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The Report of the Characteristics of Semiconductor Laser
Experiment
Masruri Masruri (186520)
22/05/2008
1 Laboratory Setup
The experiment consists of two kind of tasks:
• To measure the caracteristics of Power versus Injected Current
(P vs I) of laser by varyingthe temperature value (10o, 25o, and
50o C).Here we have to estimate the value of threshold current,
Ith, using the fitting method of thetwo segments which are the
segment before the lasing and the segment after the lasing. Wealso
estimate the conversion efficiency of the laser for the indicated
temperature. To performthis task we use the Power Meter which is
depicted in Fig. 1.
Fig.1a: The Laboratory Setup for Estimating the Threshold
Current
In Fig. 1, we connect the laser which has been connected with
the controller (to controlthe temperature and the injected current)
to the Optical Sensor which has been connectedwith the Power Meter
to measure the power. The following are the procedures to setup
theexperiment:
1. Make sure that laser is off.
2. Connect the interface of the fiber connector to the input of
Optical Sensor.
3. Power on the power meter.
4. Power on the laser
5. Set the value of the indicated temperature, for example 10o C
and fix it. Varying theinjected current of the laser and see the
power output on the power meter’s display foreach of the injected
current. Do the same procedure for the other indicated
temperatures(25o and 50oC)
• Using the Optical Spectrum Analyzer (OSA) to:
- measure the slope of wavelength, λ, with the varies of
temperatures from 10o and 50oC,fixing the injected current at
100mA.
- Measure the slope of wavelength, λ , with the varies of the
injected current from 20 mAto 150 mA, fixing the temperature at 25o
C.
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- Use the linear estimation to valutate the dependence from the
two different parameters,T and I.
To perform this task we use the Power Meter which is depicted in
Fig. 2.
Fig. 1b: The Laboratory Setup for Estimatingthe Dependence of
Wavelength from Temperature and Current.
In Fig. 2, we connect the laser, which has been conneted to the
controller (to control thetemperature and the current), to the OSA
to measure the central wavelength and its peakpower. The following
are the procedures to setup the experiment:
1. Make sure that laser is off.2. Connect the interface of the
fiber connector to the input of OSA.3. Power on the OSA.4. Turn on
the laser.5. Set the parameter of the OSA.
The parameters of OSA that we have to setup are:- Resolution
bandwidth
The ability of OSA to display two signal closely spaced in
wavelength as two distinctresponses is determined by the wavelength
resolution. Wavelength resolution is de-termined by the bandwidth
of the optical filter. The term of resolution bandwidthis used to
describe the width of the optical filter in an OSA.
- SensitivitySensitivity is defined as the minimum detectable
signal and is defined as six timesthe root-mean-square noise level
of the instrument.
- SpanThe minimum wavelength and the maximum wavelength is
desired to display in themonitor.
2 Fitting Method
In the experiment 1, we would like to find a threshold current
of the semiconductor laser. Themethod that we use is to divide the
curve into two segments which are the segment before thelasing and
the segment after the lasing. Then we make the fitting line to each
of these segments.We then find the intersection point between these
fitting lines. The point of I of this intersection isthe estimated
threshold current for the laser. Fig 3 describes the method.
The following is the method to find the threshold current:
1. Divide the data from the experiment, the first group is the
data before the lasing happenedand the second is the data in which
laser start to lase. We choose the current (which is theindependent
variable that we change during the the experiment) in which it
start to producethe power which has considered in the range of the
mW. For example the amount 0.98 mWis considered the laser to start
to lase, while the amount of 0.0012 mW is considered not yet.
2. From these two groups of data we do fitting to using the
Least Square Method to find theline regression of the data.
3. From the line we can find the intersection point to obtaine
the threshold current.
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Fig. 2: Fitting of Two Segments
3 Minimum Linear Square
From the experiment, let say that the independent variable
(current) is called xi, and the dependentvariable (Power) we call
yi. we can find the linear approach using the equation.
P (xi) = a1xi + a0 (1)
We have to find a1 and ao such that the line can pass the points
with the minimum error whichcan be formulated as below:
E(a0, a1) =m∑
i=1
yi − P (xi)
With the least square method the error function is modified as
below:
E(a0, a1) =m∑
i=1
[yi − P (xi)]2
Subsitute to the equation (1) we obtaine
E(a0, a1) =m∑
i=1
[yi − (a1xi + a0)]2
The error E(a0, a1), will be maximum/minimum if satisfies the
the requirement
∂E(a0, a1)∂ai
= 0
where i = 0, 1. In this case we find
∂E(a0, a1)∂a0
=∂
∂a0
m∑i=1
[yi − (a1xi + a0)]2 = 0
2m∑
i=1
[yi − a1xi − a0)(−1) = 0
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a0.m+ a1m∑
i=1
x1 =m∑
i=1
yi
And
∂E(a0, a1)∂a1
=∂
∂a1
m∑i=1
[yi − (a1xi + a0)]2 = 0
2m∑
i=1
[yi − a1xi − a0)(−xi) = 0
a0
m∑i=1
x1 + a1m∑
i=1
x21 =m∑
i=1
yi
And we obtaine
a0 =∑m
i=1 x2i
∑mi=1 yi −
∑mi=1 xiyi
∑mi=1 xi
m(∑m
i=1 x2i )− (
∑mi=1 xi)2
(2)
a1 =m
∑mi=1 xiyi −
∑mi=1 xi
∑mi=1 yi
m(∑m
i=1 x2i )− (
∑mi=1 xi)2
(3)
Subsitute (2) and (3) to (1) to obtain the fitting equation.We
will use this least square method to find the linear regression for
both the experiment 1 and
experiment 2.
4 Experiment I
Using the fitting method which have been expained in the
previous section, we find the linearequation and also the current
threshold which is the intersection between the fitting lines.
Theresults are summarized in Table 1.
Temperature Line Line Current Conversion Efficiency
(◦C) Equation 1 Equation 2 Threshold (mA) of Laser (mW/mA)
10 −0.001195776 −12.90368838 20.398 0.644229549+0.000386667xi
+0.644229549xi
25 −0.011535177 −12.0898828 21.008 0.57669286+0.001751647xi
+0.57669286xi
50 −0.102305636 −9.445754605 24.1996 0.396285886+0.010186882xi
+0.396285886xi
Table 1. The Fitting Lines, Threshold Current and Conversion
Efficiencyof Laser for the temperature 10o, 25o, and 50oC.
The curves for each of the temperature are depicted in Figure 4
- Figure 9. Note that for all ofthese curves using the legend as
below:
The conversion efficiency (slope efficiency) of the laser can be
obtained from the slope of thecurve after the lasing [8], in this
case is the slope of the line equation 2 which is the equation of
the
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splitting line after the lasing.
ηd(I, T ) =dP
dI(4)
From Table 1, the conversion efficiency of the laser is
0.644229549, 0.57669286, and 0.396285886mW/mA for 10oC, 25oC, and
50oC, respectively. Fig. 3 describes the conversion efficiency as
afunction of temperature. It tells us that the efficiency decreases
with an increase in the temperature.
Fig. 3: Conversion efficiency as a function of temperature
Fig. 4,6,8 are the curves for each of the indicated temperature,
and the threshold current weobtain by zooming the curves in are
indicated in Fig. 5,7,9 for the temperatures 10o,25o, and
50o,respectively.
5 Experiment II
The result of experiment 2 using the least square method is
described in Table 2.
Description Fitting Equation slope
Fixing I at 100 mA, varying T between 975.518761 + 0.312256248xi
λ versus T : 0.312256248
10o and 50oC. (Central Wavelength)
4.569116508− 0.034021823xi Ppeak versus T : - 0.034021823(Peak
Power)
Fixing T at 25oC, varying I between 980.2914604 + 0.027351485xi
λ versus I : 0.027351485
20 mA and 150 mA (Central Wavelength)
−11.49497215 + 0.12493255xi Ppeak versus I : 0.12493255(Peak
Power)
Table 2. The fitting lines for each of the reference temperature
and injected current.
Fig.10 describes that by fixing the injected current, I, at
100mA the central wavelength, λ,increases as the increase of the
temperature, T, between 10oC until 50oC. The fitting line shows
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Fig. 4: P versus I, fixing the temperature at 10oC
Fig. 5: Estimated threshold current at 10oC
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Fig. 6: P versus I, fixing the temperature at 25oC
Fig. 7: Estimated threshold current at 25oC
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Fig. 8: P versus I, fixing the temperature at 50oC
Fig. 9: Estimated threshold current at 50oC
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that the λ increases linearly as the temperature increases. From
the Table 1, it is shown that theslope for the dependence between λ
and T is 0.312256248.
Fig. 10: λ versus T, fixing I at 100mA (OSA with resolution
bandwidth 0.2 nm,sensitivity HIGH 1, span 925, 1025nm)
Figure 11 describes that by fixing the injected current, I, at
100mA the peak power, Ppeak,which is the Power (dBm) at the central
wavelength, decreases as the increase of the temperature,T, between
10oC and 50oC. The fitting line shows that the Ppeak decreases
linearly as the tem-perature increases. Table 2, it is shown that
the slope for the dependence between Ppeak and T
is-0.034021823.
Figure 12 describes that by fixing the temperature, T, at 25oC
the central wavelength, λ,increases as the increase of the injected
current, I, between 20mA and 150mA. The fitting lineshows that the
λ increases linearly as the temperature increases. From the Table
2, it is shown thatthe slope for the dependence between λ and I is
0.027351485.
Figure 13 describes that by fixing the temperature, T, at 25oC
the peak power, Ppeak, increasesas the increase of the injected
current, I, between 20mA and 150mA. The fitting line shows
thatPpeak increases linearly as the injected current increases.
Table 2 describes that the slope for thedependence between Ppeak
and I is 0.12493255.
Figure 14 describes the spectrum of laser using OSA at the
reference temperature 25oC.Figure 15 describes the spectrum of
laser using OSA as the temperature varies from 10o, 25o, and
50oC, respectively. It is shown that the central wavelength is
shifted to the right as the temperatureincreases, and the Power
(dBm) decreases as the temperature increases.
6 Theoritical Analysis
6.1 Threshold Current Varies with the Temperature
The lasing threshold current of injection lasers can have
related exponential dependences on tem-perature is reported by
Pankove [1]. The Pankove equation can be written by:
Ith = I0 expT
T0(5)
Where I0, is the threshold current extrapolated to T = 0oK and
T0 is a coefficient which iscalled caracteristic temperature.
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Fig. 11: Ppeak vs T, fixing I at 100mA (OSA with resolution
bandwidth 0.2 nm,sensitivity HIGH 1, span 925, 1025nm)
Fig. 12: λ versus I, fixing T at 25oC (OSA with resolution
bandwidth 0.2 nm,sensitivity HIGH 1, span 925, 1025nm)
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Fig. 13: Ppeak versus I, fixing T at 25oC (OSA with resolution
bandwidth 0.2 nm,sensitivity HIGH 1, span 925, 1025nm)
Fig. 14: Spectrum Laser using OSA (resolution bandwidth 0.05nm,
sensitivity HIGH 3,temperature 25oC, current 100mA)
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Fig. 15: Spectrum Laser OSA based on temperature (resolution
bandwidth 0.05nm,sensitivity HIGH 3, temperature 25oC, current
100mA)
If we take into account in the two different temperatures let
say T1 and T2, we can find thecharacteristic temperature, T0, using
the equations: [2]
Ith1 = I0 expT1T0
(6)
Ith2 = I0 expT2T0
(7)
Dividing (6) by (7) gives
Ith1Ith2
= eT1−T2
T0 (8)
T0 can then be determined by taking the natural log of both
sides of (8) and rearranging
T0 =T1 − T2
ln(Ith1/Ith2)(9)
T0 is a measure of the sensitivity of the laser to changes in
temperature. If it is very large, thethreshold current Ith will not
vary greatly with changes in temperature, on the other hand if T0
issmall, the threshold current varies with the
temperature.Researchers have investigated the factorsthat influence
a low T0. Some factors which has been investigated by Asada [3] are
depicted in Fig.16.
The threshold condition of semiconductor lasers can be expressed
as the gain being equal tothe total losses. This condition
determines the threshold carrier density nth since the material
gainand the loss depend on the carrier density. nth and the carrier
lifetime τs, determine the thresholdcurrent Ith. Thus, the
temperature characteristics of Ith are determined by those of the
gain, theloss, and the carrier lifetime. The intervalence band
absorption is related to the loss and reduces thedifferential
quantum efficiency ηd, while the nonradiative recombination (in
particular, the Augereffect) and the carrier leakage over the
heterobarrier determine the carrier lifetime. These relationsare
schematically shown in Fig. 16.
Li [2] had used simple model based on his observation that
researchers had evaluated threefactors that cause a low T0, which
is current leakage (coef A), net optical gain (coef B), and
Augerrecombination (coef C). The simple model of threshold current
that had been used by Li:
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Fig. 16: The process investigating the temperature
characteristics ofthe threshold current in the paper of Asada
[3]
Jthqt
= Anth +Bn2th + Cn3th (10)
Where: q = electron charge ; t=active layer thickness ;
If we denote the temperature sensitivity for the threshold
density as dnthdT then the temperaturesensitivity can be written
as:
dJthdT
= qt(A+Bnth + Cn2th)dnthdT
(11)
From the simulation based on the three factors explained before,
Li [2] has suggested that Augerrecombination and current leakage
through diffusion over the barrier are considered two major
pathsfor leakage currents responsible for low T0 in InGaAsP lasers.
The leakage current is caused byelectrons and holes passing the
active region without recombination.
Another experiments that give the same conclusion to Li that
auger recombination plays asignificant role for the temperature
sensitivity of the threshold current (low T0) are Dutta [4],
andHaug[5].
6.2 Auger Recombination
In semiconductors an Auger transition occurs when an electron
and a hole recombine and release en-ergy to another electron or
hole nearby in the crystal. The energy released by the captured
carrier inmultiphonon emission is used to generate lattice
phonons[6]. There are two types of Auger processesin
semiconductors, direct auger recombination which is dominant in
narrow-gap semiconductors,and phonon-asisted auger recombination
which is dominant in wide-gap semiconductors. Directauger
recombination is also called phonon-less auger recombination.
Further, both the phonon-lessand phonon-assisted auger processes
are divided by CHCC auger process (CHCC-AP) and CHHSauger process
(CHHS-AP). In CHCC, energy is transfered to an electron, while in
CHHS, energy istransfered in a hole (see Fig.17). Phonon-less AP
are strongly temperature-dependent, in contrastto phonon-assisted
AP[7].
To understand the relationship between threshold current and the
auger recombination we canrefer to the formula as follow:
Ith =qNthτc
=q
τc(N0 +
1GNτp
) (12)
The exponential increase in the threshold current with
temperature which has been explainedusing Pankove formula, can be
understood from Eq. (12). The carrier lifetime τc is generally
Ndependent because of Auger recombination and decreases with N as
N2. N is carrier population.
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Fig. 17: CHCC-AP (left) and CHHS-AP (right)Eg - band-gap; ∆Ec
(∆Ev) - conduction (valence) band barrier offset; ∆SO -
spin-orbital splitting
The rate of Auger recombination increases exponentially with
temperature and is responsible forthe temperature sensitivity of
InGaAsP laser.[9]
6.3 Power Peak Decreases with an Increase in the Temperature
Fig. 11 describes that by fixing the injected current at 100mA,
the peak power increases as anincrease in the temperature. This
phenomenon can be explained as follow:[9]
For I > Ith, the photon number P increases linearly with I
as
P =τpq
(I − Ith) (13)
The emitted power Pe is related to P by the relation
Pe =12
(νgαmir)hωP (14)
Equation (13) shows that P depends on the injected current, I,
and threshold current, Ith (asτp and q constants). As I is fixed,
in this case 100mA, P depends only on the Ith. Here P decreaseswith
an increase of Ith. From Table 1 we know that the threshold current
increases as an increaseof the temperature. Here we can say that P
decreases with an increase of the temperature. Sincefrom equation
(14), the emitted power depends on the photon number P we can
conclude that anincrease in the temperature decreases the emitted
power. In this experiment the peak power is theemitted power of the
central wavelength.
6.4 The Central Wavelength Shifts as Temperature Varies
The refractive index of silica varies linearly with temperature
via the thermal expansion and thethermooptic effects [10]. To
explain the relationship between wavelength and the refractive
indexfor simplicity we can use the equation for the fabry-perot
with the length L.[11]
λ =2nLm2
(15)
From the eq. (15), the wavelength increases linearly with an
increase in the refractive index.Since the refractive index varies
linerarly with temperature, this impacts that wavelength
changeslinearly with the temperature.
The increase of injected current can also cause the heat in the
active layer which change therefractive index and finally can shift
the wavelength.
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7 Conclusion
We can summarized the analysis of the experiment as follow:
• Threshold current depends on the temperature.Threshold current
increases with an increase in the temperature.
• Fixing the injected current, the central wavelength shifts as
the increase of temperature.
• Fixing the injected current, the peak power decreases with an
increase of temperature.
• Fixing the temperature, the central wavelength shifts as the
increase of injected current.
• Fixing the temperature, the peak power increases with an
increase in the injected current.
References
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efficiency and lasing threshold in laserdiodes,” IEEE J. Quantum
Electron.,Vol. QE-4, pp. 119-122, April 1968.
[2] Z.-M. Li and T. Bradford,”A comparative study of temperature
sensitivity of InGaAsP andAlGaAs MQW lasers using numerical
simulations,” IEEE J. Quantum Electron., Vol. 31, pp.1841-1847,
October 1995.
[3] M. Asada and Y. Suematsu, ”The effects of loss and
nonradiative Recombination on the Tem-perature Dependence of
Threshold Current in 1.5-1.6 pm GaInAsP/InP lasers,”IEEE J.
Quan-tum Electron.,vol. QE-19, pp. 917-923, June 1983.
[4] N. K. Dutta and R. J. Nelson, ”Temperature dependence of the
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[5] A. Haug, ”Theory of the temperature dependence of the
threshold current of an InGaAsPLaser,” IEEE J. Quantum
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[6] F. A. Riddoch and M. Jaros,”Auger recombination cross
section associated with deep traps insemiconductors,” J. Phys. C:
Solid St. Phys.,pp. 6181-6188, June 1980.
[7] A. Haug, ”Evidence of the importance of Auger Recombination
for InGaAsP lasers,” ElectronicLetters 19th, Vol. 20, pp. 85-86,
January 1984.
[8] U. Menzel et.all, ”Modelling the temperature dependence of
threshold current, external differ-ential efficiency and lasing
wavelength in QW laser diodes,” Semicond. Sci. Tech., pp.
1382-1392, June 1995.
[9] G.P. Agrawal, Fiber-Optic Communication Sytem, 3rd ed., John
Wiley and Son, 2002.
[10] M. Douay et.all, ”Thermal Hysteresis of Bragg Wavelengths
of Intra-core Fiber Gratings,”IEEE Photonics Tech. Letters, Vol. 5,
pp. 1331-1334, November 1993
[11] S. Selleri. Laser a Semiconduttore. pp. 13. Universita
degli Studi di Parma, 2007.
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