Capacitance and current analysis of silicon diodes Davíð Örn Þorsteinsson (1), Guðjón Henning Hilmarsson (2) and Saga Huld Helgadóttir (3) 1) [email protected] 2) [email protected] and 3) [email protected]

Abstract: I-V behavior of three different diodes of the semiconductor, which applies to all of the is observed and their ideality factors are evaluated. diodes. At very high doping levels the junction Then the capacitance of a Schottky diode as a func- becomes an ohmic contact. The most important tion of voltage is measured and the effect of hydro- difference between the p-n and Schottky diode is gen is determined. reverse recovery time, when the diode switches from conducting to non-conducting state. The p-n Introduction diode can have a reverse recovery time in order Many characteristics of semiconductor diodes can of hundreds of nanoseconds, but the Schottky be examined by measuring current as a function diode does not have a recovery time. There is of voltage. The differences between a Schottky nothing to recover from since there is no charge diode, a Zener diode and a normal p-n diode are carrier depletion region at the junction. The observed by measuring current for both forward Schottky diode is often called a majority carrier and reverse bias. By checking the exponential cur- semiconductor device. That is if the semiconduc- rent responce for forward bias the diodes ideality tor body is n-type doped, where only the n-type factor can be found. In reverse bias the leakage carriers play a significant role in normal operation current can be found as well as an additional cur- of the device. The majority carriers are quickly rent that increases the current in reverse bias lin- injected in to the conduction band in the metal early. and become free moving electrons. Therefore the Hydrogen has an important role in the deple- Schottky diode can achieve conduction faster than tion region properties in semiconductor diodes. It an ordinary p-n diode. binds with impurities in the semiconductor and neutralizes charge carriers. When the semiconduc- A Zener diode allows current to flow in the tor is heated with a negative bias on, the hydrogen forward direction like an ideal diode would, but moves deeper in to the depletion region. With fur- it also permits the current to flow in the reverse ther heating with no bias the hydrogen forms H 2 direction when the voltage is above a certain and has no influence on the semiconductor. value known as the breakdown voltage. When Theory the reverse bias breakdown voltage is exceeded A p-n diode is a type of semiconductor diode in a conventional diode it is subject to high cur- based on the p-n junction that conducts current rent. Unless this current is limited by circuitry, in only one direction. The ideal diode has zero re- the diode will be permanently damaged due to sistance in the forward bias and infinite resistance overheating. A Zener diode is specially designed in the reverse bias. The semiconductor diode is to have that breakdown voltage, a reverse biased not ideal. The diode does not conduct appreciably Zener diode will exhibit a controlled breakdown until a non-zero turn-on voltage is reached. Above and allow the current to keep the voltage across this voltage the slope of the current versus voltage the Zener diode close to the Zener breakdown curve is not infinite. In the reverse direction the voltage. The Zener diode’s operation depends diode conducts a nonzero leakage current and at on the heavy doping of its p-n junction. The a large enough reverse bias, at the breakdown depletion region is very thin because of the voltage, the current increases very rapidly with heavy doping, less than 1 µm and the electric increasing negative reverse voltages. field is consequently very high, even for a small reverse bias voltage. This allows electrons to The Schottky diode is a semiconductor diode tunnel from the valence band of the p-type mate- with a low forward voltage drop and a very fast rial to the conduction band of the n-type material. switching action. A Schottky barrier is created by forming a metal-semiconductor junction between A forward bias lowers the potential barrier be- a metal and a semiconductor. The choice of tween the two sides of the junction. The for- the combination of the metal and semiconductor ward current is expected to increase exponentially determines the forward voltage of the diode. Both with the applied voltage. A reverse bias on the n and p type semiconductors show the Schottky other hand increases the potential barrier com- effect, though the p-type usually has a much lower pared to the equilibrium. Even a small bias, any- voltage. The voltage can be too low, so the p-type thing greater than a few kT/q in magnitude, re- Schottky diodes are rarely used. The width of the duces the majority carrier current. That is the re- depletion region drops with increased doping level verse bias gives rise to the minority carrier current and is thus expected to be extremely small in mag- nitude. The minority carrier drift currents are not affected by the height of the potential barrier, it is the number of minority carriers wandering into the depletion region per second that determines the current flow. Therefore the reverse current is expected to saturate, that is become bias indepen- dent, when the majority carrier diffusion currents are reduced to a negligible level at a small reverse [1] bias. If the reverse bias saturation current is taken Fig. 2: ln(I) as a function of VA. to be −I0 then the ideal diode equation is

V 2 A VA is applied voltage. An extrapolated 1/C = 0 I = I0(e kT /q − 1) (1) intercept is equal to Vbi. Assuming the area A of the diode is known, NB can be determined from the slope. Also the straight line of the slope is a confirmation that the diode can be modeled as a step junction. But the doping variation with po- sition can be deduced directly from the C-V data without prior knowledge about the nature of the doping profile. 2 NB(x) = 2 2 (4) qKs0A |d(1/C )/dVA| [1] K  A Fig. 1: The ideal diode equation plotted. x = s 0 (5) C The I-V characteristics of the ideal diode are mod- where x is the distance into the semiconductor eled by the ideal diode equation. How the diode side of the diode measured from the junction The passes a large current when forward biased and a process of determining the doping as a function of very small current when reverse biased. For re- position is called profiling. The profile determined verse biases greater than a few kT/q, a few tenths using eqs. (2) and (3) becomes inaccurate if the of a volt at room temperature, the exponential doping is a rapidly varying function of position, voltage term in the ideal diode equation is negligi- and only a limited portion of the junction can be ble and the current goes to −I0. According to the scanned. ideal diode theory, this saturation current would be observed for a reverse bias of unlimited magni- Experimental tude. For a forward bias greater than a few kT/q VA C-V analysis the current increases exponentially with I0e kT /q . A p-type boron doped silicon Schottky diode is Because of the exponential dependance, the for- mounted in a liquid nitrogen cooled cryostat where ward bias characteristics are often plotted on a the temperature can be varied between 77 K and semilog scale, ln(I) as a function of VA, as shown 650 K. In this experiment only the heating option in fig. 2. is used. The sample holder is connected to an q Agilent LCR meter which is computer controlled. ln(I) = ln(I0) + VA (2) This experiment is fully irreversible and it is not nkT possible to repeat the measurements on the same Since for forward bias VA is positive, the semilog sample once the sample has been heated above plot has a linear region slope of q/kT and an ex- room temperature. The capacitance as a function trapolated intercept of ln(I0). of voltage for the p-type boron doped silicon C-V data is used to determine device parameters. Schottky diode is measured from 0 to −10 V in 2 Plot of 1/C as a function of VA should be a 0.1 V steps. An initial measurement at room straight line with a slope inversely proportional to temperature for comparison is taken. Then a 5 V NB, negative bias is applied and the diode is heated 1 2 up to 393 K. The diode is kept with bias on for 2 = 2 (Vbi − VA) (3) C qNBKS0A about 10 minutes at 393 K and is then cooled where C is the capacitance of the diode, q electron again to room temperature with liquid nitrogen to charge, NB the doping concentration, KS = 11.8 speed up the process. The bias is kept on during is the dielectric constant for silicon, 0 is the vac- the cooling and liquid nitrogen is used to speed up uum permittivity, A is the area of the diode and the cooling. The capacitance is closely monitored to ensure that the reverse bias is on the sample For the Zener diode the slope of the best fit line at all times. The capacitance as a function of is hze = 23.96. The ideality factor is then deter- voltage is then measured for the second time at mined nze = 1.65. The line intersects the y-axis −11 room temperature. Then the sample is heated at ln(I0) = −23.87 and I0 = 4.32 · 10 A. again, but now it is kept at 423 K for about 30 The slope of the best fit line for the Schottky diode minutes without bias. It is then cooled again is hsc = 35.59 and from that the ideality factor is to room temperature and the capacitance as a found to be nsc = 1.113. The intersection is at −6 function of voltage is measured for the third time. ln(I0) = −12.79 and I0 = 2.78 · 10 A. Conclusion I-V characterization The reasons for a higher ideality factor in the p-n For three silicon diodes, a silicon p-n diode, a sili- and Zener diode is because of recombination that con Zener diode and a silicon Schottky diode, the happens in the forward bias. Majority carriers current is measured as a function of voltage using recombine in the depletion region, reducing the a computer controlled set up that uses a Keith- current that gets through the diode. A likely ley Electrometer. The reverse and forward bias reason for the difference between the Zener and characteristics are measured seperately. The most p-n diodes is the size of their depletion region, important parameter is the current compliance of which is smaller in the Zener diode. In the the electrometer and it must be carefully chosen to Schottky diode however, the number of minority avoid destruction of the diodes. First the 1N4148 carriers is almost non-existant. This makes the silicon p-n diode is measured. The current is mea- Schottky diode very close to the ideal diode in sured as a function of the voltage between 0 and forward bias, though that isn’t the case in reverse 1.2 V with current compliance of 0.2 A, and then bias. from 0 to −160 V with a current compliance of 10 mA. Then the current for the BZX-55C10 sili- For both the Schottky diode (fig.5) and the p-n con Zener diode is measured between 0 and 1.0 V diode (fig.4) the current increases with voltage with a current compliance of 0.1 A and between 0 in the reverse bias. The reason for this current and −11 V with a current compliance of 10 mA. At change is different for the diodes. last the BYS21-45 silicon Schottky diode is mea- In the p-n diode there is a generation current, sured. The current is measured between 0 and caused by impurities that act as an intermediate 0.6 V with a current compliance of 0.2 A and be- state for electrons being excited to the conduction tween 0 and −50 V with a current compliance of band in the depletion layer. As the reverse bias 10 mA. voltage increases the depletion layer gets bigger, Calculations increasing the chance of excitation between the The slope of the best fit line of the diodes before bands. The increase grows linearly with the width the series resistance becomes dominant is used, of the depletion layer whiich is proportional to along with eq. (2), to determine the diodes ide- the square root of the voltage. ality factor n, seen in the semilog plot in fig. 3. For the p-n diode the slope is hpn = 20.75 and the ideality factor npn = 1.91. This best fit line intersects the y-axis at ln(I0) = −19.43 and thus −9 I0 = 3.63 · 10 A.

Fig. 4: I-V graph for forward and reverse bias of a 1N4148 silicon p-n diode Fig. 3: ln(I) as a function of VA for 1N4148 sili- con p-n diode, BZX-55C10 silicon Zener diode and BYS21-45 silicon Schottky diode. In the Schottky diode electrons are excited from the metal over the potential barrier at the metal-semiconductor junction. With increased voltage the potential barrier drops, allowing more electrons to be excited over the barrier.

Fig. 7: Carrier concentration as a function of dis- tance at room temperature between 0 and −10 V for various annealing temperature and time.

minutes. The hydrogen is excited from the semi- conductor and a bias forces the hydrogen deeper in to the semiconductor. There, the hydrogen atoms neutralize the carriers in the depletion layer at a certain depth. After heating the semiconductor at Fig. 5: I-V graph for forward and reverse bias of 423K for 30 minutes the concentration becomes a BYS21-45 silicon Schottky diode. almost linear. At this temperature, the hydrogen atoms recombine making H2 gas instead of binding with the carriers again. The Zener diode (fig.6) doesn’t seem to decrease linearly but has an almost constant value until References it reaches breakdown. The generation current [1] Robert F. Pierret. Semiconductor Device in the Zener diode is very small because of the Fundamentals, 2nd edition 1996. size of the depletion region. Since both sides of [2] T. Zundel and J. Weber. Dissociation energies the Zener diode are heavily doped, the depletion of shallow-acceptor-hydrogen pairs in silicon. region becomes very small and, as stated above, Physical review, volume 39, 1989. the minority carrier current is linearly dependent [3] Schottky diode. on the depletion region’s size. http://en.wikipedia.org/wiki/Schottky_diode [4] Zener diode. http://en.wikipedia.org/wiki/Zener_diode

Fig. 6: I-V graph for forward and reverse bias of a BZX-55C10 Si Zener diode

The analysis of the C-V measurements can be seen in fig. 7. The carrier concentration has shifted af- ter annealing the semiconductor at 393K for 10