Semiconductor Physics and Devices

Transcription

1 The pn Junction 1) Charge carriers crossing the junction. 3) Barrier potential Semiconductor Physics and Devices Chapter 8. The pn Junction Diode 2) Formation of positive and negative ions. 4) Formation of depletion region Seong Jun Kang Department of Advanced Materials Engineering for Information and Electronics Laboratory for Advanced Nano Technologies Depletion region: No carrier Basic structure of the pn junction Basic structure of the pn junction Figure shows the pn junction. The interface separating the n and p regions is referred to as the metallurgical junction. At the metallurgical junction, there is a very large density gradient in both electron and hole concentrations. ( Diffusion force) Majority carrier electrons in the n region will begin diffusing into the p region, while majority carrier holes in the p region will begin diffusing into the n region. The net positively and negatively charged regions are called as the space charge region. The net positive and negative charges in the n and p regions induce an electric field in the region near the metallurgical junction, in the direction from the positive to the negative charge. (n p) Since the space charge region is depleted of any mobile charge, this region is also referred to as the depletion region. In thermal equilibrium, the diffusion force and the E-field force exactly balance each other. Zero applied bias We have considered the basic pn junction structure and discussed briefly how the space charge region is formed. In chapter 7, we examined the properties of the step junction in thermal equilibrium, whereno currents exist and no external excitation is applied. We will determined the space charge region width, electric field, and potential through the depletion region. Built-in potential barrier Built-in potential barrier The Fermi energy level is constant throughout the entire system, since no voltage is applied across the pn junction and the system is in thermal equilibrium. The conduction and valence band energies must bend as we go through the space charge region as shown in the figure. Now, electrons in the conduction band of the n-region see a potential barrier in trying to move into the conduction band of the p-region. This potential barrier is referred to as the built-in potential barrier (V bi ). No voltage is applied across the pn junction, the Fermi energy level is constant.

2 Electric field and potential in pn junction Electric potential in P region The pn Junction Diode We just discussed the electrostatics of the pn junction under reverse bias. (chapter 7.) Now, consider the pn junction in a forward bias voltage. Electric potential in Built in potential barrier Equilibrium Reverse bias Forward bias pn Junction Current When a forward-bias voltage is applied to a pn junction, a current will be induced in the device. Forward bias Connect + to the p-type semiconductor and to the n-type semiconductor Qualitative Description of Charge Flow in a pn Junction Forward-biased pn junction - A positive voltage is applied to the p-region with respect to the n-region. - The Fermi level in the p-region is lower than that in the n-region. - The total potential barrier is reduced. - There will be a diffusion of holes from the p- region into the n-region, across the space charge region. - Similarly, there will be a diffusion of electrons from the n-region to the p-region. - The flow of charge generates a current through the pn junction. Equilibrium Reverse bias Forward bias Commonly used terms and notation Figure shows the conduction band energy through the pn junction in thermal equilibrium. The n-region contains many electrons, and the built-in potential barrier prevents the flow of electrons into the p-region. The built-in potential barrier was derived in the previous chapter as below. Assuming complete ionization, n n0 is the thermal-equilibrium concentration of majority carrier electrons in the n-region. n p0 is the thermal-equilibrium concentration of minority carrier electrons in the p-region.

3 The electric field E app induced by the applied voltage is in the opposite direction to the space charge electric field. This equation relates the minority carrier electron concentration on the p-side of the junction to the majority carrier electron concentration on the n-side of the junction in thermal equilibrium. Forward bias If a positive voltage is applied to the p-region with respect to the n-region, the potential barrier is reduced. The net field in the space charge region is reduced below the equilibrium value. As long as the bias V a is applied, the injection of carriers across the space charge region continues and a current is created in the pn junction. This condition is knows as forward bias. The energy band diagram of the forward biased pn junction is shown. Figure shows a forward biased pn junction with an applied voltage V a. The potential barrier V bi in equation below can be replaced by (V bi V a ) when the junction is forward biased. When a forward bias voltage is applied to the pn junction, the junction is no longer in thermal equilibrium. The total minority carrier electron concentration in the p-region is, The total minority carrier hole concentration in the n-region is, Therefore, The total minority carrier electron concentration in the p-region & the total minority carrier hole concentration in the n-region is, Assumption: Low Injection How these excess carriers behave as a function of time and spatial coordinates? From the chapter 6 (eq. 6.56), The ambipolar transport equation for excess minority carrier holes in an n-region, By applying a forward-bias voltage, excess minority carriers are created in each region of the pn junction. Here, is the excess minority carrier hole concentration. The area of interest in pn junction ( x < -x p and x > x n ) Assume no electric field (E=0), g =0 & steady state ( )

4 How these excess carriers behave as a function of time and spatial coordinates? The excess minority carrier hole concentration in the n region, The excess minority carrier hole concentration in the n region, The boundary conditions General solution is, The excess minority carrier electron concentration in the p region, The boundary conditions The excess minority carrier electron concentration in the p region, General solution is, Ideal pn Junction Current The total current in the junction is the sum of the individual electron and hole currents that are constant through the depletion region. Total PN junction current = From the equation, the minority carrier concentration decay exponentially with distance away from the junction to their thermal-equilibrium values. Minority carrier (hole) diffusion current at x = x n + Minority carrier (electron) diffusion current at x = -x p The total current density in the pn junction is, Ideal pn Junction Current The total current density in the pn junction is, Summary of Physics The minor carrier diffusion current densities as a function of distance. The equation gives a good description of the current-voltage characteristics of the pn junction. In forward bias voltage, the current increases exponentially. In reverse bias voltage (negative V a ), the current is going to -J s. J s is referred to as the reverse-saturation current density.

5 Figure shows the energy band diagram of a pn junction in thermal equilibrium when both the n and p regions are degenerately doped. (see chapter 4) The depletion region width decreases as the doping increases. The potential barrier at the junction can be approximated by a triangular potential barrier. (Tunneling phenomenon) The barrier width is small and the electric field in the space charge region is large. Energy band diagram and I-V characteristics of the tunnel diode. (a) Zero bias (b) A slight forward bias Electron in the conduction band of the n region are directly opposite to empty states in the valence band of the p region. (c) A forward bias producing maximum tunneling current. Energy band diagram and I-V characteristics of the tunnel diode. (d) A higher forward bias showing less tunneling current. As the forward-bias voltage continues to increase, the number of electrons on the n side directly opposite empty states on the p side decrease. tunneling current decrease. (e) A forward bias for which the diffusion current dominates. Electrons in the valence band on the p side are directly opposite empty states in the conduction band on the n side. So, electron can now tunnel directly from the p region into the n region. Large reverse-biased tunneling current.