Advanced Amorphous Silicon(4)

The Gaussian distribution that is used to describe the defect states in a-Si:H re?ects the concept that the structural disorder results in a distribution of states rather than in states lo-cated at a particular energy level.However,the Gaussian representation of defect states does not contain any information about the origin of the defect states.The defect pool theory based on the weak bond–dangling bond conversion model[32]has attracted a lot of atten-tion because it can successfully describe the defect state distribution in a-Si:H[33–35].The theory assumes that the energy of the defect state can take a range of values due to the in-herent disorder of the amorphous network and that the defects can be formed in different charge states.The resulting total defect density of states is the sum of three energy distri-butions,D h,D z,and D e,which correspond to positive,neutral and negative defects.The defect pool model predicts that the total number of dangling bonds in the intrinsic a-Si:H in-creases when the Fermi level shifts from the midgap towards the mobility edges of the bands. The position of the Fermi level also determines the energy dependence of the defect state distribution.

The energy states in the bandgap act as trapping and recombination centers and therefore strongly affect many electronic properties of a-Si:H and the performance of a-Si:H devices.In contrast to crystalline semiconductors,in which the recombination process is typically domi-nated by a single energy level in the bandgap,in a-Si:H,contributions from all bandgap states to the recombination–generation(R–G)rate are included.In order to model the recombination process through the single level states,such as localized tail states,Shockley—Read–Hall R–G statistics[36]is used and Sah and Shockley multilevel R–G statistics[37]are applied for the amphoteric defect states.A detailed analysis and comparison of the modeling approaches of the R–G rate in a-Si:H is given in reference[18].

A large number of experimental techniques have been applied to obtain information about the density of states in a-Si:H[26].In particular the distribution of localized tail and defect states is of interest.There is no direct method to obtain the energy distribution of states in a-Si:H. The energy distribution of states is determined indirectly from measurements of optical and electrical properties of a-Si:H?lms or from properties of a space–charge region that is formed at a-Si:H interfaces.In order to provide an understanding of procedures to determine the density of states,we?rst discuss the optical and electrical properties of a-Si:H.

5.3.4Optical properties

The optical properties of a-Si:H are usually characterized by the absorption coef?cient,the refractive index,and the value of the optical bandgap.

Figure5.3a shows the typical absorption coef?cient of a-Si:H as a function of photon energy. In Figure5.3b,the absorption coef?cient of a-Si:H is plotted with the absorption coef?cient of a-SiGe:H,p type a-SiC:H,and crystalline silicon.In the visible part of the solar spectrum, a-Si:H absorbs almost100times more than crystalline silicon.This means that a1μm thick a-Si:H layer is suf?cient to absorb90%of the usable solar energy.In practice,the thickness of a-Si:H solar cells is around than0.3μm,that is about1000times thinner than a typical single crystal silicon cell.

182THIN FILM SOLAR CELLS

(a)

(b)

0.5

1.0

1.5

2.0 2.5

3.0

Photon energy [eV]

A b s o r p t i o n c o e f f i c i e n t [1/c m ]

2.48 1.240.830.620.50

0.41

Wavelength [micrometers]10510410210110-110610310

10-2

A b s o r p t i o n c o e f f i c i e n t [1/c m ]

2.48 1.240.830.620.50

0.41

Wavelength [micrometers]10510410210110-110

6

10310

10

-2

Figure 5.3(a)Absorption coef?cient of a-Si:H as a function of photon energy,(b)absorption coef?cient as function of photon energy for a-Si:H,p type a-SiC:H and a-SiGe:H fabricated at Delft University of Technology.The absorption coef?cient of c-Si is shown for reference.

Due to the lack of translational symmetry of a unit cell in the structural network of a-Si:H,the law of crystal momentum conservation is relaxed in a-Si:H,and it behaves like a direct semiconductor.The optical absorption coef?cient,α(E),is therefore determined by optical transitions involving all pairs of occupied and unoccupied electronic states that are separated by the same photon energy E .For this reason,optical absorption measurements are widely used to determine the density of states distribution in a-Si:H.The absorption coef?cient curve is of fundamental importance for evaluating the quality of both amorphous and microcrystalline silicon ?lms.

As indicated in Figure 5.3a,the absorption spectrum of a-Si:H exhibits three regions.In region A,absorption occurs predominantly by transitions between the extended states of the valence and conduction bands.The absorption coef?cient in this region is higher than 103–104cm ?1and is commonly determined by re?ection-transmission spectroscopy mea-surement.Region B extends from α～1to 103cm ?1and is characterized by an exponential dependence of the absorption coef?cient on the photon energy.This region is called the Urbach edge.When assuming that the optical matrix element is energy independent in this region,as experimentally observed [38],the Urbach edge re?ects the transitions between the valence and conduction band tail states.The absorption coef?cient in region B can be ?tted to

α=α0exp (E /E 0),

(5.2)

ADV ANCED AMORPHOUS SILICON SOLAR CELL TECHNOLOGIES183 whereα0is a constant and E0is the Urbach energy that characterizes the exponential slope of the energy dependence.Because the conduction band tail state distribution is narrower than the valence band tail state distribution,the Urbach energy re?ects the slope of the exponential region of the valence band tail.A typical value for device quality a-Si:H?lm is E0≤50×

10?3eV.Region C,where the absorption coef?cient is less than1cm?1,is associated with the transitions involving the defect states.Regions B and C are denoted as subbandgap absorption since the absorption coef?cient re?ects transitions involving states within the bandgap.

From the absorption coef?cient of a-Si:H based materials,the so-called optical bandgap is determined.The optical bandgap is a useful material parameter for comparing the light absorption properties of a-Si:H based materials.Generally,the higher optical bandgap of a material,the less light it will absorb.The optical bandgap,E opt,is determined by extrapolating a linear part of the following function[α(E)×n(E)×E]1/(1+p+q)versus the photon energy E toα(E)=0,forα≥103cm?1:

(α(E)×n(E)×E)1/(1+p+q)=B(E?E opt)(5.3) whereα(E)is the absorption coef?cient,n(E)is the refractive index,p and q are constants that describe the shape of the density of extended states distribution for the conduction band and valence band,respectively,and B is a prefactor.When the density of state distribution near the band edges has a square root energy dependence(p=q=1/2),as is commonly the case in crystalline semiconductors,Equation(5.3)describes the so-called Tauc plot[26],and the corresponding optical bandgap is called the Tauc optical gap.When the distribution near the band edges is assumed to be linear(p=q=1),E opt is called the cubic optical gap.The Tauc gap of device quality intrinsic a-Si:H is in the range of1.70to1.80eV;usually0.1to 0.2eV smaller than this is the cubic gap of the same material.The optical bandgap increases with increasing hydrogen concentration in the?lm[39].

The refractive index of a-Si:H shows a maximum of almost5.0around425nm and then decreases as a function of wavelength in the region of interest(350nm to900nm).The refractive index slightly decreases above900nm.For device quality a-Si:H,the refractive index at900nm is above3.6.

5.3.5Electrical properties

The electrical properties of a-Si:H are usually characterized in terms of dark conductivity, photoconductivity and mobility lifetime product.Measuring these properties is a standard approach to obtain information about the quality of a-Si:H material for application in solar cells.

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