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Title: Heat flux flow of PN-junction gallium arsenide semiconductor device
Article Type: S.I.: ICT2009
Keywords: Peltier heat flow, PN-junction, laser diode, temperature profile, depletion layer
Corresponding Author: Dr. Satarou Yamaguchi, Ph.D
Corresponding Author's Institution: Chubu University
First Author: Satarou Yamaguchi, Doctor of Science
Order of Authors: Satarou Yamaguchi, Doctor of Science; Shinji Fukuda, Master degree; Toshio
Kawahara, Ph. Doctor; Yoichi Okamoto, Ph. Doctor; Hiroshi Nakatsugawa, Ph. Doctor; Hiroyuki
Kitagawa, Ph. Doctor

Manuscript
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Heat flux flow of PN-junction gallium arsenide semiconductor device
Satarou Yamaguchi, Shinji Fukuda, Toshio Kawahara, Yoichi Okamoto1), Hiroshi
Nakatsugawa2), Hiroyuki Kitagawa3)
Center for Applied Superconductivity and Sustainable Energy Research (CASER),
Chubu University, Japan
1) National Defense Academy, Japan
2) National Yokohama University, Japan
3) Shimane University, Japan
Abstract
Temperature profile inside semiconductor device is a key issue to realize its maximum
performance. One of the simplest the PN junction device is a diode, and the resistivity ofthe depletion layer is high and the heat is generated mainly in the area for usual diodes. If
the temperature of the depletion layer is high, the performance of the device is degraded,especially for the laser diode. The heat flux is transferred from the depletion layer mainlyby thermal conduction for high thermal conductivity material. However, the thermal
conductivity of single crystal gallium arsenide (GaAs) is low as 50 W/Km, and moreover
we must consider the Peltier heat flow near the PN-junction area because the directions of
the heat flows of N- and P-type’s are to the depletion layer. In order to solve this problem,
we measure the thermal conductivity, the Seebeck coefficient and the electrical resistivityof GaAs, and we estimate the temperature of the depletion layer by the computer
simulation.
Introduction
Diode is a common semiconductor device, and this is based on the structure of
PN-junction [1]. Gallium arsenide based PN-junction device is used to make solid-statelaser for the optical fiber communication [2], and therefore it is a key device for themodern life in the present time. The temperature of GaAs laser diode is controlled within
1/100 K to keep stable emission and its wavelength. This is the basis of wavelength
division multiplex (WDM) [3], and the temperature control is a key technology for thelaser diode, and the Peltier module is used with the laser diode. The temperature of the
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device is determined by both of the heat generation, heat transfer and the light emission.
Therefore, if we would estimate the performance of light emitting diode, we must know
and control the temperature profile inside the diode precisely.
Usually we use the numerical software to estimate the temperature profile inside thesemiconductor device, and it is called a numerical device stimulator [4, 5, 6]. The
software solves the heat balance equation to obtain the temperature profile, and it
includes the physical processes of the Joule heating by electric current, the heat transfer
by the thermal conduction. But we know a different process of the heat transfer by theelectric current as Peltier heat flow, and unfortunately it is not included in the present
numerical software because the thermoelectric effect is not thought to be large. However,
it is important to estimate the temperature of the PN-junction part precisely, especially forthe laser diode, we must consider the Peltier heat flow in detail because the emission andthe wavelength of the light from the GaAs diode depend on the temperature of thedepletion layer. In order to fix this problem, we measured the Seebeck coefficient of thesingle crystal GaAs for the laser diode at first. We calculate the temperature profile of thediode by ANSYS [7] in this paper.
Heat transfer model of diode by thermoelectric effectFigure 1 shows the diode structure, its symbol, its current direction and the
directions of Peltier heat flow.

current

P-typeN-typePeltier heat flo w
Fig. 1 Diode structure, symbol, current direction and the direction of Peltier heat flow
The magnitude of diode current is limited by the temperature because when thetemperature is high, the crystal of diode material would be destroyed by the electric
current. Therefore, we keep the diode low temperature, and use the cooling system for it.
Usually when the cooling system is effective, we can use the diode in high current. This
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means that when we keep the laser diode low temperature, we can expect that the light isstrong. The maximum temperature part of the diode is usually located around thedepletion layer of PN-junction because the resistivity of the depletion layer is quite highand we cannot cool the depletion layer directly. Radiation fin is usually connected to theelectrode of the diode for the cooling, and it means that we can cool it at the end of thediode or the diode electrode. As is shown in Fig. 1, since the directions of Peltier heatflows are toward the depletion layer in both sides of P- and N-types of semiconductors,
the temperature of the depletion layer will be increased by the thermoelectric effect.
Therefore, if the Seebeck coefficient is high, the heat fluxes from the both sides to thedepletion layer is high by Peltier effect, and therefore the temperature of the depletion
layer of the laser diode will be high. This phenomenon can reduce the performance of thelaser diode. This situation is common for all diodes.
Measurement of transport parameters of Gallium arsenide
We prepared two samples to measure the transport coefficients of the single crystal GaAs.
This is the laser diode grade material, and two samples were obtained from the same ingot
and they are N-type material. The carrier density of the sample is 1.3x1018 cm-3. The sizeof the sample is the length of 20 mm, the wide of 4 mm and the thickness of 1 mm. The
electrical resistivities of the samples are shown in Fig. 2.
3.0x10-5

GaAs #1
GaAs #2

Resistivity [m]

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2.8x10-5

2.6x10-5

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2.0x10

-5

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T [K]

Fig. 2 Temperature dependences of resistivity of the single crystal GaAs
The resistivities of two samples are almost same, and they are the same order of the other3/9

reported data [8].
Figure 3 shows the temperature dependence of the thermal conductivities. The
temperature difference of the samples is around 8 K to measure the thermal conductivity.
Unfortunately, we cannot measure the sample #1 in this time. The reported value of thethermal conductivity is around 50 W/Km [9], and the thermal conductivity increased with
the increase of the temperature. But the measured values are smaller than the reported
value, and the temperature dependence is also different from the report. The thermal
conductivity is decreased with the increase of the temperature around the room
temperature.
60
GaAs#250

 [W/Km]

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T [K]

Fig. 3 Temperature dependences of thermal conductivity of the single crystal GaAs
Finally, we measure the Seebeck coefficients as shown in Fig. 4. The
temperature difference of the sample is around 1.5 K to measure the Seebeck coefficientin this time. The values of two samples are similar to each other, and their temperaturedependences are also similar. This data is consisted with the reported values in the rangeof the carrier density in ref. [10].

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0

Seebeck Coefficient [V/K]

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GaAs #1
GaAs #2
-50

-100

-150

-200
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T [K]

Fig. 4 Temperature dependences of Seebeck coefficient of the N-type single crystal
GaAs.
Numerical calculation by ANSYS
After we measured the transport parameters of the single crystal GaAs, we did thenumerical calculation by ANSYS [7] to estimate the temperature profile of the diode. The
numerical model of the calculation is shown in Fig. 5.
N-GaAs

Cu

-

100

240

P-GaAs

++ -

Cu

1 1
10

100

Fig. 4 Numerical model of GaAs laser diode.
The cross-section of the diode is 100 x 100 m, and the numbers in the figure show thelengths of the parts in m. The both ends are the copper electrodes and are shown as Cu.
N-type GaAs is located left-hand side, and the minus sign (-) shows the low carrier
density part, and it is 1018 cm-3, and the plus sign (+) shows the high density part and it is1019 cm-3. The P-type parts are located in right-hand side, and the lengths are shown infigure, and the carrier densities are the same as the N-types’. This is the typical structure
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of the laser diode. The length of the depletion layer is set to be zero in this model because
it is thin, but we insert the heater into the PN-junction face to simulate the depletion layer.
The heat generation of the heater is proportional to the square of the current. The
boundary condition of the temperature is set to be 300 K at the end of the electrode ofN-type side.
However, in order to calculate the temperature in the model, we should makesome assumptions to estimate the transport parameters in different carrier density regionsof the model. We only measure the transport parameters for one sample, and its density
profile is uniform. And therefore, we did not have the data of the transport parameters in
different carrier density. Therefore, we should make the assumption for the different
carrier density. Instead of the measurements, we estimated the electrical resistivity fromthe measured values along the ref. [8]. This is based on the relation with resistivity andimpurity concentration. We also assumed the Seebeck coefficient in different carrier
density from the measured values along ref. [10]. The thermal conductivity is assumed tobe constant for the carrier density in the model both for N-type and P-type GaAs because
the phonon process is major than that of electronic process for the thermal conduction.
We could not also measure a P-type sample in this time, and unfortunately we also cannot
find the Seebeck coefficient of P-type samples in the academic journals. Therefore, we
assumes that the absolute value of the Seebeck coefficient is the same as the N-type’s forthe same carrier density. Finally, the transport parameters of the model in Fig. 4 aresummarized in Table 1.
Table 1 Transport parameters and heater model for numerical calculations

The effective resistivity of the heater is set the numerical calculation result of the device
simulator [6], and its length is 1 m. The heat generation is proportional to the square of
the current.
The calculation results of the junction temperature are shown in Fig. 5.
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400
No Peltier
Peltier
380

360

Tj [K]

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I[mA]

Fig. 5 Calculation results of the junction temperature by ANSYS [7].
We did two types of the calculations. One include the Peltier effect, and the calculation
results are shown as the squares. The other does not include the Peltier effect, and they are
shown as the circulars in the figure. When we include the Peltier effect, the temperature ishigher than the model’s that does not include the Peltier effect. These results are consistedwith the Fig. 1, and the temperature difference depends on the magnitude of the current.
When we apply large current, the temperature difference is 0.43 K at the current of 10 mA,
and 2.53 K at the current of 100 mA. These differences are 100 times larger than thevalues of the keeping temperature for the stable operation of the laser diode as mentioned
in Introduction.
Discussion and Conclusion
The calculation results shows that we must include the Peltier effect to estimate
the temperature at the depletion layer precisely, and it is important to estimate theperformance of the laser diode as shown in Fig. 5. However, we should continue toperform the experiment to obtain the actual parameters for the P-type GaAs. We also
should pay attention to make a precise model for the calculation, too. And we should take
into account the Peltier effect for all diodes. Finally the numerical simulator must include
the Peltier effect in the software.
As mentioned in Fig. 4, the Seebeck coefficient is change within short length,
and therefore we should take into account the Thomson effect because the gradient of the
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Seebeck coefficient might not be small. This situation is similar to the FGM, but it is not
same as the concept of the FMG because the transport parameters are measured andestimated in the condition of charge neutrality for the FGM, but the PN-junction is notalways keep the charge neutrality. The impurity profile around the depletion layer is notchanged by the current, and the charge neutrality is kept even for the presence of theelectric current without the area of electrode contact in the thermoelectric module.
However, the carrier density in the depletion layer depends on the magnitude of thecurrent in spite of the impurity density constant. Therefore, we must continue to discussand research the model of the calculation.
The authors thank to Prof. Makoto Sakata in Keio University for his continuos
encouragement and supports through the whole research. We acknowledge Prof. Atsuo
Iiyoshi, the President of Chubu University, for his support in Chubu University. We also
thank to Mr. Noriyuki Ishihara, Mizuho Information and Research Institute, for his
discussion about the model of diode, and also thank to Dr. Makoto Hamabe and Mr.
Hideki Yamada for their helps of the experiments and the calculations.
References[1] W. Shockley, Bell Syst. Tech. J., 28, 435 (1949).
[2] G. P. Agrawal: Fiber-Optic CommunicationSystems (3rd eds.), John Wiley & Sons
(2002).
[3] Y. Koyama, S. Arahira, Y. Kato and D. Kunimatsu, J. of Electronics, Information andCommunication Eng., Vol. J84-C, No. 1, pp. 1-10, 2001 (Japanese).
[4] http://www.synopsys.com/Tools/TCAD/DeviceSimulation/Pages/TaurusMedici.aspx[5] http://newwww.silvaco.com/products/device_simulation/atlas.html[6] Fuji Sougou Kenkyu-jo ed.: Device Simulator – Supercomputing Technology,
Maruzen, 1991 (Japanese).
http://www.mizuho-ir.co.jp/solution/research/semiconductor/devicemeister/wv/index.ht
ml[7] http://www.ansys.com/[8] S. M. Sze and J. C. Irvin, Solid State Electron., 11, 599 (1968).
[9] M. G. Holland, Phys. Rev., 134(2A), A471 (1964).
[10] G. Homm, P. J. Klar, J. Teubert and W. Heimbrodt, Applied Phys. Lett., 93, 042107
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(2008).

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