Supporting Information Air-Stable n-Doped Colloidal HgS Quantum Dots
Supporting Information
Air-Stable n-Doped Colloidal HgS Quantum Dots Kwang Seob Jeong, Zhiyou Deng, Sean Keuleyan, Heng Liu, and Philippe Guyot-Sionnest* The James Franck Institute, 929 E. 57th Street, The University of Chicago, Chicago, IL 60637
List of supplementary information 1. Experimental methods. 2. Figures. Figure S1. Absorption spectra of HgS CQDs with alternating Hg2+ and S2- exposure. Figure S2. Cyclic voltammogram of HgS CQD solid. Figure S3. Conductivity of HgTe, and HgS CQD films with alternating Hg2+ and S2- exposure. Figure S4. Resting potential of HgS CQD film with alternating Hg2+ and S2- exposure. Figure S5. Absorption spectra of HgS CQD film with alternating Hg2+ and S2- exposure. Figure S6. Size dependence of the interband and intraband transitions. Figure S7. Intraband photoluminescence (PL) sensitive to surface exposure.
3. Table. Table S1. Inductively coupled plasma optical emission spectrometry (ICP) of Hg2+ and S2treated HgS CQDs. 4. k·p prediction in Figure 2B of the main manuscript. 5. Electrochemical stability range of doped colloidal quantum dot. 6. References
1. Experimental methods Synthesis The synthesis of HgS CQD is adapted from that of HgTe. Simply replacing Te with S (for TOP: E = S, Se, Te) gave no reaction. Instead, we used several sulfur precursors: thioacetamide, bis(trimethylsilyl)sulfide (TMS)2S, or (NH4)2S with resulting particles typically giving larger mean particle size in that order. Mercury chloride (HgCl 2, 81 mg) and 10 mL of oleylamine were loaded into a 50 mL round bottom flask. The HgCl 2 oleylamine solution was heated under vacuum at 120 °C for 1 hour and then was cooled to 30°C under Ar. 0.3 mL of 1 M freshly prepared thioacetamide in oleylamine was quickly injected and the solution instantly appeared black, indicating the formation of HgS. No significant growth was observed over time between 30 min. and 1 hour. Such method produced samples typically having an exciton absorption feature near 1 μm with an absorption onset near 8000-9000 cm-1. The reaction was stopped by transferring to a solution of two volume equivalents of 10 % vol. dodecanethiol/ 1 %
trioctylphosphine tetrachloroethylene. All chemicals are purchased from Aldrich and used as received. The layer-by-layer growth was done by alternating sulfur and mercury reagents. For the sulfur step, 1 mL of formamide, 50 μL of oleylamine and 150 μL of 0.1 M (NH4)2S were added to 1 mL of HgS CQDS solution in tetrachloroethylene (the optical density of the HgS solution is about 0.1 at the interband shoulder). This mixture was stirred for about 5 minutes, and then the HgS dots were washed twice with formamide to remove extra (NH4)2S. For the mercury step, 1 mL of formamide and 150 uL of 0.1 M HgCl2 solution in formamide were added to 1 mL of sulfur-rich HgS CQD solution. This mixture was stirred for about 5 min. before being washed with formamide. Then the HgS solution was ready for the FTIR and other measurements. Film preparation HgS CQD films were prepared via multiple layer deposition. HgS CQDs (~20 mg/mL) in hexane/octane (9:1) solution and 1% hexanedithiol (HDT) in methanol were used for film preparation. The film was drop-cast onto a polished Pt disk working electrode (R=3.5mm) and then immersed in HDT methanol solution to replace the dodecanethiol bound to the CQDs. Infrared absorption spectroscopy The steady state absorption spectra were obtained with the Nexus 670 FT IR spectrometer. Spectroelectrochemistry For the spectroelectrocemical studies, the hexanedithiol crosslinked HgS CQD film was dried for 1 hour under vacuum and placed into a spectroelectrochemical cell. The electrochemical cell is comprised of three electrodes: a Ag pseudo reference electrode, Pt working electrode and Pt counter electrode. Tetrabutylammonium perchlorate (TBAP, 0.1 M) in propylene carbonate was
injected into the electrochemical cell inside the glovebox. The electrochemical cell was placed inside of the FTIR, the Pt electrode was lightly pressed against a CaF2 window and the infrared light reflected from the Pt working electrode was collected by an MCT detector. Cyclic voltammetry Hexanedithiol capped HgS CQD film were deposited on an interdigitated electrode (Abtech Scientific, 50 periods of 5mm long 10μm spaced electrodes) and immersed into 0.1 M tetrabutylammonium perchlorate (TBAP) in propylene carbonate. A Ag pseudo reference and Pt counter wire electrode were used for the cyclic voltammetry using a bipotentiostat. A function generator was used to scan the range of interest at a scan rate of 0.05 V/s scan rate. Conductivity measurement The conductance between the two working electrodes with 4.5 mV bias is measured with a TBAP propylene carbonate solution was used for the reference. Interdigitated electrode (Abtech Scienctific) was utilized to measure the conductance of HgS CQDs and a Pt wire was used for the counter electrode and the reference electrode was either a Ag/AgCl pseudo reference or a ferrocene/ferrocenium reference. Transmittance electron microscopy TEM images were obtained by using a 300 kV FEI Tecnai F 30 microscope. X-ray diffraction spectroscopy A Bruker D8 powder diffractomer was utilized for x-ray diffraction pattern of HgS CQD solid. Cu Kα X-ray source operating at 40 kV and 40 mA was incident on to the drop cast HgS CQD solid on silicon wafer.
Inductively coupled plasma optical emission spectrometry (ICP) A dried HgS CQD solid was dissolved in 1% v/v HNO3 and 1% HCl aqueous solution and analyzed using inductively coupled plasma optical emission spectrometer (Agilent 700 series). Photoluminescence measurement The as-synthesized HgS CQD solution was transferred into a liquid cell and photoexcited by 808 nm continuous laser chopped at 70 kHz. The photoluminescence was measured with a step-scan FTIR with MCT detector and a lock-in amplifier. Resting potential measurement A Pt wire was dipped into HgS CQD (10mg/mL) solution and crosslinked with ethanedithiol in methanol. For the film, after ethanedithiol crosslinking, the resting potential was ~ -50 mV. The film was then taken out, rinsed and dipped 10 s in a HgCl2/formamide solution. After rinsing with ethanol and drying with N2 gas, the resting potential was measured again, and showed a value of ~ +250 mV. The sample was then taken out, rinsed and dipped in a (NH4)2S/formamide solution, and the resting potential returned to a value close to 0 V. Tetrabutylammonium perchlorate in formamide (0.1 M) was used as an electrolyte. A Ag/AgCl pseudo reference was used.
2. Figures
Figure S1. Absorption spectra of HgS CQDs with alternating Hg2+ and S2- exposure. The absorption spectra of HgS CQDs are sensitive to surface compositions. By alternating surface composition using sulfur and mercury ion solutions, the intraband absorption at 2050 cm 1
disappears and recovers, respectively, and the reversible feature continues. In contrast, the
bandedge excitonic absorption peak shows up under sulfur treatment and disappears by mercury treatment. The vibrational absorptions observed at 2900 cm -1 (C-H asymmetric and symmetric stretch) and 1460 cm-1(C-H bend) are attributed to oleylamine in solution. The peak shown at 1650 cm-1 is from formamide used as a solvent for mercury and sulfur doping solutions. The small peak at 3600 cm-1 of the first HgS sample is presumably due to small residual methanol/ethanol in solution and it disappears with following doping steps.
Figure S2. Cyclic voltammogram of HgS CQD solid. The voltage is scanned from -1.2 V to 1 V at 0.05 V/sec, referenced to a Ag wire. The positive and negative currents at negative potential, corresponds to the reversible reduction of the CQD solid.
A A
B
Figure S3. Conductivity of HgTe and HgS CQD films with alternating Hg2+ and S2exposure. Figure 3C in the main text illustrates the conductivity change of the ambipolar HgTe CQD solid by Cd2+ and S2- exposure using a Ag/AgCl pseudoreference. Similar effects are observed with Hg2+ and S2- exposure in Figure S3A. The Hg2+ doping shifts the electron reduction potential in the positive direction whereas the S 2- doping shifts in the negative direction. However, unlike for Cd2+ and S2-, the energy difference between electron and hole injection HgTe CQD solid gradually decreases with iterating the surface doping process and this is
attributed to narrowing, or maybe closing of the HgTe quantum dot gap with HgS shell growth. Figure 3SB shows the conductivity change of HgS CQD film by Hg2+ and S2- exposure using Fc/Fc+ reference electrode. The conductivity is only observed n-type. Mercury exposure steps the redox potential in the positive direction. Sulfide exposure makes the reduction potential more negative or unchanged, and shows a hysteresis which we tentatively attribute the irreversible oxidation of sulfides to polysulfides at such positive potentials. Unlike for HgTe, where potentials are kept small, there is a net gradual positive shift of the electron injection potential to large positive values (~ 1V) which is consistent with the air-stable intraband absorption in figure S5.
Figure S4. Resting potential of HgS CQD film with alternating Hg2+ and S2- exposure. As described in the main text, the resting potential is sensitive to the type of surface treatment. The increase of the resting potential by mercury treatment corresponds to current flowing to the reference electrode (although no current is actually drawn due to the high impedance of the potentiostat), therefore electrons flowing into the quantum dots. The decrease of potential with the sulfur treatment corresponds to current flowing from the reference electrode and to the loss of electrons from the quantum dots.
Figure S5. Absorption spectra of HgS CQD film with alternating Hg2+ and S2- exposure. The intraband absorption is sensitive to surface treatment. The trend of increase and decrease by Hg2+ and S2- treatment is similar to the result of HgS in solution but, in films, the intraband absorption is not fully removed by sulfur treatment.
Figure S6. Size dependence of the interband and intraband transitions. The average sizes are determined by TEM. The interband energy is determined by the bleach peak between reducing and oxidizing potentials and the error bar is from fitting the bleach peak to a Gaussian. The intraband energy is measured in steady state as in figure.1C. The error bar is given by the fitting of the peak to a Gaussian. The red-dotted line is the k·p prediction.
Figure S7. Intraband photoluminescence (PL) sensitive to surface exposure. The intraband PL of HgS CQD solution is observed at 2000 cm-1 and very sensitive to the surface exposure of mercury or sulfur ion solutions. The black line corresponds to the PL spectrum of the nonsurface treated HgS CQDs. The red line corresponds to the mercury treated HgS-S, indicating that the intraband transition is recovered and slightly red-shifted. The consecutive sulfur treatment quenches the intraband PL, and then the mercury exposure results in a red-shifted intraband PL (green). The reversible feature of the disappearance and appearance of intraband PL by sulfur and mercury treatment continues.
3. Table Molar ratio (Hg/S) S doped HgS
1.01
Hg doped HgS
1.30
Table S1. Inductively coupled plasma optical emission spectrometry (ICP) of Hg 2+ and S2treated HgS CQDs. The sulfur treated HgS CQD has 1.01 molar ratio between Hg and S while the Hg treated has larger value, 1.30. 4. k·p prediction in Figure 2B A 2-band k·p model with a Hamiltonian H= dispersion give
gives the non parabolic energy
for the conduction band. This equation can be inverted to . The heavy hole band is assumed dispersion-less. In a spherical
box of radius R, the 1Se state has k1S= π/R, and the 1Pe state has k1P= 4.49/R. This gives the intraband energy E y= E1Pe -E1Se. The interband energy is given by E x= EG+E1Se. The equation fitting the data is then
. The Kane
parameter implicit in A in the k·p Hamiltonian is not in the fitting equation and the only parameter is the gap EG. The model neglects the valence band dispersion, and Coulomb interactions.
5. Electrochemical stability range of doped colloidal quantum dot As pointed out by Gerischer,1 the redox decomposition of a semiconductor can be estimated by its relevant surface reactions. For HgS, one may consider that the surface may undergo reduction (1) (HgS)n+2e-→(HgS)n-1Hg +S2- (solvent) or oxidation (HgS)n+2h+→(HgS)n-1S+ Hg2+ (solvent). The standard energy of formation of HgS is ΔGf0= -43 kJ/mol. The standard reduction potentials of S/S2- is E0 = -0.51 V and for Hg2+/Hg, E0 =+0.79 V, both for aqueous solutions. The potential for (1) is then Ered=E0S+ΔGf0/2F = -0.73 V, and the potential for (2) is Eox = E0Hg ΔGf0/2F = +1.01 V. HgS is unstable to oxidation if holes are present at a potential more positive than 1 V and unstable to reduction at a potential more negative than -0.73 V. If reactions can stabilize the ions in solutions, the range of potential will be smaller. For example, polysulfide formations or acidic conditions to form HS- or H2S would make the reduction easier. Similarly, the formation of stable soluble complexes with Hg2+ will facilitate oxidation. In the absence of these, the potential range of [-0.73 V, +1.01 V] provides a guideline of the stability range. The valence and conduction band have to be within that range for stable p and n-type doping respectively. A stability range for other compounds can be derived in the same manner. For CdSe, similar reactions limit the potential ranges to [-1.56 V, +0.33 V]. CdSe quantum dots are n-type at potentials of ~ -0.5 to -1.5 V depending on the size.2 Given the CdSe gap of 1.8 V and even without additional charging correction energy, p-doping of CdSe is impossible unless the surface can be stabilized against oxidative decomposition. On the other hand, for HgTe, n-type and ptype are achieved at moderate potentials within the potential range of stability [-1.09 V, + 0.96 V] and although they are not stable in ambient conditions, the n- and p-type nanoparticles are stable in anhydrous and inert conditions.
6. References 1. Gerischer, H. On the Stability of Semiconductor Electrodes against Photodecomposition. J. Electroanal. Chem. 1977, 82, 133−143. 2. Wang, C.; Shim, M.; Guyot-Sionnest, P. Electrochromic Semiconductor Nanocrystals Films. Appl. Phys. Lett. 2002, 80, 4−6.
Air-Stable n-Doped Colloidal HgS Quantum Dots Kwang Seob Jeong, Zhiyou Deng, Sean Keuleyan, Heng Liu, and Philippe Guyot-Sionnest* The James Franck Institute, 929 E. 57th Street, The University of Chicago, Chicago, IL 60637
List of supplementary information 1. Experimental methods. 2. Figures. Figure S1. Absorption spectra of HgS CQDs with alternating Hg2+ and S2- exposure. Figure S2. Cyclic voltammogram of HgS CQD solid. Figure S3. Conductivity of HgTe, and HgS CQD films with alternating Hg2+ and S2- exposure. Figure S4. Resting potential of HgS CQD film with alternating Hg2+ and S2- exposure. Figure S5. Absorption spectra of HgS CQD film with alternating Hg2+ and S2- exposure. Figure S6. Size dependence of the interband and intraband transitions. Figure S7. Intraband photoluminescence (PL) sensitive to surface exposure.
3. Table. Table S1. Inductively coupled plasma optical emission spectrometry (ICP) of Hg2+ and S2treated HgS CQDs. 4. k·p prediction in Figure 2B of the main manuscript. 5. Electrochemical stability range of doped colloidal quantum dot. 6. References
1. Experimental methods Synthesis The synthesis of HgS CQD is adapted from that of HgTe. Simply replacing Te with S (for TOP: E = S, Se, Te) gave no reaction. Instead, we used several sulfur precursors: thioacetamide, bis(trimethylsilyl)sulfide (TMS)2S, or (NH4)2S with resulting particles typically giving larger mean particle size in that order. Mercury chloride (HgCl 2, 81 mg) and 10 mL of oleylamine were loaded into a 50 mL round bottom flask. The HgCl 2 oleylamine solution was heated under vacuum at 120 °C for 1 hour and then was cooled to 30°C under Ar. 0.3 mL of 1 M freshly prepared thioacetamide in oleylamine was quickly injected and the solution instantly appeared black, indicating the formation of HgS. No significant growth was observed over time between 30 min. and 1 hour. Such method produced samples typically having an exciton absorption feature near 1 μm with an absorption onset near 8000-9000 cm-1. The reaction was stopped by transferring to a solution of two volume equivalents of 10 % vol. dodecanethiol/ 1 %
trioctylphosphine tetrachloroethylene. All chemicals are purchased from Aldrich and used as received. The layer-by-layer growth was done by alternating sulfur and mercury reagents. For the sulfur step, 1 mL of formamide, 50 μL of oleylamine and 150 μL of 0.1 M (NH4)2S were added to 1 mL of HgS CQDS solution in tetrachloroethylene (the optical density of the HgS solution is about 0.1 at the interband shoulder). This mixture was stirred for about 5 minutes, and then the HgS dots were washed twice with formamide to remove extra (NH4)2S. For the mercury step, 1 mL of formamide and 150 uL of 0.1 M HgCl2 solution in formamide were added to 1 mL of sulfur-rich HgS CQD solution. This mixture was stirred for about 5 min. before being washed with formamide. Then the HgS solution was ready for the FTIR and other measurements. Film preparation HgS CQD films were prepared via multiple layer deposition. HgS CQDs (~20 mg/mL) in hexane/octane (9:1) solution and 1% hexanedithiol (HDT) in methanol were used for film preparation. The film was drop-cast onto a polished Pt disk working electrode (R=3.5mm) and then immersed in HDT methanol solution to replace the dodecanethiol bound to the CQDs. Infrared absorption spectroscopy The steady state absorption spectra were obtained with the Nexus 670 FT IR spectrometer. Spectroelectrochemistry For the spectroelectrocemical studies, the hexanedithiol crosslinked HgS CQD film was dried for 1 hour under vacuum and placed into a spectroelectrochemical cell. The electrochemical cell is comprised of three electrodes: a Ag pseudo reference electrode, Pt working electrode and Pt counter electrode. Tetrabutylammonium perchlorate (TBAP, 0.1 M) in propylene carbonate was
injected into the electrochemical cell inside the glovebox. The electrochemical cell was placed inside of the FTIR, the Pt electrode was lightly pressed against a CaF2 window and the infrared light reflected from the Pt working electrode was collected by an MCT detector. Cyclic voltammetry Hexanedithiol capped HgS CQD film were deposited on an interdigitated electrode (Abtech Scientific, 50 periods of 5mm long 10μm spaced electrodes) and immersed into 0.1 M tetrabutylammonium perchlorate (TBAP) in propylene carbonate. A Ag pseudo reference and Pt counter wire electrode were used for the cyclic voltammetry using a bipotentiostat. A function generator was used to scan the range of interest at a scan rate of 0.05 V/s scan rate. Conductivity measurement The conductance between the two working electrodes with 4.5 mV bias is measured with a TBAP propylene carbonate solution was used for the reference. Interdigitated electrode (Abtech Scienctific) was utilized to measure the conductance of HgS CQDs and a Pt wire was used for the counter electrode and the reference electrode was either a Ag/AgCl pseudo reference or a ferrocene/ferrocenium reference. Transmittance electron microscopy TEM images were obtained by using a 300 kV FEI Tecnai F 30 microscope. X-ray diffraction spectroscopy A Bruker D8 powder diffractomer was utilized for x-ray diffraction pattern of HgS CQD solid. Cu Kα X-ray source operating at 40 kV and 40 mA was incident on to the drop cast HgS CQD solid on silicon wafer.
Inductively coupled plasma optical emission spectrometry (ICP) A dried HgS CQD solid was dissolved in 1% v/v HNO3 and 1% HCl aqueous solution and analyzed using inductively coupled plasma optical emission spectrometer (Agilent 700 series). Photoluminescence measurement The as-synthesized HgS CQD solution was transferred into a liquid cell and photoexcited by 808 nm continuous laser chopped at 70 kHz. The photoluminescence was measured with a step-scan FTIR with MCT detector and a lock-in amplifier. Resting potential measurement A Pt wire was dipped into HgS CQD (10mg/mL) solution and crosslinked with ethanedithiol in methanol. For the film, after ethanedithiol crosslinking, the resting potential was ~ -50 mV. The film was then taken out, rinsed and dipped 10 s in a HgCl2/formamide solution. After rinsing with ethanol and drying with N2 gas, the resting potential was measured again, and showed a value of ~ +250 mV. The sample was then taken out, rinsed and dipped in a (NH4)2S/formamide solution, and the resting potential returned to a value close to 0 V. Tetrabutylammonium perchlorate in formamide (0.1 M) was used as an electrolyte. A Ag/AgCl pseudo reference was used.
2. Figures
Figure S1. Absorption spectra of HgS CQDs with alternating Hg2+ and S2- exposure. The absorption spectra of HgS CQDs are sensitive to surface compositions. By alternating surface composition using sulfur and mercury ion solutions, the intraband absorption at 2050 cm 1
disappears and recovers, respectively, and the reversible feature continues. In contrast, the
bandedge excitonic absorption peak shows up under sulfur treatment and disappears by mercury treatment. The vibrational absorptions observed at 2900 cm -1 (C-H asymmetric and symmetric stretch) and 1460 cm-1(C-H bend) are attributed to oleylamine in solution. The peak shown at 1650 cm-1 is from formamide used as a solvent for mercury and sulfur doping solutions. The small peak at 3600 cm-1 of the first HgS sample is presumably due to small residual methanol/ethanol in solution and it disappears with following doping steps.
Figure S2. Cyclic voltammogram of HgS CQD solid. The voltage is scanned from -1.2 V to 1 V at 0.05 V/sec, referenced to a Ag wire. The positive and negative currents at negative potential, corresponds to the reversible reduction of the CQD solid.
A A
B
Figure S3. Conductivity of HgTe and HgS CQD films with alternating Hg2+ and S2exposure. Figure 3C in the main text illustrates the conductivity change of the ambipolar HgTe CQD solid by Cd2+ and S2- exposure using a Ag/AgCl pseudoreference. Similar effects are observed with Hg2+ and S2- exposure in Figure S3A. The Hg2+ doping shifts the electron reduction potential in the positive direction whereas the S 2- doping shifts in the negative direction. However, unlike for Cd2+ and S2-, the energy difference between electron and hole injection HgTe CQD solid gradually decreases with iterating the surface doping process and this is
attributed to narrowing, or maybe closing of the HgTe quantum dot gap with HgS shell growth. Figure 3SB shows the conductivity change of HgS CQD film by Hg2+ and S2- exposure using Fc/Fc+ reference electrode. The conductivity is only observed n-type. Mercury exposure steps the redox potential in the positive direction. Sulfide exposure makes the reduction potential more negative or unchanged, and shows a hysteresis which we tentatively attribute the irreversible oxidation of sulfides to polysulfides at such positive potentials. Unlike for HgTe, where potentials are kept small, there is a net gradual positive shift of the electron injection potential to large positive values (~ 1V) which is consistent with the air-stable intraband absorption in figure S5.
Figure S4. Resting potential of HgS CQD film with alternating Hg2+ and S2- exposure. As described in the main text, the resting potential is sensitive to the type of surface treatment. The increase of the resting potential by mercury treatment corresponds to current flowing to the reference electrode (although no current is actually drawn due to the high impedance of the potentiostat), therefore electrons flowing into the quantum dots. The decrease of potential with the sulfur treatment corresponds to current flowing from the reference electrode and to the loss of electrons from the quantum dots.
Figure S5. Absorption spectra of HgS CQD film with alternating Hg2+ and S2- exposure. The intraband absorption is sensitive to surface treatment. The trend of increase and decrease by Hg2+ and S2- treatment is similar to the result of HgS in solution but, in films, the intraband absorption is not fully removed by sulfur treatment.
Figure S6. Size dependence of the interband and intraband transitions. The average sizes are determined by TEM. The interband energy is determined by the bleach peak between reducing and oxidizing potentials and the error bar is from fitting the bleach peak to a Gaussian. The intraband energy is measured in steady state as in figure.1C. The error bar is given by the fitting of the peak to a Gaussian. The red-dotted line is the k·p prediction.
Figure S7. Intraband photoluminescence (PL) sensitive to surface exposure. The intraband PL of HgS CQD solution is observed at 2000 cm-1 and very sensitive to the surface exposure of mercury or sulfur ion solutions. The black line corresponds to the PL spectrum of the nonsurface treated HgS CQDs. The red line corresponds to the mercury treated HgS-S, indicating that the intraband transition is recovered and slightly red-shifted. The consecutive sulfur treatment quenches the intraband PL, and then the mercury exposure results in a red-shifted intraband PL (green). The reversible feature of the disappearance and appearance of intraband PL by sulfur and mercury treatment continues.
3. Table Molar ratio (Hg/S) S doped HgS
1.01
Hg doped HgS
1.30
Table S1. Inductively coupled plasma optical emission spectrometry (ICP) of Hg 2+ and S2treated HgS CQDs. The sulfur treated HgS CQD has 1.01 molar ratio between Hg and S while the Hg treated has larger value, 1.30. 4. k·p prediction in Figure 2B A 2-band k·p model with a Hamiltonian H= dispersion give
gives the non parabolic energy
for the conduction band. This equation can be inverted to . The heavy hole band is assumed dispersion-less. In a spherical
box of radius R, the 1Se state has k1S= π/R, and the 1Pe state has k1P= 4.49/R. This gives the intraband energy E y= E1Pe -E1Se. The interband energy is given by E x= EG+E1Se. The equation fitting the data is then
. The Kane
parameter implicit in A in the k·p Hamiltonian is not in the fitting equation and the only parameter is the gap EG. The model neglects the valence band dispersion, and Coulomb interactions.
5. Electrochemical stability range of doped colloidal quantum dot As pointed out by Gerischer,1 the redox decomposition of a semiconductor can be estimated by its relevant surface reactions. For HgS, one may consider that the surface may undergo reduction (1) (HgS)n+2e-→(HgS)n-1Hg +S2- (solvent) or oxidation (HgS)n+2h+→(HgS)n-1S+ Hg2+ (solvent). The standard energy of formation of HgS is ΔGf0= -43 kJ/mol. The standard reduction potentials of S/S2- is E0 = -0.51 V and for Hg2+/Hg, E0 =+0.79 V, both for aqueous solutions. The potential for (1) is then Ered=E0S+ΔGf0/2F = -0.73 V, and the potential for (2) is Eox = E0Hg ΔGf0/2F = +1.01 V. HgS is unstable to oxidation if holes are present at a potential more positive than 1 V and unstable to reduction at a potential more negative than -0.73 V. If reactions can stabilize the ions in solutions, the range of potential will be smaller. For example, polysulfide formations or acidic conditions to form HS- or H2S would make the reduction easier. Similarly, the formation of stable soluble complexes with Hg2+ will facilitate oxidation. In the absence of these, the potential range of [-0.73 V, +1.01 V] provides a guideline of the stability range. The valence and conduction band have to be within that range for stable p and n-type doping respectively. A stability range for other compounds can be derived in the same manner. For CdSe, similar reactions limit the potential ranges to [-1.56 V, +0.33 V]. CdSe quantum dots are n-type at potentials of ~ -0.5 to -1.5 V depending on the size.2 Given the CdSe gap of 1.8 V and even without additional charging correction energy, p-doping of CdSe is impossible unless the surface can be stabilized against oxidative decomposition. On the other hand, for HgTe, n-type and ptype are achieved at moderate potentials within the potential range of stability [-1.09 V, + 0.96 V] and although they are not stable in ambient conditions, the n- and p-type nanoparticles are stable in anhydrous and inert conditions.
6. References 1. Gerischer, H. On the Stability of Semiconductor Electrodes against Photodecomposition. J. Electroanal. Chem. 1977, 82, 133−143. 2. Wang, C.; Shim, M.; Guyot-Sionnest, P. Electrochromic Semiconductor Nanocrystals Films. Appl. Phys. Lett. 2002, 80, 4−6.
