Carrier capture competition between two different quantum wells in dual-wavelength semiconductor lasers

I S 2 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 8, NO. 6, JUNE 1996

Carrier Capture Competitio

Two Different Quantum

Dual-Wavelength Semicond

Jian-Jang Huang, C. C. Yang,

Senior Member, IEEE,

and Ding-Wei Huang

Absb-uct- Based on a three-level model, we have numeri- cally shown that a semiconductor gain medium with a structure consisting of two different quantum wells may lead to dual- wavelength laser operation if the balance of carrier capture competition between the two wells can be reached. The major controlling parameters for the operation are the ratio of the car- rier quantum capture times of the two wells and the absorption constant of the short-wavelength photons by the long-wavelength quantum well. It is shown that there exists a large parameter space for dual-wavelength operation.

UAL-WAVELENGTH semiconductor lasers are useful for the applications such as optical storage, wavelength- division-multiplexing and two-wavelength interferometry [ 11. Such a dual-wavelength operation has been implemented using a grating-lens-stripe-mirror setup in an external cavity [2].

Also, compact dual-wavelength laser diodes were fabricated with structures of two different quantum wells [3]-[6], in- cluding those of alternating tensile- and compressive-strain quantum wells [ 6 ] . In such a device, carriers are captured into both wells and under certain conditions the dual-wavelength oscillation can occur with the two wavelengths corresponding to the two different quantum wells.

The dual-wavelength operation in a structure with two different quantum wells may depend on many conditions; however, an important factor is the competition of carrier capture between the two wells. A balance in the competition is required so that sufficient gain can be provided for either wavelength. In this letter, we use a three-level model to numerically demonstrate that under certain conditions, such a balance is feasible and stable dual-wavelength operation can be achieved if other conditions are favorable. A similar model was proposed to describe the two-wavelength operation in such an asymmetric dual-quantum-well structure [7]. However, the model included many phenomenologic parameters and did not consider carrier quantum capture processes, explicitly. In the model of this letter, we use more fundamental physics param- eters and focus at the carrier capture competition between the two wells.

Manuscript received December 21, 199.5; revised February 2, 1996. This work was supported by NSC Grant 83-0208-M-002-015PC from National Science Council, R.O.C.

The authors are with the Institute of Electro-Optical Engineering and, De- partment of Electrical Engineering, National Taiwan University, l , Roosevelt Road, Sec. 4, Taipei, Taiwan, R.O.C.

Publisher Item Identifier S 1041-1 13.5(96)04316-9.

The basic model we use is depicted schematically in Fig. 1, in which the uncoupled wells 1 and 2 form a quantum well pair. The transition energy between the conduction subband

C1

and the heavy-hole valence subband

H1

of well 1 is assumed to be larger than that of well 2. Real structures for laser fabrication may consist of several periods of such a quantum well pair. The carrier injection process in such a quantum-well structure is modeled as a three-level system [8]. The three levels include the confinement region with carrier number N D , 3-D barrier states with carrier number N ,

and subband states with carrier numbers N g l , N92 in wells 1 and 2, respectively. The tunneling between wells is assumed to be negligible. The carrier transport time T D is used to describe the diffusion and drift processes across the separate confinement region. The quantum capture times rcl and 7c2 denote the coupling between the continuous 3-D states and ground subbands for wells 1 and 2, respectively. The model can be described with the following six rate equations:

__ d N D -

f

- NDVD -

Nc

₍₁₎ d N c - N D ~ D - N c N D N C V F I - N9i -~ - dt

4

T D rn __ - -

d t

T D rcl

(2)

NC??F2 - N92 NC - -~ 7 c 2 7 n (4) ~ (6) d S 2 - F292(N92 - Nt2)S2 s2 r27-2Ng2

+-.

- _ - d t V2 7 P ‘Tnv2

Equations (1)-(6) describe the dynamics of various carrier numbers and photon densities S1and 5’2, corresponding to the transition photon wavelengths,

X I

and X 2 , respectively, from

wells 1 and 2. The effects of nonlinear gain are neglected for mathematical simplicity. Since we have assumed that the photon energy of well 1 is larger than that of well 2, a part of the photons in S I is expected to be absorbed by well 2. 1041-1135/96$05.00 0 1996 IEEE

HUANG et nl.: CARRIER CAPTURE COMPETITION BETWEEN TWO DIFFERENT QUANTUM WELLS IN DUAL-WAVELENGTH SEMICONDUCTOR LASERS 753

~

Confinement factor of h, l-1 0 6

Confinement factor of 1, TZ 0 6

Transparent carrier population of 1, Nt, 2 . 1 4 ~ 1 0 ~

I

I

/Group velocity

well 1

V -

I

holes

7

well 2

Fig. 1. Schematic diagram of the two-quantum-well pair. The transition energy C l - H l of well 1 is assumed to be larger than that of well 2. Thus, a part of the photons emitted from well 1 is absorbed by well 2.

This photon loss from 5'1 is represented by the terms with the absorption constant a in (4) and

(5).

Because the absorption is not at band extrema and its value depends on the carrier density inside well 2, accurate a value cannot be available. In the following, we assume that a has the same order of magnitude as its value of linear absorption near the band extrema. Also, we define a parameter B as the ratio of the fourth term over the second term on the right-hand side of (4), i.e., B represents the ratio of the absorbed photon density over that due to output and other internal loss:

As can be seen in (2), the carriers supplied by the injection current is shared by the two different wells. The dependence of carrier quantum capture time on the depth and/or width is quite complicated [9]-[ll]. It is actually possible to have the carrier quantum capture time of the well of the shorter wavelength either larger or smaller than the one of the longer wavelength. For the well with a shorter carrier capture time, its higher capture rate may lead to a larger photon density

SI

and hence dominates the oscillation of the laser cavity. As will be seen in the following, two major parameters controlling the oscillation conditions are rc2/rcl and B. Those parameters in (1)-(6) not defined yet are explained on Table I.

We have numerically solved (1)-(6) at the steady state with reasonable parameter values (listed on Table I) [12]. Fig. 2 shows the L-I curves of wavelengths A1 [Fig. 2(a)] and A2

[Fig. 2(b)] with r,1 = 1 ps and rc2 = 5 ps for various B

values. In the case 13 = 0, because rc2

>

r,l, the oscillation

of XI dominates at the threshold current 63 mA until the injection current increases up to 123 mA beyond which both wavelengths oscillate. Although A2 can also oscillate, its power is much lower than that of A 1 and its differential output is smaller than that of A l . As B increases, i.e., the transfer of photons of A1 into carriers for X 2 becomes significant, the

dominance of carrier capture for A1 is canceled by the A1 photon absorption, leading to a larger 5'2 and a smaller

SI.

As

TABLE I

PARAMETER VALUES USED IN CALCULATIONS PARAMETER

Canier transport time accross the separate confinement region

Equilibrium factor between N, and N, Equilibrium factor between N, and N,, Equilibrium factor between N, and N,, Photon lifetime Gain constant of h, zp

1

1.6ps

I

g1

I

1 . 8 3 8 2 ~ 1 0 ~

I

I

1

em's-'

I

/ Gconstant of h, ~ 1 . 8 3 8 2 ~ 1 0 ~

I

cm3s-I

I

Carrier lifetime

I

7.

1

2.211s

I

Cavity volume of h,

I

VI

I

6 . 0 ~ 1 0 ~ ' ~ c m '

1

v2

I

6 . 0 ~ 1 o " ~ c m ~ Cavity volume of 1,

ISDontaneous emission factor of 1.

I

r,

I

1 . 0 ~ 1 0 - ~

I

ISDontaneous emission factor of 1-

I

r.,

I

1 . 0 ~ 1 0 - ~

I

20 n

s

E 15

2

10

-

x cu 0 a I Y

, a 5

8

0

20 n

s

E

v 15

2

2

10 cu 0

5

g

5

8

a c

0

Injection Current

(mA)

Fig. 2

of AI. (b) output power of A%. Note that rCl = 1 ps and T,L = 5 ps.

L-I curves for A 1 and A 2 with various L? values. (a) Output power

can be seen in the figure, when B = 0.5, the L-I curves for XI and A 2 are nearly identical, both with a higher threshold

current at 106 mA. When 13 = 1, within the considered injection current range A2 dominates the oscillation.

154

U

0 10 (b)

Fig. 3.

The injection current is 150 mA and T,I = 1 ps.

Output powers of XI (a) and A2 (b) with various ( T , Z / T ~ I . B ) pairs.

Fig. 3 demonstrates the 3-D curves for output power as functions of T c z / r c l and

B.

The injection current is set at 150

mA and rcl is chosen to be 1 ps. As can be seen in the figure, although it is difficult to always make the output powers of X1 and X 2 the same, there exists a quite large region in the

T , ~ / T ~ I - B space for A1 and A 2 to oscillate simultaneously.

If we define the lasing condition as that the output power is larger than 10 pW, the shaded region between the two solid lines in Fig. 4 represents the situation in which both XI and A 2 can oscillate for the parameter values considered

in Fig. 3. This large region of simultaneous oscillation implies that it might not be difficult to fabricate a semiconductor gain medium with two different types of quantum well for dual- wavelength operation. In Fig. 4, we also plot two dashed lines to form the shaded region in which dual-wavelength oscillation is possible when the injection current is reduced to 70 mA. We can see that a larger injection current leads to a larger region for dual-wavelength oscillation.

We have also studied the stability of the dual-wavelength operation with a typical perturbation method. We solved the linearized equations for a small perturbation and found that the perturbation diminished in a manner similar to relaxation oscillations for both wavelengths. This observation assures the

IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 8, NO. 6, JUNE 1996

only Lloscillates 15 10 7c2

z

C l 5

n

-

0.0 0.5 1.0 1.5 2.0

2.5 3.0

B

Fig. 4. Oscillation conditions of XI and X 2 . The injection current is 150 mA (solid lines) or 70 mA (dashed lines). The shaded region for dual-wavelength oscillation lies between the two solid (dashed) lines.

feasibility of stable dual-wavelength oscillation in a structure with two different quantum wells. In summary, we have numerically shown that there existed a quite large parame- ter space in which a semiconductor gain medium with two different quantum well structures could lead to stable dual- wavelength oscillation.

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