Chapter Three - Apparatus and Parameters
3.3 Density of States
3.4.1 Overview
The density of states (DOS) in the mobility gap of a-Si:H has been extensively studied using different experimental techniques such as field-effect measurement[3-3]-[3-4], transient and steady-state photoconductivity measurements[3-5], and deep-level transient-capacitance spectroscopy (DLTS)[3-6]. In addition, other methods such as capacitance-voltage characteristics (C-V)[3-7], and dependence of capacitance on temperature and frequency in Schottky diodes and metal-oxide-semiconductor (MOS) structures[3-8] are also used for study of the DOS in a-Si:H. Based on these experimental studies, it is demonstrated[3-9]-[3-11] that the distribution of the localized states in a-Si:H mobility gap may be modeled by exponential distributions of deep and tail states for both acceptor-like and donor-like states (see Fig. 3.6).
The localized states in the upper half of the mobility gap closer to the conduction band edge behave as acceptor-like states, while the states in the lower part of the gap closer to the valence band edge behave as donor -like states.
Acceptor-like states are neutral when empty and negatively charged when filled with an electron, whereas donor-like states are positively charged when empty and neutral when filled with an electron. Based on this exponential DOS model, the density of the acceptor-like states gA(E) as a function of energy E may be written as follow:
( )
⎟⎟ conduction band edge for the tail and deep acceptor-like states, respectively, and Etc and Edc the associated slope of the exponential distribution of the tail and deep acceptor-like states, respectively. Similarly, the density of donor-like states gD(E) may be written as follows:( )
⎟⎟ similarly defined for the exponential distribution of the tail and deep donor-like states. Typical values of these parameters for intrinsic a-Si:H are presented in Table 3.1. As can be seen from Fig. 3.6, the DOS is asymetrical in a-Si:H, i.e., the number of donor-like states in the mobility gap is higher than the number of acceptor-like states. As a result, following the neutrality condition, the position of the Fermi energy in an intrinsic a-Si:H sample in the dark (Ei) is closer to the conduction band edge. The position of the intrinsic Fermi energy is ~ 600 mV beneath the conduction band edge and is dependent on the temperature due to the asymmetrical DOS distribution[3-2][3-12].3.3.2 Evaluation of the density of states
--Activation energy method[3-13]
As it was already mentioned, the Fermi level shift with the gate voltage is strongly dependent on the density of states (DOS). At high density of states more carriers must be induced in order to fill the states from EF upward and it is necessary to apply higher gate voltage in order to induce more carriers in the
channel. On the contrary, when the density of states is low, the states from EF upward are easily filled at low concentration of the induced charge and the Fermi level is easily shifted at low gate voltages. This correlation between the DOS and the gate voltage allows to obtain the shape of the density of states by studying the dependence of Eact vs. VGS. The information on DOS shape is important for understanding the physical mechanisms responsible for the device behaviour. The DOS shape is related to the threshold voltage value, subthreshold slope, field effect mobility and the stability of the TFTs. Globus et al. [3-14] proposed a method for evaluation of DOS in a-Si:H TFTs, from the dependence of Eact vs. VGS. If it is assumed that the DOS does not suffer sharp changes for energy interval about kBT, the charge of acceptor-like states Qt, filled by the gate bias is given by
(3-7) where q is the electronic charge, Vs is the surface potential, EFo is the equilibrium Fermi level in the silicon layer g(E) is the density of states. The charge Qt can also be expressed as
(3-8)
where qnt is the surface charge, VFB is the flat-band voltage, εi and di are the gate dielectric permitivity and gate dielectric thickness, respectively, and dt is the thickness of the space-charge layer.
Per measuring the drain-source voltage at different temperatures and keeping the same drain-source current, the activation energy (i.e. the Fermi level position) can be determined from the slope of the Arrhenius plot (log(IDS) vs. 1000/T) by the following equation:[3-15]
(3-9) From eqs. (3.7) and (3.9), differentiating with respect to VGS, can be obtained
(3-10)
where Eact = EC -EFo - qVs is the activation energy, EF = EFo - qVs is the quasi Fermi level. Hence, the density of localized states can be related to the derivative of the activation energy with respect to gate bias:
(3-11)
If it is assumed that the band bending in the a-Si layer is small compared to the characteristic energy of the density of states variation, then dt ≈ t where t is the a-Si layer thickness, and eq. (3.10) reduces to
(3-12)
This method for determination of the density of states is explained in details in [3-14]. According to ref. [3-14] this technique only accounts for the acceptor-like states in the bandgap. Advantage of the method is its simplicity. It is necessary to perform only field-effect measurements at different temperatures. Using this method, the density of states can be evaluated in relatively large energy interval from the bandgap. It is suitable for evaluation of changes in the density of states due to bias stress.
Eq. (3.12) was employed to calculate the density of states in the complete
devices (with incorporated n+ layer) according to the above-mentioned assumptions. As the measurements of Eact in the simplified sample are affected by the absence of n+ contact layer, we have not performed analysis of DOS for this sample. From the experimentally measured activation energy, depicted in Fig.3.7, we estimated the density of localised acceptor-like states in the upper part of the bandgap - in the interval 0.34 to 0.15 eV below EC. The calculated density of states, in energy interval 0.15-0.33 eV, is presented in Fig.3.8. The peak of the deep bandgap states can be observed at 0.34 eV. The Fermi level is pinned in these deep states when the TFT is in off-state.
From 0.30 to 0.20 eV the shape of the acceptor-like states is nearly constant about 5⋅1017 cm-3eV-1. The Fermi level is shifted through these states in the subthreshold region of operation of the TFT.
From 0.20 eV begins the exponential increasing of the acceptor-like tail states. The Fermi level is pinned at 0.15 eV from EC when the TFT enters in the on-state.
This shape of the DOS is very similar to the obtained for the amorphous silicon TFTs by Globus et al. [3-14]. In addition, the calculated value of 5⋅1017 cm-3eV-1 for 0.30 to 0.20 eV is slightly lower than the value of the maximal density of deep bulk states (Nbs)max = 3.6⋅1018 cm-3eV-1 estimated from the subthreshold slope. This is because (Nbs)max was calculated assuming (Nss)max =0
The activation energy method is fast and simple and is suitable to observe the changes in the density of states due to bias stress, illumination, etc. The main disadvantage of this method and also of the method of the subthreshold slope is that they do not permit the separation of the bulk states from the interface sates at the channel/gate insulator. Both methods are based on field-effect measurements
that are strongly dependent on the quality of the interface between the channel material and the gate insulator. This does not permit the exact evaluation of the intrinsic DOS of the channel material (in our case nc-Si:H), independently from the properties of this interface.