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Novel Temperature Characteristics of Gain

Behaviors in Quantum-Dot Lasers

Yi Ho, Tzeng Wei-Chieh and Ching-Fuh Lin*

Graduate institute of Electro-Optical Engineering, National Taiwan University,

No.1, Sec. 4, Roosevelt Road, Taipei, 106, Taiwan, R.O.C

*also with Graduate institute of Electronics Engineering and Dept. of Electrical Engineering

cflin@cc.ee.ntu.edu.tw

Abstract In quantum dots, the increment of temperature

results in red shift of gain spectrum. Thermal state-filling and

electron-phonon scattering lead to extremely large and even

negative T0. Theoretical prediction is confirmed experimentally.

I. INTRODUCTION

Quantum dot is noted for the low threshold current, high

differential gain and high characteristics temperature which

are good for applications. [1]

II. DEPENDENCE OF GAIN SPECTRUM ON

TEMPERATURE

There are three main causes of dependence of peak

wavelength on quantum dot (QD) laser diodes: thermal

expansion, thermal state-filling,

scattering. First, thermal expansion results in decrease of

bandgap energy and red shift. The general expression for

bandgap dependence around room temperature with small

deviation is given by:

and non-equilibrium

2

0

( )

gg

T

+

E TE

T

α

β

=−

…..(1)

where the numerical values for InAs are given by [2].

Second, thermal state-filling causes blue shift . More thermal

energy provides higher probability for electrons reside in

higher energy levels. The last, non-equilibrium scattering

results in blue shift of the spectrum of lower quantized states.

In quantum dots, transition of strongly-localized electrons

involved with phonon can let electrons relax to lower

quantized states. With

electron-phonon scattering can increase the carrier density of

lower quantized states and cause blue shifts of them, in the

meanwhile, decrease the carrier density of higher quantized

states and cause red shifts of them.

III. SCATTERING DEPENDENT ON TEMPERATURE

The capture and relaxation time are determined by

electron-phonon scattering with rates as follows:

higher temperature, such

qdENM

q ifq

if

q

3

2

)( ) 1

+

(

21

τ

ω

?

δ

π

?

−=

∫

….(2)

However, the dependence of scattering rates can be expressed

in power series in positive powers. Consider operation around

room temperature with slight variance of temperature, we can

approximate the scattering ratesare inversely proportional to T.

[4]

IV. NON-EQUILIBRIUM FERMI-DIRAC DISTRIBUTION

When the carrier capture and relaxation is limited in QD,

the distribution of electrons which doesn’t follow Fermi-Dirac

distribution is given by: [3]

1

()

i

if

EE

R

k T

1*exp

B

f E

=

−

+

where

1

11

,

<

+=

se

rc

R

ττ

τ

….(3)

where

e τ

carrier recombination lifetime . The factor R<1 shows that the

, c r

τ

is overall capture/relaxation lifetime, into/in QD,

is stimulated emision lifetime out of QD, and

s τ is

phonon bottleneck can lift the Fermi level and increase the

probability for electrons in higher energy levels. The gain. is

given by :

[]

2

()(,)( ) 2 () 1

−

D

gi inhiii

N

gE gEf E dE

W

ω

?

σ

∫

ω

?

=

…(4)

With small deviation in temperature, the dependence of

e τ and

constant. So the shift of quasi-Fermi level is given by

() ln(1

fgB

ETE k T

∆∆= ∆−

On the right hand of the equation, with

term is negative and the second is positive. At certain

temperature, we can find either blue or red shift will happen at

certain photon wavelength.

In Fig 1, theoretical calculations are performed by

assuming a QD carrier density of 5*1012cm-2 in injector-well

structure layer. We can find the peak gain and peak photon

energy decrease with increment of temperature. The thermal

expansion of the lattice dominates the thermal band-filling

effect and the scattering of phonons and electrons from higher

energy levels. We find red shift finally. The peak gain

decreases with increment of temperature because of lattice

expansion.

c τ can be approximated as linear with T and

s τ as a

)

c T

− ∆

…..(5)

T

∆

>0 the first

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Fig 1. Theoretical Calculation of

Gain for 1st Quantized State Only

290295 300305

Threshold Current

310 315 320 325

2

4

6

8

10

12

14

16

18

20

22

Threshold Current(mA)

Temperature(K)

Theoretical curve

Fitting curve

T0=-295.12K

In Fig 2., we can find T0 <0 for photon energy smaller

than the peak photon energy. For ground state T0 around the

peak photon energy approximate infinitely large and even

negative such as -295.12K at photon energy 0.9 eV.

V. EXPERIMENTAL RESULTS

In Fig 3, red shift with increasing temperature is

observed as predicted by the simulation. The 1st and 2nd

quantized states lase at photon energy 0.98eV and 1.1 eV

respectively.

In Fig 4., we can find the threshold current decrease with

increment of temperature at the photon energy 0.973 eV.

Negative temperature effect is observed with different

positive and even negative T0 values at different

temperatures.

VI. CONCLUSION

In quantum dot, the increment of temperature results in

red shift by thermal expansion which dominates the blue shift

by thermal band-filling and electron-phonon scattering. The

latter two causes bring about improved temperature

characteristics with extremely large positive T0 and even

negative T0 around the peak photon energy theoretically and

experimentally.

Fig 3. Experimental Gain curves

Fig 4. Experimental Threshold Current

ACKNOWLEDGEMENT

This research is supported by NSC93-2120-M-002-011 .

REFERENCES

[1] “Carrier Dynamics and High-Speed Modulation Properties of Tunnel

Injection InGaAs–GaAs Quantum-Dot Lasers”, Pallab Bhattacharya,

Siddhartha Ghosh, Sameer Pradhan, Jasprit Singh, Zong-Kwei Wu, J.

Urayama, Kyoungsik Kim, and Theodore B. Norris, IEEE Journal of

Quantum Electronics, Vol. 39, No. 8, AUG 2003

[2] “Temperature dependence of the photoluminescence emission from InAs

quantum dots in a strained Ga0.85In0.15As quantum well”, Dan P Popescu,

Peter G Eliseev, Andreas Stintz and Kevin J Malloy, Semicond. Sci. Technol.

19 (2004) 33–38 PII: S0268-1242(04)63380-3

[3]”Nonequilibrium distribution in quantum dots lasers and influence on laser

spectral output”H. Jiang and J. Singh, J. OF App. Phys. Vol 85, Num. 10,

1999

[4] “Evalution of Hole drift mobility in glassy As2S3 in the temperature

range 77 - 330 K, A. M. Andriesh, I. P. Culeac, P. J. S. Ewen, A. E. Owen

, Journal of Optoelectronics and Advanced Materials Vol. 3, No. 1, March

2001, p. 27-31

0.80.91.0 1.11.2

-10

-5

0

5

10

15

20

25

30

35

Photon Energy(eV)

Gain(cm-1)

20

30

40

50

oC

oC

oC

oC

290 295 300305 310315 320325

2

4

6

8

10

12

14

16

18

20

22

Threshold Curremt(mA)

Temperature(K)

Theoretical curve

Fitting curve

T0=-295.12K

0.9 1.0

Photon Energy (eV)

1.1 1.21.3

0

10

20

30

40

20

30

40oC

50oC

oC

oC

Gain(cm-1)

290295300 305310315320325

24

26

28

30

32

34

Threshold Current(mA)

Temperature(K)

Fig 2. Theoretical Calculation of

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