CN106815490B - A kind of method that the band gap of determining semiconductor nanocrystal quantum dot moves in different media - Google Patents
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Abstract
A kind of method of semiconductor nanocrystal quantum dot bandgap in determining medium background, establish the quantum point model in medium background, introduce the concept of mirror charge, the size and location of image charge has been determined, electronics is added in the Hamiltonian of exciton, interaction between two particles between hole and mirror charge, the band-gap energy expression formula of quantum dot in medium background has been obtained with the Schrodinger equation that perturbation method solves exciton, at a given temperature, by the exciton Bohr radius of quantum dot, relative dielectric coefficient, partial size, body material band gap energy, the parameters such as the relative dielectric coefficient of background medium substitute into expression formula, the band gap of quantum dot in medium background can be obtained, finally determine the bandgap of quantum dot in different background media.The present invention can specifically calculate bandgap of the quantum dot of identical size in different background materials, provide directly strong tool for the design of opto-electronic device and the research of semiconductor nanocrystal materials optical characteristics.
Description
Technical field
The present invention relates to photoelectric device technologies and nano material calculating field, and in particular to determines in different medium background
The method of semiconductor nanocrystal quantum dot bandgap.By analytical expression of the invention, semiconductor can be directly determined and received
Meter Jing Ti quantum dot band gap with the dielectric coefficient of different background materials variation.
Background technique
The substance of nanoscale will appear many peculiar properties compared with body material, these properties are to be reduced to produce by size
Caused by raw quantum effect.Semiconductor crystalline material is when being all reduced to nanoscale in three dimensions, carrier therein
It can be all restricted in three dimensions, this semiconductor nanocrystals are known as quantum dot.It is measured caused by reducing due to size
Sub- effect of restraint, the energy level of quantum dot can become discrete energy level from the continuous energy level of block materials, and the size of band gap with
The size of quantum dot is related, and this characteristic is known as the dimensional effect of quantum dot.Due to this characteristic, quantum dot is in optoelectronic areas
It has a wide range of applications.Wherein most important several application aspects include: quantum dot light fiber amplifier, quantum dot laser
And the optical characteristics of quantum dot: luminescent properties and absorbent properties, and quantum is all utilized in quantum dot solar cell, these devices
The optical characteristics of point is determined by its band gap, therefore research and amount of the calculating of quantum dot band gap to quantum dot optical characteristics
The development important in inhibiting of son point opto-electronic device.
The band gap size of quantum dot is mainly related with its size, however, experimentation have shown that the band gap of quantum dot with size in addition to having
Outside the Pass, also related with background environment locating for quantum dot, this is mainly as caused by the Surface Polarization effect of quantum dot.Quantum dot
Surface Polarization effect refer to the dielectric coefficient of nanocrystalline quantum dot it is different from the dielectric coefficient of background material and in the two circle
The polarity effect that face generates, also referred to as dielectric are limited effect.Due to the presence of Surface Polarization effect, the quantum dot of identical size
When in different background materials, band gap can be moved, and cause the central wavelength of its absorption peak and emission peak that can occur partially
Move, this can design to quantum dot light fiber amplifier and quantum dot laser and research have an adverse effect.
About the research of quantum dot surface polarity effect, be earliest in nineteen eighty-three, L.E.Brus effective mass approximation
Method establishes the basic quantum mechanics model an of semiconductor nanocrystals, considers dielectric polarization generation in this model
Electrostatic potential.1984, L.E.Brus joined Surface Polarization potential energy in exciton Hamiltonian, give exciton ground-state energy amount
Approximate expression, but do not discuss on deviation caused by Surface Polarization effect and influence.Later in 1993,
It is more significant in low-dimensional and small scale structures that T.Takagahara proposes Surface Polarization effect, and is calculated with effective mass approximation
It is limited comprising dielectric the exciton power spectrum of effect, the analytical expression of exciton ground-state energy amount under strong constraint is given, in expression formula
In introduce with dielectric coefficient than related two coefficient A0And A1, for reflecting the Surface Polarization effect of quantum dot, additionally grind
Study carefully dielectric and is limited influence of the effect to exciton bind energy and Oscillator Strengthss.But for being measured caused by Surface Polarization effect
Bandgap offset of the son point in different background materials, there are no relevant calculating.
At a given temperature, the movement for determining quantum dot band gap in different background materials needs to consider Surface Polarization effect
Influence to band gap.The concept of mirror charge can be introduced into calculate the band-gap energy of quantum dot in background material.It will be by background medium
The Surface Polarized Charge that polarity effect generates is equivalent to mirror charge, calculates the phase interaction between electronics, hole and corresponding mirror charge
With potential energy, the Hamiltonian of exciton is modified, then finds out swashing comprising Surface Polarization effect by solving Schrodinger equation
Subbase state derivation of energy formula can thus calculate the band gap of quantum dot in background material, and then determine different background materials
The offset direction of middle quantum dot band gap and size.
Summary of the invention
The present invention will overcome the disadvantages mentioned above of the prior art, provide nanocrystalline quantum dot band in a kind of determining background material
The mobile new method of gap, can be convenient using this method quickly calculate quantum dot in different background materials bandgap it is big
It is small, it is quantum dot light electronics device to calculate the bias size of quantum dot first absorption peak in different background materials
Design and research provide help.
Thinking of the invention is: at a given temperature, introducing the concept in mirror charge (mirror electronic and mirror image hole) to grind
Study carefully Surface Polarization effect, the Surface Polarized Charge generated by background dielectric polorization effect is equivalent to corresponding mirror charge, electricity consumption
Interaction between two particles between son, hole and mirror charge are as the potential energy item in exciton Hamiltonian, by the Xue Ding for solving exciton
Straightforward words equation finds out the energy of exciton ground state, obtains the band-gap energy of quantum dot, so that it is determined that semiconductor nano in different background materials
The bandgap size of crystal quantum dot.
To achieve the above object, the present invention adopts the following technical scheme:
The present invention provides the method that a kind of band gap of determining semiconductor nanocrystal quantum dot moves in different media,
The following steps are included:
1) establish the model of quantum dot in background medium: because quantum dot it is small-sized, shape can approximation regard as
Spherical shape, surrounding background material near infinite is big, and a partial size is R, relative dielectric coefficient ε1Nanocrystalline quantum dot insertion
Relative dielectric coefficient is ε2Uniform background medium in, using the center of quantum dot as coordinate origin, electrons and holes in quantum dot
Position vector be respectively reAnd rh；
2) it determines that electrons and holes in quantum dot correspond to the size and location of mirror charge, electrons and holes is separated into consideration,
The size and location of the corresponding mirror charge of electronics is determined first: ball is established as polar axis in straight line using the center of quantum dot and electron institute
Coordinate system, then the potential at any point meets Poisson's equation in quantum dot
ρ (r) is electric charge volume density, and ρ (r)=- e δ (r-re), due to system have axial symmetry, in quantum dot r ≠
rePosition, equation (1) can simplify as following form
Equation (2) general solution is
Pn(cos θ) is n rank Legendre (Legendre) multinomial, and inside quantum dot, the potential Ф (r) at r=0 is answered
For finite solution, therefore the B in quantum dotn=0, it is contemplated that the potential that electronics generates at r in quantum dot is coulomb potential, will wherein
1/ | r-re| it is launched into Legnedre polynomial
r<It is r and reIn lesser one, r>It is r and reIn biggish one, it is any in addition to electronics point in quantum dot
The potential of position is
Outside quantum dot, when r → ∞, potential tends to 0, the A in general solutionn=0, therefore the electricity at the outer any point of quantum dot
Gesture is
In the interface of quantum dot and background medium, r=R, potential meets such as downstream condition
Φ1=Φ2 (7)
Wherein n is normal unit vector, by Φ1And Φ2Both the above boundary condition is substituted into obtain
Then the potential of any position is in addition to electronics point in quantum dot
Wherein Φ1It is the potential in quantum dot, ε0It is the dielectric coefficient in vacuum, ε1、ε2Respectively quantum dot and background are situated between
The relative dielectric coefficient of matter, e are the quantity of electric charge of electronics, reIt is the position vector of electronics in quantum dot, r is any one in quantum dot
The position vector of point, R is the partial size of quantum dot, θ reAngle between r, Pn(cos θ) is n rank Legnedre polynomial, above formula
It can be written as easier form
Wherein re'=reR2/re 2, x is along reDirection to the centre of sphere distance, from above formula it can easily be seen that electronic induction
The size of discrete mirror charge generated is
The position of mirror charge is re'=reR2/re 2, then the corresponding mirror image electricity in hole is determined according to above-mentioned same method
The size and location of lotus, the size for obtaining the discrete mirror charge that hole induction generates are
The corresponding mirror charge position in hole is rh'=rhR2/rh 2；
3) Hamiltonian of electron hole pair in quantum dot further, is determined, it is contemplated that quantum dot and surrounding background material
Dielectric coefficient it is different caused by Surface Polarization effect, should be plus between electronics, hole and mirror charge in exciton Hamiltonian
The interaction between two particles of interaction between two particles, electron hole areAccording to the picture in 2)
Charge size and location obtains
θ is reAnd rhAngle between vector, therefore the concrete form of exciton potential energy U is
ε in formula0It is the dielectric coefficient in vacuum, ε1、ε2Respectively the relative dielectric coefficient of quantum dot and background medium, e are
The quantity of electric charge of electronics, R are quantum point grain diameter, and θ is reAnd rhAngle between vector, reAnd rhThe respectively diameter of electrons and holes
To position, potential barrier is regarded as infinitely great, then the Hamiltonian of exciton is in quantum dot
WhereinWithIt is the effective mass of electrons and holes respectively,It is reduced Planck constant；
4) it further, determines under given temperature dependent on background material dielectric coefficient ε2Quantum dot band gap (i.e. exciton base
State energy), be according to the Schrodinger equation that the exciton Hamiltonian in 3) obtains exciton in quantum dot
Electronics in quantum dot, hole ground state wave function be
N is principal quantum number in formula, and C is normalization coefficient, and the wave function of exciton is electron wave function and hole in quantum dot
The ground state wave function of exciton is normalized, then had by the product of wave function
Wherein d τeIt is the volume element in electron motion space, d τhIt is the volume element in movement of hole space, coordinate locating for electronics
System is the spherical coordinate system established using z-axis as polar axis, and the coordinate of electronics is (θ in the coordinate systeme,re), coordinate where hole
System is the spherical coordinate system established using straight line where electronics and the centre of sphere as polar axis, the coordinate in hole for (θ,rh), θ is reAnd rhArrow
Angle between amount, then d τeWith d τhForBy d τeAnd d
τhSubstitute into (22) Shi Ke get
Therefore the normalization ground state wave function of exciton is in quantum dot
Then the ground state energy that exciton is solved with perturbation method regards interaction between two particles item U as perturbation, Hami of exciton
Amount of pausing is divided into two parts H=H0+ H', wherein H'=U, energy eigenvalues E are E=E according to Perturbation Expansion0+E1, H0Corresponding energy
Measuring characteristic value is
According to perturbation theory, the level-one perturbation E of energy eigenvalues1=< Ψ0(re,rh)|H'|Ψ0(re,rh) >, is according to Ψ0
(re,rh) expression formula, and enable a=re/ R ≠ 1, b=rh/ R ≠ 1 will integrate member d τe、dτhIt substitutes into
Numerical integration is carried out to obtain
Energy eigenvalues E is added to the band gap E of corresponding body materialg, obtain the band gap expression formula of quantum dot in background medium
(ground state energy of exciton) is
Wherein EgIt is the band gap of corresponding block of material,WithIt is the effective mass of electrons and holes respectively,It is that reduction is general
Bright gram of constant, ε0It is the dielectric coefficient in vacuum, ε1、ε2The respectively relative dielectric coefficient of quantum dot and background medium, e are electricity
The quantity of electric charge of son, R is the partial size of quantum dot, because exciton Bohr radius is
So the band gap of quantum dot can be written as more succinct form in background medium
Wherein ε0=8.854 × 10-12F/m, e=1.6 × 10-19C；
5) by the relative dielectric coefficient of quantum dot, partial size, exciton Bohr radius, the band gap of corresponding body material, background medium
Dielectric coefficient substitute into the band gap expression formula of quantum dot in step 4) and determine the band gap of nanocrystalline quantum dot in background material, into
One step can determine the size of quantum dot bandgap in different background media；
6) in the background medium for calculating step 5) band gap of quantum dot substitute into the relational expression λ of wavelength and energy=
(wherein c is the light velocity 3 × 10 to hc/ (eE)8M/s, h are Planck's constant, h=6.626 × 10-34J/s), the background medium is obtained
First absorption peak wavelength of middle quantum dot may further determine the shifting of the first absorption peak of quantum dot wavelength in different background media
It is dynamic.
Wherein, above-mentioned steps 5) in background medium be selected from the liquid, solid such as organic solvent, glass, organic glass, aqueous solution
And gas.
Wherein, above-mentioned steps 5) in quantum dot be selected from three dimensions all in the semiconductor crystal of nanoscale.
Wherein, above-mentioned steps 5) in quantum dot partial size R be 1nm~100nm.
Inventive point of the invention is: by being equivalent to the Surface Polarized Charge as caused by background dielectric polorization effect as electricity
Lotus introduces the interaction between two particles item of electronics, hole and image charge in exciton Hamiltonian, solves exciton base with perturbation method
State Schrodinger equation obtains the band gap expression formula of quantum dot in background material, creates and directly determines under given temperature at different
The method of the movement of semiconductor nanocrystal quantum dot band gap in bottom material.
It is specific not yet both at home and abroad at present to determine semiconductor nanocrystal quantum dot band gap with the dielectric of different background materials
The mobile method of coefficient.
The present invention has the advantages that the present invention provides a determining quantum dot band gap with the dielectric coefficient shifting of background material
Dynamic new method has filled up the vacancy in this field, and the band gap expression formula obtained by this method can be convenient and quickly determine
Out in background material in the band gap of quantum dot and different background materials quantum dot bandgap size, and determine bandgap
Direction provides strong work for the research of semiconductor nanocrystal quantum dot optical characteristics and the design of quantum dot optoelectronic devices
Tool.
Specific embodiment:
Following embodiment should not be construed as limiting the invention for further illustrating the present invention.
Embodiment 1
1) establish the model of quantum dot in background medium: because quantum dot it is small-sized, shape can approximation regard as
Spherical shape, surrounding background material near infinite is big, and a partial size is R, relative dielectric coefficient ε1Nanocrystalline quantum dot insertion
Relative dielectric coefficient is ε2Uniform background medium in, using the center of quantum dot as coordinate origin, electrons and holes in quantum dot
Position vector be respectively reAnd rh；
2) it determines that electrons and holes in quantum dot correspond to the size and location of mirror charge, electrons and holes is separated into consideration,
The size and location of the corresponding mirror charge of electronics is determined first: ball is established as polar axis in straight line using the center of quantum dot and electron institute
Coordinate system, then the potential at any point meets Poisson's equation in quantum dot
ρ (r) is electric charge volume density, and ρ (r)=- e δ (r-re), due to system have axial symmetry, in quantum dot r ≠
rePosition, equation (1) can simplify as following form
Equation (2) general solution is
Pn(cos θ) is n rank Legendre (Legendre) multinomial, and inside quantum dot, the potential Ф (r) at r=0 is answered
For finite value, therefore the B in quantum dotn=0, it is contemplated that the potential that electronics generates at r in quantum dot is coulomb potential, will wherein
1/ | r-re| it is launched into Legnedre polynomial
r<It is r and reIn lesser one, r>It is r and reIn biggish one, it is any in addition to electronics point in quantum dot
The potential of position is
Outside quantum dot, when r → ∞, potential tends to 0, the A in general solutionn=0, therefore the electricity at the outer any point of quantum dot
Gesture is
In the interface of quantum dot and background medium, r=R, potential meets such as downstream condition
Φ1=Φ2 (7)
Wherein n is normal unit vector, by Φ1And Φ2Both the above boundary condition is substituted into obtain
Then the potential of any position is in addition to electronics point in quantum dot
Wherein Φ1It is the potential in quantum dot, ε0It is the dielectric coefficient in vacuum, ε1、ε2Respectively quantum dot and background are situated between
The relative dielectric coefficient of matter, e are the quantity of electric charge of electronics, reIt is the position vector of electronics in quantum dot, r is any one in quantum dot
The position vector of point, R is the partial size of quantum dot, θ reAngle between r, Pn(cos θ) is n rank Legnedre polynomial, above formula
It can be written as easier form
Wherein re'=reR2/re 2, x is along reDirection to the centre of sphere distance, from above formula it can easily be seen that electronic induction
The size of discrete mirror charge generated is
The position of mirror charge is re'=reR2/re 2, then the corresponding mirror image electricity in hole is determined according to above-mentioned same method
The size and location of lotus, the size for obtaining the discrete mirror charge that hole induction generates are
The corresponding mirror charge position in hole is rh'=rhR2/rh 2；
3) Hamiltonian of electron hole pair in quantum dot further, is determined, it is contemplated that quantum dot and surrounding background material
Dielectric coefficient it is different caused by Surface Polarization effect, should be plus between electronics, hole and mirror charge in exciton Hamiltonian
The interaction between two particles of interaction between two particles, electron hole areAccording to the picture in 2)
Charge size and location obtains
θ is reAnd rhAngle between vector, therefore the concrete form of exciton potential energy U is
ε in formula0It is the dielectric coefficient in vacuum, ε1、ε2Respectively the relative dielectric coefficient of quantum dot and background medium, e are
The quantity of electric charge of electronics, R are quantum point grain diameter, and θ is reAnd rhAngle between vector, reAnd rhThe respectively diameter of electrons and holes
To position, potential barrier is regarded as infinitely great, then the Hamiltonian of exciton is in quantum dot
WhereinWithIt is the effective mass of electrons and holes respectively,It is reduced Planck constant；
4) it further, determines under given temperature dependent on background material dielectric coefficient ε2Quantum dot band gap (i.e. exciton base
State energy), be according to the Schrodinger equation that the exciton Hamiltonian in 3) obtains exciton in quantum dot
Electronics in quantum dot, hole ground state wave function be
N is principal quantum number in formula, and C is normalization coefficient, and the wave function of exciton is electron wave function and hole in quantum dot
The ground state wave function of exciton is normalized, then had by the product of wave function
Wherein d τeIt is the volume element in electron motion space, d τhIt is the volume element in movement of hole space, coordinate locating for electronics
System is the spherical coordinate system established using z-axis as polar axis, and the coordinate of electronics is (θ in the coordinate systeme,re), coordinate where hole
System is the spherical coordinate system established using straight line where electronics and the centre of sphere as polar axis, the coordinate in hole for (θ,rh), θ is reAnd rhArrow
Angle between amount, then d τeWith d τhForBy d τeAnd d
τhSubstitute into (22) Shi Ke get
Therefore the normalization ground state wave function of exciton is in quantum dot
Then the ground state energy that exciton is solved with perturbation method regards interaction between two particles item U as perturbation, Hami of exciton
Amount of pausing is divided into two parts H=H0+ H', wherein H'=U, energy eigenvalues E are E=E according to Perturbation Expansion0+E1, H0Corresponding energy
Measuring characteristic value is
According to perturbation theory, the level-one perturbation E of energy eigenvalues1=< Ψ0(re,rh)|H'|Ψ0(re,rh) >, is according to Ψ0
(re,rh) expression formula, and enable a=re/ R ≠ 1, b=rh/ R ≠ 1 will integrate member d τe、dτhIt substitutes into
Numerical integration is carried out to obtain
Energy eigenvalues E is added to the band gap E of corresponding body materialg, obtain the band gap expression formula of quantum dot in background medium
(ground state energy of exciton) is
Wherein EgIt is the band gap of corresponding block of material,WithIt is the effective mass of electrons and holes respectively,It is that reduction is general
Bright gram of constant, ε0It is the dielectric coefficient in vacuum, ε1、ε2The respectively relative dielectric coefficient of quantum dot and background medium, e are electricity
The quantity of electric charge of son, R is the partial size of quantum dot, because exciton Bohr radius is
So the band gap of quantum dot can be written as more succinct form in background medium
Wherein ε0=8.854 × 10-12F/m, e=1.6 × 10-19C；
5) quantum dot type is PbSe, relative dielectric coefficient ε1It is 23.4, exciton Bohr radius aBFor 46nm, quantum dot grain
Diameter takes 4nm, the band-gap energy E of PbSe body material under room temperaturegFor 0.28eV, background medium is positive hexane solvent, opposite dielectric system
Number ε2It is 1.58, band of the 4nmPbSe quantum dot in n-hexane solvent is obtained according to the quantum dot band gap expression formula in step 4)
Gap is 1.167eV, and background medium is changed to UV glue, relative dielectric coefficient 4.04, according to the quantum dot band gap table in step 4)
Obtaining band gap of the 4nmPbSe quantum dot in UV glue up to formula is 1.164, therefore 4nmPbSe quantum dot is in n-hexane solvent and UV
Bandgap offset amount in glue is 0.003eV；
6) band gap by 4nmPbSe quantum dot in step 5) in n-hexane background substitutes into the relational expression λ of wavelength and energy
(wherein c is the light velocity 3 × 10 to=hc/ (eE)8M/s, h are Planck's constant, h=6.626 × 10-34J/s), 4nmPbSe amount is obtained
Son point first absorption peak wavelength in n-hexane background is 1064nm, by 4nmPbSe quantum dot in step 5) in UV glue background
Band gap substitute into, obtaining 4nmPbSe quantum dot first absorption peak wavelength in UV glue background is 1067nm, therefore 4nmPbSe amount
The movement of the first absorption peak wavelength in hexane solution and UV glue of son point is 3nm.
Embodiment 2
Step 1) 2) is 3) 4) as step 1) in embodiment 1 2) 3) 4) identical；
5) quantum dot type is PbSe, relative dielectric coefficient ε1It is 23.4, exciton Bohr radius aBFor 46nm, quantum dot grain
Diameter takes 4nm, the band-gap energy E of PbSe body material under room temperaturegFor 0.28eV, background medium is toluene solvant, relative dielectric coefficient ε2
It is 2.37, obtaining band gap of the 4nmPbSe quantum dot in toluene solvant according to the quantum dot band gap expression formula in step 4) is
1.166eV, background medium are changed to UV glue, relative dielectric coefficient 4.04, according to the quantum dot band gap expression formula in step 4)
Obtaining band gap of the 4nmPbSe quantum dot in UV glue is 1.164, therefore 4nmPbSe quantum dot is in toluene solvant and UV glue
Bandgap offset amount is 0.002eV；
6) band gap by 4nmPbSe quantum dot in step 5) in toluene background substitute into the relational expression λ of wavelength and energy=
(wherein c is the light velocity 3 × 10 to hc/ (eE)8M/s, h are Planck's constant, h=6.626 × 10-34J/s), 4nmPbSe quantum is obtained
Point first absorption peak wavelength in toluene background is 1065nm, by band of the 4nmPbSe quantum dot in step 5) in UV glue background
Gap substitutes into, and obtaining 4nmPbSe quantum dot first absorption peak wavelength in UV glue background is 1067nm, therefore 4nmPbSe quantum dot
The movement of the first absorption peak wavelength is 2nm in toluene solvant and UV glue.
Embodiment 3
Step 1) 2) is 3) 4) as step 1) in embodiment 1 2) 3) 4) identical；
5) quantum dot type is PbS, relative dielectric coefficient ε1It is 17.2, exciton Bohr radius aBFor 18nm, quantum point grain diameter
4nm is taken, the band-gap energy E of PbS body material under room temperaturegFor 0.41eV, background medium is positive hexane solvent, relative dielectric coefficient ε2
It is 1.58, obtaining band gap of the 4nmPbS quantum dot in n-hexane solvent according to the quantum dot band gap expression formula in step 4) is
0.893eV, background medium are changed to UV glue, relative dielectric coefficient 4.04, according to the quantum dot band gap expression formula in step 4)
Obtaining band gap of the 4nmPbS quantum dot in UV glue is 0.888, therefore 4nmPbS quantum dot is in n-hexane solvent and UV glue
Bandgap offset amount is 0.005eV；
6) band gap by 4nmPbS quantum dot in step 5) in n-hexane background substitute into the relational expression λ of wavelength and energy=
(wherein c is the light velocity 3 × 10 to hc/ (eE)8M/s, h are Planck's constant, h=6.626 × 10-34J/s), 4nmPbS quantum is obtained
Point first absorption peak wavelength in n-hexane background is 1390nm, by band of the 4nmPbS quantum dot in step 5) in UV glue background
Gap substitutes into, and obtaining 4nmPbS quantum dot first absorption peak wavelength in UV glue background is 1398nm, therefore 4nmPbS quantum dot exists
The movement of the first absorption peak wavelength is 8nm in n-hexane solvent and UV glue.
Embodiment 4
Step 1) 2) is 3) 4) as step 1) in embodiment 1 2) 3) 4) identical；
5) quantum dot type is PbSe, relative dielectric coefficient ε1It is 23.4, exciton Bohr radius aBFor 46nm, quantum dot grain
Diameter takes 5nm, the band-gap energy E of PbSe body material under room temperaturegFor 0.28eV, background medium is positive hexane solvent, opposite dielectric system
Number ε2It is 1.58, band of the 5nmPbSe quantum dot in n-hexane solvent is obtained according to the quantum dot band gap expression formula in step 4)
Gap is 0.85eV, and background medium is changed to UV glue, and relative dielectric coefficient 4.04 is expressed according to the quantum dot band gap in step 4)
It is 0.848eV that formula, which obtains band gap of the 4nmPbSe quantum dot in UV glue, therefore 5nmPbSe quantum dot is in n-hexane solvent and UV
Bandgap offset amount in glue is 0.002eV；
6) band gap by 5nmPbSe quantum dot in step 5) in n-hexane background substitutes into the relational expression λ of wavelength and energy
(wherein c is the light velocity 3 × 10 to=hc/ (eE)8M/s, h are Planck's constant, h=6.626 × 10-34J/s), 5nmPbSe quantum dot
The first absorption peak wavelength is 1462nm in n-hexane background, by band of the 5nmPbSe quantum dot in step 5) in UV glue background
Gap substitutes into, and obtaining 5nmPbSe quantum dot first absorption peak wavelength in UV glue background is 1466nm, therefore 5nmPbSe quantum dot
The movement of the first absorption peak wavelength is 4nm in n-hexane solvent and UV glue.
Content described in this specification embodiment is only enumerating to the way of realization of inventive concept, protection of the invention
Range should not be construed as being limited to the specific forms stated in the embodiments, and protection scope of the present invention is also and in art technology
Personnel conceive according to the present invention it is conceivable that equivalent technologies mean.
Claims (4)
1. a kind of method of semiconductor nanocrystal quantum dot bandgap in determining medium background, which is characterized in that including with
Lower step:
1) establish the model of quantum dot in background medium: because the shape approximation of quantum dot regards spherical as, surrounding background material is close
Like infinity, a partial size is R, relative dielectric coefficient ε1Nanocrystalline quantum dot insertion relative dielectric coefficient be ε2It is equal
In even background medium, using the center of quantum dot as coordinate origin, the position vector of electrons and holes is respectively r in quantum doteWith
rh；
2) it determines that electrons and holes in quantum dot correspond to the size and location of mirror charge, electrons and holes is separated into consideration, first
The size and location for determining the corresponding mirror charge of electronics establishes spherical coordinates as polar axis in straight line using the center of quantum dot and electron institute
System, then the potential at any point meets Poisson's equation in quantum dot, and equation general solution is n rank Legendre (Legendre) multinomial,
It can determine the coefficient in Legnedre polynomial according to finite solution and boundary condition, can obtain any in addition to electronics point in quantum dot
The potential of position
Wherein re' be mirror charge corresponding to electronics position vector, re'=reR2/re 2, Φ1It is the potential in quantum dot, ε0It is true
Aerial dielectric coefficient, ε1、ε2The respectively relative dielectric coefficient of quantum dot and background medium, e are the quantity of electric charge of electronics, reIt is
The position vector of electronics in quantum dot, r are the position vectors at any point in addition to electronics point in quantum dot, and R is quantum dot
Partial size, θ reAngle between r, Pn(cos θ) is n rank Legnedre polynomial, and x is along reDirection to the centre of sphere distance, by
Above formula can obtain the size and location of the discrete mirror charge of electronic induction generation, can similarly obtain the discrete mirror charge that hole induction generates
Size and location；
3) Hamiltonian of electron hole pair in quantum dot further, is determined, it is contemplated that the dielectric system of quantum dot and background material
Surface Polarization effect caused by difference is counted, it should be plus the interaction between electronics, hole and mirror charge in exciton Hamiltonian
Potential energy, the interaction between two particles of electron holeSubscript indicates two of interaction
Charge, e indicate that electronics, h indicate hole, qe' indicate the corresponding mirror charge of electronics, qh' indicate the corresponding mirror charge in hole, it utilizes
2) mirror charge size and location obtained in obtains the concrete form of exciton potential energy U according to the definition of interaction between two particles
ε in formula0It is the dielectric coefficient in vacuum, ε1、ε2The respectively relative dielectric coefficient of quantum dot and background medium, e are electronics
The quantity of electric charge, R is quantum point grain diameter, and θ is electronic position vector reWith VOID POSITIONS vector rhBetween angle, reAnd rhRespectively
For the radial position of electrons and holes, potential barrier is regarded as infinitely great, according to effective mass approximation, the Hamilton of exciton in quantum dot
AmountExciton potential energy U is added for the kinetic energy of electrons and holes, in kinetic energy termWithIt is the effective of electrons and holes respectively
Quality；
4) it further, determines under given temperature dependent on background material dielectric coefficient ε2Quantum dot band gap, according to the exciton in 3)
Hamiltonian obtains the Schrodinger equation of exciton in quantum dot, electronics in quantum dot, hole and exciton ground state wave function, use is micro-
The ground state energy that method solves exciton is disturbed, regards interaction between two particles item U as perturbation, the Hamiltonian of exciton is write as H=H0+ H',
Wherein H'=U, energy eigenvalues E is according to Perturbation Expansion E=E0+E1, wherein E0For the sum of the kinetic energy of electrons and holes, according to micro-
It disturbs theory and obtains E1, energy eigenvalues E is added to the band gap of corresponding body material, it is effective using exciton Bohr radius and electron hole
QualityBetween relationship, the band gap of quantum dot in background material can be obtained
Wherein EgIt is the band gap of corresponding body material, aBFor exciton Bohr radius, ε0It is the dielectric coefficient in vacuum, ε1、ε2Respectively
The relative dielectric coefficient of quantum dot and background medium, e are the quantities of electric charge of electronics, and R is the partial size of quantum dot,
5) by the relative dielectric coefficient of quantum dot, partial size, exciton Bohr radius, the band gap of corresponding body material, background medium Jie
The band gap expression formula that electrostrictive coefficient substitutes into quantum dot in step 4) determines the band gap of nanocrystalline quantum dot in background material, further
It can determine the size of quantum dot bandgap in different background media；
6) in the background medium for calculating step 5) quantum dot band gap substitute into wavelength and energy relational expression, obtain this
First absorption peak wavelength of quantum dot in the medium of bottom may further determine that quantum dot first absorbs spike in different background media
Long movement.
2. the method as described in claim 1, it is characterised in that background medium is selected from organic solvent, glass, organic in step 5)
Glass, the liquid of aqueous solution, solid and gas.
3. the method as described in claim 1, it is characterised in that quantum dot is selected from three dimensions all in nanometer ruler in step 5)
The semiconductor crystalline material of degree.
4. the method as described in claim 1, it is characterised in that the partial size of quantum dot is 1nm~100nm in step 5).
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