CN111812477A - Method for representing junction characteristics of semiconductor device - Google Patents
Method for representing junction characteristics of semiconductor device Download PDFInfo
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- CN111812477A CN111812477A CN202010596223.4A CN202010596223A CN111812477A CN 111812477 A CN111812477 A CN 111812477A CN 202010596223 A CN202010596223 A CN 202010596223A CN 111812477 A CN111812477 A CN 111812477A
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Abstract
The invention discloses a method for representing junction characteristics of a semiconductor device, which is a systematic method for accurately representing a diode by combining forward alternating current characteristics with direct current I-V measurement based on a parallel or series mode, overcomes the defect of small information amount of the traditional semiconductor device representation technology, and can obtain accurate functional relations of junction capacitance, junction conductance, series resistance, ideal factors and junction voltage along with external voltage and current in the device. The method solves the difficult problem of characterization of the internal junction characteristics of the semiconductor device, discloses the internal electrical transport mechanism of the semiconductor device in actual work, and provides technical guidance for designing and preparing the high-performance semiconductor optoelectronic device.
Description
Technical Field
The present invention relates to semiconductor devices, and more particularly to an accurate method for accurately characterizing the internal junction characteristics of two-terminal semiconductor devices (including schottky junctions, light emitting diodes, laser diodes, PN junctions, etc.) at forward voltages.
Background
Semiconductor optoelectronic devices are one of the most widely used optoelectronic devices at present. P-n junction semiconductor diodes, including schottky junctions and including LDs and LEDs, operate primarily in the forward direction, but methods for characterization and measurement of the forward electrical characteristics of the diodes have long been too simple and crude, which has been a "soft rib" that has limited device characterization and micro-mechanical research.
The research on the forward electrical characteristics of various devices at home and abroad depends on an I-V method to a great extent, but the information content of the I-V method is very limited, and the functional relation between the internal junction parameter of the device and the applied voltage and current cannot be accurately given only by treating the series resistance and the idealized factor as constants.
Although the method is convenient and intuitive, under the condition of a larger voltage after the diode is started, the influence of the series resistance is more and more obvious, and in addition, the ideal factor and the series resistance are not constant generally, so that the practical solution of the electrical parameters of the diode is very difficult.
The conductance number technique (IdVdI) has become a common method for detecting the performance of a laser diode and determining its threshold, ideality factor, and series resistance. However, for a considerable part of actual semiconductor lasers, the IdVdI curve is not in a straight line shape before the threshold, which is mainly caused by the fact that the ideality factor or the series resistance of the diode is not constant, and therefore, the values of the ideality factor and the series resistance cannot be solved by the linear method, and even if the ideality factor or the series resistance is barely solved, an accurate value cannot be obtained.
Other methods based on the expansion of the I-V technology have no limitation beyond that of assuming that the series resistance or other physical parameters are constant.
The existing method for researching the alternating current C-V characteristic is mainly suitable for reverse measurement, and people always take a diode as a black box to directly test the obtained forward parallel apparent capacitance as a junction capacitance, but the forward parallel apparent capacitance and the junction capacitance are far from each other under larger forward voltage. Thus, a variety of troublesome phenomena have emerged in this area. For example, the forward diffusion capacitance theory of p-n junctions has been developed by people such as the applicants (transistor founders, nociceptors), but experimental data cannot be found for decades. There are at least two reasons for this: firstly, researchers often equate apparent capacitance with junction capacitance; secondly, the characteristics of the actual devices are far from as simple as they are theoretically demonstrated.
At present, an accurate characterization method capable of directly characterizing electrical and physical parameters such as internal junction voltage, series resistance, ideal factors, quasi-Fermi level difference and the like of a semiconductor two-terminal device is not available.
Disclosure of Invention
The invention aims to overcome the defect of small information quantity provided by the traditional semiconductor device characterization technology, and provides a method capable of accurately characterizing the internal junction characteristics of a semiconductor device so as to characterize the functional relation between the internal junction characteristics of the device and an applied voltage and current in real time.
The invention relates to a method for characterizing the junction characteristics of a semiconductor device, which comprises the following steps:
firstly, the direct current I-V characteristic of a two-terminal device is measured by using a precision instrument, and simultaneously, the conclusion that series resistance or an ideal factor is assumed to be constant is abandoned, and n is set to be n (V)j) And rS＝rS(Vj) Then, the equation of Shockley is simplified as:
wherein n is an ideal factor, IsFor reverse saturation current, VjIs the device junction voltage, rsThe series resistance of the device, k is Boltzmann constant, T is temperature, and the relation between junction voltage and series resistance is Vj＝V-Irs. Taking the logarithm of both sides of equation (1) can obtain:
the relationship between the ideality factor and the junction voltage can be derived from equation (2):
then, the junction voltage is differentiated by the Shockley equation (1), and the relation of the junction differential conductance G can be obtained:
(II) measuring the AC impedance spectrum characteristics of the device in parallel mode by using the precise impedance spectrum under the condition of AC small signal, mainly measuring the relation (C) between the apparent conductance and the apparent capacitance along with the applied voltage or currentp-V and Gp-V). Using actual diodesThe relationship equal to the complex impedance in the parallel-mode equivalent circuit diagram (as in fig. 1(a) and 1(b)) can be found among the apparent capacitance, apparent conductance and junction capacitance, junction conductance and series resistance inside the device:
considering the range of the actual working voltage of the device, G > omega C is satisfied, and equations (5) and (6) are naturally simplified into:
then according to the equations (3), (4), (7) and the relation V of junction voltage and applied voltagej＝V-IrsThen the following system of equations can be obtained and then iteratively fitted or approximately solved:
wherein G ispAnd CpApparent conductance and apparent capacitance.
If step (three) is performed in the series mode, then r in equation (9) is only required to be measuredS＝1/Gp-1/G is converted into the equation rS＝RS-1/G, wherein RsIs a series resistor in an equivalent circuit in series mode.
The accurate functional relation of physical parameters in the equation, including junction voltage, series resistance, ideal factors and junction conductance along with the applied voltage and current, can be obtained through the solution of the equation set; at the same time, the measured apparent capacitance C is reusedpAnd the resulting junctionThe derivative G also allows for an accurate function of junction capacitance as a function of external voltage or current.
The invention mainly considers various methods for representing two-terminal devices at present, and finds that none of the methods is established on certain assumption; the transportation mechanism of the two-terminal device under the work of large forward voltage is mainly solved; the difficulty of the invention lies in unifying the direct current characteristic and the alternating current characteristic, and compiling software to solve together; the innovation point of the invention is that the forward direct current electrical characteristics and the alternating current characteristics of the two-terminal device are directly represented and solved together without assuming that physical parameters such as series resistance or ideal factors of an actual device are constants, so as to obtain the internal physical parameters of the device which actually works.
The invention solves the difficult problem of characterization of the internal junction characteristics of the semiconductor device, discloses the internal electrical transport mechanism of the semiconductor device in actual work, and provides technical guidance for designing and preparing high-performance semiconductor optoelectronic devices.
The invention can accurately obtain the functional relation of internal physical parameters such as series resistance ideal factors of devices such as p-n, semiconductor Light Emitting Diodes (LEDs), semiconductor laser diodes, Schottky diodes and the like along with the external voltage or current, thereby clearly judging the transportation mechanism of the devices and promoting the physical development of the semiconductor devices. For example, from the magnitude of the ideality factor n, it can be determined whether radiative recombination or non-radiative recombination occurs inside the device at different voltages; from the observed junction voltage of the multiple quantum well laser, it is obtained that the junction voltage of two physical concepts and the quasi-Fermi energy level difference of electron holes are different inside and outside the well. Meanwhile, the method can be used for accurately representing the characteristics of the internal physical parameters of the device, and providing guidance for designing and preparing the device with higher performance, for example, the series resistance characteristics are combined with the ideal factor characteristics, and a guidance scheme can be provided for further reducing the series resistance, thereby reducing the power consumption and improving the device characteristics.
Drawings
FIG. 1 is an equivalent circuit diagram of a method of characterizing a junction of a semiconductor device in accordance with the present invention;
FIG. 2 is a graph of junction voltage, series resistance as a function of current for example 1;
FIG. 3 is a graph of junction voltage and series resistance as a function of current for example 2.
The reference numbers are as follows:
c-junction capacitance G-junction conductance
rs-series resistance CpDirectly measured apparent capacitance
Gp-directly measured apparent conductance Rs-resistance measured directly in series mode
CsCapacitance, V, measured directly in series modejJunction voltage
Detailed Description
The invention is further illustrated by the following specific examples.
Unless otherwise specified, the technical means used in the present invention are well known to those skilled in the art.
Example 1
The characteristics of junction voltage, series resistance and ideality factor of a GaAs-based Laser Diode (LD) with the wavelength of 780nm are illustrated by way of example, and refer to FIG. 2, wherein a square open frame curve represents a device junction voltage curve, and a solid circle curve represents a device series resistance curve.
(1) The direct current I-V characteristics of the device are measured by a precision impedance analysis instrument (all instruments can be made by Hewlett packard, Agilent and China), and the step length of the current can be selected (1mA or lower) in consideration of the internal resistance of all the measurement instruments.
(2) And measuring the alternating current characteristic under the alternating current small signal. Fig. 1 is an equivalent circuit diagram of a method for characterizing a junction of a semiconductor device according to the present invention, in which fig. 1(a) is an equivalent circuit diagram of an actual device, fig. 1(b) is an equivalent circuit diagram of a parallel mode employed in a measurement process, and fig. 1(c) is an equivalent circuit diagram of a series mode.
The impedance instrument was selected in parallel mode with the equivalent circuit as in fig. 1 (b). Series mode is also possible, as in FIG. 1 (c). The amplitude and frequency of the AC small signal (in this example, 50mV, 100kHz is selected) and the current step size, which is the same as the step size of the DC I-V characteristic of the measuring device in step (1), are set, and the apparent capacitance and the apparent conductance characteristics are measured.
(3) Comparing the equivalent circuit diagram 1(a) of the actual diode with the equivalent circuit diagram 1(b) in the parallel measurement mode, the measured apparent conductance G can be obtained by using the complex impedance equalitypAnd CpSeries resistance r of junction characteristics with actual devicesRelation between junction capacitance C and junction conductance G:
under the condition of large voltage (including the condition of extra large voltage), G > omega C is satisfied, and the method can obtain
And C ═ 1+ rSG)2CpAnd then combining the formulas (3) and (4) in the invention content obtained according to the Shockley equation, namely
Formula (II) and
formula (VI), and the relationship between junction voltage and applied voltage (V)j＝V-IrsThe system of equations (9) in the summary of the invention is obtained:
(4) the equation is solved, and the specific solving process can be iterated by a computer. This is mainly the differential involved in the equation, which can be mathematically viewed as the data of the next point minus the data of the previous point. Therefore, in the above equation, the initial value needs to be set before the solution can be continuously performed. Research shows that the initial value is selected within a recognized reasonable range, the characteristic that the physical parameter changes along with the current is not influenced, and only the value is slightly influenced. The above equation set only needs to know two initial values. For exampleInitial values of n and IsCan be obtained from the linear part and the intercept of the lnI-V curve; the values of the ideality factor n and the series resistance for a laser diode can be obtained from the slope and intercept of the linear portion of the conductance IdVdI-I curve. Then the current I, the voltage V and the apparent conductance G which is directly measured at each point are measuredpAnd an apparent capacitance CpThe substitution results in the junction voltage characteristics at each current or voltage, as shown in FIG. 2.
The end result is a junction voltage V at threshold for a narrow band GaAs based Multiple Quantum Well (MQW) laser with 780nm wavelengthj(corresponding to the quasi-fermi level difference of electrons and holes in the active region) does not reach saturation immediately at the threshold as predicted by classical theory, but rather a considerable jump occurs first and then saturation occurs; the start and end points of the junction voltage jump we define the threshold region of the laser. Also, in solving for the junction voltage, other various electrical properties (i.e., series resistance, ideality factor, junction capacitance, and junction conductance) may also be solved together. Fig. 2 only shows the function of the series resistance as a function of the applied current, and it can be seen that the series resistance gradually decreases with the increase of the current, and a sudden dip occurs in the threshold region, which is mainly because the resistance decreases when the laser suddenly exhibits stimulated emission in the threshold region and the radiative recombination is enhanced.
Example 2
Junction characteristics (junction voltage, series resistance, ideality factor junction capacitance and junction conductance as a function of applied current) of a wide bandgap GaN-based quantum well laser with a wavelength of 450 nm: the procedure was as in example 1. Firstly, measuring I-V of the device; secondly, measuring the relation between the apparent conductance and the apparent capacitance of the device along with voltage or current in a parallel mode; and finally, substituting the measured data into an equation set (9) in the invention content for solving.
As a result, the junction voltage characteristics of the wide bandgap GaN-based laser are different from those of the narrower bandgap semiconductor laser, and in the threshold region, the wide bandgap GaN-based laser VjExhibiting a transient 'pinning' (or dip), as shown by the square-symbol curve in FIG. 3, with increasing implant, VjThe rise continues. While the narrow bandgap GaAs in example 1The fundamental laser junction voltage is a jump up in the threshold region and then saturates as in fig. 2. Existing laser theory holds that above threshold, after the laser forms stable lasing, the device junction voltage should be 'pinned', which is exactly the same as the above-threshold characteristic of the narrow bandgap LD in example 1. Obviously, this non-saturation effect of the junction voltage of the wide bandgap GaN-based laser is difficult to be explained under the existing theoretical framework of lasers. In addition, the precise function relation of other junction parameters such as an ideal factor, series resistance and the like along with the current is obtained. The circular sign curve of fig. 3 shows the characteristic of the series resistance, and it can be seen that the series resistance is not constant but varies with the current, so that the conventional I-V method is obviously disadvantageous assuming that it is constant. The measurement result also shows that all the electrical parameters including the two electrical parameters have mutation phenomena in the lasing threshold region.
Example 3
Series resistance of LD and LED: the procedure was as in example 1. The series resistance of these devices is variable and has characteristics similar to example 2, except that these devices do not have a threshold region, so the curve is continuously variable, i.e., as the current increases, the series resistance gradually decreases, and the smaller the current, the larger the series resistance value. This non-linearity of the series resistance, which mainly results from the ohmic contact resistance and the high resistance layers of some heterojunctions, generally corresponds to a dipole layer and a spatial barrier, which is equivalent to a parallel connection of a non-linear resistance and a capacitance.
Example 4
LED and LD junction capacitance characteristics: the procedure was as in example 1. After the series resistance and junction conductance characteristics are obtained, the junction capacitance characteristics can be obtained by using equation (8). The measurement result is that the devices show a negative junction capacitance phenomenon under low frequency and large forward voltage, and the accurate expression of the negative capacitance along with the voltage and the frequency can be obtained by continuing data analysis, and the phenomenon is quite opposite to the inference of the classical Shockley theory on diffusion capacitance, which shows that the approximation of the Shockley classical depletion layer and the boundary condition thereof cannot be established under the large forward voltage.
Example 5
The LED junction voltage and the ideal factor are accurately related with the current change: the procedure was as in example 1. The measurement result is that the junction voltage of the LED gradually increases along with the applied voltage or current, but under the condition of large current (or voltage), the junction voltage of the device gradually tends to be completely saturated, at the moment, the quasi-Fermi energy levels of electrons and holes are 'pinned', the result is similar to that of a GaAs-based laser, but the junction voltage curve of the LED is smooth, and the jump phenomenon does not occur; the ideality factor decreases with increasing current. Previously, people can only measure the junction voltage and the ideality factor under small current, and the measurement of the junction voltage and the ideality factor under large current is valuable for researching the internal mechanism and the working characteristic of the LED under the actual working state.
It will be apparent to those skilled in the art that various changes or modifications to the parallel or series mode and initial values used in the process of measuring the C-V characteristic of the ac small signal in these embodiments are within the scope of the invention without departing from the spirit and scope of the invention. And the invention is not limited to the embodiments set forth in the description.
Claims (2)
1. A method of characterizing a junction of a semiconductor device, having the steps of:
firstly, the direct current I-V characteristic of a two-terminal device is measured by using a precision instrument, and simultaneously, the conclusion that series resistance or an ideal factor is assumed to be constant is abandoned, and n is set to n (V)j) And rS＝rS(Vj) Then, the equation of Shockley is simplified as:
wherein n is an ideal factor, IsFor reverse saturation current, VjIs the device junction voltage, rsThe series resistance of the device, k is Boltzmann constant, T is temperature, and the relation between junction voltage and series resistance is Vj＝V-Irs(ii) a Taking the logarithm of both sides of equation (1) yields:
the relationship between the ideality factor and the junction voltage can be derived from equation (2):
then, the junction voltage is differentiated by the Shockley equation (1), and the relation of the junction differential conductance G can be obtained:
(II) measuring the AC impedance spectrum characteristics of the device in parallel mode by using the precise impedance spectrum under the condition of AC small signal, mainly measuring the relation (C) between the apparent conductance and the apparent capacitance along with the applied voltage or currentp-V and Gp-V). By utilizing the relationship that complex impedances in an actual diode equivalent circuit and an equivalent circuit in a parallel measurement mode are equal, the relationship among the apparent capacitance, the apparent conductance, the junction capacitance, the junction conductance and the series resistance in the device can be obtained:
considering the range of the actual working voltage of the device, G > > omega C is satisfied, and equations (5) and (6) are naturally simplified into:
according to equations (3), (4), (7) andrelation V of junction voltage and applied voltagej＝V-IrsThen the following system of equations can be obtained and then iteratively fitted or approximately solved:
wherein G ispAnd CpApparent conductance and apparent capacitance.
2. The method according to claim 1, wherein the step (iii) is performed in series mode by measuring the ac impedance only in the equation (9)S＝1/Gp-1/G is converted into the equation rS＝RS-1/G, wherein RsIs a series resistor in an equivalent circuit in series mode.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112285519A (en) * | 2020-10-26 | 2021-01-29 | 中国科学院上海微系统与信息技术研究所 | Method for measuring series resistance and ideal factor in diode gating array |
| CN113252991A (en) * | 2021-05-07 | 2021-08-13 | 清华大学深圳国际研究生院 | Method for calculating junction capacitance of diode |
-
2020
- 2020-06-28 CN CN202010596223.4A patent/CN111812477A/en active Pending
Non-Patent Citations (1)
| Title |
|---|
| 冯列峰: "半导体激光器光电特性的研究", 《中国博士学位论文全文数据库 信息科技辑》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112285519A (en) * | 2020-10-26 | 2021-01-29 | 中国科学院上海微系统与信息技术研究所 | Method for measuring series resistance and ideal factor in diode gating array |
| CN113252991A (en) * | 2021-05-07 | 2021-08-13 | 清华大学深圳国际研究生院 | Method for calculating junction capacitance of diode |
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