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Unformatted text preview: Midterm
ECE 227A November 7, 2007 Department of Electrical and Computer Engineering University of California, Santa Barbara (70 pts)
1. An AlGaAs/GaAs based VCSEL is wafer is grown with an active region consisting of 3 — 8nm thick GaAs quantum—wells surrounded by AlogGanAs all sandwiched between two AlGaAs
DBR mirrors. Emission is expected at 860 nm. Before the VCSELs are fabricated, diagnostic edgeemitting lasers are cleaved out of a portion of
the wafer. T we sets of broadarea cleaved—facet chips are formed, both with active widths, w, of
50 um, but with lengths, L, of either 300 or 600 pm. From a numerical modal analysis, the
transverse conﬁnement factor is found to be 0.06 for the in—plane propagating mode. Pulsed light vs. current measurements give the following data for the threshold current and differential
quantum efficiency: Diagnostic Edge—emitters (pulsed): L I_,;, both ends
300 pm 102 mA 71.2%
600 pm 160 mA 59.0% Next the desired 5 x 5 tun square etched—pillar VCSELs are created from this wafer. In this case
' we calculate an axial confinement factor of 0.04, including an enhancement factor of 1.8, for the
vertically propagating mode. This indicates a total effective cavity length of 1.08 pm. We
assume that the lateral—transverse conﬁnement factor is unity, neglect any lateral current or
carrier spreading, and assume that the back mirror is totally reﬂecting, so that all of the light is emitted out of the top surface. In this case we measure the following threshold current and
differential quantum efﬁciency: VCSEL (pulsed 25 C):
It}, : mA 7],; : 40% (all out of the top) We wish to de—embed a number of the internal parameters and use them to predict other
characteristics. For the diagnostic edge—emitters:
(a) What is the injection (internal) efficiency? (7pts)
(b) What is the average internal modal loss? (7 pts) (c) What are the active region g0, and J,, within each quantum well assuming a logarithmic
gain model, g = g0, ln(J/J,,) (15 pts) For the VCSELs:
(d) What is the VCSEL injection efficiency? (7 pts)
(e) What is the VCSEL average internal modal loss? (7 pts)
(i) What is the VCSEL top mirror amplitude reﬂectivity (assuming the bottom mirror has a
unity value)? (12 pts)
(g) What is the expected relaxation resonance frequency at a bias current of 10 mA, if we assume only radiative carrier recombination and neglect any heating? [Assume B = 10—
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2. We now consider cw operation of the VCSELs in which selfheating must be included. Chips
measuring 500 x 500 um are mounted substrate side down to a good heat sink for top emission. From I—V measurements we determine an effective series resistance of 150 Q and a diode ideality
factor of 4, in a simple resistordiode model. We assume an effective substrate thermal
conductivity of 0.45 W/CmK. From additional pulsed measurements with a heat sink temperature of 125 C, we observe that the threshold current doubles to 0.6 mA, and the
differential quantum efficiency is reduced to 30%. (a) What is the thermal impedance of the VCSELS? (7 pts) (b) What are the threshold current and differential efficiency characteristic temperatures, To
and T”? (7 pts) (c) How much cw power is emitted for a 10 mA bias at a 25 C heat sink temperature? (8 pts) (d) Estimate the cw relaxation resonance frequency at 85 C. [Assume the drop in mi is due
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