CSE251 CSE251 Lecture 2 and 5

Carrier Transport 2 The net flow of electrons and holes generate currents. The flow of ”holes” within a solid–state material is, in all respects, equivalent to a flow of positive charge carriers. The process by which these charged particles move is called Carrier Transport. There are 2 carrier transport mechanism in semiconductor. - Diffusion – the flow of charge due to density gradients. - Drift – the movement of charge due to electric fields

Carrier Transport: Diffusion 3 Diffusion is the process whereby particles flow from a region of high concentration toward a region of low concentration (charge density gradients). If the particles have charge, the net flow of charge would result in a diffusion current.

Carrier Transport: Drift 4 An electric field applied to a semiconductor will produce a force on electrons and holes so that they will experience a net acceleration and net movement. This net movement of charge due to an electric field is called drift. The net drift of charge gives rise to a drift current.

5 p>>nn>>p excess electrons diffuse to the p-type region excess holes diffuse to the n-type region Before junction is formed: - Uniform distribution of holes in p-type semiconductor - Uniform distribution of electrons in n-type semiconductor. After junction is formed: p-n Junction at Thermal Equilibrium

p>>n n>>p Diffusion current & Drift current Hole diffusion:Electron diffusion: Total diffusion current Electron drift:Hole drift: Total drift current

7 - Excess holes diffuse to the n- region and excess electrons diffuse to the p-region giving rise to diffusion current, I D. - The excess holes diffused recombine with the excess electrons in the n-region, thus uncovering bound positively charged donor atoms in the n- region near the junction. - The excess electrons diffused to the p-region recombine with the excess holes thus uncovering bound negatively charged acceptor atoms in the p- region near the junction - The charged region created at the junction is called the depletion region (depleted of free carriers) or the space charge region. OR Space charge region The Diffusion Current and the Space Charge Region p-n Junction at Thermal Equilibrium

8 The Barrier Voltage : The depletion region or the space charge region creates an electric field and establishes a potential barrier know as barrier voltage or the built-in voltage, V 0. - It is also called the contact potential as the voltage is developed due to contact between p and n materials. - The developed electric field opposes further diffusion of electrons and holes and hence the name barrier voltage. - Drift Current : Further, the developed electric field will sweep minority carriers across the junction, i.e., holes from n to p and electrons from p to n, giving rise to minority carrier drift current, I S. The Drift Current and the Barrier / Built-in / Contact Potential p-n Junction at Thermal Equilibrium

9 Diffusion and Drift Current Equilibrium -The process of diffusion continues until the depletion region expands to a width such that the electric field in the depletion region is large enough so that the diffusion current due to majority carriers is exactly balanced by the drift current due to minority carrier. - The net flow of current through the junction is zero. So for a p-n junction at thermal equilibrium, Hole diffusion Electron diffusion Total diffusion current Electron drift Hole drift Total drift current E Total diffusion current = Total drift current

10 Reverse-Bias Condition (V D < 0V) p>>n n>>p VDVD IsIs VDVD IDID The number of uncovered positive ions in the depletion region of n-type will increase due to large number of free electrons drawn to the positive potential Similarly, the number of uncovered negative ions will increase in p-type resulting in widening of depletion region The wider space charge region increases the barrier height by the reverse voltage, V B = V 0 + V D. The increased barrier height reduced the diffusion of majority carriers – resulting in a much reduced diffusion current I D. p-n Junction : Steady State Condition

11 p>>n n>>p VDVD IsIs VDVD IDID Reverse-Bias Condition (V D < 0V) The drift current I S due to minority carriers does not change as the number of minority carriers entering the depletion region remains same I S depends only on the minority carrier concentration and is independent of the voltage applied. I S is called the reverse saturation current as it keeps flowing under reverse biased condition Therefore, the diode current under reverse-biased condition, I = I D – I s ≈ - I S p-n Junction : Steady State Condition

The number of uncovered positive ions in the depletion region of n-type will increase due to large number of free electrons drawn to the positive potential The number of uncovered negative ions will increase in p-type resulting widening of depletion region This region established great barrier for the majority carriers to overcome – resulting I majority = 0 The number of minority carriers find themselves entering the depletion region will not change resulting in minority-carrier flow vectors of the same magnitude The current exists under reverse-bias conditions is called the reverse saturation current and represented by I s Therefore, I D = -I s Reverse-Bias Condition (V D < 0V)

13 Forward-Bias Condition (V D > 0V) p>>nn>>p VDVD IsIs IDID I= I D -I s I VDVD - In the forward-biased condition positive potential on the p-side and negative potential on n-side. - The forward voltage will pressure the electrons in n-type and holes in p-type to neutralize some of the uncovered ions near the boundary and reduce the width of the depletion region - The reduced depletion region will reduce the barrier voltage V 0 by the forward voltage V D. The new barrier height, V B = V 0 – V D. p-n Junction : Steady State Condition

14 p-n Junction : Steady State Condition Forward-Bias Condition (V D > 0V) p>>nn>>p VDVD IsIs IDID I= I D -I s I VDVD - Due to reduced barrier height, more electrons and holes can now diffuse across the junction, thus greatly increasing the diffusion current I D. - But the drift current I S due to minority carriers remains unchanged, since the minority carrier concentration is same. - Thus in the forward-biased condition, the diode current is almost equal to the diffusion current, I = I D – I S ≈ I D

Forward-Bias Condition (V D >0) Positive potential on the p-side and negative potential on n-side The application of forward-bias potential will pressure the electrons in n-type and hole in p-type to recombine with ions near the boundary and reduce the width of depletion region Minority carrier flow unchanged, but heavy majority carrier (diffusion current) flow across the depletion region An electron of the n-type material sees a reduced barrier at the junction due to the reduced depletion region and a strong attraction for the positive potential applied to the p-type material

p-n Junction Diode: Structure and Symbol 16 p-typen-type anode cathode p-typen-type Metal Contacts Circuit Symbol (Arrow head indicates the normal direction of current flow) p-n junction diode: A two terminal one way device.

17 p-n Junction Diode Characteristics Ideal Diode Characteristics Forward-biased: - On during forward bias - Zero forward resistance (short-circuit) - Zero forward voltage drop Reversed-biased: - Off during reverse bias - Infinite resistance (open-circuit) - Zero diode current

18 Ideal Diode Characteristics The ideal diode: (a) diode circuit symbol; (b) i–v characteristic; (c) equivalent circuit in the reverse direction; (d) equivalent circuit in the forward direction. p-n Junction Diode Characteristics

19 Carrier Transport: Drift The net flow of the electrons and holes in a semiconductor will generate currents. The process by which these charged particles move is called transport. In this chapter we will consider the two basic transport mechanisms in a semiconductor crystal: - Drift – the movement of charge due to electric fields. - Diffusion – the flow of charge due to density gradients. Carrier Drift An electric field applied to a semiconductor will produce a force on electrons and holes so that they will experience a net acceleration and net movement, provided there are available energy states in the conduction and valence bands. This net movement of charge due to an electric field is called drift. The net drift of charge gives rise to a drift current. Drift and Diffusion

20 The flow of ”holes” within a solid–state material is, in all respects, equivalent to a flow of positive charge carriers. They are identical to the concept of a flux of bubbles, which are a flow of negative (absence of) matter, but do not exist unless the space is the ’filled’ solid or liquid molecular environment. Because of their mobility, the ”holes” in the valence band are just like electrons in the conduction band, except they fall in the opposite direction of that of the electrons when subject to the drift force of an electric field. Carrier Transport: Drift

21 Hole Drift Velocity and Mobility The equation of motion of a positively charged hole in the presence of an electric field E is a is the acceleration, is the effective mass of hole, and e is the charge of a hole. For a constant electric field, we expect the velocity to increase linearly with time. However, charged particles in a semiconductor are involved in collisions with ionized atoms and with thermally vibrating lattice atoms. This accelerate, collide, accelerate, collide motion results in an average drift velocity v d. Hole Mobility At low electric fields, the drift velocit is directly proportional to the electric field. where v dp is the hole drift velocity and μ p is called the hole mobility (cm 2 /V-sec). Carrier Transport: Drift

22 Hole Drift Current If p is the concentration of holes, then the hole drift current in the presence of an electric field E is The drift current due to holes is in the same direction as the applied electric field. Electron Drift Current Similarly, If n is the concentration of electrons,  n is their mobility, then the electron drift current in the presence of an electric field E is The conventional drift current due to electrons is also in the same direction as the applied electric field even though electrons move is in the opposite direction. Total Drift Current Carrier Transport: Drift

23 Typical Mobility Values Exercise: Consider a sample of silicon at T = 300 K doped at an impurity concentration of: N d = cm -3 and N a = cm -3. Assume electron and hole mobilities are given in Table 5.1. Calculate the drift current density if the applied electric field is E = 35 V/cm.. Carrier Transport: Drift

24 Exercise: Consider a sample of silicon at T = 300 K doped at an impurity concentration of: N d = cm -3 and N a = cm -3. Assume electron and hole mobilities are given in Table 5.1. Calculate the drift current density if the applied electric field is E = 35 V/cm. Carrier Transport: Drift

25 The drift current density may be written as, where  (siemens/cm) is the conductivity of the semiconductor. Resistivity  is the reciprocal of conductivity σ: For a bar of semiconductor with a voltage V applied that produces a current I, Carrier Transport: Conductivity