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Reversible modulation of spontaneous emission by strain in silicon nanowires.

Shiri D, Verma A, Selvakumar CR, Anantram MP - Sci Rep (2012)

Bottom Line: Our main finding is that a one to two orders of magnitude change in spontaneous emission time occurs due to two distinct mechanisms: (A) Change in wave function symmetry, where within the direct bandgap regime, strain changes the symmetry of wave functions, which in turn leads to a large change of optical dipole matrix element. (B) Direct to indirect bandgap transition which makes the spontaneous photon emission to be of a slow second order process mediated by phonons.These results promise new applications of silicon nanowires as optoelectronic devices including a mechanism for lasing.Our results are verifiable using existing experimental techniques of applying strain to nanowires.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

ABSTRACT
We computationally study the effect of uniaxial strain in modulating the spontaneous emission of photons in silicon nanowires. Our main finding is that a one to two orders of magnitude change in spontaneous emission time occurs due to two distinct mechanisms: (A) Change in wave function symmetry, where within the direct bandgap regime, strain changes the symmetry of wave functions, which in turn leads to a large change of optical dipole matrix element. (B) Direct to indirect bandgap transition which makes the spontaneous photon emission to be of a slow second order process mediated by phonons. This feature uniquely occurs in silicon nanowires while in bulk silicon there is no change of optical properties under any reasonable amount of strain. These results promise new applications of silicon nanowires as optoelectronic devices including a mechanism for lasing. Our results are verifiable using existing experimental techniques of applying strain to nanowires.

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Wave function symmetry change with strain.(a) Effect of compressive strain on second valence sub band (V2) which results in the change of wave function symmetry. From left to right, it can be seen that compressive strain raises the energy of V2 faster than it lowers the energy of C2. (b) Normalized squared value of wave function (/Ψ/2) in the cross sectional plane of a 1.7 nm [110] SiNW. From left to right strain values are −2%, 0% and +2%, respectively. Valence and conduction band states (VB and CB) are at BZ center. As can be seen in the left panel (for −2% strain) the change of symmetry is more pronounced for valence sub band.
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f2: Wave function symmetry change with strain.(a) Effect of compressive strain on second valence sub band (V2) which results in the change of wave function symmetry. From left to right, it can be seen that compressive strain raises the energy of V2 faster than it lowers the energy of C2. (b) Normalized squared value of wave function (/Ψ/2) in the cross sectional plane of a 1.7 nm [110] SiNW. From left to right strain values are −2%, 0% and +2%, respectively. Valence and conduction band states (VB and CB) are at BZ center. As can be seen in the left panel (for −2% strain) the change of symmetry is more pronounced for valence sub band.

Mentions: As long as the bandgap is direct, photon emission is a first order process and its rate is governed by equation (2). The average spontaneous emission times for [110] axially aligned SiNWs in this study are tabulated in Table 1. As can be seen in Table 1, compressive strain leads to an increase of spontaneous emission time by one to two orders of magnitude. This is due to the movement of sub bands in the compressive strain regime. As pictured in the graphics of Fig. 2a, the rise of the second valence sub band (V2) due to its anti-bonding nature is more dominant than the rate with which the first valence sub band (V1) rises or the conduction sub band (C2) falls. As a result, V2 determines the new highest valence band. The aforementioned mechanism can be further understood by looking at Fig. 2b that shows the normalized probability density (/Ψ/2) of conduction and valence states at BZ center. Comparing the valence/conduction bands (VB/CB) at 0% and −2% strain values shows that the dominant change is due to the valence band symmetry change induced by compressive strain (e.g. −2% ). Left panel of Fig. 2b shows that the newly raised valence sub band (V2) has different wave function symmetry as opposed to the centro-symmetric nature of valence band V1 at 0% and +2% strains. Therefore the matrix element, <Ψc/r/Ψv>, changes accordingly and modulates the spontaneous emission time (rate) through equation (2). Comparing wave function symmetries of valence and conduction bands at strain values of 0% and +2%, as in Fig. 2b (center and right panel), further illustrates why the spontaneous emission time is almost unchanged within this tensile strain regime.


Reversible modulation of spontaneous emission by strain in silicon nanowires.

Shiri D, Verma A, Selvakumar CR, Anantram MP - Sci Rep (2012)

Wave function symmetry change with strain.(a) Effect of compressive strain on second valence sub band (V2) which results in the change of wave function symmetry. From left to right, it can be seen that compressive strain raises the energy of V2 faster than it lowers the energy of C2. (b) Normalized squared value of wave function (/Ψ/2) in the cross sectional plane of a 1.7 nm [110] SiNW. From left to right strain values are −2%, 0% and +2%, respectively. Valence and conduction band states (VB and CB) are at BZ center. As can be seen in the left panel (for −2% strain) the change of symmetry is more pronounced for valence sub band.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3375500&req=5

f2: Wave function symmetry change with strain.(a) Effect of compressive strain on second valence sub band (V2) which results in the change of wave function symmetry. From left to right, it can be seen that compressive strain raises the energy of V2 faster than it lowers the energy of C2. (b) Normalized squared value of wave function (/Ψ/2) in the cross sectional plane of a 1.7 nm [110] SiNW. From left to right strain values are −2%, 0% and +2%, respectively. Valence and conduction band states (VB and CB) are at BZ center. As can be seen in the left panel (for −2% strain) the change of symmetry is more pronounced for valence sub band.
Mentions: As long as the bandgap is direct, photon emission is a first order process and its rate is governed by equation (2). The average spontaneous emission times for [110] axially aligned SiNWs in this study are tabulated in Table 1. As can be seen in Table 1, compressive strain leads to an increase of spontaneous emission time by one to two orders of magnitude. This is due to the movement of sub bands in the compressive strain regime. As pictured in the graphics of Fig. 2a, the rise of the second valence sub band (V2) due to its anti-bonding nature is more dominant than the rate with which the first valence sub band (V1) rises or the conduction sub band (C2) falls. As a result, V2 determines the new highest valence band. The aforementioned mechanism can be further understood by looking at Fig. 2b that shows the normalized probability density (/Ψ/2) of conduction and valence states at BZ center. Comparing the valence/conduction bands (VB/CB) at 0% and −2% strain values shows that the dominant change is due to the valence band symmetry change induced by compressive strain (e.g. −2% ). Left panel of Fig. 2b shows that the newly raised valence sub band (V2) has different wave function symmetry as opposed to the centro-symmetric nature of valence band V1 at 0% and +2% strains. Therefore the matrix element, <Ψc/r/Ψv>, changes accordingly and modulates the spontaneous emission time (rate) through equation (2). Comparing wave function symmetries of valence and conduction bands at strain values of 0% and +2%, as in Fig. 2b (center and right panel), further illustrates why the spontaneous emission time is almost unchanged within this tensile strain regime.

Bottom Line: Our main finding is that a one to two orders of magnitude change in spontaneous emission time occurs due to two distinct mechanisms: (A) Change in wave function symmetry, where within the direct bandgap regime, strain changes the symmetry of wave functions, which in turn leads to a large change of optical dipole matrix element. (B) Direct to indirect bandgap transition which makes the spontaneous photon emission to be of a slow second order process mediated by phonons.These results promise new applications of silicon nanowires as optoelectronic devices including a mechanism for lasing.Our results are verifiable using existing experimental techniques of applying strain to nanowires.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

ABSTRACT
We computationally study the effect of uniaxial strain in modulating the spontaneous emission of photons in silicon nanowires. Our main finding is that a one to two orders of magnitude change in spontaneous emission time occurs due to two distinct mechanisms: (A) Change in wave function symmetry, where within the direct bandgap regime, strain changes the symmetry of wave functions, which in turn leads to a large change of optical dipole matrix element. (B) Direct to indirect bandgap transition which makes the spontaneous photon emission to be of a slow second order process mediated by phonons. This feature uniquely occurs in silicon nanowires while in bulk silicon there is no change of optical properties under any reasonable amount of strain. These results promise new applications of silicon nanowires as optoelectronic devices including a mechanism for lasing. Our results are verifiable using existing experimental techniques of applying strain to nanowires.

Show MeSH
Related in: MedlinePlus