Mobility is an important parameter to measure the conductive properties of semiconductors. It determines the conductivity of semiconductor materials and affects the working speed of devices. Many articles have studied the importance of carrier mobility, but few have mentioned its measurement methods. This article provides a summary of carrier measurement methods. Related concepts of mobility μ In semiconductor materials, carriers generated for some reason are in irregular thermal motion. When an external voltage is applied, the carriers inside the conductor are affected by the electric field force and perform directional movement to form a current, that is, For drift current, the speed of directional movement becomes the drift velocity, and the direction is determined by the carrier type. Under an electric field, the average drift velocity v of carriers is proportional to the electric field strength E:
v=μE
where μ is the drift mobility of carriers, referred to as Mobility represents the average drift speed of charge carriers per unit electric field, and the unit is m2/Vs or cm2/Vs.
Mobility is an important parameter that reflects the conductivity of carriers in semiconductors. At the same doping concentration, the greater the mobility of carriers, the higher the conductivity of the semiconductor material. The size of the mobility is not only related to the strength of the conductive ability, but also directly determines the speed of carrier movement. It has a direct impact on the operating speed of semiconductor devices.
The relationship between conductivity and mobility is. That is to say, under a certain electron concentration n and charge amount, electron mobility and conductivity are positively related.
Under the action of a constant electric field, the average drift speed of carriers can only take a certain value, which means that carriers in semiconductors are not constantly accelerated without any resistance. In fact, during the process of thermal motion, carriers constantly collide with the crystal lattice, impurities, defects, etc., and change their direction of motion irregularly, that is, scattering occurs. Inorganic crystals are not ideal crystals, and organic semiconductors are essentially amorphous, so there are lattice scattering, ionized impurity scattering, etc., so the carrier mobility can only have a certain value.
2 Measurement method (1) Transit time (TOP) method The transit time (TOP) method is suitable for measuring the carrier mobility of materials with good photogenerated carrier function. Measure low mobility of organic materials. Apply an appropriate DC voltage to the sample, select pulse light with an appropriate pulse width, and excite the sample through the transparent electrode to generate a thin layer of electron-hole pairs. The holes are pulled to the direction of the negative electrode and move in a thin layer. Assuming that the condition of the thin layer remains unchanged, the moving speed is μE. If it is assumed that there are only limited traps in the sample and the trap density is uniform, the power loss is related to the carrier lifetime τ. At this time, an induced current will be formed on the lower electrode due to carrier movement, and will increase with time. At time t:
If L in the formula is the thickness of the sample, the electric field is strong enough, t≤τ, and the transit time is t0lt;τ. Then
At time t0, the voltage will change significantly, which can be measured experimentally. In the formula, L, V and t0 are all physical quantities that can be measured experimentally, so the μ value can be found. (2) Hall effect method The Hall effect method is mainly suitable for measuring the carrier mobility of larger inorganic semiconductors. If a semiconductor sheet carrying a current I is placed in a magnetic field with a magnetic induction intensity B, an electric potential U proportional to the current and magnetic induction intensity will be generated at both ends of the sheet perpendicular to the current and magnetic field. This is called the Hall effect. Since holes and electrons have opposite charge signs, the Hall effect can directly distinguish the conductivity type of carriers. The measured electric field can be expressed as
where R is the Hall coefficient, which can be calculated from the Hall effect The current density, vertical drift velocity component of the electric field, etc. are obtained to find R, and then determine μ. (3) Voltage decay method: The mobility of carriers is measured by monitoring the surface voltage decay of the corona charging sample. The charge accumulated in the charged sample leaks from the top to the grounded bottom electrode. The initial downward flow of charge has a good front, and the time it takes to pass through the sample with thickness L can be determined, and thus the μ value of the material can be determined. (4) Radiation-induced conductivity (SIC) method The radiation-induced conductivity (SIC) method is suitable for materials whose conduction mechanism is space charge limited conductivity.
In this method, the upper half of the study sample is subjected to continuous electron beam excitation irradiation to produce a steady-state SIC, and the lower half of the material acts as an injection contact. This space charge limited current (SCLC) is then flowed to the lower electrode. According to theoretical analysis, the relationship between SCLC conductivity current and mobility is J=pμε1ε0V2/εDd3 (7). By measuring the signal current as a function of electron beam current, irradiation energy and applied voltage, the μ value can be calculated.
(5) Surface wave transmission method places the semiconductor film to be measured within the field surface wave field generated by the piezoelectric crystal, then the electric field associated with the field surface wave is coupled to the semiconductor film and The carriers are driven to move along the surface acoustic wave transmission direction, and two separate electrodes set on the sample detect an acoustic current or voltage. The expression is Iae=μP/Lv. (8) In the formula, P is the sound power, L is the distance between the two poles of the sample to be measured, and v is the surface acoustic wave speed. With this formula, the value of μ can be derived. (6) Applied electric field polarity reversal method: When an external electric field is applied when the polarity is completely closed, ions will gather in a thin plate shape near the electrode, causing a space charge effect. When the polarity of the external electric field is reversed, the carriers will migrate toward the other electrode in a plate shape. Due to the influence of the electric field applied to the front and rear edges of the carrier thin layer, the current reaches its maximum value at t time after the polarity reversal. t is equivalent to the time for a thin layer of carriers to travel in the sample. The μ value can be determined based on the thickness of the sample, electric field, etc. (7) Current-voltage characteristic method This method is mainly suitable for measuring the carrier mobility of the inversion layer of MOSFET operating at room temperature. When a general MOSFET works at high temperature, the drain-source current Ids is equal to the sum of the channel current Ich and the leakage current Ir. However, when it works at room temperature, the leakage current Ir decreases sharply and is approximately zero, making the drain-source current Ids is the channel current Ich. Therefore, for general MOSFET inversion layer carrier mobility, it can be calculated based on measuring the IV characteristics of the linear region.
3 Summary In summary, this article *** pointed out seven methods for measuring carrier mobility. In addition, drift experiments, analysis of ion diffusion, and analysis of pyroelectric current can also be used The carrier mobility is measured using polarization charge transient response and other methods.