5.4 Capacitance-voltage characteristics

Capacitance-voltage characteristics are crucial for understanding semiconductor device behavior. They reveal how charge storage and distribution change with applied voltage, impacting device performance and functionality.

C-V measurements provide insights into doping profiles, built-in potentials, and carrier lifetimes. This information is vital for device design, optimization, and quality control in semiconductor manufacturing processes.

Capacitance in semiconductor devices

• Capacitance plays a crucial role in the operation and characterization of semiconductor devices
• Understanding capacitance-voltage (C-V) characteristics is essential for designing and optimizing semiconductor devices
• Capacitance in semiconductor devices arises from the charge storage in depletion regions, diffusion of carriers, and junction effects

Depletion region capacitance

Depletion width vs applied voltage

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• The depletion width in a semiconductor junction varies with the applied voltage
• Reverse bias increases the depletion width, while forward bias decreases it
• The relationship between depletion width and applied voltage is given by $W_D = \sqrt{\frac{2\varepsilon_s(V_{bi} - V_A)}{qN}}$, where $W_D$ is the depletion width, $\varepsilon_s$ is the semiconductor permittivity, $V_{bi}$ is the built-in potential, $V_A$ is the applied voltage, $q$ is the elementary charge, and $N$ is the doping concentration

Capacitance vs depletion width

• The depletion region capacitance is inversely proportional to the depletion width
• As the depletion width increases, the capacitance decreases, and vice versa
• The capacitance per unit area is given by $C = \frac{\varepsilon_s}{W_D}$, where $C$ is the capacitance per unit area, $\varepsilon_s$ is the semiconductor permittivity, and $W_D$ is the depletion width

Capacitance-voltage relationship derivation

• Combining the depletion width-voltage and capacitance-depletion width relationships yields the capacitance-voltage relationship
• The capacitance-voltage relationship is derived as $C = \sqrt{\frac{q\varepsilon_sN}{2(V_{bi} - V_A)}}$, where $C$ is the capacitance per unit area, $q$ is the elementary charge, $\varepsilon_s$ is the semiconductor permittivity, $N$ is the doping concentration, $V_{bi}$ is the built-in potential, and $V_A$ is the applied voltage
• This relationship shows that the capacitance decreases with increasing reverse bias and increases with increasing forward bias

Diffusion capacitance

Minority carrier distribution

• Diffusion capacitance arises from the diffusion of minority carriers in the quasi-neutral regions of a semiconductor device
• The minority carrier distribution varies with the applied voltage, leading to changes in the diffusion capacitance
• Under forward bias, the minority carrier concentration increases exponentially, resulting in a higher diffusion capacitance

Diffusion capacitance vs applied voltage

• The diffusion capacitance increases exponentially with increasing forward bias voltage
• In the forward bias regime, the diffusion capacitance dominates over the depletion capacitance
• The diffusion capacitance is given by $C_D = \frac{dQ}{dV} = \frac{I_0\tau}{V_T}e^{V_A/V_T}$, where $C_D$ is the diffusion capacitance, $Q$ is the charge, $V$ is the voltage, $I_0$ is the reverse saturation current, $\tau$ is the minority carrier lifetime, $V_T$ is the thermal voltage, and $V_A$ is the applied voltage

Junction capacitance

Junction capacitance components

• The total junction capacitance consists of two components: depletion capacitance and diffusion capacitance
• Depletion capacitance arises from the charge storage in the depletion region, while diffusion capacitance arises from the diffusion of minority carriers
• The relative contribution of each component depends on the applied voltage and the operating frequency

Junction capacitance vs applied voltage

• The junction capacitance varies with the applied voltage
• Under reverse bias, the depletion capacitance dominates, and the total capacitance decreases with increasing reverse bias
• Under forward bias, the diffusion capacitance dominates, and the total capacitance increases exponentially with increasing forward bias
• The transition between depletion and diffusion capacitance occurs around the built-in potential

Measurement of C-V characteristics

Low and high frequency C-V

• C-V characteristics can be measured at low and high frequencies
• Low-frequency C-V measurements capture both the depletion and diffusion capacitance contributions
• High-frequency C-V measurements primarily capture the depletion capacitance, as the diffusion capacitance cannot respond to the rapid voltage changes
• The frequency at which the transition between low and high frequency behavior occurs depends on the device parameters and the measurement setup

Depletion and inversion regions in C-V

• C-V characteristics exhibit distinct regions: accumulation, depletion, and inversion
• In the depletion region, the capacitance decreases with increasing reverse bias due to the widening of the depletion region
• In the inversion region, the capacitance reaches a minimum value and remains constant with further increase in reverse bias
• The transition between depletion and inversion regions occurs when the surface potential equals the bulk potential

Applications of C-V characteristics

Determination of doping profile

• C-V measurements can be used to determine the doping profile of a semiconductor device
• The doping concentration can be extracted from the slope of the 1/C^2 vs voltage plot
• The doping profile provides valuable information about the spatial distribution of impurities in the device

Extraction of device parameters

• C-V characteristics can be used to extract various device parameters
• The built-in potential can be determined from the intercept of the 1/C^2 vs voltage plot
• The minority carrier lifetime can be estimated from the diffusion capacitance in the forward bias regime
• The oxide thickness in MOS structures can be determined from the accumulation capacitance

C-V in MOS structures

• C-V measurements are widely used to characterize metal-oxide-semiconductor (MOS) structures
• The C-V characteristics of MOS structures provide information about the oxide quality, interface states, and substrate doping
• The flatband voltage, threshold voltage, and oxide charges can be extracted from the C-V curves of MOS capacitors

Frequency effects on C-V characteristics

Low vs high frequency behavior

• The frequency of the applied voltage significantly affects the C-V characteristics
• At low frequencies, both depletion and diffusion capacitance contribute to the total capacitance
• At high frequencies, the diffusion capacitance cannot respond fast enough, and the depletion capacitance dominates
• The transition frequency between low and high frequency behavior depends on the device parameters, such as the minority carrier lifetime and the doping concentration

Deep-level traps and interface states

• Deep-level traps and interface states can influence the C-V characteristics, especially at low frequencies
• Traps and interface states can capture and emit carriers, leading to additional capacitance contributions
• The presence of traps and interface states can cause frequency dispersion in the C-V curves
• Analyzing the frequency dependence of C-V characteristics can provide insights into the trap density and energy levels

Small-signal capacitance models

Equivalent circuit representation

• Small-signal capacitance models are used to represent the capacitive behavior of semiconductor devices in circuit simulations
• The equivalent circuit representation typically includes the depletion capacitance, diffusion capacitance, and series resistance
• The depletion capacitance is modeled as a voltage-dependent capacitor, while the diffusion capacitance is modeled as a conductance in parallel with a capacitor
• The series resistance accounts for the resistive effects in the device, such as contact resistance and bulk resistance

Capacitance in device modeling

• Accurate modeling of capacitance is crucial for predicting the high-frequency performance of semiconductor devices
• Capacitance models are incorporated into device simulators and circuit simulators to analyze the transient and AC behavior of circuits
• The capacitance models are based on the physical principles governing the charge storage and distribution in semiconductor devices
• Empirical models, such as the SPICE models, are often used to represent the capacitance-voltage relationships in circuit simulations