Theory, techniques for Schottky barrier diode evaluation

 Introduction:

In the previous discussions, I have clearly discussed the reason for forming Schottky contact. So, to evaluate the Schottky contact (SC), it is necessary to understand the relevant parameters those are governing the Schottky contact response. The parameters are Schottky barrier height (SBH), (Φ_B), ideality factor (η), effective Richardson’s constant (A**), doping concentration (N_D), and series resistance (R_s). The current (I)- voltage (V) characteristics are mainly for the thermionic emission model for a Schottky barrier diode (SBD). The SBD is very promising for fast switching, high current, low noise, and high-frequency applications. 

Theory of SBD:

The SC of SBD governing equation is shown in equation (1). Where, S Schottky contact area, T operating temperature in Kelvin, V applied voltage, K_B Boltzmann constant,  Richardson’s constant, A* material’s properties.  

The A* is influenced by the optical phonon scattering, quantum-mechanical reflection, electron tunneling over the barrier, inhomogeneous barrier distribution, and, metal contact properties. Therefore, taking these into consideration, A* becomes A**. Then equation (1) can be replaced by (2), where I_s reverse saturation current or leakage current and Φ_B0 Schottky barrier-height at zero bias.

The ideality factor is unity for the TE model. This measure deviation from the TE model of the Schottky contact. The ideality factor considers all the factors that affect the TE model. The factors come from carrier generation, field emission, recombination, thermionic field emission, image-force lowering (Δϕ_B) of the SBH, inhomogeneity of barrier, bias dependence of the SBH, edge leakage etc. For high-quality SC the ideality factor is within 1-1.3.  The image force lowering SBD can be expressed by equation (3), 

where, E_MS maximum electric field strength at the interface, this is more pronounced in reverse bias. The E_MS value is related to the bias voltage and can be expressed by equation (4). However, if the diode series resistance plays a crucial role when the current becomes too high. Then the total voltage drops across the diode and series resistance. The I-V relation is modified by the IRs drop. Then equation (2) becomes like (5) is known as Cheung’s method. 

SBD Evaluation: I-V and C-V methods

When we apply forward bias, and the bias V ≥ 3k_BT/q, then equation (2) can be represented by equation (6). Equation (6) can be written in linear form like (7). The linear fitting intercept gives a reverse saturation current, and the slope represents the ideality factor. Hence using the reverse saturation current relation shown in (2), we can estimate the SBH at zero bias with the known value of the Richardson constant. 

Along with the I-V relation, it is also necessary capacitance-voltage (C-V) relation to extracting the SC parameters. The reverse bias generates a depletion region which means the SBD behaves like a parallel plate capacitor. For an n-type semiconductor under the reverse bias condition, the C-V relation is shown in equation (8). C capacitance per unit area. The slope of 1/C² – V plot represents doping concentration N_D. Also, the intercept, Vi, of the plot related to built-in potential, V_bi. 

Then the zero bias SBH can be calculated by equation (9). where E_C-E_F is related to the effective carrier density (N_c) of the state and follows the relation in (10). 

The Nc strongly depends on the effective mass and operating temperature (equation (11)). 

Hence, from I-V and C-V, we can judge SBD applicability. You may find useful of SBD example in my previous explanation. If you need some help with your understanding, then feel free to comment or reach me.