ECE170A Project 2

Note: All the codes should be submitted in (.mlx) form and remember to write
can still use MATLAB to calculate the results, or you can solve problems by hand
and scan them to PDF file. All the files should be named in ID_Name_problem.

Assignments:
1. InGaAs LED: Calculate the emission spectrum of a GaAs LED with bandgap
energy equal to 1.4 eV at 350K, assume the emission spectrum is given by
n(E)=g(E)*f(E), with g(E)=(E-Ec)^(1/2), f(E)=e^(-(E-Ec)/KT). then assuming the
density states, Fermi distribution and electron concentration are normalized so
that the absolute amplitude value of it is not important. We are only interested
in the shape of the spectrum. Its absolute magnitude is not needed.

(a) plot the density of states g(E) versus energy (eV) for wavelength ranged
from 0.8μm to 1.0 μm
(b) plot the distribution f(E) versus energy (eV) for wavelength ranged
from 0.8μm to 1.0 μm
(c) plot the electron concentration n(E) versus Energy (eV) for wavelength
ranged from 0.8μm to 1.0 μm
(d) calculate the full-width-at-half-max linewidth
(e) estimate the emission peak wavelength (in microns) and frequency (in THz)

2. GaAs LED and SiO2 (glass) Fabry-Perot (FP) Cavity: Assume the GaAs LED output
spectrum is now being passed into a SiO2 resonant cavity (similar to the one in
Project 1). Assume mirror separation is 500 μm and the mirror reflectivity are
95%, and the Sellmeier coefficients of SiO2 can be found in chapter 1 lecture
slide.

(a) plot the output spectrum of FP cavity versus energy (eV) from 0.8μm to 1.0
μm
(b) plot the same versus wavelength from 0.8μm to 1.0 μm
(b) find the nearest resonance mode at 870 nm

3. Temperature dependence of GaAs LED and SiO2 Fabry Perot Cavity: Instead of
assuming the temperature is constant at room temperature, now, consider
GaAs LED bandgap changes with temperature by using Varshni equation.

(a) plot the bandgap energy with temperature ranged from 298K to 398K
(b) plot the wavelength corresponding to the bandgap energy with temperature
ranging from 298K to 398K
(c) plot the peak emission wavelength with temperature ranging from 298K to
398K. How much does the peak emission change?
(d) compare the full-width-at-half-max linewidth for 298K, and 398K, does the

Varshni constants for GaAs are, Ego = 1.519 eV, A = 5.41 × 10−4 eV K−1, B = 204K.
Varshni equation:
Eqs. (3.11.1) → Eph = hv0 ≈ Eg+(1/2) kBT
Eqs. (3.11.2) → Eg = Ego − AT2/ (B + T)

4. LED efficiencies (problem 3.29): A particular 890 nm infrared (IR) LED for use in
instrumentation has an AlGaAs chip. The active region has been doped p-type
forward current of 50 mA, the voltage across it is 1.4 V, and the emitted optical
power is 10 mW. Calculate the PCE, IQE, EQE, and estimate the light extraction
ratio. For AlGaAs, the lifetime parameter is B ≈ 1×10-16 m3 s-1.

5. LED luminous flux (problem 3.30):
(a) Consider a particular green LED based on InGaN MQW active region. The
emission wavelength is 528 nm. At an LED current of 350 mA, the forward
voltage is 3.4 V. The emitted luminous flux is 92 lm. Find the power conversion
efficiency, external quantum efficiency, luminous efficacy and the emitted
optical power (radiant flux)? (Data for Osram LT CPDP)
(b) A red LED emits 320 mW of optical power at 656 nm when the current is 400
mA and the forward voltage is 2.15 V. Calculate the power conversion efficiency,
external quantum efficiency and the luminous efficacy. (Data for thin film
InGaA1P Osram LH W5AM LED)
(c) A deep blue LED emits at an optical power of 710 mW at 455 nm when the
current is 350 mA and the forward voltage is 3.2 V. Calculate the power conversion
efficiency, external quantum efficiency and the luminous efficacy. (Data for a GaN
Osram LD W5AM LED)  