Band Energy Modification of

Ferroelectric ZnSnO3 for photovoltaic applications

B.Smith, C. Kons, A. Datta

University of South Florida, Department of Physics

NSF REU grant # DMR-1263066 REU site in Applied Physics at USF

Florida Cluster for Advanced Smart Sensor Technologies1

Blackbody Radiation Comps Problem

The question is broken up into 5 parts (Will discuss each individually)

Uses mainly the power per unit area over a small wavelength interval at location λ which is R(λ) radiated by an ideal thermal radiator at some temperature T.

I will refer to two constants with unchanging variables throughout, C1 and C2

2

C1 = 2πc2h = 3.747 E -16 m4 s-3 kg C2 = hc/k = 0.01440 K m

Part A

For a Blackbody at Temperature T, find an expression for the wavelength at which the maximum power is radiated (λmax(T)). Then evaluate the expression at the temperature of the photosphere of the sun and explain it’s significance.

Took the derivative of R(λ) and set it equal to zero to find maximum and got to here:

Replace C2/λT with u and graphed to find intersection

3

Intersection point occurs when u = 4.965

Final Equation =

The Sun’s photosphere is the surface of the sun and the source thermal radiation collected by solar panels that is converted into energy. 4

0 2 4 6 8 10 12

Grapical Determination of u (hc/λkT)

5ue (̂u) / e (̂u) -1

Part B Integrate R(λ) over all wavelengths and show that the total radiated power per unit

area is proportional to T4.

By plugging in u = hc/λkT we simplify the integral to

5

Constant *

∫ hc

ukT ___( ()5 1 ___( ) eu - 1 kT

-hc( ) ___) u ___

2

1 du

Reduces to:

Constant *

∫4T ( ) hc

k ___4

eu - 1 ____ u( )

3

du

hc k ___

Part C Find the fraction of radiated power in the region of the spectrum

below λmax(T).

We already know we can model the function with a single variable u so we find

Power radiated below λmax(T) = 0.251 or approximately 25 percent of the total area.6

u3

eu - 1______ du = ∫ u3

eu - 1______ du = ∫

infinity

0

infinity

4.965

6.4810

1.62351

Constant *

4

T ( )4

eu - 1 ____ u( )

3

du

Solar Spectrum Curve

7

Part D Starting with the expression for R(λ), derive an expression for the radiated

power per unit area as a function of frequency.

8

ν2

-c ___dλ =

dν

Part E Plot both R(λ)dλ and R(ν)dν for the temperature of the solar photosphere. For each

R, find the value of the independent variable (λmax, νmax) at the respective R has its maximum.

9

Max = 500nmW/m^2 8.42E+13

Solar Spectrum Curve

10

Power v.s. Frequency

11

Max = 3.33E+14W / m^2 1.15992E-07

Frequency v.s. Wavelength

12

Questions

13

Design Slide

14

R(ν)dν = C1ν3 1

c4 e(hν/kT) - 1

________ _________ dν

R’(λ)dλ = 0after

simplification

5 = Tλ (e(C2/λT) - 1)

C2e(C2/λT) _____________

λmax(T) = ukT

hc ____ = 500 nm at 5800 K

Constant *

∫ λ5

1 ___ = Constant * λ4

- 1 ____ λ = ukT

hc ____Constant * T4

=

R(λ)dλ =ukT 1

hc eu - 1____ ______ du2πc2h ( )

5 u5

eu - 1______ du = ∫

15

Design Slide 2

ν

c __ λ =

ν

ν2

-c ___dλ =

dν