AddendumWESTBROOK, L.D.: 'Measurement of dg/dN anddn/dN and their dependence on photon energy inX = 1.5 ^m InGaAsP laser diodes', IEE Proc. J, Optoelec-tron., 1986,133, (2), pp. 135-142

In the paper the carrier lifetime was assumed to be equalto the differential lifetime as measured using the tech-nique of Olshansky et al. [1]. In this addendum thatassumption is critically examined. The values of dg/dNand dn/dN are re-evaluated and found to be approx-imately 15% lower than previously estimated. The valueof the a parameter, which depends on the ratio of theseparameters, is unaffected, however.

Olshansky [1] expresses the current / and total recombi-nation rate R as power series in N the carrier density,

— = R(N) =eV

bN2 + cN (1)

where a, b, c etc. are coefficients, e is the electronic chargeand V is the active volume. The differential carrier life-time is then

dR(N)

dN= a + 2bN + 3cJV2

(2)

Now, for the purpose of calculating N from the injectedcurrent /, an effective lifetime T* is defined thus:

R(N) = J (3)

If both linear and quadratic terms in R(N) are nonzeroi.e. R(N) = (aN + bN2), the ratio of the effective carrierlifetime to the differential lifetime can be written as

x* a + 2bN 2

xd a + bN 1 + axd(4)

The magnitude of the coefficient a can be found [1] byplotting (l/xd)

2 against current / since, from eqns. 1 and 2,

eV(5)

Fig. 1 shows such a plot for one of the lasers used in theoriginal study. The data appear to fit to a straight linethereby justifying the neglecting of higher powers of N.From the Figure I estimate (I/a) « 3 ns.

Using this value for a it is possible to evaluate the correc-tion needed to the original estimates for T*, dg/dN and

dn/dN. At / = 15 mA, I measured xd « 2.1 ns. This givesan effective lifetime T* « 2.47ns (=1.17 x xd). Similarly,at / = 30 mA, xd « 1.7 ns, and therefore T* « 2.17 ns ( =1.27 x xd).

0.3

0.2

0.1

10 15 20I, mA

25 30 35

Fig. 1 Plot of(l/zd)2 against injected current for device number 2244

Vertical intercept = a1

In my original paper I took an average of T* « 2 ns. Thisvalue would now appear to represent an underestimate ofT* (and hence of N) of 8-23%. Taking the median value,it would seem that the values of dg/dN and dn/dN shouldbe reduced by about 15%, yielding the following dataat the lasing wavelength; dg/dndn/dN « 1.6 x 10-2 0cm3.

2.4 x l (T 1 6 cm 2 and

AcknowledgmentThe author would like to thank C. Stubkjaer, H. Olsenand P. Hanson of the Technical University of Denmarkfor bringing this matter to his attention. The Director ofResearch, British Telecom, is acknowledged for per-mission to publish this addendum.

Reference1 OLSHANSKY, R., SU, C.B., MANNING, J., and POWAZINIK,

W.: 'Measurement of radiative and non-radiative recombination ratesin InGaAsP and AlGaAs light sources', IEEE J. Quantum Electron.,1984, QE-20, pp. 838-854

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122 IEE PROCEEDINGS, Vol. 134, Pt. J, No. 2, APRIL 1987