CHAPTER 8 The PN Junction Diode Consider the process by which the potential barrier of a PN junction is lowered when a forward bias voltage is applied, so holes and electrons can flow across the junction generating a diode current. Derive the ideal current voltage relation of the forward biased PN junction diode. Non-ideal effects such as high level injection, and generation and recombination currents. Develop a small signal equivalent circuit of the PN junction diode. Discuss large signal diode switching characteristics. Describe a specialized PN junction called a tunnel diode. 1
8.1 PN JUNCTION CURRENT In Figure 8.1c, the total potential barrier is reduced. There will be a diffusion of holes from the p region across the space charge region where they will flow into the n region. Similarly, there will be a diffusion of electrons from the n region across the space charge region where they will flow into the p region. 2
8.1 PN JUNCTION CURRENT
8.1 PN JUNCTION CURRENT
8.1.2 Ideal Current Voltage Relationship The ideal current voltage relationship of a PN junction is derived on the basis of four assumptions. The abrupt depletion layer approximation applies. The space charge regions have abrup t boundaries, and the semiconductor is neutral outside of the depletion region. The Maxwell Boltzmann approximation applies to carrier statistics. The concepts of low injection and complete ionization apply. The total current is a constant throughout the entire PN structure. The individual electron and hole currents are continuous functions through the PN structure. The individual electron and hole currents are constant throughout the depletion region. 3
8.1.3 Boundary Conditions The electric field Eapp induced by the applied voltage is in the opposite direction to the thermal equilibrium space charge electric field. Electric field in the space charge region is reduced below the equilibrium value. majority carrier electrons from the n side are now injected across the depletion region into the p m aterial, and majority carrier holes from the p side are injected across the depletion region into the n material. 5
8.1.3 Boundary Conditions V bi Fn Fp kt N d kt N a ln ln e ni e ni kt NaN d NaN d ln V ln 2 t 2 e ni ni If a reverse biased voltage greater than a few tenths of a volt is applied to the PN junction, then we see from Equations that the minority carrier concentrations at the space charge edge are essentially zero. 6
8.1.3 Boundary Conditions
8.1.3 Boundary Conditions
8.1.4 Minority Carrier Distribution The boundary conditions: 2 L D n p n0 for (x >=x n ) for (x <=-x p )
8.1.4 Minority Carrier Distribution
8.1.5 Ideal PN Junction Current The total PN junction current will be the minority carrier hole diffusion current at x = xn plus the minority carrier electron diffusion current at x = xp. 10
8.1.5 Ideal PN Junction Current 10
8.1.6 Summary of Physics 14
8.1.7 Temperature Effect For a silicon PN junction, the ideal reverse saturation current density will increase by approximately a factor of 4 for every 10 increase in temperature. As temperature increases, less forward bias voltage is required to obtain the same diode current. If the voltage is held constant, the diode current will increase as temperature increases. Example 15
8.1.8 The Short Diode The length Wn is assumed to be much smaller than the minority carrier hole diffusion length Lp. 15
8.2 GENERATION RECOMBINATION CURRENTS AND HIGH INJECTION LEVELS The recombination rate of excess electrons and holes, given by the Shockley Read Hall recombination theory, was written as Reverse-Biased Generation Current The negative sign implies a negative recombination rate; hence, we are really generating electron hole pairs within the reverse biased space charge region. 17
8.2 GENERATION RECOMBINATION CURRENTS AND HIGH INJECTION LEVELS The recombination rate of excess electrons and holes, given by the Shockley Read Hall recombination theory, was written as Reverse-Biased Generation Current The total reverse-biased current density is the sum of the ideal reverse saturation current density and the generation current density. 17
8.2 GENERATION RECOMBINATION CURRENTS AND HIGH INJECTION LEVELS Forward Bias Recombination Current 20
8.2 GENERATION RECOMBINATION CURRENTS AND HIGH INJECTION LEVELS Total Forward Bias Current Sum of the recombination and the ideal diffusion current densities. where the parameter n is called the ideality factor. For a large forward-bias voltage, n 1 when diffusion dominates, and for low forward-bias voltage, n 2 when recombination dominates. There is a transition region where 1<n <2. 22
8.2.2 High Level Injection In the derivation of the ideal diode I V relationship, we assumed that low injection was valid. Low injection implies that the excess minority carrier concentrations are always much less than the majority carrier concentration. In the high level injection region, it takes a larger increase in diode voltage to produce a given increase in diode current. np ( n 0 n)( p 0 p) n p n 2 i V exp( V a t ) C C 24
8.3 SMALL SIGNAL MODEL OF THE PN JUNCTION
8.3.2 Small-Signal Admittance Qualitative Analysis The shaded areas represents the charge Q that is alternately charged and discharged during the ac voltage cycle. The mechanism of charging and discharging of holes in the n region and electrons in the p region leads to a capacitance, called diffusion capacitance. The magnitude of the diffusion capacitance in a forward biased PN junction is usually substantially larger than the junction capacitance.
8.3.2 Small-Signal Admittance Mathematical Analysis 28
8.3.2 Small-Signal Admittance dc ac 29
8.3.2 Small-Signal Admittance One consequence of the approximations ωt p0 <<1 and ωt n0 << 1 is that there are no wiggles in the minority carrier curves. The sinusoidal frequency is low enough, so that the exponential curves are maintained at all times. 30
8.3.3 Equivalent Circuit 31
7.3.2 Junction Capacitance
8.3.3 Equivalent Circuit 31
*8.4 CHARGE STORAGE AND DIODE TRANSIENTS I I R V R R R
*8.4 CHARGE STORAGE AND DIODE TRANSIENTS the reverse biased density gradient is constant; thus, the minority carrier concentrations at the space charge edge decrease with time This reverse current IR will be approximately constant for 0< t< ts, where ts is called the storage time. 33
*8.5 THE TUNNEL DIODE The tunnel diode is a PN junction in which both the n and p regions are degenerately doped. The depletion region width decreases as the doping increases and may be on the order of approximately 100 Å. 34
*8.5 THE TUNNEL DIODE (b) There is a finite probability that some of these electrons will tunnel directly into the empty states, producing a forward bias tunneling Current. (e) The tunneling current will be zero and the normal ideal diffusion current will exist. 35
8.6 SUMMARY Electrons in the valence band on the p side are directly opposite empty states in the conduction band on the n side, so electrons can now tunnel directly from the p region into the n region, resulting in a large reversebiased tunneling current. 36