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

[1] J. I. Pankove, ”Temperature dependence of emission 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 lasing characteristics of the 1.3µm InGaAsP-lnP and GaAs − AI0.36Ga0.64As DH Lasers,” IEEE J. Quantum Electron.,vol.QE-18, pp. 871-878, May 1982.

[5] A. Haug, ”Theory of the temperature dependence of the threshold current of an InGaAsPLaser,” IEEE J. Quantum Electron.,vol. QE-21, pp. 716-718, June 1985.

[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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