1.54 μm Lasing from Silicon in Presence of Erbium Doping

M. Q. Huda, M. Z. Hossain

Department of Electrical & Electronic Engineering, Bangladesh University of Engineering & Technology Dhaka 1000, Bangladesh

E-mail: mqhuda@eee.buet.ac.bd

Abstract – Lasing at 1.54 μm from Erbium doped silicon has been studied. A model has been developed for the mechanism of energy transfer to erbium by electron-hole recombination through erbium sites. Emission rates of erbium through intra 4f shell transitions by spontaneous and stimulated processes have been equated with the excitation rates. Detailed analysis on rate equations show the feasibility of achieving population inversion and lasing threshold for incorporation of 1019 cm−3 of optically active erbium sites. Low threshold current densities of the order of A/cm2 has been estimated for optimized lasing conditions. Linear increase of laser output with excitation current has been simulated. Modulation compatibility of the erbium doped silicon lasing system has been studied by introducing small signal components at various operating conditions. It was found that direct modulation of the 1.54 μm erbium emission with frequencies up to Gega hertz level is feasible. The 3 dB bandwidth of laser response was found to be a strong function of the power output. Rate equations of laser operation were also solved for large signal conditions. Turn-on delays of the order of tens of nanoseconds have been estimated.

I. Introduction Erbium doped silicon has been extensively studied in recent times for its prospective application in silicon based optoelectronics [1]-[4]. The motivation is to develop a light emitting source in silicon which is compatible with standard processing technology. This would allow the enormous optical bandwidth to be utilized in on-chip distribution of data and clock signals. The bottleneck of present Integrated Circuit technology in realizing Aluminum/Copper data bus networks for high-speed low dimensional chips can thus be eliminated. Silicon is the material for the semiconductor industry at present and in the foreseeable future. It has tremendous advantages regarding the availability, processing techniques, and cost-effectiveness. It also supports optical processes of waveguiding and detection techniques. However, being an in-direct material, silicon is not radiative. As a result, achieving an on-chip light emitter has been the main hurdle towards the realization of silicon based optoelectronics. Several approaches have been considered in recent years to achieve luminescence in silicon. Among them, the incorporation of Erbium in silicon has attracted lot of interest for its atomically sharp emission at the minimum loss window of fiber optic communication. Different

aspects of silicon erbium systems have been studied and light emitting diode operation have been reported several years ago [5]. Si:Er LEDs however, are yet to be applied in practical circuits due to the lack of sufficient emission power. Also, the relatively larger lifetime of erbium luminescence in silicon makes it unsuitable for direct modulation at high frequencies of operation.

Large emphasis has been given in recent times on prospects of light amplification and lasing action on silicon. Most of the work is being carried out on silica based silicon nanocrystals doped with erbium [6]-[8]. Such structures are process compatible with silicon technology. Erbium atoms sensitized by an external source are reported to provide sufficient stimulus for light amplification at 1.54 μm. Laser operation has also been reported. These silica based structures although promising have the inherent problem of requiring an additional exciting source typically with photon energies larger than the silicon bandgap. On-chip photonic application of these structures would most likely involve external modulators. Attachment of on-chip/off-chip modulators along with the lasing device would demand more silicon space inside the chip.

Achieving lasing action from erbium in silicon in the form of a laser diode would be a proper approach for the silicon photonics. However, due to practical limitations of erbium incorporation related issues in silicon and the moderate or low power emission from Si:Er through electroluminescence, such possibilities have not been explored in depth. Xie et al. [9] first discussed the phenomenon of light amplification and laser operation in erbium doped silicon. Not much work, either in theories or experiments have been done on this topic. We have shown in previous publications that sustained stimulated emission in erbium doped silicon is feasible [10]-[11]. In this paper, we show that, laser action in Si:Er is theoretically possible with the present technology of erbium incorporation. We also make analysis on performance and characteristics of prospective erbium doped silicon lasers.

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II. Erbium Emission in Silicon Erbium atoms when incorporated in silicon produce

energy states in the bandgap. Electron-hole recombination through these sites produce the energy for pumping erbium atoms from their ground state of 4I15/2 to the first excited level of 4I13/2. Radiative transition of erbium atoms from their excited state to the ground state produce the luminescence at 1.54 μm. Thus the 1.54 μm emission in erbium incorporated silicon can be described as radiation via a non-radiative route. The process of light amplification and the subsequent lasing action in erbium-doped silicon can be considered to be a quasi-two level laser system, where erbium atoms are pumped electronically and then interact optically in the lasing system. Unlike a two level system where saturation occurs at the onset of population inversion, erbium-doped silicon can be designed to maintain a sustained level of population inversion through proper excitation of erbium atoms. The electron-hole mediated process of erbium excitation can be represented by a Shockley-Rheed-Hall model [3]. In case of a laser diode, erbium atoms would be excited from the ground state 4I15/2 to the first excited state of 4I13/2 through carrier injection under forward bias. A part of transition of erbium atoms from the excited state to the ground state provide the 1.54 µm emission.

Let NEr be the density of erbium atoms in the active volume, and suppose at a certain condition of electrical excitation, the density of atoms in the 4I13/2 state is given as NEr*. Under this condition, the fraction of erbium sites in the bandgap that are occupied by electrons is given as:

.pcncee

nceNnf

pnpn

np

Er

Ert +++

+== (1)

where, en and ep are the electron and hole emission coefficients from the erbium trap; and cn, cp are the capture coefficients. n and p are the carrier densities.

Rate of electrical pumping of erbium atoms is given as: ( )*

ErErptex NNpcfR −= (2)

Rate equations representing the density of excited atoms, and the optical power density inside the cavity (S) are then given as[12]:

,*

* vkSNdtd

Er

ErexEr

NR −−=τ

(3)

,*

prad

Er SNvkSdtdS

ττβ −+=

(4)

where, ft is the fraction of erbium sites occupied by electrons, cp is the capture coefficients, p is the carrier density, τEr represents the lifetime of erbium decay, τrad is the radiative lifetime, τp is the lifetime of photon decay inside the cavity, v is the velocity of light, and k is the gain coefficient of light. Three terms on the right hand side of (3) represent the rate of excitation of erbium through electron-hole recombination, overall decay rate of erbium atoms, and the net generation rate of photons through stimulated emission, respectively. The last two

Fig. 1. Density of Erbium atoms in excited state as a function of excess carriers. Erbium density is taken as 1019/cm3.Threshold level of population inversion is seen to be a function of optical losses in the cavity. terms on (4) represent contribution of light in the laser cavity through spontaneous emission and the rate of photon loss in the cavity. The fraction β has been estimated to be of the order of 10-3 [6].

Threshold value of gain coefficient for the laser is given as:

.)(

1ln21

21RRLk mth +=+= ααα (5)

where, α represents the internal losses due to scattering, absorption, etc., and αm is the losses of light through the end mirrors. R1 and R2 represent the reflectivities of the two end mirrors.

At threshold, the gain reaches its thresold value of kth and the density of erbium atoms in the excited state gets pinned down at NErTh*. Density of erbium atoms as a function of excess carrier density in the active medium is shown in Figure 1. Cavity length of 300 μm with mirror reflectivities of 90% have been assumed. It is obvious that the internal loss coefficient is a key parameter in

Fig. 2. Density of Erbium atoms in excited state as a function of excess carriers. Erbium density is taken as 1020/cm3.Threshold level can be achieved for cavity losses well above 50 cm-1.

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determining the degree of population inversion necessary for the lasing. Absorption losses of 5 cm-1 or smaller is found to be required for the erbium concentration of 1019/cm3. To accommodate larger values of loss parameters in the laser cavity higher concentrations of erbium density would be necessary. This is shown in Figure 2 where lasing threshold is seen to be achievable at loss coefficients above 50 cm-1 for erbium concentration of 1020/cm3. Erbium concentrations of these order has been demonstrated in silica hosts, but remains a challenge to be incorporated in good quality silicon.

III. Lasing Threshold and Output Power Current density corresponding to the lasing threshold is

given as:

qLnJ eqth

th τ= , (6)

where, nth is the threshold level of excess carrier density, τ is the carrier lifetime in silicon, Leq is the effective depth of erbium incorporated active layer, q is the electronic charge. For current densities above the threshold, photon density builds up inside the cavity due to stimulated emission, and the lasing output is given as[13]:

.mopt SALvhcP αλ

= (7)

Here, λ is the wavelength, L is the cavity length, αm represents the coefficient of light output through end mirrors. The photon density S in lasing condition is given by (3) and (4). Calculated values of laser output as a function of the drive curent is shown in Figure 3. Doping density of 1019/cm3 with emission linewidth of 1 Å is assumed[11],[14]. As seen, laser output in mW range is estimated for drive current densities of the order of A/cm2. It is obvious that larger carrier lifetime of silicon results in smaller lasing

Fig 3 Calculated laser output as a function of drive current density for different silicon lifetime parameters. Lasing threshold of the order of A/cm2 is estimated for erbium concentration of 1019/cm3.

Fig 4 Calculated laser output as a function of drive current density for different emission linewidths for erbium concentration of 1020/cm3. threshold with larger optical output for a specific excitation condition. However, it needs to be mentioned that upper limit of the carrier lifetime in silicon is controlled by the recombination rate of carriers through erbium sites, i.e. the condition when the silicon is of extreme high quality and all recombination routes can be considered negligible in comparison to that through erbium sites. Figure 4 shows the calculated laser output against drive current for different emission linewidth. It is seen that smaller emission linewidth corresponds a smaller lasing threshold with larger optical output. Erbium emission although atomic in nature is typically found to be in the range of 100 Å in photoluminescence measurements [14]. This is due to the coexistence of a number of erbium atomic site symmetry. However, with careful processing, emission linewidth of the order of 1 Å has been reported [15].

IV. Frequency Response Let us assume that the Si:Er laser is biased above

threshold by DC current J0>Jth and a time-varying current ΔJ(t) is added as:

)()( 0 tJJtJ Δ+= (8) Under steady state conditions, the excited erbium atom

and photon density would respond similarly with the drive current and given by:

* * *( ) ( )Er Erth ErN t N N t= + Δ , )()( 0 tSStS Δ+= (9) Putting the time variations in equations (3) and (4), and

assuming sinusoidal signals, the small signal modulation response function can be expressed as [12]:

( )14

213 12

( )( )( )

S AMJ A j A

ωωω ω ω

Δ= =Δ − + (10)

where, A12, A13, and A14 are constants consisting of system parameters. Response of the prospective Si:Er laser normalized to that at zero frequency is given as:

( )13

213 12

( )( )(0)

AMHM A j A

ωωω ω

= =− +

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( )2

2 2r

r jω

ω ω ωγ=

− + (11)

where

and 12A=γ ωr is the relaxation oscillation frequency

and γ is the damping constant of the relaxation oscillation respectively. These two terms play an important role in governing the dynamic characteristics of Si:Er laser. The resonance peak fp is obtained by setting the first derivative of |H(ω) | to zero. The analytic expression of fp is

21

22

221

⎟⎟⎠

⎞⎜⎜⎝

⎛−= γω

π rpf (12)

The 3-dB modulation bandwidth f3dB is defined as the frequency at which |H(ω) | is reduced by 3 dB from its DC value. Eq. (10) provides the following analytic expression for f3dB:

( ) ( ) 21

422222

3 2422

21

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ +−+−= rrr

dBfωωγγω

π

or,

( ) 21

21

4423 2

1⎟⎠

⎞⎜⎝

⎛ ++= rrpdBf ωωωπ (13)

The amplitude of the resonance peak Hp which occurs at frequency ωp=(2π fp ) is obtained by inserting Eq. (11) into Eq. (10):

21

42

41

1

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

rr

pH

ωγ

ωγ

(14)

Fig. 5 Normalized frequency response for erbium-doped silicon laser. Direct modulation up to GHz. level is seen feasible for 1 watt power.

Fig. 6 Profile of the density of photons in the laser cavity against time. Turn on delay around 60 ns with initial spikes are simulated before the continuous mode of lasing.

Normalized frequency response of a laser structure is shown in Fig. 5. It is seen that, direct modulation in Gega hertz. level is feasible for laser outputs in the range of watt.

V. Time Response At the time of laser switching with a drive current above the threshold, a finite amount of time is spent to pump erbium atoms to the threshold level of population inversion. The onset of lasing is marked by an enhanced decay of erbium atoms due to stimulated emission. This creates momentary depopulation of erbium atoms below the threshold level followed by subsequent pumping. The result is a typical turn-on delay accompanied by laser oscillations. The effect can be calculated by numerical solution of (3) and (4). Photon density inside the laser cavity, representing the time function of laser output is shown in Fig. 6. A drive current of 276 A/cm2 with erbium concentration of 1020/cm3 was used. It was found that larger drive currents result in smaller turn-on delays with less effect of initial oscillations.

VI. Conclusions We have studied the prospects of erbium doped silicon laser for its application in on-chip optical communications. A model based on Shockley-Rheed-Hall recombination kinetics and quasi two level lasing analysis was used. Detailed analysis show that erbium doped silicon lasing system is feasible for certain conditions of erbium incorporation. It has been shown that direct modulation of Si:Er laser with frequencies of the order of Gegahertz is possible. Turn-on delays of the order of tens of ns is estimated.

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13Ar =ω

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