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hydrogenic impurities , including donors and acceptors , have been widely studied in theoretical and experimental approaches .
recently , mahieu et al . investigated the energy and symmetry of zn and be dopant - induced acceptor states in gaas using cross - sectional scanning tunneling microscopy and spectroscopy at low temperatures .
the ground and first excited states were found to have a non - spherical symmetry . in particular , the first excited acceptor state has td symmetry .
bernevig and zhang proposed a spin manipulation technique based entirely on electric fields applied to acceptor states in p - type semiconductors with spin - orbit coupling . while interesting on its own , the technique could also be used to implement fault - resilient holonomic quantum computing .
studied tunneling transport through the depletion layer under a gaas surface with a low temperature scanning tunneling microscope .
their findings suggest that the complex band structure causes the observed anisotropies connected with the zinc blende symmetry .
kundrotas et al . investigated the optical transitions in be - doped gaas / alas multiple quantum wells with various widths and doping levels .
the fractional dimensionality model was extended to describe free - electron acceptor ( free hole - donor ) transitions in a quantum well ( qw ) .
the measured photoluminescence spectra from the samples were interpreted within the framework of this model , and acceptor - impurity induced effects in the photoluminescence line shapes from multiple quantum wells of different widths were demonstrated .
presented results on the ground - state binding energies for donor and acceptor impurities in a deformed quantum well wire ( qww ) .
the impurity effective - mass schrdinger equation was reduced to a one - dimensional equation with an effective potential containing both the coulomb interaction and the effects of the wire surface irregularities through the boundary conditions . studying the ground - state wave functions for different positions of the impurity along the wire axis
, they found that there are wire deformation geometries for which the impurity wave function is localized either on the wire deformation or on the impurity , or even on both .
calculated the magnetic - field dependence of low - lying spectra of a single - electron magnetic quantum ring and dot , formed by inhomogeneous magnetic fields using the numerical diagonalization scheme .
the effects of on - center acceptor and donor impurities were also considered . in the presence of an acceptor impurity , transitions in the orbital angular momentum
were found for both the magnetic quantum ring and the magnetic quantum dot when the magnetic field was varied .
galiev and polupanov calculated the energy levels and oscillator strengths from the ground state to the odd excited states of an acceptor located at the center of a spherical quantum dot ( qd ) in the effective mass approximation .
they also used an infinite potential barrier model . using variational envelope functions , janiszewski and suffczynski computed the energy levels and oscillator strengths for transitions between the lowest states of an acceptor located at the center of a spherical qd with a finite potential barrier in the effective mass approximation .
calculated the spectrum of a mn ion in a p - type inas quantum disk in a magnetic field as a function of the number of holes described by the luttinger - kohn hamiltonian . for simplicity
, we will study the electronic structures and binding energy of a hydrogenic acceptor impurity in semiconductor nano - structures in the framework of effective - mass envelope - function theory . in our calculations , the finite potential barrier and the mixing effects of heavy- and light - holes are all taken into account .
throughout this paper , the units of length and energy are given in terms of the bohr radius   and the effective rydberg constant   where m0 and 0 are the mass of a free electron and the permittivity of free space .
for a hydrogenic acceptor impurity located at   in a semiconductor nano - structure , the electron envelope function equation in the framework of the effective - mass approximation is(1 ) in the above equations , 1,2 , and 3are the luttinger parameters and   the subscript n = 0 , 1 , 2 , ... correspond to the ground- , first excited- , second excited- , ... states , respectively .
the quantum confinement potential   can be written in different forms for various nano - structures . in eq .
1 ,  is 0 when there are no acceptors and 1 when there are acceptors in the nano - structure .
the binding energy of the n - order hydrogenic donor impurity state is explicitly calculated by the following equation:(2 ) we express the wave function of the impurity state as ( 3 ) where lxly , and lz are the side lengths of the unit cell in the x , y , and z directions , respectively . kx = 2  /lx , ky = 2  /ly , kz = 2  /lz , nx  {  mx ,  , mx } , ny  {  my ,  , my } , and nz  {  mz ,  , mz}. the plane wave number is nxyz   =   nxnynz = ( 2 mx   + 1)(2 my   + 1)(2 mz   + 1 ) , where mxmy , and mz are positive integers .
we take lx   =   ly   =   lz = l = wmax + 25 nm , kx = ky = kz = k = 2 /l , and nx = ny = nz = 7 in the following calculation , where wmax is the maximum side length of the nano - structures .
if we take larger nxny , and nz , the calculation precision will be increased somewhat .
the matrix elements for solving the energy latent root of the impurity states can be found from eqs . 1 and 5 .
the electronic structures and binding energy in the nano - structure can be calculated from the matrix elements .
in the following sections , we will give some numerical results for the electronic structure and binding energy of a hydrogenic acceptor impurity in several typical gaas / ga1xalxas nano - structures .
1   =   6.98,2   =   2.06 ,  3   =   2.93 .
the band gaps eg ( ev ) of bulk gaas and al0.35ga0.65as are 1.519 and 2.072 ev , respectively .
the valence - band offset is assumed to be 35% of the band gap difference , so v0   =   193.55 mev .
we adopt a square potential energy model in the following calculation , i.e. , v(r ) = 0 inside and v(r ) = v0 outside of the nano - structures .
figures 1 and 2 show the first five energy levels and binding energy levels of an impurity in a qw as functions of the qw width w for an acceptor at the qw center .
figure 1 shows that the energy levels monotonically and quickly decrease as the well width increases .
it is well known that the donor binding energy has a peak as the qw width increases . however , fig .
2 shows that the changes of the acceptor binding energies are very complex as the qw widthwincreases .
this is because the holes have asymmetric effective masses , and there are mixing effects between heavy- and light - hole states .
the energy levels of the first five states as functions of the qw width w for an acceptor at the qw center the binding energy levels of the first five states as functions of the qw width w for an acceptor at the qw center figure 3 shows the binding energy levels of the first five states as functions of the donor positionz0for the qw widthw =   10 nm .
this figure shows that the binding energies monotonically decrease as the acceptor moves away from the qw center .
the binding energy levels of the first five states as functions of the donor position z0 for the qw width w = 10 nm figure 4a and b shows the impurity energy levels of the first five states as functions of the square qww side length l0(a ) and the cylindrical qww radius   ( b ) for an acceptor at the qww center . compared with fig . 1 , we find from fig .
4 that the impurity energy levels decrease slowly as the qww size increases . this is because the acceptor is confined in two directions .
the impurity energy levels of the first five states as functions of the square qww side length l0(a ) and the cylindrical qww radius   ( b ) for an acceptor at the qww center figure 5a and b is the same as fig . 4a and b , respectively , but are for the binding energy levels instead of the impurity energy levels .
the binding energy of the acceptor in the qww is larger than that in the qw because the quantum confinement effects in the qww are larger than in the qw . the same as fig . 4 but for the binding energy levels of the first five states figure 6a and b shows the binding energy of the first five states as a function of the impurity position for a square qww with side widthl0 =   10 nm ( a ) and for a cylindrical qww with radius   ( b ) . the positions of o , a , and b in fig .
it is easy see that the binding is the weakest for the impurity located at the corner of the square qww .
the binding energy of the first five states as functions of the impurity position for the square qww side length l0 =   10 nm ( a ) and the cylindrical qww radius   ( b ) .
the positions of o , a , and b in ( a ) are indicated in the inserted figure figure 7(a ) , b , and c gives the impurity energy levels as functions of the spherical qd radius r0(a ) , the square qd side length w(b ) , and the cylindrical qd radius   and height w ( ) ( c ) for an acceptor at the qd center . compared with figs . 1 and 4 , we find that the impurity energy levels decrease more slowly in the qd than in the qw or the qww .
this is because the quantum confinement effect is larger in the qd than in the qw and qww .
the impurity energy levels as functions of the spherical qd radius r0(a ) , the square qd side width w(b ) , and the cylindrical qd radius   and height   ( c ) for an acceptor at the qd center figure 8a , b , and c is the same as fig .
7a , b , and c , respectively , but are for the binding energy levels . from fig .
8(a ) , we find that there is only one binding energy for which r0 is greater than about 2.2 nm . the first two quantum states are degenerate and correspond to the first energy level , due to the symmetry of the spherical qd .
figure 8(b ) shows that there is only one binding energy level when the side length is between 3 and 10.5 nm . if the side length is greater than 10.3 nm , the second binding energy level arises once again .
figure 8(c ) shows that the first two binding energy levels diverge quickly , and the other binding energy levels disappear as the qd radius and height become larger than about 2.5 nm . the same as fig .
7 but for the binding energy levels of the first five states figure 9a , b , and c shows the binding energy as a function of the impurity position with a spherical qd radius of r0 =   5 nm ( a ) , with a cubic qd side length of w =   10 nm ( b ) , and a cylindrical qd radius   and height w equal to 5 nm ( c ) .
9b and c are indicated on the inserted qd figure , respectively . as the acceptor moves away from the center , the symmetry decreases ,
figure 9c shows that there are two binding energy levels when the cylindrical qd radius   and height w equal 5 nm .
the binding energy is the largest when the impurity is at the qd center , and it is least when the impurity is at the corner .
the binding energy as a function of the impurity position with the spherical qd radius of r0 = 5 nm ( a ) , with the cubic qd side length w =   10 nm ( b ) , and the cylindrical qd radius   and height w equal to 5 nm ( c ) .
the impurity positions of o , a , b and c in ( b ) and ( c ) are indicated on the inserted qd figure , respectively
in summary , we have calculated the electronic structures and binding energy levels of a hydrogenic acceptor impurity in 2 , 1 , and 0-dimensional semiconductor nano - structures in the framework of effective - mass envelope - function theory .
our method can be widely applied in the calculation of the electronic structures and binding energy levels of a hydrogenic acceptor impurity in semiconductor nano - structures of other shapes and other semiconductor material systems .
this work was supported by the national natural science foundation of china under grant nos 60325416 , 60521001 , and 90301007 .
the electronic structure and binding energy of a hydrogenic acceptor impurity in 2 , 1 , and 0-dimensional semiconductor nano - structures ( i.e. quantum well ( qw ) , quantum well wire ( qww ) , and quantum dot ( qd ) ) are studied in the framework of effective - mass envelope - function theory . 
 the results show that ( 1 ) the energy levels monotonically decrease as the quantum confinement sizes increase ; ( 2 ) the impurity energy levels decrease more slowly for qwws and qds as their sizes increase than for qws ; ( 3 ) the changes of the acceptor binding energies are very complex as the quantum confinement size increases ; ( 4 ) the binding energies monotonically decrease as the acceptor moves away from the nano - structures center ; ( 5 ) as the symmetry decreases , the degeneracy is lifted , and the first binding energy level in the qd splits into two branches . 
 our calculated results are useful for the application of semiconductor nano - structures in electronic and photoelectric devices .