An automated method a method of determining the bulk states and interface states of a polysilicon thin film transistor from a current-voltage measurement and a capacitance-voltage measurement, the current-voltage measurement being source/drain current measurements relative to gate/source voltage:
- comprising the steps of:
- a determining the minima of the capacitance-voltage measurement and assigning this value as the flat band voltage;
- b using the flat band voltage and the capacitance-voltage measurement to calculate the relationship between the gate surface potential and gate/source voltage, using the relationship that the charge on the gate is equal to the integral of the product of the oxide capacitance per unit area and the voltage drop across the oxide and the relationship that the derivative of the gate surface potential with respect to the gate/source voltage is a function of the gate width, channel length, the capacitance measured between the gate and the drain/source contacts electrically connected together;
- c using the calculated relationship between the gate surface potential and gate/source voltage, the relationship that the charge on the gate is equal to the integral of the product of the oxide capacitance per unit area and the voltage drop across the oxide, the relationship that the charge on the gate is the sum of the surface charge and the bulk charge where the bulk charge is the product of the dielectric permittivity of silicon and the surface field, which is the derivative of the calculated profile of the surface potential;
- to calculate and output the interface states information;
- d dividing the source/drain current with the drain/source voltage to obtain conductance/gate voltage data;
- and
- e using the conductance/gate voltage data and the flat band voltage to provide inputs to an initialisation process and to an iteration process, the initialisation process also receiving as an input the calculated relationship between the gate surface potential and gate/source voltage;
- f the initialisation process comprising the steps of:
- 1 calculating the conductance at the flat band voltage from the conductance/gate voltage data;
- 2 initialising a calculation of the profile of the surface potential using Poisson's equation, in which the Fermi function is used and in which the density of states is separated into a plurality of discrete blocks, using the calculated conductance at the flat band voltage and using the calculated relationship between the gate surface potential and gate/source voltage in a function for the profile of the surface potential based on the variables of the gate surface potential, the density of states, and the active layer thickness;
- and
- 3 applying a least squares method to the initialises calculation of the profile of the surface potential so as to calculate intialised values for :the electron conductance at the flat band voltage, the hole conductance at the flat band voltage, the density of states, and the Fermi energy;
- g the iteration process comprising the steps of:
- 1 using the calculated conductance/gate voltage data and the initalised values of the electron conductance at the flat band voltage and the hole conductance at the flat band voltage in making a comparison of experimental conductance with conductance calculated as the sum of a function of the electron conductance at the flat band voltage and a function of the hole conductance at the flat band voltage;
- 2 using the result of the comparison to calculate the electron conductance, the hole conductance, the density of states at the flat band voltage, and Fermi energy;
- 3 using the result of the comparison to adjust the profile of the surface potential;
- 4 using the adjusted profile of the surface potential and the initialised values of the density of states at the flat band voltage, and Fermi energy to calculate the profile of the surface potential using Poisson's equation, in which the Fermi function is used and in which the density of states is separated into a plurality of discrete blocks;
- 5 adopting a relaxation by applying the boundary conditions ψ(0)=ψs and dψ/dx|x=d=0, where d is the active layer thickness to calculate a value for the profile of the surface potential ψx;
- and
- 6 repeating steps 1 to 5 inclusive of the iteration process a plurality of times;
- h whereby the result of the iteration process is an output of the bulk states information.