\$


*dt* <sup>=</sup> *<sup>α</sup> fv*(<sup>1</sup> <sup>−</sup> *fc*)*Nph* <sup>−</sup> *est fc*(<sup>1</sup> <sup>−</sup> *fv*)*Nph* <sup>−</sup> *esp fc*(<sup>1</sup> <sup>−</sup> *fv*) (26)

 

 

Fig. 17. Comparison of the carrier distribution and the light emission process between (a)

denote the scattering strength of absorption, stimulated emission, and spontaneous emission at photon energy *hν* are *α*(*hν*), *est*(*hν*), and *esp*(*hν*) respectively. *α*(*hν*) is the same absorption coefficient that we calculated earlier in the photodetector section. The rate equation of carriers

where *Nph* is the number of photons and *fc* and *fv* are the occupation probabilities of the electron with respect to the electron quasi Fermi level at *E*<sup>1</sup> and the hole with respect to the

*<sup>E</sup>*<sup>2</sup> <sup>=</sup> *Ev* <sup>−</sup> *<sup>h</sup><sup>ν</sup>* <sup>−</sup> *Eg*

are the energy levels associated with the optical transition at photon energy *hν* and are related by *E*<sup>1</sup> − *E*<sup>2</sup> = *hν*. Since quasi Fermi level depends on the injection level, *fc* (*fv*) is an implicit function of the density of electrons (holes) which include equilibrium electrons (holes) and

The meaning of *fc*(1 − *fv*) is the joint probability of the existence of an electron at *E*<sup>1</sup> in the conduction band and the absence of a hole at *E*<sup>2</sup> in the valence band, which is the condition satisfied when an optical transition occurs at a given photon energy *hν*. It represents both stimulated emission and spontaneous emission. Optical absorption is the opposite process of

Optical gain *g*(*hν*) is determined by the competition of the stimulated emission and the

*g*(*hν*) = *est fc*(1 − *fv*) − *α fv*(1 − *fc*). (29)

*hν* − *Eg* 1 + *mc*/*mv*

1 + *mv*/*mc*

 !"-

n-type doped 0.25% tensile-strained Ge and (b) In0.53Ga0.47As under injection.

*E*<sup>1</sup> = *Ec* +

 


 

*N* related to radiative recombinations is *dN*

hole quasi Fermi level at *E*2, respectively. And

the stimulated emission therefore *fv*(1 − *fc*) is used instead.

 

 -

injected electrons (holes).

absorption:

of direct and indirect band gaps are also reduced under tensile strain. Based on the calculation a tensile strain of about 1.8% is required to make germanium direct band gap. It is difficult to achieve such high strain in epitaxial germanium. By using a thermal mismatch approach to stress epitaxial germanium on silicon as explained earlier, the maximal tensile strain is below 0.20∼0.25%. The energy difference between the direct and the indirect gaps at this condition is only reduced by 20 meV therefore the majority of the injected electrons still occupy the indirect *L* valleys.

N-type doping can be used to solve this problem. When the indirect *L* valleys are filled with the extrinsic electrons thermally activated from n-type donors, the Fermi level is raised to push more injected electrons into the direct Γ valley. An example of the Fermi level versus active n-type doping concentration for 0.25% tensile-strained germanium is shown in Fig. 16. The Fermi level becomes equal to the bottom of <sup>Γ</sup> valley at a doping concentration of 7 <sup>×</sup> 1019 cm−3, where most states of the indirect *L* valleys are filled by electrons and Ge behaves as a direct band gap material.

Fig. 16. Calculations of the Fermi level as a function of active n-type doping concentration in 0.25% tensile-strained Ge is shown in black line. The direct band gap and the indirect band gap at the same strain level is shown in red and in blue respectively. All energies are referred to the top of the valence band.

The carrier distribution and the light emission process of n-type doped 0.25% tensile-strained germanium under injection are schematically shown in Fig. 17 (a). Since the lower quantum states of the indirect *L* valleys are filled by electrons, the energy levels of the available states in both the direct Γ valley and the indirect *L* valleys are equal in energy. The excess electrons are injected into both valleys and the electrons in the direct Γ valley contribute to the direct gap light emission. The heavy n-type doping introduces free carrier absorption which negatively affects the occurrence of net gain, therefore the amount of doping should be carefully modeled and optimized.

#### **3.3 Germanium gain modeling**

Direct band-to-band optical transition includes three processes: optical absorption, stimulated emission, and spontaneous emission. The rate of these electron-photon scattering processes can be described by the product of scattering strength and carrier occupation probabilities. We 20 Will-be-set-by-IN-TECH

of direct and indirect band gaps are also reduced under tensile strain. Based on the calculation a tensile strain of about 1.8% is required to make germanium direct band gap. It is difficult to achieve such high strain in epitaxial germanium. By using a thermal mismatch approach to stress epitaxial germanium on silicon as explained earlier, the maximal tensile strain is below 0.20∼0.25%. The energy difference between the direct and the indirect gaps at this condition is only reduced by 20 meV therefore the majority of the injected electrons still occupy the

N-type doping can be used to solve this problem. When the indirect *L* valleys are filled with the extrinsic electrons thermally activated from n-type donors, the Fermi level is raised to push more injected electrons into the direct Γ valley. An example of the Fermi level versus active n-type doping concentration for 0.25% tensile-strained germanium is shown in Fig. 16. The Fermi level becomes equal to the bottom of <sup>Γ</sup> valley at a doping concentration of 7 <sup>×</sup> 1019 cm−3, where most states of the indirect *L* valleys are filled by electrons and Ge behaves as a

<sup>1017</sup> <sup>1018</sup> <sup>1019</sup> <sup>1020</sup> 0.5

0.25% strain

indirect band gap

direct band gap

Active N−Type Doping (cm−<sup>3</sup>

Fig. 16. Calculations of the Fermi level as a function of active n-type doping concentration in 0.25% tensile-strained Ge is shown in black line. The direct band gap and the indirect band gap at the same strain level is shown in red and in blue respectively. All energies are referred

The carrier distribution and the light emission process of n-type doped 0.25% tensile-strained germanium under injection are schematically shown in Fig. 17 (a). Since the lower quantum states of the indirect *L* valleys are filled by electrons, the energy levels of the available states in both the direct Γ valley and the indirect *L* valleys are equal in energy. The excess electrons are injected into both valleys and the electrons in the direct Γ valley contribute to the direct gap light emission. The heavy n-type doping introduces free carrier absorption which negatively affects the occurrence of net gain, therefore the amount of doping should be carefully modeled

Direct band-to-band optical transition includes three processes: optical absorption, stimulated emission, and spontaneous emission. The rate of these electron-photon scattering processes can be described by the product of scattering strength and carrier occupation probabilities. We

)

7×1019 cm−<sup>3</sup>

Fermi level

indirect *L* valleys.

direct band gap material.

0.55

0.6

0.65

Energy (eV)

to the top of the valence band.

**3.3 Germanium gain modeling**

and optimized.

0.7

0.75

0.8

 - !"- -- - # \$

Fig. 17. Comparison of the carrier distribution and the light emission process between (a) n-type doped 0.25% tensile-strained Ge and (b) In0.53Ga0.47As under injection.

denote the scattering strength of absorption, stimulated emission, and spontaneous emission at photon energy *hν* are *α*(*hν*), *est*(*hν*), and *esp*(*hν*) respectively. *α*(*hν*) is the same absorption coefficient that we calculated earlier in the photodetector section. The rate equation of carriers *N* related to radiative recombinations is

$$\frac{dN}{dt} = a f\_{\upsilon} (1 - f\_{\upsilon}) N\_{\text{ph}} - e\_{\text{st}} f\_{\text{c}} (1 - f\_{\upsilon}) N\_{\text{ph}} - e\_{\text{sp}} f\_{\text{c}} (1 - f\_{\upsilon}) \tag{26}$$

where *Nph* is the number of photons and *fc* and *fv* are the occupation probabilities of the electron with respect to the electron quasi Fermi level at *E*<sup>1</sup> and the hole with respect to the hole quasi Fermi level at *E*2, respectively. And

$$E\_1 = E\_\emptyset + \frac{h\nu - E\_\emptyset}{1 + m\_\emptyset/m\_\upsilon} \text{and} \tag{27}$$

$$E\_2 = E\_\upsilon - \frac{h\nu - E\_\mathcal{S}}{1 + m\_\upsilon/m\_\circ} \tag{28}$$

are the energy levels associated with the optical transition at photon energy *hν* and are related by *E*<sup>1</sup> − *E*<sup>2</sup> = *hν*. Since quasi Fermi level depends on the injection level, *fc* (*fv*) is an implicit function of the density of electrons (holes) which include equilibrium electrons (holes) and injected electrons (holes).

The meaning of *fc*(1 − *fv*) is the joint probability of the existence of an electron at *E*<sup>1</sup> in the conduction band and the absence of a hole at *E*<sup>2</sup> in the valence band, which is the condition satisfied when an optical transition occurs at a given photon energy *hν*. It represents both stimulated emission and spontaneous emission. Optical absorption is the opposite process of the stimulated emission therefore *fv*(1 − *fc*) is used instead.

Optical gain *g*(*hν*) is determined by the competition of the stimulated emission and the absorption:

$$g(h\nu) = e\_{\rm st} f\_{\rm c} (1 - f\_{\rm v}) - \alpha f\_{\rm v} (1 - f\_{\rm c}).\tag{29}$$


Silicon Photonics 23

Germanium-on-Silicon for Integrated Silicon Photonics 25

In n-typed doped germanium, additional free carrier absorption exists due to the existence of

where *nc* and *pv* are the densities of electrons and holes and *ke*, *kh*, *ae* and *ah* are the constants of a material. *ae* and *ah* are usually between 1.5 and 3.5. By fitting the free carrier absorption data in n+Ge Spitzer et al. (1961) and p+Ge Newman & Tyler (1957) in a carrier density range

<sup>1018</sup> <sup>1019</sup> <sup>1020</sup> <sup>−</sup><sup>1000</sup>

The optical gain, the free carrier absorption, and the net material gain which is the difference between first two are calculated with respect to injection level at the photon energy of 0.8 eV (1550 nm) for Ge with 0.25% tensile strain and 7 <sup>×</sup> 1019 cm−<sup>3</sup> n-type doping. The results are shown in Fig. 19. The free carrier absorption is significant even at low injections since the material is heavily doped. The optical gain overcomes the free carrier loss above the injection level of 1.2 <sup>×</sup> <sup>10</sup><sup>18</sup> cm−<sup>3</sup> where germanium becomes a gain medium. At very high carrier injection levels (> 1020 cm−3), the free carrier absorption exceeds the optical gain leading to net loss. Between a large injection range of 1018 cm−<sup>3</sup> and 10<sup>20</sup> cm−3, the tensile-strained n+Ge is a gain medium. For photon energies other than 0.8 eV, the net gain range varies but

The comparison of the net material gain versus injection level of germanium with both tensile strain and n-type doping, with either of the two, and with neither of two are shown in Fig. 20. Since the optical gain spectrum varies with strain, the net gain for each condition is calculated at the photon energy where maximal gain is achieved. Net gain can not be achieved for intrinsic Ge no matter with or without 0.25% tensile strain because the free carrier absorption

Fig. 19. The optical gain, the free carrier absorption, and the net material gain of Ge with 0.25% tensile strain and 7 <sup>×</sup> 1019 cm−<sup>1</sup> n-type doping at various injection levels at the photon

Injection level (cm−<sup>3</sup>

)

free carrier absorption

net material gain

0.8 eV (1550 nm)

*α*fc(*λ*) = *kencλae* + *kh pvλah* , (31)

*<sup>α</sup>*fc(*λ*) = <sup>−</sup>3.4 <sup>×</sup> <sup>10</sup>−25*ncλ*2.25 <sup>−</sup> 3.2 <sup>×</sup> <sup>10</sup>−<sup>25</sup> *pvλ*2.43, (32)

Free carrier absorption *α*fc can be expressed in the following empirical formula:

where *αf c* is in unit of cm−1, *nc* and *pv* in units of cm−3, and *λ* in units of nm.

optical gain

of 10<sup>19</sup> <sup>−</sup> 1020 cm−<sup>3</sup> at room temperature, we obtain

−500

Gain coefficient (cm−1

energy of 0.8 eV (1550 nm).

the same characteristic holds.

)

0

500

1000

extrinsic electrons.

A detailed balance analysis proves that all the three scattering strength coefficients, *α*, *est*, and *esp*, are equal at any photon energy *hν*. Therefore optical gain can be rewritten as

$$\lg(h\nu) = \mathfrak{a}(f\_{\mathfrak{c}} - f\_{\mathfrak{v}}).\tag{30}$$

(*fc* − *fv*) is called population inversion factor. It is negative at equilibrium or low injection indicating a net optical loss (absorption). It becomes positive at high injection, when the population of the electrons inverts indicating a net optical gain. By using the absorption data presented in the photodetector section, optical gain can be calculated with this formula.

Fig. 18. Calculated optical gain spectrum of Ge with 0.25% tensile strain and 7 <sup>×</sup> 1019*cm*−<sup>3</sup> n-type doping at various injection levels with respect to photon energies close to its direct band gap energy.

As demonstrated earlier, a combination of 0.25% tensile strain and 7 <sup>×</sup> 1019 cm−<sup>3</sup> n-type doping results in an effective direct band gap germanium. The optical gain spectrum of such engineered germanium is shown in Fig. 18. The optical gain occurs at 0.76 eV which is the energy gap between the direct Γ valley and the light-hold band under 0.25% tensile strain. Since the effective masses are very light for these bands, population inversion occurs at low injection levels of <sup>∼</sup> 1017 cm−3. As the injection level increases, the separation of the electron and the hole quasi Fermi levels becomes larger than the energy gap between the direct Γ valley and the heavy-hole band. Thus the optical gain contributed by electron heavy-hole recombination occurs, which can be seen from the fast raise of the optical gain at 0.78 eV at injection levels above 1018 cm−3. A peak gain over 1000 cm−<sup>1</sup> around 0.8 eV (1550 nm) is achieved at injection level of 8 <sup>×</sup> <sup>10</sup><sup>18</sup> cm−3.

The occurrence of optical gain in a material does not necessarily lead to lasing which requires that the optical gain overcomes optical losses from all sources. The material related optical loss is dominated by free carrier absorption. Free carrier absorption is a process that an electron or a hole absorbs the energy of a photon and moves to an empty higher energy state without inter-band recombination. Free carrier absorption increases with wavelength and becomes significant at high carrier densities. When a material is under carrier injection for population inversion, free carrier absorption caused by large amount of injected carriers competes against optical gain. Free carrier absorption is usually the major obstacle for lasing in a gain medium. 22 Will-be-set-by-IN-TECH

A detailed balance analysis proves that all the three scattering strength coefficients, *α*, *est*, and

(*fc* − *fv*) is called population inversion factor. It is negative at equilibrium or low injection indicating a net optical loss (absorption). It becomes positive at high injection, when the population of the electrons inverts indicating a net optical gain. By using the absorption data presented in the photodetector section, optical gain can be calculated with this formula.

0.75 0.8 0.85

Photon Energy (eV)

n−doped

7×1019/cm3

0.25% strained

Fig. 18. Calculated optical gain spectrum of Ge with 0.25% tensile strain and 7 <sup>×</sup> 1019*cm*−<sup>3</sup> n-type doping at various injection levels with respect to photon energies close to its direct

As demonstrated earlier, a combination of 0.25% tensile strain and 7 <sup>×</sup> 1019 cm−<sup>3</sup> n-type doping results in an effective direct band gap germanium. The optical gain spectrum of such engineered germanium is shown in Fig. 18. The optical gain occurs at 0.76 eV which is the energy gap between the direct Γ valley and the light-hold band under 0.25% tensile strain. Since the effective masses are very light for these bands, population inversion occurs at low injection levels of <sup>∼</sup> 1017 cm−3. As the injection level increases, the separation of the electron and the hole quasi Fermi levels becomes larger than the energy gap between the direct Γ valley and the heavy-hole band. Thus the optical gain contributed by electron heavy-hole recombination occurs, which can be seen from the fast raise of the optical gain at 0.78 eV at injection levels above 1018 cm−3. A peak gain over 1000 cm−<sup>1</sup> around 0.8 eV (1550 nm) is

The occurrence of optical gain in a material does not necessarily lead to lasing which requires that the optical gain overcomes optical losses from all sources. The material related optical loss is dominated by free carrier absorption. Free carrier absorption is a process that an electron or a hole absorbs the energy of a photon and moves to an empty higher energy state without inter-band recombination. Free carrier absorption increases with wavelength and becomes significant at high carrier densities. When a material is under carrier injection for population inversion, free carrier absorption caused by large amount of injected carriers competes against optical gain. Free carrier absorption is usually the major obstacle for lasing in a gain medium.

100

achieved at injection level of 8 <sup>×</sup> <sup>10</sup><sup>18</sup> cm−3.

101

102

Gain Coefficient (cm−1

band gap energy.

)

103

*g*(*hν*) = *α*(*fc* − *fv*). (30)

8×1018cm−<sup>3</sup> 2×1018cm−<sup>3</sup> 1×1018cm−<sup>3</sup> 5×1017cm−<sup>3</sup>

*esp*, are equal at any photon energy *hν*. Therefore optical gain can be rewritten as

In n-typed doped germanium, additional free carrier absorption exists due to the existence of extrinsic electrons.

Free carrier absorption *α*fc can be expressed in the following empirical formula:

$$
\alpha\_{\rm fc}(\lambda) = k\_{\rm c} n\_{\rm c} \lambda^{a\_{\rm c}} + k\_{\rm h} p\_{\rm v} \lambda^{a\_{\rm h}} \,\,\,\,\,\tag{31}
$$

where *nc* and *pv* are the densities of electrons and holes and *ke*, *kh*, *ae* and *ah* are the constants of a material. *ae* and *ah* are usually between 1.5 and 3.5. By fitting the free carrier absorption data in n+Ge Spitzer et al. (1961) and p+Ge Newman & Tyler (1957) in a carrier density range of 10<sup>19</sup> <sup>−</sup> 1020 cm−<sup>3</sup> at room temperature, we obtain

$$u\_{\rm fc}(\lambda) = -3.4 \times 10^{-25} n\_{\rm c} \lambda^{2.25} - 3.2 \times 10^{-25} p\_{\rm v} \lambda^{2.43},\tag{32}$$

where *αf c* is in unit of cm−1, *nc* and *pv* in units of cm−3, and *λ* in units of nm.

Fig. 19. The optical gain, the free carrier absorption, and the net material gain of Ge with 0.25% tensile strain and 7 <sup>×</sup> 1019 cm−<sup>1</sup> n-type doping at various injection levels at the photon energy of 0.8 eV (1550 nm).

The optical gain, the free carrier absorption, and the net material gain which is the difference between first two are calculated with respect to injection level at the photon energy of 0.8 eV (1550 nm) for Ge with 0.25% tensile strain and 7 <sup>×</sup> 1019 cm−<sup>3</sup> n-type doping. The results are shown in Fig. 19. The free carrier absorption is significant even at low injections since the material is heavily doped. The optical gain overcomes the free carrier loss above the injection level of 1.2 <sup>×</sup> <sup>10</sup><sup>18</sup> cm−<sup>3</sup> where germanium becomes a gain medium. At very high carrier injection levels (> 1020 cm−3), the free carrier absorption exceeds the optical gain leading to net loss. Between a large injection range of 1018 cm−<sup>3</sup> and 10<sup>20</sup> cm−3, the tensile-strained n+Ge is a gain medium. For photon energies other than 0.8 eV, the net gain range varies but the same characteristic holds.

The comparison of the net material gain versus injection level of germanium with both tensile strain and n-type doping, with either of the two, and with neither of two are shown in Fig. 20. Since the optical gain spectrum varies with strain, the net gain for each condition is calculated at the photon energy where maximal gain is achieved. Net gain can not be achieved for intrinsic Ge no matter with or without 0.25% tensile strain because the free carrier absorption

Silicon Photonics 25

Germanium-on-Silicon for Integrated Silicon Photonics 27

level, in which net gain occurs. Doping concentration higher than a few 1019 cm−<sup>3</sup> is required for net gain occurrence at photon energy of 0.8 eV. Net loss occurs at either very high doping concentrations or very high injection levels because the free carrier loss trumps the optical gain. The intercept of the 3-D plot at zero gain surface is a threshold boundary surrounding the net gain region. The threshold boundary varies at photon energies other than 0.8 eV.

Photoluminescence (PL) and electroluminescence (EL) are commonly used material characterization experiments. The intensity and spectral content of the luminescence is a direct measure of various important material properties. The carrier recombination

Germanium is a multi-valley indirect band gap material therefore both the direct and the indirect band-to-band radiative recombination exist. As discussed earlier indirect transition is an inefficient process as most injected electron-hole pairs recombine non-radiatively before the occurrence of radiative recombination. Therefore indirect PL can only be observed in ultra high quality germanium at cryogenic temperatures at which non-radiative recombinations are greatly suppressed. On the contrary, direct transition is a fast process with radiative recombination rate 4-5 orders of magnitude higher than that of the indirect transition(Haynes & Nilsson, 1964). However, the lack of sufficient injected electrons in the direct Γ valley results in weak overall light emission. The tensile strain and n-type doping techniques improve the electron concentration in the direct valley hence more efficient luminescence is expected.

0.75 0.8 0.85

Fig. 22. PL spectra of tensile-strained Ge film with various n-type doping levels. The PL of a <sup>1</sup> <sup>×</sup> 1019 cm−<sup>3</sup> doped Ge film is over 50 times brighter than that of an undoped one. (Sun

The effect of n-type doping and tensile-strain on PL is investigated using a series of epitaxial germanium samples with doping concentrations from less than 1 <sup>×</sup> <sup>10</sup>16cm−<sup>3</sup> (approximately undoped) to 2 <sup>×</sup> <sup>10</sup><sup>19</sup> cm−3. The doping is achieved by in situ phosphorous incorporation during germanium epitaxy. Some PL spectrum examples are shown in Fig. 22. All PL spectra are measured at room temperature. The doping dependence of PL intensities agrees with the analysis earlier that direct gap light emission is enhanced with n-type doping owing to

Energy (eV)

1.0×1019cm−<sup>3</sup> 4.3×1018cm−<sup>3</sup> 1.0×1018cm−<sup>3</sup> 4.9×1017cm−<sup>3</sup> intrinsic

> Experiment 300K

0

0.2

0.4

0.6

Nd

Photoluminescence (a.u.)

et al., 2009a)

0.8

1

**3.4 Germanium photoluminescence and electroluminescence**

characteristics of germanium can be studied with these experiments.

Fig. 20. Comparison of the calculated net material gain versus injection level of the Ge with both tensile strain and n-type doping, with either of two, and with neither of two at peak gain photon energy respectively.

always exceeds the optical gain. It is the reason that net gain has not been experimentally observed from germainium in the history. With n-type doping, the net gain can be achieved in both tensile-strained and unstrained cases. Tensile strain increases the population of the injected electrons in the direct Γ valley leading to a lower net gain threshold as well as higher net gain above threshold.

Fig. 21. Dependence of the calculated net material gain of Ge on n-type doping level (*Nd*) and carrier injection level at the photon energy of 0.8 eV.

The dependence of the net gain on n-type doping level and on injection level is calculated and shown in Fig. 21. There exists a range of n-type doping concentration and carrier injection 24 Will-be-set-by-IN-TECH

=7×1019cm−<sup>3</sup>

=7×1019cm−<sup>3</sup>

at 0.8eV

at 0.82eV

=0 at 0.8eV

)

<sup>1018</sup> <sup>1019</sup> <sup>1020</sup> <sup>1021</sup>

(cm−<sup>3</sup>

Nd

=0 at 0.82eV

Injection level (cm−<sup>3</sup>

<sup>1018</sup> <sup>1019</sup> <sup>1020</sup> <sup>−</sup><sup>1000</sup>

Fig. 20. Comparison of the calculated net material gain versus injection level of the Ge with both tensile strain and n-type doping, with either of two, and with neither of two at peak

always exceeds the optical gain. It is the reason that net gain has not been experimentally observed from germainium in the history. With n-type doping, the net gain can be achieved in both tensile-strained and unstrained cases. Tensile strain increases the population of the injected electrons in the direct Γ valley leading to a lower net gain threshold as well as higher

1018

Eph=0.8 eV

) Injection (cm−<sup>3</sup>

Fig. 21. Dependence of the calculated net material gain of Ge on n-type doping level (*Nd*) and

The dependence of the net gain on n-type doping level and on injection level is calculated and shown in Fig. 21. There exists a range of n-type doping concentration and carrier injection

1019

)

1020

carrier injection level at the photon energy of 0.8 eV.

0

1000

2000

−1000

<sup>ε</sup>=0.25%, Nd

<sup>ε</sup>=0, Nd

−500

Gain coefficient (cm−1

gain photon energy respectively.

net gain above threshold.

Material gain (cm−1

)

)

0

500

<sup>ε</sup>=0.25%, Nd

<sup>ε</sup>=0, Nd

1000

level, in which net gain occurs. Doping concentration higher than a few 1019 cm−<sup>3</sup> is required for net gain occurrence at photon energy of 0.8 eV. Net loss occurs at either very high doping concentrations or very high injection levels because the free carrier loss trumps the optical gain. The intercept of the 3-D plot at zero gain surface is a threshold boundary surrounding the net gain region. The threshold boundary varies at photon energies other than 0.8 eV.

#### **3.4 Germanium photoluminescence and electroluminescence**

Photoluminescence (PL) and electroluminescence (EL) are commonly used material characterization experiments. The intensity and spectral content of the luminescence is a direct measure of various important material properties. The carrier recombination characteristics of germanium can be studied with these experiments.

Germanium is a multi-valley indirect band gap material therefore both the direct and the indirect band-to-band radiative recombination exist. As discussed earlier indirect transition is an inefficient process as most injected electron-hole pairs recombine non-radiatively before the occurrence of radiative recombination. Therefore indirect PL can only be observed in ultra high quality germanium at cryogenic temperatures at which non-radiative recombinations are greatly suppressed. On the contrary, direct transition is a fast process with radiative recombination rate 4-5 orders of magnitude higher than that of the indirect transition(Haynes & Nilsson, 1964). However, the lack of sufficient injected electrons in the direct Γ valley results in weak overall light emission. The tensile strain and n-type doping techniques improve the electron concentration in the direct valley hence more efficient luminescence is expected.

Fig. 22. PL spectra of tensile-strained Ge film with various n-type doping levels. The PL of a <sup>1</sup> <sup>×</sup> 1019 cm−<sup>3</sup> doped Ge film is over 50 times brighter than that of an undoped one. (Sun et al., 2009a)

The effect of n-type doping and tensile-strain on PL is investigated using a series of epitaxial germanium samples with doping concentrations from less than 1 <sup>×</sup> <sup>10</sup>16cm−<sup>3</sup> (approximately undoped) to 2 <sup>×</sup> <sup>10</sup><sup>19</sup> cm−3. The doping is achieved by in situ phosphorous incorporation during germanium epitaxy. Some PL spectrum examples are shown in Fig. 22. All PL spectra are measured at room temperature. The doping dependence of PL intensities agrees with the analysis earlier that direct gap light emission is enhanced with n-type doping owing to

Silicon Photonics 27

Germanium-on-Silicon for Integrated Silicon Photonics 29

0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88

Fig. 24. PL Comparison of in situ doped Ge and implanted Ge. Post-implantation annealing

Compared to PL, EL emission is excited electrically other than optically. EL is usually described as an electrical-optical phenomenon in which a material emits light in response to an electric current passed through it, or to a strong electric field. Due to different injection

Si/Ge/Si structure forms a natural hetetojunction for a light-emitting diode. In the EL experiment on such Si/Ge/Si diodes, the onset of EL at forward bias has been observed at room temperature. In author's own work, EL was observed at 0.5 V forward bias or 1.3 mA

The EL spectrum measured at room temperature at 50 mA forward current is shown in Fig. 25 (a). The EL peak is located at 0.76 eV corresponding to the direct band-to-band optical transition in 0.2% tensile-strained Ge. The full width at half maximum (FWHM) of the peak is about 60 meV (∼2 kT) consistent with the direct band-to-band transition model. The sharp peaks are from the Fabry-Perot resonance of the air gap between device surface and the flat facet of the fiber used for light collection. These resonances are reproducible in the experiments and can be filtered by fast Fourier transformation (FFT). After the FFT filtering, the smoothed curve represents the "real" EL characteristics which is shown with red solid line. The EL spectrum is consistent with the room temperature photoluminescence (PL) spectrum measured from a 0.2% tensile-strained epitaxial germanium sample shown in Fig. 25 (b). The small red shift in the EL peak position compared to PL peak position is a result of heating

The injection dependence of the direct gap EL emission was measured. The results show unique direct gap light emission characteristics of germanium which is different from that of

A superlinear relation of the integral direct gap EL intensity with the injected electrical current is shown in Fig. 26. In a direct band gap semiconductor, the relation is expected to be linear at lower injection levels and to roll over at higher injecion levels due to increasingly significant non-radiative recombinations. This superlinear dependence on injection is a unique feature of direct gap light emission in germanium. As discussed earlier, direct light emission intensity is

mechanisms, the characteristics observed in EL are not necessary the same as in PL.

Photon energy (eV)

post−implantation activation annealing has been performed

in situ, 1×1019 cm−<sup>3</sup> implantation, 1×1020 cm−<sup>3</sup> implantation, 1×1019 cm−<sup>3</sup> implantation, 1×1018 cm−<sup>3</sup>

0

injection current for a 20 *μ*m by 100 *μ*m diode.

from current injection which slightly reduces the band gap.

a direct gap semiconductor.

has been performed for implanted Ge films for dopant activation.

0.2

0.4

0.6

Photoluminescence (a.u.)

0.8

1

the indirect valley states filling with extrinsic electrons. The PL of a 1 <sup>×</sup> 1019 cm−<sup>3</sup> doped epitaxial germanium is over 50 times brighter than that of an undoped one. All spectra exhibit the same spectral characteristic. The same PL peak position implies that phosphorous doping has negligible effect on band structure or tensile strain in germanium.

Fig. 23. A summary of integral PL intensity versus active doping concentration. The theoretical calculation is represented in red solid line and describes the trend of the experimental data.(Sun et al., 2009a)

A plot of the enhancement of integral PL intensity with active doping concentration is shown in Fig. 23. The integral PL-doping relation can be calculated by

$$I(N\_d) \propto n\_e^{\Gamma}(N\_d) n\_h \propto n\_e^{\Gamma}(N\_d) \tag{33}$$

It shows the direct gap integral PL intensity is proportional to the product of the electron concentration in the Γ valley and the hole concentration at quasi-equilibrium under excitation. The hole concentration remains the same for each sample at the same excitation level therefore the PL intensity is only determined by the electron concentration in the direct Γ valley. This concentration is a function of n-type doping concentration. Higher n-type doping results in more injected electrons in the direct Γ valley. A theoretical calculation based on this analysis is shown in Fig. 23 with red solid line, exhibiting good agreement with the experimental data. Ion-implantation is an effective way to achieve high doping concentration at the cost of crystalline damage. The lattice damages introduce defects acting as non-radiative recombination centers and reduce lifetime in materials. Fig. 24 shows the PL from epitaxial germanium implanted with phosphorus at three doses aiming for doping concentrations of <sup>1</sup> <sup>×</sup> 1018 cm−3, 1 <sup>×</sup> 1019 cm−3, and 1 <sup>×</sup> <sup>10</sup><sup>20</sup> cm−3, respectively. All samples were annealed at 800 *<sup>o</sup>*C after implantation for dopant activation and subsequent Hall effect measurement confirmed over 80% dopants were activated. PL increases with the doping level in implanted germanium as expected. But all the implanted samples show weaker PL than the in situ doped one confirming the negative effect of lattice damage on radiative recombination. In general, in situ doping is a superior approach to achieve n-type doping in epitaxial germanium for light emission applications.

26 Will-be-set-by-IN-TECH

the indirect valley states filling with extrinsic electrons. The PL of a 1 <sup>×</sup> 1019 cm−<sup>3</sup> doped epitaxial germanium is over 50 times brighter than that of an undoped one. All spectra exhibit the same spectral characteristic. The same PL peak position implies that phosphorous doping

1017 1018 1019 1020

Active Doping (cm−<sup>3</sup>

A plot of the enhancement of integral PL intensity with active doping concentration is shown

It shows the direct gap integral PL intensity is proportional to the product of the electron concentration in the Γ valley and the hole concentration at quasi-equilibrium under excitation. The hole concentration remains the same for each sample at the same excitation level therefore the PL intensity is only determined by the electron concentration in the direct Γ valley. This concentration is a function of n-type doping concentration. Higher n-type doping results in more injected electrons in the direct Γ valley. A theoretical calculation based on this analysis is shown in Fig. 23 with red solid line, exhibiting good agreement with the experimental data. Ion-implantation is an effective way to achieve high doping concentration at the cost of crystalline damage. The lattice damages introduce defects acting as non-radiative recombination centers and reduce lifetime in materials. Fig. 24 shows the PL from epitaxial germanium implanted with phosphorus at three doses aiming for doping concentrations of <sup>1</sup> <sup>×</sup> 1018 cm−3, 1 <sup>×</sup> 1019 cm−3, and 1 <sup>×</sup> <sup>10</sup><sup>20</sup> cm−3, respectively. All samples were annealed at 800 *<sup>o</sup>*C after implantation for dopant activation and subsequent Hall effect measurement confirmed over 80% dopants were activated. PL increases with the doping level in implanted germanium as expected. But all the implanted samples show weaker PL than the in situ doped one confirming the negative effect of lattice damage on radiative recombination. In general, in situ doping is a superior approach to achieve n-type doping in epitaxial germanium for light

*<sup>e</sup>* (*Nd*)*nh* <sup>∝</sup> *<sup>n</sup>*<sup>Γ</sup>

Fig. 23. A summary of integral PL intensity versus active doping concentration. The theoretical calculation is represented in red solid line and describes the trend of the

)

*<sup>e</sup>* (*Nd*) (33)

has negligible effect on band structure or tensile strain in germanium.

300K 30W/cm2

in Fig. 23. The integral PL-doping relation can be calculated by

*<sup>I</sup>*(*Nd*) <sup>∝</sup> *<sup>n</sup>*<sup>Γ</sup>

experiment modeling

0.2

0.4

0.6

0.8

Integral PL (a.u.)

experimental data.(Sun et al., 2009a)

emission applications.

1

1.2

1.4

Fig. 24. PL Comparison of in situ doped Ge and implanted Ge. Post-implantation annealing has been performed for implanted Ge films for dopant activation.

Compared to PL, EL emission is excited electrically other than optically. EL is usually described as an electrical-optical phenomenon in which a material emits light in response to an electric current passed through it, or to a strong electric field. Due to different injection mechanisms, the characteristics observed in EL are not necessary the same as in PL.

Si/Ge/Si structure forms a natural hetetojunction for a light-emitting diode. In the EL experiment on such Si/Ge/Si diodes, the onset of EL at forward bias has been observed at room temperature. In author's own work, EL was observed at 0.5 V forward bias or 1.3 mA injection current for a 20 *μ*m by 100 *μ*m diode.

The EL spectrum measured at room temperature at 50 mA forward current is shown in Fig. 25 (a). The EL peak is located at 0.76 eV corresponding to the direct band-to-band optical transition in 0.2% tensile-strained Ge. The full width at half maximum (FWHM) of the peak is about 60 meV (∼2 kT) consistent with the direct band-to-band transition model. The sharp peaks are from the Fabry-Perot resonance of the air gap between device surface and the flat facet of the fiber used for light collection. These resonances are reproducible in the experiments and can be filtered by fast Fourier transformation (FFT). After the FFT filtering, the smoothed curve represents the "real" EL characteristics which is shown with red solid line. The EL spectrum is consistent with the room temperature photoluminescence (PL) spectrum measured from a 0.2% tensile-strained epitaxial germanium sample shown in Fig. 25 (b). The small red shift in the EL peak position compared to PL peak position is a result of heating from current injection which slightly reduces the band gap.

The injection dependence of the direct gap EL emission was measured. The results show unique direct gap light emission characteristics of germanium which is different from that of a direct gap semiconductor.

A superlinear relation of the integral direct gap EL intensity with the injected electrical current is shown in Fig. 26. In a direct band gap semiconductor, the relation is expected to be linear at lower injection levels and to roll over at higher injecion levels due to increasingly significant non-radiative recombinations. This superlinear dependence on injection is a unique feature of direct gap light emission in germanium. As discussed earlier, direct light emission intensity is

Silicon Photonics 29

Germanium-on-Silicon for Integrated Silicon Photonics 31

0 10 20 30 40 50 60

Current (mA)

Fig. 26. Integral direct gap EL intensity of a 0.2% tensile-strained Si/Ge/Si light emitting diode. The EL intensity increases superlinearly with electrical current. The theoretical

experiment greatly support this theory. Investigating the capability of net gain in germanium

A non-degenerate pump-probe experiment with a tunable laser as probe and a high power laser as pump is used for optical gain measurement. The fiber outputs of the pump laser and the probe laser are combined through a wavelength division multiplexing (WDM) coupler and illuminate to the top of n-type doped, tensile-strained epitaxial germanium. The transmitted optical power is measured by an integral optical sphere for transmissivity calculation with respect to incident light. The probe light is modulated at a few kHz and is filtered by a lock-in

The measured transmissivity is correlated with the optical gain or absorption under optical

The relation between transmissivity and optical gain/absorption can be modeled by transfer

The inversion factor (*fc* − *fv*) ranges from -1 to 1. In the absence of pumping, (*fc* − *fv*) = −1, i.e. *g*(*hν*) = −*α* is pure absorption. As the material is increasingly pumped, (*fc* − *fv*) increases from -1 towards 0. The optical absorption becomes less which is called optical bleaching effect. At sufficiently high pumping levels, the material becomes transparent and a gain medium for

For heavily n-type doped germanium, the measured net gain/absorption includes both

where *α*fc represents free carrier absorption. The existence of free carrier absorption increases the injection level required for transparency or net gain. The effective inversion factor can be

*<sup>α</sup>* <sup>=</sup> <sup>−</sup>*α*tot

(*fc* <sup>−</sup> *fv*) <sup>−</sup> *<sup>α</sup>*fc

*g*(*hν*) = *α*(*fc* − *fv*). (35)

*g*tot(*hν*) = −*α*tot(*hν*) = *α*(*fc* − *fv*) − *α*fc, (36)

*<sup>α</sup>* , (37)

0

amplifier for precise transmission measurement.

calculation (solid line) agrees well with the experimental result.

matrix method (TMM). The detailed calculated is omitted here.

the inversion factor equals to and more than 0, respectively.

optical gain/absorption and free carrier absorption:

0.2

0.4

0.6

experiment modeling

Integral EL (a.u.)

and to achieving lasing are next tasks.

pumping:

expressed by

0.8

1

Fig. 25. (a) Direct gap EL spectrum of a 20 *μ*m by 100*μ*m 0.2% tensile-strained Si/Ge/Si light-emitting diode measured at room temperature. The periodic sharp peaks are due to Fabry-Perot resonances. (b) Room temperature direct gap photoluminescence of a 0.2% tensile-strained Ge film epitaxially grown on Si. (Sun et al., 2009b)

determined by the injected electrons in the direct Γ valley *ne*<sup>Γ</sup> and can be further expressed as

$$P\_{\Gamma} \propto n\_{\varepsilon \Gamma} = n\_{\text{tot}} \cdot f\_{\Gamma \prime} \tag{34}$$

where *n*tot is the total injected electron density and *f*<sup>Γ</sup> is the fraction of the electrons injected into the direct Γ valley. The total injected electron scales linearly with the injected electrical current. The fraction term also increases with the injection level due to the increase of the electron quasi Fermi level leading to larger portion of electrons in the direct Γ valley. The multiplication of the two terms results in a superlinear behavior with injection current. A theoretical calculation based on this analysis is shown in solid line in Fig. 26. It agrees well with the experimental data. The small difference between the theoretical and the experimental result is due to the small deviation from the ideal square-root density of states near the band edge.

#### **3.5 Germanium net gain and lasing**

It has been theoretically shown that germanium can be engineered by tensile strain and n-type doping for better direct gap light emission at room temperature. The direct gap PL and EL 28 Will-be-set-by-IN-TECH

experiment FFT smoothed

0.7 0.75 0.8 0.85 0.9 0.95

Photon Energy (eV)

0.7 0.75 0.8 0.85 0.9 0.95

Photon Energy (eV)

(b)

determined by the injected electrons in the direct Γ valley *ne*<sup>Γ</sup> and can be further expressed as

where *n*tot is the total injected electron density and *f*<sup>Γ</sup> is the fraction of the electrons injected into the direct Γ valley. The total injected electron scales linearly with the injected electrical current. The fraction term also increases with the injection level due to the increase of the electron quasi Fermi level leading to larger portion of electrons in the direct Γ valley. The multiplication of the two terms results in a superlinear behavior with injection current. A theoretical calculation based on this analysis is shown in solid line in Fig. 26. It agrees well with the experimental data. The small difference between the theoretical and the experimental result is due to the small deviation from the ideal square-root density of states near the band

It has been theoretically shown that germanium can be engineered by tensile strain and n-type doping for better direct gap light emission at room temperature. The direct gap PL and EL

*P*<sup>Γ</sup> ∝ *ne*<sup>Γ</sup> = *n*tot · *f*Γ, (34)

Fig. 25. (a) Direct gap EL spectrum of a 20 *μ*m by 100*μ*m 0.2% tensile-strained Si/Ge/Si light-emitting diode measured at room temperature. The periodic sharp peaks are due to Fabry-Perot resonances. (b) Room temperature direct gap photoluminescence of a 0.2%

(a)

1

0

tensile-strained Ge film epitaxially grown on Si. (Sun et al., 2009b)

0.5

PL (a.u.)

edge.

**3.5 Germanium net gain and lasing**

EL power (pW)

Fig. 26. Integral direct gap EL intensity of a 0.2% tensile-strained Si/Ge/Si light emitting diode. The EL intensity increases superlinearly with electrical current. The theoretical calculation (solid line) agrees well with the experimental result.

experiment greatly support this theory. Investigating the capability of net gain in germanium and to achieving lasing are next tasks.

A non-degenerate pump-probe experiment with a tunable laser as probe and a high power laser as pump is used for optical gain measurement. The fiber outputs of the pump laser and the probe laser are combined through a wavelength division multiplexing (WDM) coupler and illuminate to the top of n-type doped, tensile-strained epitaxial germanium. The transmitted optical power is measured by an integral optical sphere for transmissivity calculation with respect to incident light. The probe light is modulated at a few kHz and is filtered by a lock-in amplifier for precise transmission measurement.

The measured transmissivity is correlated with the optical gain or absorption under optical pumping:

$$
\sigma\_{\mathcal{S}}(h\nu) = \mathfrak{a}(f\_{\mathcal{C}} - f\_{\mathcal{U}}).\tag{35}
$$

The relation between transmissivity and optical gain/absorption can be modeled by transfer matrix method (TMM). The detailed calculated is omitted here.

The inversion factor (*fc* − *fv*) ranges from -1 to 1. In the absence of pumping, (*fc* − *fv*) = −1, i.e. *g*(*hν*) = −*α* is pure absorption. As the material is increasingly pumped, (*fc* − *fv*) increases from -1 towards 0. The optical absorption becomes less which is called optical bleaching effect. At sufficiently high pumping levels, the material becomes transparent and a gain medium for the inversion factor equals to and more than 0, respectively.

For heavily n-type doped germanium, the measured net gain/absorption includes both optical gain/absorption and free carrier absorption:

$$g\_{\rm tot}(h\nu) = -\mathfrak{a}\_{\rm tot}(h\nu) = \mathfrak{a}(f\_{\mathfrak{c}} - f\_{\mathfrak{v}}) - \mathfrak{a}\_{\rm fc} \tag{36}$$

where *α*fc represents free carrier absorption. The existence of free carrier absorption increases the injection level required for transparency or net gain. The effective inversion factor can be expressed by

(*fc* <sup>−</sup> *fv*) <sup>−</sup> *<sup>α</sup>*fc *<sup>α</sup>* <sup>=</sup> <sup>−</sup>*α*tot *<sup>α</sup>* , (37)

Silicon Photonics 31

Germanium-on-Silicon for Integrated Silicon Photonics 33

Fig. 28. Comparison of the effective inversion factors of tensile-strained Ge film and mesa with various n-type doping concentrations. The observed optical bleaching effect increases

Fig. 29. Edge emission spectra of a Ge waveguide with mirror polished facets under excitation. The three spectra at 1.5, 6.0 and 50 *μ*J/pulse pumping power correspond to spontaneous emission, threshold for lasing, and laser emission, respectively. The inset shows

a cross-sectional SEM picture of the Ge waveguide and a schematic drawing of the

with n-type doping concentration.

experimental setup for optical pumping.

which can be obtained from the experimental results.

A tensile-strained n<sup>+</sup> doped germanium mesa was fabricated for pump-probe measurement. The germanium is 1.0 <sup>×</sup> <sup>10</sup><sup>19</sup> cm−<sup>3</sup> n-type doped and 0.2% tensile-strained. The transmissivity spectra were measured at 0 and 60 mW optical pumping powers, respectively. The absorption is then calculated by using transfer matrix method with the consideration of Kramer-Kronig relations.

Fig. 27. The absorption spectra of the n+ Ge mesa under 0 and 60 mW optical pumping, respectively. Negative absorption corresponding to the onset of net gain was observed in wavelength between 1600 nm and 1608 nm. The error bars in the inset represent the transmissivity measurement errors. Liu et al. (2009).

Fig. 27 shows the absorption spectra of the n+Ge mesa under pumping powers of 0 and 60W, respectively. The absorption at photon energies above 0.77 eV (at wavelengths below 1610 nm) decreases significantly upon optical pumping. Negative absorption corresponding to the onset of optical gain is observed in the wavelength range of 1600-1608 nm, as shown in the inset of Fig. 27. The maximum gain coefficient is *<sup>g</sup>*tot <sup>=</sup> <sup>−</sup>*α*tot <sup>=</sup> <sup>50</sup> <sup>±</sup> 25 cm−<sup>1</sup> at 1605 nm. The error bars represent the transmissivity measurement errors.

Like PL in doped germanium, the optical bleaching effect also increases with the n-type doping concentration. The effective inversion factor is calculated from the experimental results for germanium with different doping concentrations.

The comparison of the effective inversion factor spectra of tensile-strained Ge for both blanket film and mesa samples with various n-type doping concentrations is shown in Fig. 28. The optical bleaching effect (inversion factor more than -1) can be seen from all samples. The bleaching increases with n-type doping concentration confirming the theory of the effect of n-type doping on optical gain. The Ge mesa sample exhibits a positive inversion factor at the direct band edge (1600-1608 nm) underlying the occurrence of net gain. The effective inversion factors at longer wavelengths are less than -1 for all samples because free carrier absorption overcomes optical bleaching. The optical bleaching in the Ge mesa sample is more than any Ge film samples as a result of the lateral confinement of injected carriers by the mesa structure. With the observation of net gain in tensile-strained n-doped germanium, a optically pumped Fabry-Perot germanium laser was realized (Liu et al., 2010). The waveguide laser was excited 30 Will-be-set-by-IN-TECH

A tensile-strained n<sup>+</sup> doped germanium mesa was fabricated for pump-probe measurement. The germanium is 1.0 <sup>×</sup> <sup>10</sup><sup>19</sup> cm−<sup>3</sup> n-type doped and 0.2% tensile-strained. The transmissivity spectra were measured at 0 and 60 mW optical pumping powers, respectively. The absorption is then calculated by using transfer matrix method with the consideration of Kramer-Kronig

> 0.82 0.81 0.8 0.79 0.78 0.77 0.76 Photon energy (ev)

> > > 1595 1600 1605 1610

Gain

1500 1550 1600 1650

Wavelength (nm)

Fig. 27. The absorption spectra of the n+ Ge mesa under 0 and 60 mW optical pumping, respectively. Negative absorption corresponding to the onset of net gain was observed in wavelength between 1600 nm and 1608 nm. The error bars in the inset represent the

Fig. 27 shows the absorption spectra of the n+Ge mesa under pumping powers of 0 and 60W, respectively. The absorption at photon energies above 0.77 eV (at wavelengths below 1610 nm) decreases significantly upon optical pumping. Negative absorption corresponding to the onset of optical gain is observed in the wavelength range of 1600-1608 nm, as shown in the inset of Fig. 27. The maximum gain coefficient is *<sup>g</sup>*tot <sup>=</sup> <sup>−</sup>*α*tot <sup>=</sup> <sup>50</sup> <sup>±</sup> 25 cm−<sup>1</sup> at 1605 nm.

Like PL in doped germanium, the optical bleaching effect also increases with the n-type doping concentration. The effective inversion factor is calculated from the experimental

The comparison of the effective inversion factor spectra of tensile-strained Ge for both blanket film and mesa samples with various n-type doping concentrations is shown in Fig. 28. The optical bleaching effect (inversion factor more than -1) can be seen from all samples. The bleaching increases with n-type doping concentration confirming the theory of the effect of n-type doping on optical gain. The Ge mesa sample exhibits a positive inversion factor at the direct band edge (1600-1608 nm) underlying the occurrence of net gain. The effective inversion factors at longer wavelengths are less than -1 for all samples because free carrier absorption overcomes optical bleaching. The optical bleaching in the Ge mesa sample is more than any Ge film samples as a result of the lateral confinement of injected carriers by the mesa structure. With the observation of net gain in tensile-strained n-doped germanium, a optically pumped Fabry-Perot germanium laser was realized (Liu et al., 2010). The waveguide laser was excited

which can be obtained from the experimental results.

transmissivity measurement errors. Liu et al. (2009).

The error bars represent the transmissivity measurement errors.

results for germanium with different doping concentrations.

pump: 0mW pump: 60mW

Absorption Coefficient (cm−1

)

relations.

Fig. 28. Comparison of the effective inversion factors of tensile-strained Ge film and mesa with various n-type doping concentrations. The observed optical bleaching effect increases with n-type doping concentration.

Fig. 29. Edge emission spectra of a Ge waveguide with mirror polished facets under excitation. The three spectra at 1.5, 6.0 and 50 *μ*J/pulse pumping power correspond to spontaneous emission, threshold for lasing, and laser emission, respectively. The inset shows a cross-sectional SEM picture of the Ge waveguide and a schematic drawing of the experimental setup for optical pumping.

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Germanium-on-Silicon for Integrated Silicon Photonics 35

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by a 1064 nm Q-switched laser through a cylindrical focusing lens. The lasing measurement is schematically shown in the inset of Fig. 29. The light emission spectra of the laser under different injection levels are shown in Fig. 29. At 1.5 *μ*J/pulse of pump laser power, the spectrum is a typical spontaneous emission consistent with PL results discussed earlier. As the pump power increases to 6.0 *μ*J/pulse, a few peaks emerge which occurs at the pump power corresponding to the threshold condition in Fig. 30. It marks the onset of transparency. The occurrence of emission peaks between 1600 and 1610 nm is consistent with the optical gain spectrum peaked at 1605 nm shown earlier. As pump power increases to 50 *μ*J/pulse, the widths of the emission peaks at 1594, 1599 and 1605 nm significantly decrease and the polarization became to predominant TE other than a mixture of TE and TM at lower injections. These results represent a typical lasing behavior. The multiple emission peaks are most likely due to multiple guided modes in the germanium waveguide as a result of high refractive index contrast. A similar multimode behavior has been observed in an early work on III-V semiconductor lasers (Miller et al., 1977).

Fig. 30 shows the integral edge emission intensity as a function of pump power. An obvious threshold behavior is observed. The threshold pumping power is about 5 *μ*J/pulse. The absorbed pump power density at the threshold is about 30 kW/cm2 by considering various optical losses of the incident pump light. The threshold is expected to further decrease with increased n-type doping concentration based on the calculation earlier. With lower injection threshold requirement, an electrically pumped germanium laser diode can be realized. As shown in the EL experiment discussion, Ge/Si/Ge heterojunction may be suitable diode structure for such lasers which will eventually complete the integrated silicon photonic circuits for the next generation of data communication and interconnects.

Fig. 30. Integral edge emission power versus optical pump power showing a lasing threshold behavior.

#### **4. References**

Adeola, G. W., Jambois, O., Miska, P., Rinnert, H. & Vergnat, M. (2006). Luminescence efficiency at 1.5 *μ*m of er-doped thick sio layers and er-doped sio / sio2 multilayers, *Appl. Phys. Lett.* 89: 101920.

32 Will-be-set-by-IN-TECH

by a 1064 nm Q-switched laser through a cylindrical focusing lens. The lasing measurement is schematically shown in the inset of Fig. 29. The light emission spectra of the laser under different injection levels are shown in Fig. 29. At 1.5 *μ*J/pulse of pump laser power, the spectrum is a typical spontaneous emission consistent with PL results discussed earlier. As the pump power increases to 6.0 *μ*J/pulse, a few peaks emerge which occurs at the pump power corresponding to the threshold condition in Fig. 30. It marks the onset of transparency. The occurrence of emission peaks between 1600 and 1610 nm is consistent with the optical gain spectrum peaked at 1605 nm shown earlier. As pump power increases to 50 *μ*J/pulse, the widths of the emission peaks at 1594, 1599 and 1605 nm significantly decrease and the polarization became to predominant TE other than a mixture of TE and TM at lower injections. These results represent a typical lasing behavior. The multiple emission peaks are most likely due to multiple guided modes in the germanium waveguide as a result of high refractive index contrast. A similar multimode behavior has been observed in an early work on III-V

Fig. 30 shows the integral edge emission intensity as a function of pump power. An obvious threshold behavior is observed. The threshold pumping power is about 5 *μ*J/pulse. The absorbed pump power density at the threshold is about 30 kW/cm2 by considering various optical losses of the incident pump light. The threshold is expected to further decrease with increased n-type doping concentration based on the calculation earlier. With lower injection threshold requirement, an electrically pumped germanium laser diode can be realized. As shown in the EL experiment discussion, Ge/Si/Ge heterojunction may be suitable diode structure for such lasers which will eventually complete the integrated silicon photonic

Fig. 30. Integral edge emission power versus optical pump power showing a lasing threshold

Adeola, G. W., Jambois, O., Miska, P., Rinnert, H. & Vergnat, M. (2006). Luminescence

efficiency at 1.5 *μ*m of er-doped thick sio layers and er-doped sio / sio2 multilayers,

circuits for the next generation of data communication and interconnects.

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**1. Introduction**

(2001)).

**2. Background**

Entangled photons are a crucial resource for linear optical quantum communication and quantum computation. Besides the remarkable progress of photon state engineering using atomic memories (Kimble (2008); Yuan et al. (2008)) the majority of current experiments is based on the production of photon pairs in the process of spontaneous parametric down-conversion (SPDC), where the entangled photon pair is concluded from post-selection of randomly occurring coincidences. Here we present new insights into the heralded generation of photon states (Barz et al. (2010); Wagenknecht et al. (2010)) that are maximally entangled in polarization (Schrödinger (1935)) with linear optics and standard photon detection from SPDC (Kwiat et al. (1995)). We utilize the down-conversion state corresponding to the generation of three pairs of photons, where the coincident detection of four auxiliary photons unambiguously heralds the successful preparation of the entangled state (Sliwa & Banaszek (2003)). This controlled generation of entangled photon states is ´ a significant step towards the applicability of a linear optics quantum network (Nielsen & Chuang (2000)), in particular for entanglement distribution (Bennett et al. (1996)), entanglement swapping (Kaltenbaek et al. (2009); Pan et al. (1998)), quantum teleportation (Bouwmeester et al. (1997)), quantum cryptography (Bennett & Brassard (1984); Ekert (1991); Jennewein et al. (2000)) and scalable approaches towards photonics-based quantum computing schemes (Browne & Rudolph (2004); Gottesman & Chuang (1999); Knill et al.

**Experimental Engineering of** 

*2Atominstitut, Technische Universität Wien, Vienna* 

*University of Vienna, Vienna* 

*Austria* 

**2**

**Photonic Quantum Entanglement** 

Stefanie Barz1, Gunther Cronenberg1,2 and Philip Walther1

*1Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics,* 

Photons are generally accepted as the best candidate for quantum communication due to their lack of decoherence and their possibility of photon broadcasting (Bouwmeester et al. (2000)). However, it has also been discovered that a scalable quantum computer can in principle be realized by using only single-photon sources, linear-optics elements and single-photon detectors (Knill et al. (2001)). Several proof-of-principle demonstrations for linear optical quantum computing have been given, including controlled-NOT gates (Gasparoni et al. (2004); O'Brien et al. (2003); Pittman et al. (2003; 2001); Sanaka et al. (2004)), Grover's search algorithm (Grover (1997); Kwiat et al. (2000); Prevedel et al. (2007)), Deutsch-Josza

