}/(N_{d}+ N_{a}); andSpace charge neutrality: N_{d}x_{n}=N_{a}x_{p}.

1) **Review** (*optional*): If you are not familiar with
the Energy Band concepts, study the “Fermi
Level and Carrier Concentration Applet” and its worksheet before continuing
with this virtual laboratory. The applet is at http://jas2.eng.buffalo.edu/applets/education/semicon/fermi/bandAndLevel/fermi.html.
You need to know at least the Energy Band concepts for bulk semiconductors,
the significance of Fermi level, carrier concentrations and their relationship
to the Fermi level, and the formulas to calculate the carrier concentrations.

2) **Calculate** the PN Junction parameters: For a Si PN junction
diode with N_{a}=10^{17}/cm^{3}, N_{d}=10^{16}/cm^{3}
and T=300 K,

a) Find built-in voltage, V_{o}

b) The width of the depletion region., W_{dep}

c) The distance depletion extends on the n and p side , x_{n}and x_{p}.

** Procedure**:

1) Visit the applet entitled “Formation of PN Junction Energy Band Diagram” at http://jas2.eng.buffalo.edu/applets/education/pn/pnformation/pnformation.html. This applet lets you visualize the Energy Band Diagram of a PN Junction under thermal equilibrium (i.e., under the Open Circuit condition).

2) **Select Si, Na=1E15, Nd=1E15, click “SetNewValue” button, and click
“FormJunction” button**. Repeat clicking the “FormJunction/Separate”
button until you are able to visualize the final Energy Band Diagram of
the PN junction. Now, repeat the procedure with Na=1E17 and Nd=1E15.
Pay attention to the condition when the animation of Energy Band Diagram
finally comes to completion. [Hint: watch the green horizontal line
in the band. What is this green line ?]

3) **Click “Separate” button. Select Si, Na=1E15, Nd=1E15, click
the “SetNewValue” button, click the “ShowParameters” button, and click
the “FormJunction” button. ** From the applet, find the built-in
voltage **V _{o}**, the distance depletion extends on the n-side

From applet: V_{o} = (
) volts, x_{n }= (
)mm, x_{p} = (
) mm, and W_{dep} = (
) mm.

Use the formulas given at the beginning of PreLab and calculate the
above parameters below:

Calculation of V_{o}, x_{n}, x_{p}, and W_{dep}:

From calculation in PreLab: V_{o}
= ( ) volts, x_{n
}=
( )mm,
x_{p} = ( ) mm,
and W_{dep} = ( ) mm.

4) **Click “Separate” button. Select Si, Na=1E17, Nd=1E16, click
the “SetNewValue” button, click the “ShowParameters” button, and click
the “FormJunction” button.** From the applet find the following
parameters:

From applet: V_{o}
= ( ) volts, x_{n
}=
( )mm,
x_{p} = ( ) mm,
and W_{dep} = ( ) mm.

Compare this with your calculation in the PreLab:

From calculation in PreLab: V_{o}
= ( ) volts, x_{n
}=
( )mm,
x_{p} = ( ) mm,
and W_{dep} = ( ) mm.

5) **Self-graded Quiz**: For a Si PN junction with **Na=1E15, Nd=1E16
**at
room temperature (300K), **calculate** the Fermi level **E _{f}**
deep inside the p-side and n-side bulks, relative to the intrinsic Fermi
level

[Hint: “Fermi Level and Carrier Concentration Applet”]Calculation

n-side: Ef-Ei = ( ) eV

p-side: Ef-Ei = ( ) eV.

Calculate other PN junction parameters: V

V

Sketch the Energy Band Diagram below without looking at the applet.
In your diagram you must have all the important parameters indicated clearly:
E_{c}, E_{v}, E_{f}, E_{i}, V_{o},
W_{dep},
x_{n}, and x_{p}..

__Energy Band Diagram Sketch__:

__Grade your work using the applet__.
`Give 1 point for each for correctly calculated parameters and 5
points for the Energy Band Diagram (partial credit allowed).
Write your total grade here(max=11. Honor system)`:______